JP3930311B2 - Molding mold manufacturing method, fθ lens manufacturing method, molding mold, fθ lens, optical apparatus, image forming apparatus - Google Patents

Description

【００８２】
（１）式において、Ｃ_１は光軸近傍における母線方向の曲率（以下、適宜、母線方向の近軸曲率という）、Ｃ_２は光軸近傍における子線方向の曲率（以下、適宜、子線方向の近軸曲率という）、Ｋ_１は母線方向の円錐定数、Ｋ_２は子線方向の円錐定数、Ｓは子線断面形状のシフト量である。なお、Ｃ_２，Ｋ_２，Ｓは母線方向のレンズ高さＸの関数、Ｃ_２（Ｘ），Ｋ_２（Ｘ），Ｓ（Ｘ）として与えられる。また、（１）式の第３項は多項式であり、ｍ及びｎはそれぞれＸ及びＹの次数、Ｍ及びＮはそれぞれＸ及びＹの最大次数、Ａ_ｍｎは多項式の係数である。
【００８３】
この成形品である光学素子１は、母線方向（この例で、光学素子１は露光走査用のｆθレンズであるため、母線方向は主走査方向となる）及び子線方向（同じく、光学素子１は露光走査用のｆθレンズであるため、子線方向は副走査方向となる）と直交する方向側の両側面３のラインと４のラインとが不揃いである。そして、応力を受けていない状態では母線には歪みが生じていて、この光学素子１が装着されるべき特定の装置、この例では、後述の画像形成装置２０に組み付けた状態では、その歪みが修正される。
【００８４】
この場合に、応力を受けていない状態では両側面３，４に歪みがなく、特定の装置（画像形成装置２０）に組み付けた状態では両側面３，４に歪みが生じる。
【００８５】
また、この光学素子１のように、本来、理想的には母線と両側面３，４とが平行となるべき成形品については、母線と両側面３，４のラインとは、組み付けられるべき特定の装置（この例では、後述の画像形成装置２０）に組み付けられて応力を受けている状態でも、応力を受けていない状態でも、何れの場合も非平行である。そして、応力を受けていない状態では母線には歪みが生じていて、特定の装置に組み付けた状態ではその歪みが修正される。
【００８６】
そして、応力を受けていない状態では側面３と４とが非対称であり、特定の装置（画像形成装置２０）に組み付けた状態では、側面３と４とが非対称である状態に比べて対称に近づくように変形する。
【００８７】
図３（ａ）は、前記のように応力を受けていない状態にある光学素子１の光学機能面４の概念図であり、図３（ｂ）は、特定の装置（この例では、後述の画像形成装置２０）に組み付けられて、応力（矢印１１で示す）を受けている状態にある光学素子１の光学機能面４の概念図である。図３（ａ）（ｂ）において、破線１２は母線を示している。
【００８８】
図４は、このような成形品としての光学素子の一例である光学素子１を組み付けた光学機器の一例である電子写真方式の画像形成装置の概略構成を説明する図である。この画像形成装置２０は、画像読取装置であるイメージスキャナ２２と、イメージスキャナ２２で読み取った画像データに基づく画像形成を用紙上に行なうプリンタユニット２３と、イメージスキャナ２２上に設けられたＡＤＦ（Automatic Document Feeder）２４とを備えている。
【００８９】
イメージスキャナ２２の上面には、読み取る原稿が載置されるコンタクトガラス２５が設けられている。コンタクトガラス２５の下方には、照明ランプ２６およびミラー２７を備えてコンタクトガラス２５に沿って走行可能な第１キャリッジ２８と、ミラー２９，３０を備えてコンタクトガラス２５に沿って走行可能な第２キャリッジ３１と、結像レンズ３２と、光電変換素子であるＣＣＤ（Charge Coupled Device）３３とを備えた走査光学系３４が設けられている。第１および第２キャリッジ２８，３１は、ステッピングモータ等のキャリッジモータ（図示せず）によって駆動されて、図４に示すホームポジション（右側）から左側へ２：１の速度比で走行する。
【００９０】
プリンタユニット２３には、用紙を積層する給紙トレイ３５から、電子写真方式で用紙上に画像の形成を行なうプリンタエンジン３６、定着装置３７等を経由して排紙スタッカ部３８へ至る用紙搬送路３９が形成されている。プリンタエンジン３６は、感光体５１と、感光体５１の表面を一様に帯電させる帯電装置５２と、イメージスキャナ２２で読み取った画像データに基づいて感光体５１を露光し、静電潜像を形成する露光装置４２と、感光体５１の表面に形成された静電潜像をトナーで現像する現像ユニット５３と、用紙搬送路３９中を搬送されてきた用紙に感光体５１上のトナー画像を転写する転写器４４と、この転写後の感光体５１上をクリーニングするクリーニング装置５４とを備えている。
【００９１】
ＡＤＦ２４は、ＡＤＦ２４によってコンタクトガラス２５に給紙する原稿が載置される原稿台４５と、読み取りが終了した原稿が排出される排紙部４６とを備えている。ＡＤＦ２４の内部には、原稿台４５から排紙部４６へ連通する原稿搬送経路４７が形成されている。原稿搬送経路４７中には、複数対のローラ４８に巻回された無端帯４９、搬送ローラ５０等の搬送機構が設けられている。この搬送機構は、ステッピングモータ等のＡＤＦモータ（図示せず）によって駆動されて、原稿台４５に載置された原稿を一枚ずつコンタクトガラス２５へ向けて搬送する。ＡＤＦ２４の上面には、キーボードとディスプレイとを備えた本体操作パネル５２が設けられている。
【００９２】
図５は、露光装置４２の一構成例を示す斜視図である。この露光装置４２は、光源である半導体レーザ６１、この半導体レーザ６１からの光を所定角度範囲で等角速度的に偏向する偏向面を有する回転多面鏡（ポリゴンミラー）６４、この回転多面鏡６４で偏向された光を等速度的な光に変換する光学系であるレーザ走査光学系６５、及び、このレーザ走査光学系６５からの光の方向を変更する（光路を折り曲げる）折り返しミラー６８等を備えている。ここで、レーザ走査光学系６５には走査レンズ６５ａ，６５ｂ，６５ｃが用いられている。そして、この走査レンズ６５ａ，６５ｂ，６５ｃは、いずれも前記の構成の光学素子１である。
【００９３】
露光装置４２の動作について説明する。半導体レーザ６１から出射された光は、レンズ６２及び６３を介して、回転多面鏡６４の偏向面近傍に一旦結像される。回転多面鏡６４は一定の角速度で図５中の矢印６９方向に回転しており、偏向面近傍に結像された光は回転多面鏡６４の回転に伴って等角速度的に偏向される。偏向された光は、fθレンズ６５ａ、６５ｂ、６５ｃを順次透過することで等速度的な光に変換され、折り返しミラー６８で反射されて走査対象である感光体５１の表面を露光走査する。
【００９４】
図６は、露光装置４２について、図５を参照して前記したものとは別の例を示す斜視図である。
【００９５】
図６において、図５と同様の部材については同一の符号を付している。すなわち、半導体レーザ６１から出射された光は、レンズ６２及び６３を介して、回転多面鏡６４の偏向面近傍に一旦結像する。回転多面鏡６４は一定の角速度で図中の矢印方向に回転しており、偏向面近傍に結像した光は回転多面鏡６４の回転に伴って等角速度的に偏向される。偏向した光は、走査ミラー１５１ａ及び折返ミラー１５２ａを介して、光学素子１５１ｂに入射することで等速度的な光に変換され、折り返しミラー１５２ｂで反射されて、走査対象である感光体５１の表面を露光走査する。走査ミラー１５１ａ及び光学素子１５１ｂによりレーザ走査光学系１５１をなしている。
【００９６】
画像形成装置２０において、図５や図６に示す露光装置４２を使用した場合には、半導体レーザ６１の光は、複写画像に対応する画像情報によって、その光強度が変調されており、この光が感光体５１の表面に結像することによって、感光体５１表面に複写画像の静電潜像が形成される。従って、走査レンズ６５ａ，６５ｂ，６５ｃや走査ミラー１５１ａ等で構成される走査光学系６５，１５１の精度、例えば、光学機能面の形状精度、光学素子の配置精度等が、複写画像品質に大きな影響を与えることになる。例えば、走査レンズ６５ａ，６５ｂ，６５ｃや走査ミラー１５１ａが、図示しない光学ベースに接着固定された状態において、母線曲がりが存在していると、感光体５１上の走査線も湾曲してしまう。
【００９７】
従って、画像形成装置２０では、後述するような製造方法によって製造された後述する型部材７１（図７参照）を含む成形用型を用いて、例えば、射出成形により成形された光学素子１であるレンズやミラーを、走査レンズ６５ａ，６５ｂ，６５ｃや走査ミラー１５１ａとして使用しているために、光学システムに固定された実使用状態において、設計形状との形状誤差が小さく、設計時の光学的機能を有しており、その結果として正確な走査が可能となり、高画質の画像を形成することができる。特に、カラーレーザプリンタやカラーデジタル複写機に適用した場合に、色ずれの少ない高画質のカラー画像を形成することができる。
【００９８】
図７は、光学素子１を成形するための成形用型である金型の型部材（鏡面駒（オプティカルインサート））の一例を示す斜視図である。通常、金型は複数個の型部材で構成されているが、図７では、光学素子１の光学機能面４を成形する型部材７１のみを図示している。すなわち型部材７１は、光学素子１の光学機能面４とほぼ合った形状（表面形状）の面７２を有しており、この型部材７１によって形成されるキャビティに溶融した樹脂が注入され、冷却、固化することにより、面７２の表面形状が樹脂に転写されて、前記のような構成の光学素子１が成形される。
【００９９】
したがって、型部材７１の面７２は、光学素子１の光学機能面４を前記の（１）式で表されるような非球面形状に成形する形状である。
【０１００】
そして、型部材７１の面７２は、光学素子１を、母線方向及び子線方向と直交する方向側の側面２のラインと側面３のラインとが不揃いとなり、応力を受けていない状態では母線には歪みが生じていて、この光学素子１が装着されるべき特定の装置（この例では画像形成装置２０）に組み付けた状態では、その歪みが修正されるような形状に成形する形状である。
【０１０１】
この場合に、型部材７１の面７２は、光学素子１を、応力を受けていない状態では両側面３，４に歪みがなく、特定の装置（画像形成装置２０）に組み付けた状態では両側面３，４に歪みが生じるような形状に成形する形状である。
【０１０２】
また、型部材７１の面７２は、この光学素子１のように、本来、理想的には母線と両側面３，４とが平行となるべき成形品については、母線と両側面３，４のラインとは、組み付けられるべき特定の装置（この例では、後述の画像形成装置２０）に組み付けられて応力を受けている状態でも、応力を受けていない状態でも、何れの場合も非平行である。そして、応力を受けていない状態では母線には歪みが生じていて、特定の装置に組み付けた状態ではその歪みが修正されるような形状に成形する形状である。
【０１０３】
そして、型部材７１の面７２は、光学素子１を、応力を受けていない状態では側面３と４とが非対称であり、特定の装置（画像形成装置２０）に組み付けた状態では、側面３と４とが非対称である状態に比べて対称に近づくように変形するような形状に成形する形状である。
【０１０４】
以下では、この型部材７１の製造方法について、図８のフローチャートを参照して詳細に説明する。なお、ここでは、光学素子１の光学機能面４の設計形状は、前記の（１）式で与えられるものとし、便宜的にこれを（２）式で略述する。
Ｚ＝ｆ（Ｘ，Ｙ） …… （２）
【０１０５】
図８のステップＳ１〜Ｓ１０は設計工程を実施するもので、まず、光学素子１の成形素材である樹脂のＸ，Ｙ，Ｚ軸方向に関する収縮率の初期見込値（ｍ_Ｘ ^＊，ｍ_Ｙ ^＊，ｍ_Ｚ ^＊）を決定する（ステップＳ１）。ここでは、成形素材として非晶質ポリオレフィン樹脂を用い、その収縮率の初期見込値を、例えば、“ｍ_Ｘ ^＊＝ ｍ_Ｙ ^＊ ＝ ｍ_Ｚ ^＊ ＝ ０．９９３”とする。
【０１０６】
次に、型部材７１の面７２の表面形状を決定する（ステップＳ２）。ここでは、光学素子１の設計形状に対して、各収縮変形率の初期見込値で与えられる収縮変形量を考慮して、（３）式で示される形状を、型部材７１の面７２の表面形状とする。すなわち、光学素子１の設計形状よりも，この例では全体的に０．７％だけ大きめのキャビティが形成されるように型部材７１の面７２の表面形状を設定する。
Ｚ＝−ｆ（−０．９９３Ｘ，０．９９３Ｙ）／０．９９３ …… （３）
ただし、子線方向の近軸曲率：Ｃ_２（−０．９９３・Ｘ）
子線方向の円錐定数：Ｋ_２（−０．９９３・Ｘ）
子線断面形状のシフト量：Ｓ（−０．９９３・Ｘ）
【０１０７】
なお、本例では、光学素子１の座標系と型部材７１の座標系とは、図８に示すように、Ｙ軸に関しては正負の方向は同一だが、Ｚ軸及びＸ軸に関しては正負の方向が逆の関係にある。一方、例えば、図１０に示すように、Ｘ軸が同一関係で、Ｚ軸及びＹ軸に関して正負の方向が逆の関係にある場合には、型部材７１の面７２の表面形状は、（３）式ではなく、次の（４）式で示される形状となる。
Ｚ＝−ｆ（０．９９３Ｘ，−０．９９３Ｙ）／０．９９３ …… （４）
ただし、子線方向の近軸曲率：Ｃ_２（０．９９３・Ｘ）
子線方向の円錐定数：Ｋ_２（０．９９３・Ｘ）
子線断面形状のシフト量：Ｓ（０．９９３・Ｘ）
【０１０８】
（３）式と（４）式を比較すると、ＸとＹの各係数の正負符号が異なるのみであるため、以下では、Ｙ軸が同一関係にある、図８に相当する場合について説明する。なお、Ｘ軸が同一関係にある場合には、後述する式において、ＸとＹの各係数の正負符号をそれぞれ変えることにより、以下の手順をそのまま用いることができる。
【０１０９】
図８に示すように、型部材７１の面７２の表面形状が決定されると（ステップＳ２）、その表面形状に基づいて型部材７１の製作を行なう（ステップＳ３）。ステップＳ３により成形型予備製作工程を実現している。型部材７１の製作には、高い加工精度を得るためにＮＣ旋盤等の数値制御による自動工作機械（以下、金型加工機という）を用いる。そこで型部材７１の面７２の表面形状は、数値制御用データ（ＮＣデータ等）に変換され、金型加工機８１（図１１参照）に入力される。
【０１１０】
図１１は、金型加工機８１の一例を説明する説明図である。図１１に示すように、金型加工機は、単結晶ダイヤモンド工具８２と工具スピンドル８３とを有しており、Ｙ軸回りに一定速度で回転する工具スピンドル８３の外周面に単結晶ダイヤモンド工具８２が保持されている。また、型部材７１は、図示しない移動ステージによってＸ，Ｙ，Ｚの３軸方向に移動可能である。
【０１１１】
そして、型部材７１形成用の素材（例えば工具用特殊鋼等）が金型加工機８１の所定位置にセットされると、図示しない制御装置の指示に従って、工具スピンドル８３は一定速度で回転し、単結晶ダイヤモンド工具８２によって、まずＸＹ同時２軸制御により、最初の加工ライン８４に沿った切削加工が行われる。そして加工ライン８４の切削加工が終了すると、次に型部材をＹ軸方向に一定ピッチだけ移動させて次の加工ラインの切削加工を行なう。これを繰り返すことにより、設定された表面形状が型部材７１に形成される。なお切削工具は単結晶ダイヤモンド工具８２でなくてもよく、型部材７１の材質や要求される形状精度等により、ほかの切削工具を用いることが可能である。
【０１１２】
図８に示すように、このようにして型部材７１を製作したら（ステップＳ３）、この型部材７１を用いて、種々の条件（金型温度、樹脂温度、射出速度、射出圧力、及び冷却時間等）で射出成形を行い、ほぼ同一形状の光学素子１が安定して成形されるような成形条件を決定する（ステップＳ４）。これらの成形条件は、成形品の形状や樹脂の種類によって変化するものであり、ここでは、一例として、金型温度が１３５℃、樹脂温度が２８０℃、射出速度が２０ｍｍ／ｓｅｃ、射出圧力が５０Ｍｐａ、冷却時間が３００ｓｅｃ、という成形条件を決定したものとして、以下説明する。なお、射出成形用の金型として必要な他の型部材等は予め準備されているものとする。
【０１１３】
このように、成形条件を決定すると（ステップＳ４）、その成形条件で射出成形を行なって、光学素子１を製作する（ステップＳ５）。ステップＳ５により成形品予備製作工程を実現している。射出成形には、電動式射出成形機その他の射出成形機を用いることができる。また、同一表面形状の型部材７１を複数個製作し、金型に各型部材７１をセットすることにより、１回の射出成形で複数個の成形品を成形することも可能である。
【０１１４】
次に、製作した成形品である光学素子１の表面形状を測定する（ステップＳ６）。ステップＳ６により測定工程を実現している。以下では、この測定の具体的な手段について説明する。
【０１１５】
まず、測定に際しては、光学素子１を、この光学素子１が組みつけられるべき特定の装置、この例では画像形成装置２０に組み付けたときに、その組付けにより光学素子１に作用する外力を想定し、その外力と同等の応力を光学素子１に作用させた状態で測定する。
【０１１６】
このような外力を作用させるためには、例えば、図１２に示すような治具９１を用いることができる。この治具９１は、治具９１の本体９２の基準面９３に、光学素子１の基準面となる側面２又は３を当接させて、本体９２に取付けられている板バネ９４の弾性力により光学素子１を本体９２に支持する。このように板バネ９４の弾性力を光学素子１に作用させることにより、光学素子１は基準面９３と板バネ９４から応力を受けるが、この応力は、光学素子１を画像形成装置２０に組み付けたときのものを再現している。
【０１１７】
また、図１３に示すような治具９５を用いてもよい。この治具９５は、本体９６に位置決めピン９７が取付けられていて、光学素子１は、この位置決めピン９７により位置決めされて支持される。本体９６には、真空チャック部９８が設けられ、図示しない真空ポンプにより吸引することで、真空チャック部９８は光学素子１を吸引する。真空チャック部９８の吸引により、基準面となる真空チャック部９８の表面に、光学素子１の基準面となる側面２又は３は当接して、真空チャック部９８の表面から応力を受ける。この応力は、光学素子１を画像形成装置２０に組み付けたときのものを再現している。
【０１１８】
そして、このように、治具９１，９５などを用いて特定の装置に組み付けた状態の外力の作用を再現した状態で、光学素子１の光学機能面４の形状（以下、レンズ形状という）を超高精度の３次元形状測定装置で測定する。
【０１１９】
具体的な３次元形状測定装置としては、例えば、プローブを用いた３次元測定装置を用いることができる。このような３次元測定装置としては、触針式プローブ等の接触式プローブを用いた装置と、光学式変位計による非接触式プローブを用いた装置とがある。ここでは、接触式プローブを用いた３次元形状測定装置による形状測定について説明する。
【０１２０】
図１４は、接触式プローブを用いた３次元形状測定装置の概要を示す模式図である。図中、矢印で示す方向をそれぞれＸ軸、Ｚ軸とし、紙面と垂直方向をＹ軸とする。
【０１２１】
接触式のプローブ１０１は、被測定面１０２との間で、Ｘ，Ｙ，Ｚの各方向に相対的に移動自在に支持されている。そのための構造として、Ｘ軸ステージ１０３、Ｙ軸ステージ１０４及びＺ軸ステージ１０５がそれぞれ設けられている。各軸ステージ１０３，１０４，１０５は、それぞれ、駆動用モータ１０６，１０７，１０８によって駆動され、プローブ１０１と被測定面１０２とをＸ，Ｙ，Ｚ方向に相対移動させる。また、Ｘ，Ｙ，Ｚ軸ステージ１０３，１０４，１０５には、それぞれ、Ｘ軸ステージ１０３、Ｙ軸ステージ１０４及びＺ軸ステージ１０５のそれぞれの移動軌跡を検出するためのリニアエンコーダ１０９，１１０，１１１が設けられている。
【０１２２】
このような３次元形状測定装置では、各駆動用モータ１０６，１０７，１０８に対して、それぞれの駆動装置、つまり、ＸＹ軸駆動装置１１２及びＺ軸駆動装置１１３から駆動制御信号に基づく電力供給がなされることで、各駆動用モータ１０６，１０７，１０８が駆動される。そして、ＸＹ軸駆動装置１１２及びＺ軸駆動装置１１３は、制御／解析用コンピュータ１１４からの駆動制御信号に応じて動作する。
【０１２３】
制御／解析用コンピュータ１１４は、マイクロコンピュータであり、ＣＰＵ、ＲＯＭ、ＲＡＭ（全て図示せず）等を主体として構成されるプロセッサ１１５と、ＨＤＤやその他の記憶手段等によって構成される記憶部１１６とによって構築される。このような制御／解析用コンピュータ１１４には、形状測定用コンピュータプログラムが記憶されており、この形状測定用コンピュータプログラムに従いプローブ１０１を用いた形状測定のための各種の処理を実行する。
【０１２４】
図１４に示すように、接触式のプローブ１０１は、被測定面１０２との接触力を検出する機能を有し、接触力の大きさに応じた接触力信号が出力される。接触力信号は、制御／解析用コンピュータ１１４に取り込まれる。そして、制御／解析用コンピュータ１１４では、接触力信号を常に一定に保つような駆動信号を生成し、これをＺ軸駆動装置１１３へ送る。これにより、Ｚ軸駆動装置１１３から駆動用モータ１０８に駆動電力が供給され、この駆動用モータ１０８によってＺ軸ステージ１０５が駆動されてプローブ１０１と被測定面１０２との接触力を一定に維持する。また、制御／解析用コンピュータ１１４は、内部の記憶部１１６に記憶するＸ、Ｙ座標に基づく駆動信号をＸＹ軸駆動装置１１２へ送る。これにより、ＸＹ軸駆動装置１１２から駆動用モータ１０６、１０７に駆動電力が供給され、これらの駆動用モータ１０６、１０７によってＸ軸ステージ１０３及びＹ軸ステージ１０４が駆動されてプローブ１０１と被測定面１０２とがＸ、Ｙ方向に位置制御される。
【０１２５】
こうして、予め設定された経路に従い、被測定面１０２の表面が走査される。走査中、各軸ステージ１０３、１０４、１０５に備えられたリニアエンコーダ１０９、１１０、１１１の信号は、制御／解析用コンピュータ１１４によって適切なサンプリング間隔で逐次測定され、被測定面１０２の表面形状データがＸ、Ｙ、Ｚ座標点群データとして取得される。さらに詳しくは、取得されたＸ、Ｙ、Ｚに対して後述するデータ処理を施して表面形状データとする。
【０１２６】
図１５は、接触式のプローブ１０１の縦断側面図である。プローブ１０１は、先端部に先端球１１７を備える直動スライダ１１８をハウジング１１９に収納し、その直動スライダ１１８を静圧空気軸受１２０によって非接触状態で支持する構造を有する。これにより、直動スライダ１１８の水平方向の運動が拘束され、直動スライダ１１８は上下方向に摺動抵抗なく運動する。また、直動スライダ１１８の荷重は、ハウジング１１９内でコイルばね１２１によって受けられている。このような基本構造のもと、ハウジング１１９内には、直動スライダ１１８の後端に対面させて変位計１２２が備えられており、この変位計１２２の出力によって直動スライダ１１８の変位を検出し、これによって被測定面１０２（光学素子１の光学機能面４）をトレースする先端球１１７の変位を検出するものである。この際、形状測定の際の動作としては、先端球１１７が被測定面１０２に押しつけられると、コイルばね１２１が変形し、変位計１２２の出力が変化する。そこで、Ｚ軸ステージ１１１を駆動して変位計１２２の出力が一定になるように制御することにより、先端球１１７の接触荷重を一定に保つ。このような接触荷重制御を行なうことで、Ｚ軸方向に大きく湾曲した被測定面１０２の面も測定が可能となる。
【０１２７】
なお、光学式変位計による非接触式プローブを用いた装置としては、例えば、特許第２７９７５２１号公報や特開平２−２５４６３４号公報等に開示されている装置を用いることができる。
【０１２８】
このようなプローブを用いた３次元形状測定装置のほか、レーザ光等の干渉を用いて形状測定する３次元形状測定装置を用いてもよい。このような３次元形状測定装置としては、例えば、Ｚｙｇｏ社のレーザ干渉システム等のレーザ干渉計、同じくＺｙｇｏ社の三次元表面構造解析顕微鏡等の走査型白色干渉計等を用いることができる。
【０１２９】
ここでは、レーザ光等の干渉を用いて形状測定する３次元形状測定装置の一例の概要について説明する。図１６は、かかる３次元形状測定装置の概略構成を示すブロック図である。図１６に示すように、この表面形状測定装置は、光源となるＨｅ−Ｎｅレーザ１３１と、その出力するレーザ光の被測定物１４４（光学素子１）への照射光強度を調整するためのＮＤフィルタ１３２と、レーザ光を拡大するためのビームエキスパンダ１３３とを備えている。
【０１３０】
ビームエキスパンダ１３３にて拡大された光は、ミラー１３４にて折り返され、ビームスプリッタ１３５に入射する。ビームスプリッタ１３５で反射した光は、光を球面波に変換するための光学素子１３６を通り、ミラー１３７で折り返され、光強度を調整するためのＮＤフィルタ１３８、ハーフミラー１３９を介して撮像素子であるＣＣＤ１４０に入射する。この光は、被測定物１４４の反射光と干渉するための参照光となる。
【０１３１】
一方、ビームスプリッタ１３５を透過した光は、ミラー１４１にて折り返され、光学素子１４２により球面波に変換され、ハーフミラー１３９を透過して、対物光学素子１４３によりほぼ平行光に変換されて、被測定物１４４に照射する。被測定物１４４で反射した光は、対物光学素子１４３を通過し、ハーフミラー１３９で反射して物体光としてＣＣＤ１４０に到達し、前記の参照光との間に干渉をおこして干渉縞を発生する。この干渉縞はＣＣＤ１４０にて撮像され、フレームグラバー１４５を介してコンピュータ１４６に転送され、コンピュータ１４６に記録される。
【０１３２】
ビームスプリッタ１３５で分岐された後の参照光路と物体光路の長さは、光源であるＨｅ−Ｎｅレーザ１３１のコヒーレンス長以下になるように設定されている。また、被測定物１４４からの反射光がＣＣＤ１４０で撮像するのに適した強度になるように、ＮＤフィルタ１３２により被測定物１４４への照射光強度を調整してあり、さらに、被測定物１４４からの反射光と参照光との干渉により発生する干渉縞のコントラストが高くなるように、ＮＤフィルタ１３８により参照光強度が調整されている。
【０１３３】
対物光学素子１４３は被測定物１４４の反射光を球面波に変換するように作用し、これにより後述のように被測定物１４４の反射光の複素振幅（被測定物１４４の像）を再生したときに、像が拡大して観測される。光学素子１４２と対物光学素子１４３の位置関係は、被測定物１４４にほぼ平行光が照射されるように調整されている。光学素子１３６は、参照光を球面波に変換するように作用し、対物光学素子１４３により球面波に変換された被測定物１４４の反射光の曲率と、参照光の曲率とが、ＣＣＤ１４０の撮像位置においてほぼ一致するように、位置が調整されている。
【０１３４】
被測定物１４４の像を拡大しない場合は、対物光学素子１４３は不要であり、それに伴い、光学素子１３６、光学素子１４２も不要である。また後で詳細を説明するが、ここでは干渉縞をホログラムとして扱い、ＣＣＤ１４０にて撮像したホログラム干渉縞に仮想的に参照光を照射して、その回折光波により被測定物１４４からの反射光（被測定物１４４の像）の複素振幅を再生する。単一の干渉縞データをＣＣＤ１４０にて撮像し、被測定物１４４の反射光を再生する場合、ホログラムを透過する０次回折光と実像と虚像の３つが再生されるため、この３つを分離して再生できるように、被測定物１４からの反射光の光軸と参照光の光軸との間に適当な傾きを与えて、干渉縞にキャリヤ周波数がのるようにしている。前記の両光軸に傾きを与えるためには、例えば、ミラー１３７、被測定物１４４又はハーフミラー１３９かの傾きを調整すればよい。
【０１３５】
次に、被測定物１４４からの反射光（被測定物１４４の像）の複素振幅（光の振幅と位相を併せて、以下、複素振幅という）を再生計算する方法について説明する。
【０１３６】
まず、被測定物１４４からの反射光と参照光との干渉により発生する干渉縞のＣＣＤ１０の撮像位置での強度は、（５）式で与えられる。
【０１３７】
【数２】

【０１３８】
ここで、Ｉは干渉縞の強度であり、ｘ，ｙはＣＣＤ１０の撮像位置のｘ，ｙ座標、Ｒは参照光の複素振幅であり、Ａ，φはそれぞれ被測定物１４４の反射光の振幅と位相である。
【０１３９】
干渉縞をＣＣＤ１４０にて撮像し、ホログラム画像データとしてコンピュータ１４６に記憶する。乾板を用いたホログラフィでは、干渉縞を記録した乾板（ホログラム）に改めて参照光を照射すると、参照光がホログラムに記録された干渉縞にて回折し、それが記録時の物体反射光として振舞うので、これにより、物体反射光（物体像）が再生されることになった。ここでは、実際に参照光を照射せずに、仮想的に参照光がホログラムに照射されたものとして、ＣＣＤ１４０にて記録したホログラム画像からフレネル近似のもとに物体反射光（物体像）を再生する。ホログラムに参照光として平行光が照射されたとすると、ホログラムによる回折光、すなわち物体反射光は（６）式のように表される。
【０１４０】
【数３】

【０１４１】
ここで、Ｕは再生距離ｄだけ離れた像面位置での物体反射光波の複素振幅、ｘ’，ｙ’は像面位置でのｘ，ｙ座標、ｃは複素定数、λは光源波長を表す。
【０１４２】
したがって、再生距離ｄを入力し、収録した干渉縞データを用いて（６）式を計算することにより、再生距離ｄにおける物体反射光の複素振幅が再生されることになる。被測定物１４４の像を拡大しない場合は、再生距離ｄにＣＣＤ１４０の撮像位置と被測定物１４４の表面との距離を代入すればよい。図１６に示した装置のように、被測定物１４４の像を拡大する場合は、対物光学素子１４３による被測定物１４４の拡大像面とＣＣＤ１４０の撮像位置との距離を、再生距離ｄとして入力する。
【０１４３】
例えば以上のような各種３次元形状測定装置を用い、光学素子１の光学機能面４の形状の測定は次のように行なう。すなわち、まず、光学素子１の母線１２（図３参照）の中央部をＸ軸方向に走査してＺ方向の高さ（デプス）を測定し、Ｙ軸方向に走査する。Ｙ軸方向の測定は、Ｘ軸方向に対して複数位置について行なう。
【０１４４】
図８に示すように、この光学素子１の形状を測定した後（ステップＳ６）、Ｘ軸方向及びＹ軸方向におけるデプスを設計値と比較し、その形状誤差が所定の公差内かどうか判断する（ステップＳ７）。すなわち、応力を受けていない状態では光学素子１の母線１２と両側面２，３のラインとが非平行であり、かつ、母線１２には歪みが生じていて、特定の装置である画像形成装置２０に組み付けた状態ではその歪みが修正されるものとして、光学素子１の形状誤差が公差内かどうか判断する。また、光学素子１の形状が側面２と３のラインが本来不揃いであるような場合には、応力を受けていない状態では母線１２には歪みが生じていて、特定の装置である画像形成装置２０に組み付けた状態では、その歪みが修正されるものとして、光学素子１の形状誤差が公差内かどうか判断する。
【０１４５】
この判断対象となる形状誤差としては、Ｘ軸方向及びＹ軸方向の断面プロファイルの誤差や、Ｙ軸方向断面の近軸曲率誤差のほか、特に母線１２の曲がりについて判断する。この母線曲がりとは、（１）式における子線方向の断面形状のシフト量Ｓに関連する形状誤差であり、設計値における母線位置をＳ（Ｘ）、測定値における母線位置をＳ’（Ｘ）とするとき、“Ｓ’（Ｘ）−Ｓ（Ｘ）”として与えられる量である。なお、Ｓ’（Ｘ）は、具体的には、計算機を使って次のようにして求められる。
【０１４６】
初めに、測定値の各Ｙ軸方向の測定ラインにおいては、Ｘ座標がほぼ同一の値Ｘ_ｉ（本実施形態の場合はｉ＝１〜２３）であることを利用して、ＹＺ断面形状に対して最小自乗近似を行い、近軸曲率中心の座標（Ｙ_ｉ，Ｚ_ｉ）を求める。次に、近軸曲率中心をＸＹ平面に投影してできる点列（Ｘ_ｉ，Ｙ_ｉ）をＸの多項式で近似してＳ’（Ｘ）とする。例えば、４次の多項式で近似した場合、Ｓ’（Ｘ）は次の（７）式のように表される。
【０１４７】
【数４】

【０１４８】
もし、前記した各種の形状誤差が許容し得る所定の公差内であれば（ステップＳ７のＹ）、型部材７１の修正は不要なので、一連の製造工程を終了する。所定の公差内でなければ（ステップＳ７のＮ）、すなわち型部材７１の設計の修正が必要となり、次のステップＳ８に移行する。
【０１４９】
ステップＳ８においては、新たに３つのパラメータ（ｍ_Ｘ，ｍ_Ｙ，ｍ_Ｚ）を用いて、次の（８）式で示される形状回帰式を考える。
【０１５０】
【数５】

【０１５１】
ただし、子線方向の近軸曲率：Ｃ_２（ｍ_Ｘ ^＊／ｍ_Ｘ・Ｘ）
子線方向の円錐定数：Ｋ_２（ｍ_Ｘ ^＊／ｍ_Ｘ・Ｘ）
子線断面形状のシフト量：Ｓ（ｍ_Ｘ ^＊／ｍ_Ｘ・Ｘ）
すなわち、本例では、次の（９）式となる。
【０１５２】
【数６】

【０１５３】
ただし、子線方向の近軸曲率：Ｃ_２（０．９９３／ｍ_Ｘ・Ｘ）
子線方向の円錐定数：Ｋ_２（０．９９３／ｍ_Ｘ・Ｘ）
子線断面形状のシフト量：Ｓ（０．９９３／ｍ_Ｘ・Ｘ）
【０１５４】
そして、光学素子１の形状の測定値と（９）式との差を最小とする前記パラメータ（ｍ_Ｘ，ｍ_Ｙ，ｍ_Ｚ）の最適値を最小自乗法に基づいて計算機を使って求める。本例では、一例として、（ｍ_Ｘ，ｍ_Ｙ，ｍ_Ｚ）＝（0.99325，0.99215，0.99206）という値が得られたものとする。すなわち、形状回帰式は、次の（１０）式となる。
【０１５５】
【数７】

【０１５６】
ただし、子線方向の近軸曲率：Ｃ_２（０．９９３／０．９９３２５・Ｘ）
子線方向の円錐定数：Ｋ_２（０．９９３／０．９９３２５・Ｘ）
子線断面形状のシフト量：Ｓ（０．９９３／０．９９３２５・Ｘ）
このようにして求められた各パラメータの最適値（ｍ_Ｘ，ｍ_Ｙ，ｍ_Ｚ）が、それぞれ、Ｘ，Ｙ，Ｚ軸方向における成形品の収縮率である。
【０１５７】
次に、ステップＳ２で決定した型部材７１の表面形状を、次の（１１）式で示される形状に修正する（ステップＳ９）。
【０１５８】
【数８】

【０１５９】
ただし、子線方向の近軸曲率：Ｃ_２（−ｍ_Ｘ・Ｘ）
子線方向の円錐定数：Ｋ_２（−ｍ_Ｘ・Ｘ）
子線断面形状のシフト量：Ｓ（−ｍ_Ｘ・Ｘ）−Ｓ’（−ｍ_Ｘ・Ｘ）
すなわち、本例では、（１２）式となる。
【０１６０】
【数９】

【０１６１】
ただし、子線方向の近軸曲率：Ｃ_２（-0.99325・Ｘ）
子線方向の円錐定数：Ｋ_２（-0.99325・Ｘ）
子線断面形状のシフト量：Ｓ（-0.99325・Ｘ）−Ｓ’（-0.99325・Ｘ）
【０１６２】
次に、（１２）式で示される表面形状に基づいて、型部材７１の修正加工又は再度の製作を行なう（ステップＳ１０）。そして、ステップＳ５に戻り、修正加工又は再製作された型部材７１を用いて、前記と同じ成形条件で射出成形を行ない（ステップＳ５）、成形された光学素子１の形状の測定が前記と同様にして行われる（ステップＳ６）。そして、再度、光学素子１の形状の測定値と設計形状とを比較し、その形状誤差が所定の公差内か否かを判断する（ステップＳ７）。ここで、所定の公差内であれば（ステップＳ７のＹ）、型部材７１の再修正は不要なので、一連の製造工程を終了する。しかし、所定の公差内でなければ（ステップＳ７のＮ）、型部材７１の再修正が必要となり、次のステップＳ８以降の工程を繰り返す。
【０１６３】
以上説明した型部材７１の製造方法によれば、光学素子１の実使用状態、すなわち、画像形成装置２０に組付けた状態を再現するので、光学素子１の基準面２（又は３）が、画像形成装置２０に組付けたときと同様に変形し、実使用状態での光学素子１の形状を測定することができる。そして、このようにして測定された測定値と型部材７１の設計形状とを比較し、形状誤差を低減するように型部材７１を修正又は再製作するので、修正又は再製作された型部材７１を含む金型を用いて新たに成形された光学素子１は、実使用状態、画像形成装置２０に組付けた状態で、設計形状に最も近づくよう、光学素子１の成形形状を最適化することができる。
【０１６４】
図１７は、前記の方法で製作した型部材７１の成形面７２の平面図である。破線７３は、光学素子１の光学機能面４の母線１２に対応する位置を示すラインであり、このラインは湾曲している。（１）式で示される光学素子１の設計式において、より一般性をもたせるために、子線の断面形状のシフト量Ｓがレンズ高さＸの関数Ｓ（Ｘ）で表されるものとして、これまで説明しできたが、一般には、設計値は“Ｓ（Ｘ）＝０”とするのが通例であると思われるので、成形した光学素子１が実使用状態、すなわち、画像形成装置に組み付けた状態において、母線１２の湾曲と、図１７に示した成形面７２の破線７３の湾曲とを比較したとき、成形面７２の破線７３の湾曲の方がより大きいならば、前記した製造方法を適用して製造された型部材７１であることが強く示唆されることになる。
【０１６５】
以上のようにして設計した型部材７１を製作することにより、成形型本製作工程を実現することができる。そして、この成形用型を用い、例えば前記したような成形材料を使用して、プラスチック射出成形等を行なうことにより、成形品であるレンズ、ミラーなどの光学素子１を製造することができる。
【０１６６】
なお、光学素子１の成形法及び材質は前記の例に限定されるものではない。例えば、ガラスプレス成形に対して前記の方法を適用することもできる。また、成形品もレンズ、ミラーなどの光学素子１に限定するものではなく、各種の製品の成形に前記の方法を使用して、本発明の成形品を製作することができる。
【０１６７】
図８などを参照して説明した方法とは別の型部材７１の製造方法について、図１８のフローチャートを参照して説明する。
【０１６８】
図１８のステップＳ１１〜Ｓ１６は、設計工程を実現するもので、まず、光学素子１の成形素材である樹脂のＸ，Ｙ，Ｚ軸方向に関する収縮率の初期見込値（ｍ_Ｘ ^＊，ｍ_Ｙ ^＊，ｍ_Ｚ ^＊）を決定し（ステップＳ１１）、型部材７１の面７２の表面形状を決定する（ステップＳ１２）。これらの工程は、前記したステップＳ１，Ｓ２と同様に行なうことができる。
【０１６９】
次に、この決定した表面形状の型部材７１を製作したとして、その型部材７１で成形した成形品である光学素子１を特定の装置である画像形成装置２０に組み付けたときに、その光学素子１に加わる応力を想定し、その応力が加わったときの光学素子１の形状変形を計算機上でシミュレートして、その変形を生じている状態の光学素子１の変形を割り出す（ステップＳ１３）。かかるシミュレートは、光学素子１に加わる応力の加わる位置、方向、大きさ、光学素子１の材質の弾力など、様々なファクターを考慮して計算を行なう。
【０１７０】
そして、この変形状態の光学素子１の形状誤差が所定の公差内かどうか判断する（ステップＳ１４）。この判断は、前記ステップＳ７と同様に行なえばよい。そして、形状誤差が所定の公差内であるときは（ステップＳ１４のＹ）、一連の工程を終了する。形状誤差が所定の公差内でないときは（ステップＳ１４のＹ）、前記ステップＳ８と同様の処理（ステップＳ１５）と、前記ステップＳ９と同様の処理（ステップＳ１６）とを行ない、このようにして修正された新たな型部材７１の表面形状に基づいて、ステップＳ１３以下の工程を繰り返せばよい。
【０１７１】
なお、この例では、一度、光学素子１の形状を設計し、その設計した光学素子１を画像形成装置２０に組み付けたときに、その光学素子１に加わる応力を想定したシミュレートを行い、その結果から光学素子１の形状を再度設計しなおすようにしているが、最初から光学素子１の形状誤差が所定の公差内となるような光学素子１の形状を計算機上でシミュレートするようにしてもよい。
【０１７２】
そして、このようにして設計された型部材７１を製作することにより、成形型本製作工程を実現することができる。
【０１７３】
以上、図８、図１８を参照して説明した型部材７１の製造方法によれば、製造後の型部材７１を含む成形用型を用いて製作した成形品である光学素子１は、特定の装置である画像形成装置２０に組み付けたときには理想形状となり、画像形成装置２０に組み付けた実使用状態では、成形の冷却過程に起因して発生する形状誤差以外の成形品の形状誤差、すなわち、光学機能面の第二の変形等も修正される。
【０１７４】
図８を参照して説明した型部材７１の製造方法によれば、実際に成形用型、その成形品である光学素子１を試作し、その光学素子１の形状を測定して、特定の装置である画像形成装置２０に組み付けたときには歪みのない光学素子１の理想形状との誤差を知り、その誤差を反映して成形用型の設計を行なうことができるので、成形用型の設計を具体的で容易なものにすることができる。
【０１７５】
図１８を参照して説明した型部材７１の製造方法によれば、特定の装置である画像形成装置２０に組み付けたときには歪みのない理想形状の光学素子１を製作するための型部材７１を計算で設計することができるので、実際に成形用型、その成形品である光学素子１の試作を行なう手間を省くことができる。この場合に、最初から光学素子１の形状誤差が所定の公差内となるような光学素子１の形状を計算機上でシミュレートするようにすれば、光学素子１の設計を複数回行なう手間を省くことができる。
【０１７６】
図８に示す型部材７１の製造方法において、例えば図１４、図１５を参照して説明したような接触式（又は非接触式）のプローブを用いて形状の測定を行なう３次元形状測定装置、あるいは、例えば図１６を参照して説明したような光の干渉を用いて形状の測定を行なう３次元形状測定装置により光学素子１の形状の測定（ステップＳ６）を行なうようにすれば、成形品である光学素子１の表面形状を精密に測定することができる。
【０１７７】
この際、例えば図１２に示すような治具９１でバネの弾性力により光学素子１に想定される応力を加えるようにするか、例えば図１３に示すような治具９５で真空吸着により光学素子１に想定される応力を加えるようにすれば、当該応力の再現が容易で、成形品である光学素子１を傷めることもない。
【０１７８】
成形品である光学素子１の設計を行なうに際しては、図１に示されるＸ，Ｙ，Ｚ方向において、（１）式のように、Ｘ、Ｙ、さらに、Ｘの関数であるＳの関数として表わされるＺを示す式を用いて行なうので、設計を容易なものとすることができる。
【０１７９】
このような製造方法で製作した型部材７１を含む成形用型を用いて成形した成形品である光学素子１は、特定の装置である画像形成装置２０に組み付けたときには両側面２，３は歪み、応力が加わっていないときより両側面２，３は対称に近づくように変形して、母線１２の歪みのない理想形状となり、画像形成装置２０に組み付けた実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差、すなわち、光学機能面の第二の変形等も修正される。
【０１８０】
このような光学素子１である走査レンズ６５ａ，６５ｂ，６５ｃ，１５１ｂや走査ミラー１５１ｂを露光装置４２に備えている画像形成装置２０によれば、これらの光学素子１は、成形の冷却過程に起因して発生する形状誤差以外の形状誤差、すなわち、光学機能面の第二の変形等も修正されているので、正確な露光走査を行なうことができる画像形成装置２０を提供することができる。
【０１８１】
なお、レンズ、ミラーなどの光学素子１のみならず、各種の成形品及びその製造方法に本発明を適用することができる。また、このような成形品としての光学素子１も、電子写真方式の画像形成装置２０のみならず、各種の光学機器に適用することができる。
【０１８２】
【発明の効果】
請求項１に記載の発明は、成形品の実使用状態では成形の冷却過程に起因して発生する形状誤差以外の成形品の形状誤差も修正される。
【０１８３】
請求項２に記載の発明は、請求項１に記載の成形用型の製造方法において、成形用型の設計を具体的で容易なものにすることができる。
【０１８４】
請求項３に記載の発明は、請求項１に記載の成形用型の製造方法において、実際に成形用型、その成形品の試作を行なう手間を省くことができる。
【０１８５】
請求項４に記載の発明は、請求項２に記載の成形用型の製造方法において、試作した成形用型で成形した成形品の表面形状を精密に測定することができる。
【０１８６】
請求項５に記載の発明は、請求項２に記載の成形用型の製造方法において、試作した成形用型で成形した成形品の表面形状を精密に測定することができる。
【０１８７】
請求項６に記載の発明は、請求項２，４又は５に記載の成形用型の製造方法において、特定の装置に組み付けたとき成形品にかかる応力の再現が容易で、成形品を傷めることもない。
【０１８８】
請求項７に記載の発明は、請求項２，４又は５に記載の成形用型の製造方法において、特定の装置に組み付けたとき成形品にかかる応力の再現が容易で、成形品を傷めることもない。
【０１８９】
請求項８に記載の発明は、請求項２，４〜７のいずれかの一に記載の成形用型の製造方法において、成形用型の設計が容易になる。
【０１９５】
請求項１０に記載の発明は、特定の装置に組み付けたときには母線の歪みのない理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正される成形品を成形できる。
【０１９７】
請求項１１に記載の発明は、特定の装置に組み付けたときには両側面は歪んで全体としては理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正される成形品を成形できる。
【０１９８】
請求項１２に記載の発明は、特定の装置に組み付けたときには両側面は対称に近づくように変形して全体としては理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正される成形品を成形できる。
【０１９９】
請求項１３に記載の発明は、特定の装置に組み付けたときには母線の歪みのない理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正される光学素子を提供できる。
【０２０１】
請求項１４に記載の発明は、特定の装置に組み付けたときには両側面は歪んで全体としては理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正される光学素子を提供できる。
【０２０２】
請求項１５に記載の発明は、特定の装置に組み付けたときには両側面は対称に近づくように変形して全体としては理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正される光学素子を提供できる。
【０２０３】
請求項１６に記載の発明は、特定の装置に組み付けたときには母線の歪みのない理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正されるレンズを提供できる。
【０２０５】
請求項１７に記載の発明は、特定の装置に組み付けたときには両側面は歪んで全体としては理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正されるレンズを提供できる。
【０２０６】
請求項１８に記載の発明は、特定の装置に組み付けたときには両側面は対称に近づくように変形して全体としては理想形状となり、実使用状態では成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正されるレンズを提供できる。
【０２０７】
請求項１９に記載の発明は、成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正されている光学素子又はレンズが用いられ、正確な光学機能を発揮する光学機器を提供することができる。
【０２０８】
請求項２０に記載の発明は、成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正されている光学素子又はレンズが用いられ、正確な露光走査を行なうことができる画像形成装置を提供することができる。
【０２０９】
請求項２１に記載の発明は、成形の冷却過程に起因して発生する形状誤差以外の形状誤差も修正されている光学素子又はレンズが用いられ、読み取った画像データに基づいて正確な露光走査を行なうことができる画像形成装置を提供することができる。
【図面の簡単な説明】
【図１】この発明の課題を説明する説明図である。
【図２】この発明の一実施の形態である光学素子の斜視図である。
【図３】前記光学素子の光学機能面の平面図である。
【図４】前記光学素子を備えた画像形成装置の概略構成を説明する説明図である。
【図５】前記画像形成装置の露光装置の斜視図である。
【図６】前記画像形成装置の露光装置の別例を示す斜視図である。
【図７】この発明の一実施の形態である成形用型を構成する型部材の斜視図である。
【図８】この発明の一実施の形態である型部材の製造方法を説明するフローチャートである。
【図９】前記製造方法を説明する説明図である。
【図１０】同説明図である。
【図１１】同説明図である。
【図１２】前記製造方法に使用する治具の一例を示す斜視図である。
【図１３】前記治具の他の例を示す斜視図である。
【図１４】前記製造方法に使用する３次元形状測定装置の一例を示すブロック図である。
【図１５】前記３次元形状測定装置のプローブ部分の縦断面図である。
【図１６】前記製造方法に使用する３次元形状測定装置の他の例を示すブロック図である。
【図１７】この発明の一実施の形態である成形用型を構成する型部材の成形面の平面図である。
【図１８】この発明の別の実施の形態である型部材の製造方法を説明するフローチャートである。
【符号の説明】
１ 光学素子、レンズ、成形品
２ 側面
３ 側面
１２ 母線
２０ 画像形成装置
４２ 露光装置
６５ａ レンズ、光学素子
６５ｂ レンズ、光学素子
６５ｃ レンズ、光学素子
７１ 成形用型
９１ 治具
９５ 治具
１５１ａ 光学素子
１５１ｂ レンズ、光学素子[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for manufacturing a molding die, a method for manufacturing a molded product, a molded product, a molding die, an optical element, a lens, an optical instrument, an image forming apparatus, and a jig.
[0002]
[Prior art]
Since optical elements such as lenses are inexpensive and light, relatively many optical elements such as plastic are used. Most of the optical elements made of resin are manufactured by an injection molding method and similar techniques. In the injection molding method, a molding die such as a mold having a cavity having a shape similar to that of a molded product is used. The surface of the mold member constituting the mold is processed into a predetermined surface shape based on the design shape of the optical element that is a molded product in order to form a cavity. Then, a molten resin is injected into the mold cavity while applying pressure, and after cooling, the solidified resin is separated from the mold so that the surface shape of the mold is transferred to a predetermined shape. As an optical element can be obtained.
[0003]
For injection molding, thermoplastic resins such as amorphous polyolefin and acrylic are used for optical elements. The resin is heated and melted at around 200 ° C, and the mold is kept in a molten state. Injected into. Therefore, due to shrinkage that occurs when the injected resin is solidified, thermal shrinkage that occurs when the injected resin is cooled to room temperature, the optical element that is a molded product is deformed, and its shape is smaller than the molding cavity. As a countermeasure, the deformation generated in the cooling process of the optical element is approximated as a similar deformation, and the molding die is designed to be slightly larger than the molded product in consideration of the similar deformation rate.
[0004]
However, in reality, the deformation that occurs in the cooling process of the optical element is not only similar deformation, but also non-uniformity caused by non-uniform cooling rate, non-uniform resin temperature, asymmetry of the shape of the optical element as a molded product, etc. Non-similar deformation due to internal stress, resin density non-uniformity, and the like. Therefore, an optical element having sufficient shape accuracy cannot be obtained with a molding die designed by approximating the deformation generated in the cooling process of the optical element as a similar deformation.
[0005]
Therefore, in the technique disclosed in Japanese Patent No. 2898197, the shape of the optical functional surface of the optical element, which is a molded product molded using a mold member having a predetermined surface shape, is measured. An attempt is made to improve the shape accuracy of the optical element by obtaining a shape error which is a dimensional difference from the design shape and correcting the shape of the mold member again so as to reduce the shape error.
[0006]
[Problems to be solved by the invention]
However, in the technique disclosed in Japanese Patent No. 2898197, only the improvement of the shape error (for example, curvature error) of the optical function surface of the optical element caused by the cooling process of molding is targeted. Other than the deformation of the outer shape and the deformation of the optical function surface related to the deformation of the outer shape (in the sense of distinguishing from the above-mentioned `` shape error of the optical function surface caused by the cooling process of molding ''), There is a problem that “the second deformation of the optical function surface”) cannot be solved at all. Here, “deformation of the optical functional surface related to the deformation of the outer shape” means that the deformation of the optical functional surface of the optical element is also corrected at the same time when the deformation of the outer shape can be corrected by external force. For example, it refers to a “bus bend” described later.
[0007]
The object of the present invention is to correct the shape error of the molded product other than the shape error caused by the cooling process of the molded product in the actual use state of the molded product, as in the second modification of the optical functional surface described above. Is to do.
[0008]
Another object of the present invention is to make the design of the molding die concrete and easy in correcting the second deformation or the like of the optical function surface.
[0009]
Another object of the present invention is to save the labor of making a prototype of a molded product when correcting the second deformation or the like of the optical function surface.
[0010]
Another object of the present invention is to accurately measure the surface shape of a molded product molded with a prototype molding die when correcting the second deformation or the like of the optical functional surface.
[0011]
Another object of the present invention is to make it easy to reproduce the stress applied to the molded product when it is assembled in a specific device when correcting the second deformation of the optical function surface, etc., so that the molded product is not damaged. It is to be.
[0012]
Another object of the present invention is to provide a suitable jig for correcting the second deformation or the like of the optical function surface.
[0013]
[Means for Solving the Problems]
  The invention of claim 1 has a long direction and a short direction perpendicular to the optical axis direction, has a concave shape or a convex shape with respect to the optical axis direction, and is assembled to an optical apparatus.fθ lensA method for manufacturing a molding die according to claim 1, wherein a line connecting the lowest point of the concave shape or the highest point of the convex shape along the longitudinal direction is a busbar, and is assembled to the optical device. When not mounted, the bus bar is distorted. When mounted on the optical apparatus, the bus bar is distorted by the stress at the time of mounting.To be closer to the design shape than when the fθ lens is not assembled.The abovefθ lensThis is a method for manufacturing a molding die, which includes a design step of designing a molding die in which the molding die is molded and a molding die main manufacturing step of manufacturing the molding die according to the design.
[0014]
Therefore, a molded product manufactured using a mold for manufacturing after manufacture becomes an ideal shape when assembled to a specific apparatus.
[0015]
  The invention according to claim 2 provides thefθ lensThe mold pre-manufacturing process for manufacturing the mold for molding, and using the manufactured moldfθ lensThe pre-manufacturing process of the molded product and the manufacturedfθ lensIn a state where stress that is assumed to be applied when assembled to the optical device is actually applied.fθ lensA measuring step for measuring the shape of the mold, and the designing step is for designing the molding die based on the measurement result.
[0016]
Therefore, when you actually prototype the mold and the molded product, measure the shape of the molded product, know the error from the ideal shape of the molded product without distortion when assembled to a specific device, and reflect that error Thus, the molding die can be designed.
[0017]
  According to a third aspect of the present invention, in the design step, the stress, the shape, and the deformation before and after the deformation are performed by performing a predetermined calculation.fθ lensThe shape of the mold is designed by simulating the shape.
[0018]
Therefore, it is possible to design a molding die for producing an ideal-shaped molded product having no distortion when assembled in a specific apparatus.
[0019]
  According to a fourth aspect of the present invention, the measurement step uses a contact or non-contact type probe.SaidThe measurement is performed by a three-dimensional shape measuring apparatus that measures the shape.
[0020]
Therefore, the shape of the molded product can be measured by a three-dimensional shape measuring apparatus using a contact type or non-contact type probe.
[0021]
  According to a fifth aspect of the present invention, the measurement step uses light interference.SaidThe measurement is performed by a three-dimensional shape measuring apparatus that measures the shape.
[0022]
Therefore, the shape of the molded product can be measured by a three-dimensional shape measuring apparatus using light interference.
[0023]
  The invention according to claim 6 is characterized in that the measuring step is performed by an elastic force of a spring.fθ lensThe above-mentioned assumed stress is applied to the above.
[0024]
Therefore, the stress applied to the molded product when it is assembled to a specific device is reproduced by the elastic force of the spring.
[0025]
  The invention according to claim 7 is characterized in that the measurement step is performed by vacuum adsorption.fθ lensThe above-mentioned assumed stress is applied to the above.
[0026]
Therefore, the stress applied to the molded product when it is assembled to a specific device is reproduced by vacuum suction.
[0027]
The invention according to claim 8 is characterized in that the design step includes the step offθ lensWhen the concavo-convex direction of a predetermined line on the surface of the surface is the Z direction, and the direction orthogonal to the Z direction is the X direction and the Y direction, S is a function of X indicating the concavo-convex, and is expressed as a function of the X and Y. The above design is performed using the above-described formula indicating Z.
[0028]
Therefore, when designing a molding die by measuring a molded product molded with the prototype molding die, an expression expressed using S that is a function of X can be used.
[0029]
  The invention according to claim 9 uses the molding die manufactured by the method for manufacturing a molding die according to any one of claims 1 to 8.fθ lensMakefθ lensIt is a manufacturing method.
[0030]
Therefore, the molded product after manufacture becomes an ideal shape when assembled to a specific device.
[0039]
The invention according to claim 10 has a long direction and a short direction perpendicular to the optical axis direction, has a concave shape or a convex shape with respect to the optical axis direction, and is assembled to an optical apparatus.fθ lensThe mold is not assembled to the optical device when a line connecting the lowest point of the concave shape or the highest point of the convex shape along the longitudinal direction is a busbar. In the state, the bus bar is distorted. In the state where the bus bar is assembled in the optical apparatus, the distortion of the bus bar is corrected by the stress during the assembly.To be closer to the design shape than when the fθ lens is not assembled.The abovefθ lensIs a mold for molding.
[0040]
Therefore, when assembled in a specific device, it has an ideal shape with no busbar distortion.
[0043]
  The invention according to claim 11 is characterized in that thefθ lensIn a state where the stress is not received, the side surface in the lateral direction is not distorted, and when assembled in the optical apparatus, the side surface is distorted.
[0044]
Therefore, when assembled in a specific device, both side surfaces are distorted and become an ideal shape as a whole.
[0047]
  Claim12The described invention has a long direction and a short direction perpendicular to the optical axis direction, has a concave shape or a convex shape with respect to the optical axis direction, and is assembled to an optical apparatus.fθ lensAnd when the lowest point of the concave shape or the highest point of the convex shape is a line connecting the longitudinal direction as a bus, in a state where it is not assembled to the optical instrument, The busbar is distorted, and in the state assembled to the optical device, the distortion of the busbar is corrected by the stress at the time of assembly,Fθ lens that is closer to the design shape than when it is not assembled.
[0048]
Therefore, when assembled in a specific device, it has an ideal shape with no busbar distortion.
[0051]
  Claim13In the described invention, the side surface is not distorted in a state where the stress is not received, and the side surface is distorted in the short direction when assembled in the optical apparatus.fθ lensIt is.
[0052]
Therefore, when assembled in a specific device, both side surfaces are distorted and become an ideal shape as a whole.
[0055]
  Claim14The described invention has a long direction and a short direction perpendicular to the optical axis direction, has a concave shape or a convex shape with respect to the optical axis direction, and is assembled to an optical apparatus.fθIn a state where the lens is not assembled to the optical device when the bus line is formed by connecting the lowest point of the concave shape or the highest point of the convex shape along the longitudinal direction, The busbar is distorted, and when assembled in the optical apparatus, the busbar distortion is corrected by the stress during assembly.Fθ closer to the design shape than when the fθ lens is not assembled.It is a lens.
[0056]
Therefore, when assembled in a specific device, it has an ideal shape with no busbar distortion.
[0059]
  Claim15In the described invention, the side surface in the short side direction is not distorted in a state where the stress is not received, and the side surface is distorted when assembled in the optical apparatus.fθ lensIt is.
[0060]
Therefore, when assembled in a specific device, both side surfaces are distorted and become an ideal shape as a whole.
[0063]
  Claim16The described inventionClaim 12 or 13Described infθ lensOr claim14 or 15Described infθThe distortion of the lens is corrected,The fθ lens is arranged so that it is closer to the design shape than when not assembled.It is an optical device equipped with an optical system.
[0064]
Accordingly, the optical device is provided with an optical element or a lens in which a shape error other than the shape error generated due to the cooling process of the molding is corrected.
[0065]
  Claim17The described invention is claimed.14 or 15Described inFθThe lens
  ConcernedfθThe distortion of the lens is corrected,The fθ lens is closer to the design shape than when it is not assembled.The image forming apparatus includes an exposure apparatus assembled in this manner and forms an image on a sheet by electrophotography.
[0066]
Therefore, the image forming apparatus includes an optical element such as a lens in which a shape error other than the shape error generated due to the cooling process of the molding is corrected.
[0067]
  Claim21The described invention includes an image reading device that reads an image of a document, and performs the image formation based on image data read by the image reading device.
[0068]
Accordingly, an image forming apparatus having an image reading apparatus includes an optical element such as a lens in which a shape error other than a shape error generated due to a cooling process of molding is corrected.
[0075]
DETAILED DESCRIPTION OF THE INVENTION
An embodiment of the present invention will be described.
[0076]
First, the reason why the outer shape of a conventional optical element, which is a molded product, is deformed will be specifically described taking the optical element shown in FIG. 1 as an example. In the cavity when the optical element 201 shown in FIG. 1 is molded, it is assumed that the resin temperature is higher on the side 203 side, which is the opposite side of the side 202, than on the side 202 of the optical element 201. It is clear that the side 203 has a larger amount of resin shrinkage during the cooling process. As a result, the outer shape of the optical element 201 is deformed into a convex shape in the positive direction of the Y axis direction in FIG. Since the resin temperature filled in the actual cavity has a more complicated temperature distribution, it is not only a convex shape or a concave shape, but also an S shape or a shape twisted around the X axis in FIG. In addition, the outer shape is deformed.
[0077]
Next, a second modification of the optical function surface will be described. When the optical element 201, which is a molded product, is fixed to the optical base or lens holder of the optical device, if the external element can be fixed by applying an external force sufficient to correct the deformation of the outer shape, the second deformation is simultaneously performed as described above. In practice, the optical element 201 must be fixed so that the thermal expansion and contraction of the optical element 201 can be appropriately released in order to prevent the optical function from deteriorating due to thermal deformation in actual use. In other words, a fixing means that is strong enough to completely correct the deformation of the outer shape cannot be employed. Therefore, the second deformation is not completely corrected and some of it remains. As an example, when the optical element 201 whose side 202 (or side 203) as a reference mounting surface is curved by 50 μm is bonded and fixed only at the center without both ends being constrained, the side 202 (or side 203) that is the reference mounting surface. In addition, a curvature of about 15 μm to 25 μm remains at the same time, and the same degree of curvature also remains on the optical function surface 204, resulting in deterioration of optical performance.
[0078]
When such an optical element 201 is used as a scanning optical element of an exposure apparatus in an electrophotographic image forming apparatus such as a laser printer or a digital copying machine, for example, the optical function surface 204 as described above. Such a curvature causes a deterioration in optical performance such as a curvature of the scanning line of the scanning beam on the surface of the photosensitive member. In particular, in a color image forming apparatus, this causes a color misregistration, resulting in a problem that the image quality is greatly affected.
[0079]
FIG. 2 is a perspective view of an example of an optical element that is a molded article that solves such a problem. The optical element 1 is, for example, a lens, and more specifically a scanning lens (fθ lens) used in an optical apparatus such as an electrophotographic image forming apparatus such as a laser printer. Here, the optical axis direction of the optical element 1 is the Z-axis direction, the long direction is the X-axis direction, and the short direction is the Y-axis direction. In this specification, a line connecting the highest (or lowest) positions of the convex (or concave) shape in the longitudinal direction of the object is referred to as a “bus line”, and a line in the short direction of the object is referred to as a “child line”. It will be called appropriately. The side surface 3 that is the surface opposite to the side surface 2 of the optical element 1 serves as a reference surface for fixing to the mounting reference surface on the optical device side. The optical element 1 uses, for example, an amorphous polyolefin resin as a molding material.
[0080]
The optical functional surface 4 of the optical element 1 has an aspheric shape represented by the formula (1).
[0081]
[Expression 1]

[0082]
In the formula (1), C₁Is the curvature in the busbar direction in the vicinity of the optical axis (hereinafter referred to as the paraxial curvature in the busbar direction as appropriate), C₂Is the curvature in the sub-wire direction in the vicinity of the optical axis (hereinafter referred to as the paraxial curvature in the sub-wire direction as appropriate), K₁Is the conic constant in the direction of the bus, K₂Is the conic constant in the direction of the strand, and S is the shift amount of the strand cross-sectional shape. C₂, K₂, S is a function of the lens height X in the generatrix direction, C₂(X), K₂(X) and S (X). The third term of equation (1) is a polynomial, m and n are the orders of X and Y, respectively, M and N are the maximum orders of X and Y, respectively, A_mnIs a polynomial coefficient.
[0083]
The optical element 1 which is this molded product has a busbar direction (in this example, since the optical element 1 is an fθ lens for exposure scanning, the busbar direction is the main scanning direction) and a slave line direction (also the optical element 1 Is an exposure scanning fθ lens, and therefore, the lines on both side surfaces 3 and 4 on the direction orthogonal to the sub-scanning direction are not aligned. The bus bar is distorted in a state where no stress is applied. In a state where the optical element 1 is to be mounted, in this example, in a state where the optical element 1 is assembled to the image forming apparatus 20 described later, the distortion is generated. Will be corrected.
[0084]
In this case, the side surfaces 3 and 4 are not distorted in a state where no stress is applied, and the side surfaces 3 and 4 are distorted when assembled in a specific apparatus (image forming apparatus 20).
[0085]
Further, in the case of a molded product that should ideally be parallel to the bus bar and the side surfaces 3 and 4 like the optical element 1, the bus bar and the lines of the side surfaces 3 and 4 are specified to be assembled. In either case, the apparatus is assembled in the apparatus (in this example, an image forming apparatus 20 described later) and is in a state of being stressed, or in a state of being not subjected to the stress. The bus bar is distorted when it is not subjected to stress, and the distortion is corrected when it is assembled to a specific device.
[0086]
The side surfaces 3 and 4 are asymmetric in a state where no stress is applied, and in a state where the side surfaces 3 and 4 are asymmetric in the state where the side surfaces 3 and 4 are assembled to a specific apparatus (image forming apparatus 20). It deforms as follows.
[0087]
FIG. 3A is a conceptual diagram of the optical functional surface 4 of the optical element 1 in a state where it is not subjected to stress as described above, and FIG. 3B is a specific device (in this example, which will be described later). It is a conceptual diagram of the optical function surface 4 of the optical element 1 assembled in the image forming apparatus 20) and receiving a stress (indicated by an arrow 11). 3A and 3B, a broken line 12 indicates a bus.
[0088]
FIG. 4 is a diagram illustrating a schematic configuration of an electrophotographic image forming apparatus which is an example of an optical apparatus in which the optical element 1 which is an example of the optical element as such a molded product is assembled. The image forming apparatus 20 includes an image scanner 22 that is an image reading apparatus, a printer unit 23 that performs image formation on a sheet based on image data read by the image scanner 22, and an ADF (Automatic) provided on the image scanner 22. Document Feeder) 24.
[0089]
A contact glass 25 on which an original to be read is placed is provided on the upper surface of the image scanner 22. Below the contact glass 25, a first carriage 28 that includes the illumination lamp 26 and the mirror 27 and can travel along the contact glass 25, and a second carriage that includes the mirrors 29 and 30 and can travel along the contact glass 25. A scanning optical system 34 including a carriage 31, an imaging lens 32, and a CCD (Charge Coupled Device) 33 that is a photoelectric conversion element is provided. The first and second carriages 28 and 31 are driven by a carriage motor (not shown) such as a stepping motor, and travel from the home position (right side) shown in FIG. 4 to the left side at a speed ratio of 2: 1.
[0090]
In the printer unit 23, a paper transport path from a paper feed tray 35 for stacking paper to a paper discharge stacker unit 38 via a printer engine 36, a fixing device 37, etc. for forming an image on the paper by electrophotography. 39 is formed. The printer engine 36 exposes the photoconductor 51 based on image data read by the image scanner 22, the charging device 52 that uniformly charges the surface of the photoconductor 51, and the image scanner 22 to form an electrostatic latent image. The exposure device 42, the developing unit 53 that develops the electrostatic latent image formed on the surface of the photoconductor 51 with toner, and the toner image on the photoconductor 51 is transferred to the paper conveyed through the paper conveyance path 39. And a cleaning device 54 for cleaning the surface of the photoconductor 51 after the transfer.
[0091]
The ADF 24 includes a document table 45 on which a document to be fed to the contact glass 25 by the ADF 24 is placed, and a paper discharge unit 46 from which the document that has been read is discharged. Inside the ADF 24, a document conveyance path 47 that communicates from the document table 45 to the paper discharge unit 46 is formed. In the document conveyance path 47, conveyance mechanisms such as an endless belt 49 wound around a plurality of pairs of rollers 48 and a conveyance roller 50 are provided. This transport mechanism is driven by an ADF motor (not shown) such as a stepping motor, and transports the originals placed on the original table 45 one by one toward the contact glass 25. A main body operation panel 52 including a keyboard and a display is provided on the upper surface of the ADF 24.
[0092]
FIG. 5 is a perspective view showing a configuration example of the exposure apparatus 42. The exposure apparatus 42 includes a semiconductor laser 61 as a light source, a rotating polygon mirror (polygon mirror) 64 having a deflecting surface for deflecting light from the semiconductor laser 61 in a predetermined angular range at a constant angular velocity, and the rotating polygon mirror 64. A laser scanning optical system 65 that is an optical system that converts the deflected light into constant-speed light, a folding mirror 68 that changes the direction of light from the laser scanning optical system 65 (folds the optical path), and the like are provided. ing. Here, the scanning lens 65a, 65b, 65c is used for the laser scanning optical system 65. Each of the scanning lenses 65a, 65b, and 65c is the optical element 1 having the above-described configuration.
[0093]
The operation of the exposure device 42 will be described. The light emitted from the semiconductor laser 61 forms an image once in the vicinity of the deflection surface of the rotary polygon mirror 64 via the lenses 62 and 63. The rotating polygon mirror 64 rotates at a constant angular velocity in the direction of the arrow 69 in FIG. 5, and the light imaged in the vicinity of the deflection surface is deflected at a constant angular velocity with the rotation of the rotating polygon mirror 64. The deflected light is sequentially transmitted through the fθ lenses 65a, 65b, and 65c to be converted into constant speed light, reflected by the folding mirror 68, and exposed and scanned on the surface of the photoconductor 51 that is a scanning target.
[0094]
FIG. 6 is a perspective view showing another example of the exposure apparatus 42 different from that described above with reference to FIG.
[0095]
In FIG. 6, the same members as those in FIG. That is, the light emitted from the semiconductor laser 61 forms an image once in the vicinity of the deflection surface of the rotary polygon mirror 64 via the lenses 62 and 63. The rotating polygon mirror 64 rotates at a constant angular velocity in the direction of the arrow in the drawing, and the light imaged in the vicinity of the deflecting surface is deflected at a constant angular velocity as the rotating polygon mirror 64 rotates. The deflected light enters the optical element 151b through the scanning mirror 151a and the folding mirror 152a, is converted to constant velocity light, is reflected by the folding mirror 152b, and is reflected on the surface of the photoconductor 51 that is the scanning target. Is scanned by exposure. The scanning mirror 151a and the optical element 151b constitute a laser scanning optical system 151.
[0096]
In the image forming apparatus 20, when the exposure device 42 shown in FIG. 5 or FIG. 6 is used, the light intensity of the light from the semiconductor laser 61 is modulated by image information corresponding to the copy image. Is formed on the surface of the photoconductor 51, whereby an electrostatic latent image of a copy image is formed on the surface of the photoconductor 51. Accordingly, the accuracy of the scanning optical systems 65 and 151 including the scanning lenses 65a, 65b, and 65c, the scanning mirror 151a, and the like, for example, the shape accuracy of the optical function surface, the placement accuracy of the optical elements, and the like have a great influence on the copy image quality. Will give. For example, in the state where the scanning lenses 65a, 65b, 65c and the scanning mirror 151a are bonded and fixed to an optical base (not shown), if there is a bend in the bus line, the scanning line on the photoconductor 51 is also curved.
[0097]
Therefore, in the image forming apparatus 20, the optical element 1 is formed by, for example, injection molding using a molding die including a mold member 71 (see FIG. 7) described later manufactured by a manufacturing method described later. Since the lenses and mirrors are used as the scanning lenses 65a, 65b, 65c and the scanning mirror 151a, in the actual use state fixed to the optical system, the shape error with the design shape is small, and the optical function at the time of design As a result, accurate scanning is possible, and a high-quality image can be formed. In particular, when applied to a color laser printer or a color digital copying machine, a high-quality color image with little color misregistration can be formed.
[0098]
FIG. 7 is a perspective view showing an example of a mold member (a mirror piece (optical insert)) that is a mold for molding the optical element 1. Normally, the mold is composed of a plurality of mold members, but FIG. 7 shows only the mold member 71 for molding the optical functional surface 4 of the optical element 1. That is, the mold member 71 has a surface 72 having a shape (surface shape) substantially matching the optical function surface 4 of the optical element 1, and molten resin is injected into a cavity formed by the mold member 71 to cool the mold member 71. By solidifying, the surface shape of the surface 72 is transferred to the resin, and the optical element 1 configured as described above is molded.
[0099]
Therefore, the surface 72 of the mold member 71 has a shape that molds the optical functional surface 4 of the optical element 1 into an aspherical shape as expressed by the above-described equation (1).
[0100]
Then, the surface 72 of the mold member 71 causes the optical element 1 to be a busbar in a state where the line of the side surface 2 and the line of the side surface 3 on the direction side orthogonal to the busbar direction and the childline direction are not aligned and are not subjected to stress. Is a shape that is deformed and molded into a shape that corrects the distortion in a state in which the optical element 1 is assembled to a specific device (image forming apparatus 20 in this example) to be mounted.
[0101]
In this case, the surface 72 of the mold member 71 is formed on both side surfaces when the optical element 1 is not distorted on both side surfaces 3 and 4 when it is not subjected to stress, and when it is assembled to a specific apparatus (image forming apparatus 20). The shape is formed into a shape in which distortion occurs in 3 and 4.
[0102]
In addition, the surface 72 of the mold member 71 is essentially formed of the bus bar and the side surfaces 3 and 4 for a molded product in which the bus bar and the side surfaces 3 and 4 should ideally be parallel. The line is non-parallel both in a state where it is attached to a specific device to be assembled (in this example, an image forming apparatus 20 described later) and is in a stressed state or in a state where the stress is not received. . And it is the shape which shape | molds in the shape where distortion has arisen in the bus-bar in the state which has not received stress, and the distortion is corrected in the state assembled | attached to the specific apparatus.
[0103]
The surface 72 of the mold member 71 is asymmetric with the side surfaces 3 and 4 when the optical element 1 is not subjected to stress, and with the side surface 3 when assembled with a specific apparatus (image forming apparatus 20). 4 is a shape that is shaped so as to be deformed so as to approach symmetry as compared to the state of being asymmetric.
[0104]
Below, the manufacturing method of this type | mold member 71 is demonstrated in detail with reference to the flowchart of FIG. Here, it is assumed that the design shape of the optical functional surface 4 of the optical element 1 is given by the above-described equation (1), and this is briefly described by the equation (2) for convenience.
Z = f (X, Y) (2)
[0105]
Steps S1 to S10 in FIG. 8 are for carrying out the design process. First, an initial expected value (m_X ^*, M_Y ^*, M_Z ^*) Is determined (step S1). Here, an amorphous polyolefin resin is used as a molding material, and the initial expected value of the shrinkage is, for example, “m_X ^*= M_Y ^* = M_Z ^* = 0.993 ".
[0106]
Next, the surface shape of the surface 72 of the mold member 71 is determined (step S2). Here, considering the amount of shrinkage deformation given by the initial expected value of each shrinkage deformation rate with respect to the design shape of the optical element 1, the shape represented by the expression (3) is changed to the surface of the surface 72 of the mold member 71. Shape. That is, in this example, the surface shape of the surface 72 of the mold member 71 is set so that a cavity larger by 0.7% than the design shape of the optical element 1 is formed.
Z = −f (−0.993X, 0.993Y) /0.993 (3)
However, paraxial curvature in the sub-wire direction: C₂(−0.993 · X)
Conical constant in the direction of the strand: K₂(−0.993 · X)
Shift amount of the cross-sectional shape of the strand: S (−0.993 · X)
[0107]
In this example, as shown in FIG. 8, the coordinate system of the optical element 1 and the coordinate system of the mold member 71 have the same positive and negative directions with respect to the Y axis, but with positive and negative directions with respect to the Z axis and the X axis. Are in the opposite relationship. On the other hand, for example, as shown in FIG. 10, when the X axis is the same and the positive and negative directions are opposite with respect to the Z and Y axes, the surface shape of the surface 72 of the mold member 71 is (3 ), Not the following formula (4).
Z = −f (0.993X, −0.993Y) /0.993 (4)
However, paraxial curvature in the sub-wire direction: C₂(0.993 · X)
Conical constant in the direction of the strand: K₂(0.993 · X)
Shift amount of the cross-sectional shape of the strand: S (0.993 · X)
[0108]
When the equations (3) and (4) are compared, only the signs of the X and Y coefficients are different. Therefore, a case corresponding to FIG. 8 in which the Y axes are in the same relationship will be described below. When the X-axis is in the same relationship, the following procedure can be used as it is by changing the sign of each of the X and Y coefficients in the formula described later.
[0109]
As shown in FIG. 8, when the surface shape of the surface 72 of the mold member 71 is determined (step S2), the mold member 71 is manufactured based on the surface shape (step S3). Step S3 realizes a mold pre-manufacturing process. For the production of the mold member 71, an automatic machine tool (hereinafter referred to as a mold processing machine) by numerical control such as an NC lathe is used in order to obtain high machining accuracy. Therefore, the surface shape of the surface 72 of the mold member 71 is converted into numerical control data (NC data or the like) and input to the mold processing machine 81 (see FIG. 11).
[0110]
FIG. 11 is an explanatory diagram for explaining an example of the die processing machine 81. As shown in FIG. 11, the die processing machine has a single crystal diamond tool 82 and a tool spindle 83, and a single crystal diamond tool 82 is provided on the outer peripheral surface of a tool spindle 83 that rotates at a constant speed around the Y axis. Is held. In addition, the mold member 71 can be moved in three axial directions of X, Y, and Z by a moving stage (not shown).
[0111]
When a material for forming the mold member 71 (for example, special steel for tools) is set at a predetermined position of the die processing machine 81, the tool spindle 83 rotates at a constant speed according to an instruction of a control device (not shown), The single crystal diamond tool 82 first performs cutting along the first processing line 84 by XY simultaneous biaxial control. Then, when the cutting of the processing line 84 is completed, the die member is then moved by a fixed pitch in the Y-axis direction, and the next processing line is cut. By repeating this, the set surface shape is formed on the mold member 71. Note that the cutting tool may not be the single crystal diamond tool 82, and other cutting tools can be used depending on the material of the mold member 71 and the required shape accuracy.
[0112]
As shown in FIG. 8, when the mold member 71 is manufactured in this way (step S3), various conditions (mold temperature, resin temperature, injection speed, injection pressure, and cooling time are used by using the mold member 71. Etc.) and injection molding is performed to determine molding conditions for stably molding the optical element 1 having substantially the same shape (step S4). These molding conditions vary depending on the shape of the molded product and the type of resin. Here, as an example, the mold temperature is 135 ° C., the resin temperature is 280 ° C., the injection speed is 20 mm / sec, and the injection pressure is The following description will be made assuming that the molding conditions of 50 Mpa and cooling time of 300 sec have been determined. It is assumed that other mold members and the like necessary as a mold for injection molding are prepared in advance.
[0113]
When the molding conditions are thus determined (step S4), injection molding is performed under the molding conditions, and the optical element 1 is manufactured (step S5). Step S5 realizes a molded product preliminary manufacturing process. For injection molding, an electric injection molding machine or other injection molding machines can be used. It is also possible to form a plurality of molded products by one injection molding by manufacturing a plurality of mold members 71 having the same surface shape and setting each mold member 71 in a mold.
[0114]
Next, the surface shape of the optical element 1 which is the manufactured molded product is measured (step S6). The measurement process is realized by step S6. Below, the concrete means of this measurement is demonstrated.
[0115]
First, upon measurement, when the optical element 1 is assembled to a specific apparatus to which the optical element 1 is to be assembled, in this example, the image forming apparatus 20, an external force acting on the optical element 1 by the assembly is assumed. Then, measurement is performed in a state where a stress equivalent to the external force is applied to the optical element 1.
[0116]
In order to apply such an external force, for example, a jig 91 as shown in FIG. 12 can be used. The jig 91 is brought into contact with the reference surface 93 of the main body 92 of the jig 91 with the side surface 2 or 3 serving as the reference surface of the optical element 1, and the elastic force of the leaf spring 94 attached to the main body 92 is used. The optical element 1 is supported on the main body 92. By applying the elastic force of the leaf spring 94 to the optical element 1 in this way, the optical element 1 receives stress from the reference surface 93 and the leaf spring 94, and this stress is assembled to the image forming apparatus 20. It reproduces what it was when.
[0117]
Further, a jig 95 as shown in FIG. 13 may be used. The jig 95 has a positioning pin 97 attached to a main body 96, and the optical element 1 is positioned and supported by the positioning pin 97. The main body 96 is provided with a vacuum chuck portion 98, and the vacuum chuck portion 98 sucks the optical element 1 by sucking with a vacuum pump (not shown). By suction of the vacuum chuck unit 98, the side surface 2 or 3 serving as the reference surface of the optical element 1 comes into contact with the surface of the vacuum chuck unit 98 serving as the reference surface and receives stress from the surface of the vacuum chuck unit 98. This stress is reproduced when the optical element 1 is assembled to the image forming apparatus 20.
[0118]
In this manner, the shape of the optical function surface 4 of the optical element 1 (hereinafter referred to as a lens shape) is reproduced in a state in which the action of an external force in a state assembled to a specific device using the jigs 91 and 95 is reproduced. Measure with an ultra-high precision 3D shape measuring device.
[0119]
As a specific three-dimensional shape measuring apparatus, for example, a three-dimensional measuring apparatus using a probe can be used. As such a three-dimensional measuring apparatus, there are an apparatus using a contact probe such as a stylus probe and an apparatus using a non-contact probe using an optical displacement meter. Here, shape measurement by a three-dimensional shape measuring apparatus using a contact probe will be described.
[0120]
FIG. 14 is a schematic diagram showing an outline of a three-dimensional shape measuring apparatus using a contact probe. In the figure, the directions indicated by the arrows are the X axis and the Z axis, respectively, and the direction perpendicular to the paper surface is the Y axis.
[0121]
The contact-type probe 101 is supported so as to be relatively movable with respect to the surface to be measured 102 in each of the X, Y, and Z directions. For this purpose, an X-axis stage 103, a Y-axis stage 104, and a Z-axis stage 105 are provided. The axis stages 103, 104, and 105 are driven by driving motors 106, 107, and 108, respectively, to move the probe 101 and the surface to be measured 102 in the X, Y, and Z directions relative to each other. The X, Y, and Z axis stages 103, 104, and 105 include linear encoders 109, 110, and 111 for detecting the movement trajectories of the X axis stage 103, the Y axis stage 104, and the Z axis stage 105, respectively. Is provided.
[0122]
In such a three-dimensional shape measuring apparatus, power is supplied to each of the driving motors 106, 107, 108 from the respective driving apparatuses, that is, the XY axis driving apparatus 112 and the Z axis driving apparatus 113, based on the drive control signal. As a result, the driving motors 106, 107, 108 are driven. The XY axis driving device 112 and the Z axis driving device 113 operate in accordance with a drive control signal from the control / analysis computer 114.
[0123]
The control / analysis computer 114 is a microcomputer, and includes a processor 115 mainly composed of a CPU, ROM, RAM (all not shown), etc., and a storage unit 116 composed of an HDD, other storage means, and the like. Built by. Such a control / analysis computer 114 stores a shape measurement computer program, and executes various processes for shape measurement using the probe 101 in accordance with the shape measurement computer program.
[0124]
As shown in FIG. 14, the contact-type probe 101 has a function of detecting a contact force with the surface to be measured 102, and a contact force signal corresponding to the magnitude of the contact force is output. The contact force signal is taken into the control / analysis computer 114. Then, the control / analysis computer 114 generates a drive signal that keeps the contact force signal constant, and sends this to the Z-axis drive device 113. As a result, driving power is supplied from the Z-axis driving device 113 to the driving motor 108, and the Z-axis stage 105 is driven by the driving motor 108 to keep the contact force between the probe 101 and the measured surface 102 constant. . Further, the control / analysis computer 114 sends a drive signal based on the X and Y coordinates stored in the internal storage unit 116 to the XY axis drive device 112. As a result, driving power is supplied from the XY axis driving device 112 to the driving motors 106 and 107, and the X axis stage 103 and the Y axis stage 104 are driven by these driving motors 106 and 107, and the probe 101 and the surface to be measured. 102 is controlled in the X and Y directions.
[0125]
In this way, the surface of the measurement target surface 102 is scanned according to a preset path. During scanning, the signals of the linear encoders 109, 110, and 111 provided in the respective axis stages 103, 104, and 105 are sequentially measured by the control / analysis computer 114 at appropriate sampling intervals, and the surface shape data of the measured surface 102 is measured. Is acquired as X, Y, Z coordinate point cloud data. More specifically, the acquired X, Y, and Z are subjected to data processing described later to obtain surface shape data.
[0126]
FIG. 15 is a vertical side view of the contact-type probe 101. The probe 101 has a structure in which a linear slider 118 having a tip sphere 117 at the tip is housed in a housing 119, and the linear slider 118 is supported by a hydrostatic air bearing 120 in a non-contact state. Thereby, the horizontal movement of the linear slider 118 is restricted, and the linear slider 118 moves in the vertical direction without sliding resistance. Further, the load of the linear slider 118 is received by the coil spring 121 in the housing 119. Under such a basic structure, a displacement gauge 122 is provided in the housing 119 so as to face the rear end of the linear slider 118, and the displacement of the linear slider 118 is detected by the output of the displacement gauge 122. Thus, the displacement of the tip sphere 117 tracing the measured surface 102 (the optical function surface 4 of the optical element 1) is detected. At this time, as an operation at the time of shape measurement, when the tip sphere 117 is pressed against the surface to be measured 102, the coil spring 121 is deformed and the output of the displacement meter 122 changes. Therefore, the contact load of the tip sphere 117 is kept constant by driving the Z-axis stage 111 to control the output of the displacement meter 122 to be constant. By performing such contact load control, the surface of the surface 102 to be measured that is greatly curved in the Z-axis direction can also be measured.
[0127]
In addition, as an apparatus using the non-contact type probe by an optical displacement meter, the apparatus currently disclosed by patent 2975521, Unexamined-Japanese-Patent No. 2-254634, etc. can be used, for example.
[0128]
In addition to the three-dimensional shape measuring apparatus using such a probe, a three-dimensional shape measuring apparatus that measures the shape using interference such as laser light may be used. As such a three-dimensional shape measuring apparatus, for example, a laser interferometer such as a laser interference system manufactured by Zygo, or a scanning white interferometer such as a three-dimensional surface structure analysis microscope manufactured by Zygo can be used.
[0129]
Here, an outline of an example of a three-dimensional shape measuring apparatus that measures the shape using interference such as laser light will be described. FIG. 16 is a block diagram showing a schematic configuration of such a three-dimensional shape measuring apparatus. As shown in FIG. 16, this surface shape measuring apparatus is an ND for adjusting the irradiation light intensity of the He—Ne laser 131 serving as a light source and the laser beam output from the laser beam to be measured 144 (optical element 1). A filter 132 and a beam expander 133 for expanding the laser beam are provided.
[0130]
The light expanded by the beam expander 133 is folded by the mirror 134 and enters the beam splitter 135. The light reflected by the beam splitter 135 passes through an optical element 136 for converting the light into a spherical wave, is folded back by a mirror 137, and passes through an ND filter 138 and a half mirror 139 for adjusting the light intensity. It enters a certain CCD 140. This light becomes reference light for interfering with the reflected light of the object to be measured 144.
[0131]
On the other hand, the light transmitted through the beam splitter 135 is folded back by the mirror 141, converted into a spherical wave by the optical element 142, transmitted through the half mirror 139, and converted into substantially parallel light by the objective optical element 143. Irradiate the measurement object 144. The light reflected by the measurement object 144 passes through the objective optical element 143, is reflected by the half mirror 139, reaches the CCD 140 as object light, and causes interference with the reference light to generate interference fringes. . The interference fringes are imaged by the CCD 140, transferred to the computer 146 via the frame grabber 145, and recorded on the computer 146.
[0132]
The lengths of the reference optical path and the object optical path after being branched by the beam splitter 135 are set to be equal to or less than the coherence length of the He—Ne laser 131 which is a light source. In addition, the irradiation light intensity to the object to be measured 144 is adjusted by the ND filter 132 so that the reflected light from the object to be measured 144 has an intensity suitable for imaging by the CCD 140. Further, the object to be measured 144 is further measured. The reference light intensity is adjusted by the ND filter 138 so that the contrast of the interference fringes generated by the interference between the reflected light from the light and the reference light becomes high.
[0133]
The objective optical element 143 acts to convert the reflected light of the measured object 144 into a spherical wave, thereby reproducing the complex amplitude (image of the measured object 144) of the reflected light of the measured object 144 as described later. Sometimes the image is observed magnified. The positional relationship between the optical element 142 and the objective optical element 143 is adjusted so that the object to be measured 144 is irradiated with substantially parallel light. The optical element 136 acts to convert the reference light into a spherical wave, and the curvature of the reflected light of the object to be measured 144 converted into the spherical wave by the objective optical element 143 and the curvature of the reference light are captured by the CCD 140. The position is adjusted so that the positions substantially coincide.
[0134]
When the image of the measurement object 144 is not enlarged, the objective optical element 143 is unnecessary, and accordingly, the optical element 136 and the optical element 142 are also unnecessary. Although details will be described later, here, the interference fringes are handled as holograms, the reference light is virtually irradiated to the hologram interference fringes imaged by the CCD 140, and the reflected light from the object 144 to be measured (the diffracted light wave) The complex amplitude of the measured object 144) is reproduced. When a single interference fringe data is imaged by the CCD 140 and the reflected light of the object to be measured 144 is reproduced, the zero-order diffracted light that transmits the hologram, the real image, and the virtual image are reproduced. Thus, an appropriate inclination is provided between the optical axis of the reflected light from the object to be measured 14 and the optical axis of the reference light so that the carrier frequency is placed on the interference fringes. In order to give the inclination to both the optical axes, for example, the inclination of the mirror 137, the measured object 144 or the half mirror 139 may be adjusted.
[0135]
Next, a method for reproducing and calculating the complex amplitude of the reflected light from the object to be measured 144 (image of the object to be measured 144) (hereinafter, the light amplitude and phase are collectively referred to as complex amplitude) will be described.
[0136]
First, the intensity at the imaging position of the CCD 10 of the interference fringes generated by the interference between the reflected light from the object to be measured 144 and the reference light is given by equation (5).
[0137]
[Expression 2]

[0138]
Here, I is the intensity of the interference fringes, x and y are the x and y coordinates of the imaging position of the CCD 10, R is the complex amplitude of the reference light, and A and φ are the amplitudes of the reflected light of the measured object 144, respectively. And the phase.
[0139]
The interference fringes are picked up by the CCD 140 and stored in the computer 146 as hologram image data. In holography using a dry plate, when the reference light is irradiated again on the dry plate (hologram) on which interference fringes are recorded, the reference light is diffracted by the interference fringes recorded on the hologram, and it behaves as object reflected light during recording. As a result, the object reflected light (object image) is reproduced. Here, the object reflected light (object image) is reproduced based on Fresnel approximation from the hologram image recorded by the CCD 140, assuming that the reference light is virtually irradiated to the hologram without actually irradiating the reference light. To do. Assuming that the hologram is irradiated with parallel light as reference light, the diffracted light by the hologram, that is, the object reflected light, is expressed as in equation (6).
[0140]
[Equation 3]

[0141]
Here, U is the complex amplitude of the object reflected light wave at the image plane position separated by the reproduction distance d, x ′ and y ′ are the x and y coordinates at the image plane position, c is a complex constant, and λ is the light source wavelength. .
[0142]
Therefore, by inputting the reproduction distance d and calculating the expression (6) using the recorded interference fringe data, the complex amplitude of the object reflected light at the reproduction distance d is reproduced. When the image of the measurement object 144 is not enlarged, the distance between the imaging position of the CCD 140 and the surface of the measurement object 144 may be substituted for the reproduction distance d. When the image of the object to be measured 144 is enlarged as in the apparatus shown in FIG. 16, the distance between the enlarged image plane of the object to be measured 144 by the objective optical element 143 and the imaging position of the CCD 140 is input as the reproduction distance d. To do.
[0143]
For example, using the various three-dimensional shape measuring devices as described above, the shape of the optical functional surface 4 of the optical element 1 is measured as follows. That is, first, the central portion of the bus 12 (see FIG. 3) of the optical element 1 is scanned in the X-axis direction to measure the height (depth) in the Z direction, and then scanned in the Y-axis direction. Measurement in the Y-axis direction is performed at a plurality of positions in the X-axis direction.
[0144]
As shown in FIG. 8, after measuring the shape of the optical element 1 (step S6), the depths in the X-axis direction and the Y-axis direction are compared with design values to determine whether the shape error is within a predetermined tolerance. (Step S7). That is, in a state where no stress is applied, the bus bar 12 of the optical element 1 and the lines of the side surfaces 2 and 3 are non-parallel, and the bus bar 12 is distorted. It is determined whether the shape error of the optical element 1 is within the tolerance on the assumption that the distortion is corrected in the state assembled to 20. Further, when the shape of the optical element 1 is such that the lines of the side surfaces 2 and 3 are originally uneven, the bus bar 12 is distorted in a state where no stress is applied, and the image forming apparatus which is a specific apparatus In the state assembled to 20, it is determined whether or not the distortion of the optical element 1 is within the tolerance, assuming that the distortion is corrected.
[0145]
As the shape error to be determined, in addition to an error in the cross-sectional profile in the X-axis direction and the Y-axis direction, a paraxial curvature error in the cross-section in the Y-axis direction, particularly a bending of the bus 12 is determined. The bus-bending is a shape error related to the shift amount S of the cross-sectional shape in the sub-wire direction in the equation (1). The bus position in the design value is S (X), and the bus position in the measurement value is S ′ (X ) Is an amount given as “S ′ (X) −S (X)”. S ′ (X) is specifically obtained as follows using a computer.
[0146]
First, in the measurement line in each Y-axis direction of the measurement value, the X coordinate is substantially the same value X_i(In the present embodiment, i = 1 to 23), the least square approximation is performed on the YZ cross-sectional shape, and the coordinates of the paraxial curvature center (Y_i, Z_i) Next, a point sequence (X_i, Y_i) Is approximated by a polynomial of X to be S ′ (X). For example, when approximated by a quartic polynomial, S ′ (X) is expressed as the following equation (7).
[0147]
[Expression 4]

[0148]
If the above-described various shape errors are within the allowable tolerances (Y in step S7), the mold member 71 need not be corrected, and the series of manufacturing steps is completed. If it is not within the predetermined tolerance (N in step S7), that is, the design of the mold member 71 needs to be corrected, and the process proceeds to the next step S8.
[0149]
In step S8, three new parameters (m_X, M_Y, M_Z), The shape regression equation represented by the following equation (8) is considered.
[0150]
[Equation 5]

[0151]
However, paraxial curvature in the sub-wire direction: C₂(M_X ^*/ M_X・ X)
Conical constant in the direction of the strand: K₂(M_X ^*/ M_X・ X)
Shift amount of the cross section of the strand: S (m_X ^*/ M_X・ X)
That is, in this example, the following equation (9) is obtained.
[0152]
[Formula 6]

[0153]
However, paraxial curvature in the sub-wire direction: C₂(0.993 / m_X・ X)
Conical constant in the direction of the strand: K₂(0.993 / m_X・ X)
Shift amount of the cross-sectional shape of the wire: S (0.993 / m_X・ X)
[0154]
The parameter (m) that minimizes the difference between the measured value of the shape of the optical element 1 and the equation (9)._X, M_Y, M_Z) Using a computer based on the least square method. In this example, (m_X, M_Y, M_Z) = (0.99325, 0.99215, 0.99206). That is, the shape regression equation is the following equation (10).
[0155]
[Expression 7]

[0156]
However, paraxial curvature in the sub-wire direction: C₂(0.993 / 0.9925 · X)
Conical constant in the direction of the strand: K₂(0.993 / 0.9925 · X)
Shift amount of the cross-sectional shape of the strand: S (0.993 / 0.9925 · X)
The optimum values (m_X, M_Y, M_Z) Are shrinkage rates of the molded product in the X, Y, and Z axis directions, respectively.
[0157]
Next, the surface shape of the mold member 71 determined in step S2 is corrected to the shape represented by the following equation (11) (step S9).
[0158]
[Equation 8]

[0159]
However, paraxial curvature in the sub-wire direction: C₂(-M_X・ X)
Conical constant in the direction of the strand: K₂(-M_X・ X)
Shift amount of the cross section of the strand: S (−m_X* X) -S '(-m_X・ X)
That is, in this example, equation (12) is obtained.
[0160]
[Equation 9]

[0161]
However, paraxial curvature in the sub-wire direction: C₂(-0.99325 ・ X)
Conical constant in the direction of the strand: K₂(-0.99325 ・ X)
Shift amount of the cross-sectional shape of the strand: S (-0.99325 · X) −S ′ (− 0.99325 · X)
[0162]
Next, based on the surface shape shown by the equation (12), the mold member 71 is corrected or manufactured again (step S10). Then, returning to step S5, injection molding is performed under the same molding conditions as above using the mold member 71 that has been modified or remanufactured (step S5), and the measurement of the shape of the molded optical element 1 is the same as described above. (Step S6). Then, again, the measured value of the shape of the optical element 1 is compared with the design shape, and it is determined whether or not the shape error is within a predetermined tolerance (step S7). Here, if it is within the predetermined tolerance (Y in Step S7), the mold member 71 does not need to be re-corrected, and thus the series of manufacturing steps is finished. However, if the tolerance is not within the predetermined tolerance (N in Step S7), the mold member 71 needs to be re-corrected, and the subsequent steps after Step S8 are repeated.
[0163]
According to the manufacturing method of the mold member 71 described above, the actual use state of the optical element 1, that is, the state assembled to the image forming apparatus 20 is reproduced. Therefore, the reference surface 2 (or 3) of the optical element 1 is It is possible to measure the shape of the optical element 1 in the actual use state by being deformed in the same manner as when assembled in the image forming apparatus 20. The measured value thus measured is compared with the design shape of the mold member 71, and the mold member 71 is corrected or remanufactured so as to reduce the shape error. The optical element 1 that is newly molded using a mold including the shape of the optical element 1 is optimized so as to be closest to the design shape in a state of actual use and assembled in the image forming apparatus 20. Can do.
[0164]
FIG. 17 is a plan view of the molding surface 72 of the mold member 71 manufactured by the above method. A broken line 73 is a line indicating a position corresponding to the generatrix 12 of the optical function surface 4 of the optical element 1, and this line is curved. In the design formula of the optical element 1 represented by the formula (1), in order to give more generality, the shift amount S of the cross-sectional shape of the child wire is expressed as a function S (X) of the lens height X. Although it has been explained so far, it is generally considered that the design value is usually “S (X) = 0”, so that the molded optical element 1 is in an actual use state, that is, in the image forming apparatus. In the assembled state, when the curve of the bus bar 12 and the curve of the broken line 73 of the molding surface 72 shown in FIG. 17 are compared, if the curve of the broken line 73 of the molding surface 72 is larger, the manufacturing method described above. It is strongly suggested that the mold member 71 is manufactured by applying the above.
[0165]
By manufacturing the mold member 71 designed as described above, the main mold manufacturing process can be realized. Then, by using this molding die and performing plastic injection molding or the like using, for example, the molding material as described above, the optical element 1 such as a lens or a mirror that is a molded product can be manufactured.
[0166]
The molding method and material of the optical element 1 are not limited to the above examples. For example, the above method can be applied to glass press molding. Further, the molded product is not limited to the optical element 1 such as a lens or a mirror, and the molded product of the present invention can be manufactured by using the above-described method for molding various products.
[0167]
A method of manufacturing the mold member 71 different from the method described with reference to FIG. 8 and the like will be described with reference to the flowchart of FIG.
[0168]
Steps S11 to S16 in FIG. 18 realize the design process. First, an initial expected value (m of shrinkage in the X, Y, and Z axis directions of the resin that is the molding material of the optical element 1_X ^*, M_Y ^*, M_Z ^*) Is determined (step S11), and the surface shape of the surface 72 of the mold member 71 is determined (step S12). These steps can be performed in the same manner as steps S1 and S2.
[0169]
Next, assuming that the mold member 71 having the determined surface shape is manufactured, when the optical element 1 which is a molded product molded by the mold member 71 is assembled to the image forming apparatus 20 which is a specific apparatus, the optical element 1 1 is assumed, the deformation of the optical element 1 when the stress is applied is simulated on a computer, and the deformation of the optical element 1 in the state where the deformation is generated is determined (step S13). Such simulation is performed in consideration of various factors such as the position, direction, and size of the stress applied to the optical element 1 and the elasticity of the material of the optical element 1.
[0170]
Then, it is determined whether the shape error of the deformed optical element 1 is within a predetermined tolerance (step S14). This determination may be performed in the same manner as in step S7. When the shape error is within a predetermined tolerance (Y in step S14), the series of steps is finished. If the shape error is not within the predetermined tolerance (Y in step S14), the same processing as in step S8 (step S15) and the same processing as in step S9 (step S16) are performed and corrected in this way. Based on the surface shape of the new mold member 71 that has been made, the steps after step S13 may be repeated.
[0171]
In this example, the shape of the optical element 1 is designed once, and when the designed optical element 1 is assembled to the image forming apparatus 20, a simulation is performed assuming the stress applied to the optical element 1. From the result, the shape of the optical element 1 is redesigned. From the beginning, the shape of the optical element 1 in which the shape error of the optical element 1 is within a predetermined tolerance is simulated on the computer. Also good.
[0172]
Then, by forming the mold member 71 designed in this way, the forming mold main manufacturing process can be realized.
[0173]
As described above, according to the method for manufacturing the mold member 71 described with reference to FIGS. 8 and 18, the optical element 1 that is a molded product manufactured using the molding die including the molded mold member 71 is a specific product. When the image forming apparatus 20 is assembled to the image forming apparatus 20, an ideal shape is obtained. In an actual use state assembled to the image forming apparatus 20, the shape error of the molded product other than the shape error caused by the cooling process of the molding, that is, the optical shape is obtained. The second functional deformation is also corrected.
[0174]
According to the method of manufacturing the mold member 71 described with reference to FIG. 8, a specific apparatus is manufactured by actually making a prototype of the molding die and the optical element 1 which is the molded product, and measuring the shape of the optical element 1. When the image forming apparatus 20 is assembled, it is possible to know an error from the ideal shape of the optical element 1 having no distortion, and to design the molding die by reflecting the error. And easy.
[0175]
According to the method for manufacturing the mold member 71 described with reference to FIG. 18, the mold member 71 for manufacturing the optical element 1 having an ideal shape without distortion when assembled in the image forming apparatus 20 that is a specific apparatus is calculated. Therefore, it is possible to save the trouble of actually making a prototype of the molding die and the optical element 1 which is the molded product. In this case, if the shape of the optical element 1 in which the shape error of the optical element 1 is within a predetermined tolerance is simulated on the computer from the beginning, the trouble of designing the optical element 1 multiple times can be saved. be able to.
[0176]
In the manufacturing method of the mold member 71 shown in FIG. 8, for example, a three-dimensional shape measuring apparatus that measures the shape using a contact (or non-contact) probe as described with reference to FIGS. Alternatively, for example, if the shape of the optical element 1 is measured (step S6) by a three-dimensional shape measuring device that measures the shape using the interference of light as described with reference to FIG. The surface shape of the optical element 1 can be measured accurately.
[0177]
At this time, for example, an assumed stress is applied to the optical element 1 by the elastic force of a spring with a jig 91 as shown in FIG. 12, or the optical element is obtained by vacuum suction with a jig 95 as shown in FIG. If the stress assumed in 1 is applied, the stress can be easily reproduced, and the optical element 1 that is a molded article is not damaged.
[0178]
When designing the optical element 1 that is a molded product, in the X, Y, and Z directions shown in FIG. 1, X, Y, and further, as a function of S, which is a function of X, as shown in Equation (1) Since the calculation is performed using an expression indicating Z, the design can be facilitated.
[0179]
When the optical element 1 which is a molded product formed by using a molding die including the mold member 71 manufactured by such a manufacturing method is assembled to the image forming apparatus 20 which is a specific apparatus, both side surfaces 2 and 3 are distorted. The side surfaces 2 and 3 are deformed so as to approach symmetry as compared with when no stress is applied, and the bus bar 12 has an ideal shape without distortion. In the actual use state assembled to the image forming apparatus 20, the side surfaces 2 and 3 are caused by the cooling process of molding. Thus, the shape error other than the shape error generated, that is, the second deformation of the optical functional surface is corrected.
[0180]
According to the image forming apparatus 20 having the exposure device 42 provided with the scanning lenses 65a, 65b, 65c, 151b and the scanning mirror 151b, which are such optical elements 1, these optical elements 1 are caused by a cooling process of molding. Since the shape error other than the shape error generated, that is, the second deformation of the optical function surface is also corrected, the image forming apparatus 20 capable of performing accurate exposure scanning can be provided.
[0181]
Note that the present invention can be applied not only to the optical element 1 such as a lens and a mirror but also to various molded products and manufacturing methods thereof. Further, the optical element 1 as such a molded product can be applied not only to the electrophotographic image forming apparatus 20 but also to various optical devices.
[0182]
【The invention's effect】
According to the first aspect of the present invention, the shape error of the molded product other than the shape error generated due to the cooling process of the molded product in the actual use state of the molded product is also corrected.
[0183]
According to the second aspect of the present invention, in the manufacturing method of the molding die according to the first aspect, the design of the molding die can be made concrete and easy.
[0184]
According to a third aspect of the present invention, in the method for manufacturing a molding die according to the first aspect, it is possible to save the labor of actually making a prototype of the molding die and its molded product.
[0185]
According to a fourth aspect of the present invention, in the method for manufacturing a molding die according to the second aspect, the surface shape of a molded product molded with the prototyped molding die can be accurately measured.
[0186]
According to a fifth aspect of the present invention, in the method for manufacturing a molding die according to the second aspect, the surface shape of a molded product molded with the prototype molding die can be accurately measured.
[0187]
The invention according to claim 6 is a method for manufacturing a molding die according to claim 2, 4 or 5, wherein the stress applied to the molded product is easily reproduced when it is assembled to a specific device, and the molded product is damaged. Nor.
[0188]
The invention according to claim 7 is a method for manufacturing a molding die according to claim 2, 4 or 5, wherein when applied to a specific device, the stress applied to the molded product can be easily reproduced and the molded product is damaged. Nor.
[0189]
According to an eighth aspect of the present invention, in the method for manufacturing a molding die according to any one of the second, fourth to seventh aspects, the molding die can be easily designed.
[0195]
Claim10The invention described in (3) forms a molded product that has an ideal shape with no distortion of the busbar when assembled to a specific device, and in which the shape error other than the shape error caused by the cooling process of the molding is corrected in actual use. it can.
[0197]
Claim11According to the invention described in (2), both sides are distorted when assembled to a specific device, resulting in an ideal shape as a whole, and a shape error other than a shape error caused by a cooling process of the molding is corrected in an actual use state. The product can be molded.
[0198]
Claim12According to the invention described in (2), both sides are deformed so as to approach symmetry when assembled in a specific device, and the overall shape becomes an ideal shape. In actual use, shapes other than shape errors caused by the cooling process of molding are formed. A molded product whose error is also corrected can be molded.
[0199]
Claim13The present invention provides an optical element that has an ideal shape with no distortion of the busbar when assembled in a specific device, and can correct shape errors other than shape errors caused by the cooling process of molding in actual use conditions. it can.
[0201]
Claim14According to the invention described in the optical system, both sides are distorted when assembled in a specific device, resulting in an ideal shape as a whole, and in an actual use state, the shape error other than the shape error caused by the molding cooling process is also corrected. An element can be provided.
[0202]
Claim15According to the invention described in (2), both sides are deformed so as to approach symmetry when assembled in a specific device, and the overall shape becomes an ideal shape. In actual use, shapes other than shape errors caused by the cooling process of molding are formed. An optical element in which errors are also corrected can be provided.
[0203]
  Claim16The invention described in (1) can provide a lens that has an ideal shape with no distortion of the busbar when assembled to a specific device, and can correct shape errors other than shape errors caused by the cooling process of molding in actual use conditions. .
[0205]
  Claim17According to the invention described in the above, when assembled to a specific device, both side surfaces are distorted to become an ideal shape as a whole, and a shape error other than the shape error caused by the cooling process of molding is corrected in an actual use state. Can provide.
[0206]
  Claim18According to the invention described in the above, when assembled to a specific device, both side surfaces are deformed so as to approach symmetry, and become an ideal shape as a whole, and shapes other than shape errors caused by the molding cooling process in actual use conditions A lens can be provided in which errors are also corrected.
[0207]
  Claim19The invention described in the above can provide an optical device that uses an optical element or a lens in which a shape error other than a shape error caused by a cooling process of molding is corrected, and exhibits an accurate optical function. .
[0208]
  Claim20The present invention provides an image forming apparatus that uses an optical element or a lens in which a shape error other than a shape error generated due to a cooling process of molding is corrected, and can perform accurate exposure scanning. be able to.
[0209]
  Claim21In the invention described in the above, an optical element or a lens in which a shape error other than a shape error generated due to a cooling process of molding is corrected is used, and accurate exposure scanning can be performed based on the read image data. An image forming apparatus that can be used can be provided.
[Brief description of the drawings]
BRIEF DESCRIPTION OF DRAWINGS FIG. 1 is an explanatory diagram illustrating a problem of the present invention.
FIG. 2 is a perspective view of an optical element according to an embodiment of the present invention.
FIG. 3 is a plan view of an optical function surface of the optical element.
FIG. 4 is an explanatory diagram illustrating a schematic configuration of an image forming apparatus including the optical element.
FIG. 5 is a perspective view of an exposure apparatus of the image forming apparatus.
FIG. 6 is a perspective view showing another example of an exposure apparatus of the image forming apparatus.
FIG. 7 is a perspective view of a mold member constituting a molding die according to an embodiment of the present invention.
FIG. 8 is a flowchart for explaining a mold member manufacturing method according to an embodiment of the present invention;
FIG. 9 is an explanatory diagram explaining the manufacturing method.
FIG. 10 is an explanatory view of the same.
FIG. 11 is an explanatory diagram of the same.
FIG. 12 is a perspective view showing an example of a jig used in the manufacturing method.
FIG. 13 is a perspective view showing another example of the jig.
FIG. 14 is a block diagram showing an example of a three-dimensional shape measuring apparatus used in the manufacturing method.
FIG. 15 is a longitudinal sectional view of a probe portion of the three-dimensional shape measuring apparatus.
FIG. 16 is a block diagram showing another example of a three-dimensional shape measuring apparatus used in the manufacturing method.
FIG. 17 is a plan view of a molding surface of a mold member constituting the molding die according to one embodiment of the present invention.
FIG. 18 is a flowchart illustrating a method for manufacturing a mold member according to another embodiment of the present invention.
[Explanation of symbols]
1 Optical elements, lenses, molded products
2 side
3 side
12 Busbar
20 Image forming apparatus
42 Exposure equipment
65a Lens, optical element
65b Lens, optical element
65c Lens, optical element
71 Mold
91 Jig
95 Jig
151a Optical element
151b Lens, optical element

Claims (18)

Method for manufacturing mold for molding fθ lens having long direction and short direction perpendicular to optical axis direction, concave shape or convex shape with respect to optical axis direction, and assembled to optical apparatus Because
When a line connecting the lowest point of the concave shape or the highest point of the convex shape along the longitudinal direction is a bus,
In a state where it is not assembled to the optical device, the bus bar is distorted,
When assembled in the optical device, the fθ lens is molded so that the distortion of the bus bar is corrected by the stress at the time of assembly and the design shape is closer to the design shape than the state where the fθ lens is not assembled. A design process for designing the mold for molding,
A mold main production process for producing the mold according to this design,
The manufacturing method of the shaping | molding die which comprises this. A mold pre-production process for producing a mold for molding the fθ lens ;
A molded product preliminary manufacturing process for manufacturing the fθ lens using the manufactured mold,
A measurement step of measuring the shape of the fθ lens in a state where stress that is assumed to be applied when the manufactured fθ lens is assembled to the optical device is actually applied;
The design step is to design the molding die based on the measurement result.
The manufacturing method of the shaping | molding die of Claim 1. The design step is to design the mold by simulating the stress, the shape, and the shape of the fθ lens before and after the deformation by performing a predetermined calculation.
The manufacturing method of the shaping | molding die of Claim 2. In the measurement step, the measurement is performed by a three-dimensional shape measurement apparatus that measures the shape using a contact-type or non-contact type probe.
The manufacturing method of the shaping | molding die of Claim 2. In the measurement step, the measurement is performed by a three-dimensional shape measurement apparatus that measures the shape using light interference.
The manufacturing method of the shaping | molding die of Claim 2. The method for manufacturing a molding die according to claim 2, 4 or 5, wherein the measuring step applies the assumed stress to the fθ lens by an elastic force of a spring. The method for manufacturing a molding die according to claim 2, 4 or 5, wherein the measuring step applies the assumed stress to the fθ lens by vacuum suction. The design step is a function of X indicating the unevenness when the uneven direction of a predetermined line on the surface of the fθ lens is the Z direction, and the direction orthogonal to the Z direction is the X direction and the Y direction. The design is performed using an expression representing the Z expressed as a function of the X and Y.
The manufacturing method of the shaping | molding die as described in any one of Claim 2, 4-7. Method for producing a fθ lens for fabricating the fθ lens using mold fabricated in mold manufacturing method according to one of any claims 1 to 8. A mold for forming an fθ lens that has a long direction and a short direction perpendicular to the optical axis direction, has a concave shape or a convex shape with respect to the optical axis direction, and is assembled to an optical device. ,
When a line connecting the lowest point of the concave shape or the highest point of the convex shape along the longitudinal direction is a bus,
In a state where it is not assembled to the optical device, the bus bar is distorted,
When assembled in the optical device, the fθ lens is molded so that the distortion of the bus bar is corrected by the stress at the time of assembly and the design shape is closer to the design shape than the state where the fθ lens is not assembled. Mold for molding. The molding die according to claim 10, wherein the fθ lens has a shape in which a side surface in a short-side direction has no distortion in a state where the stress is not received, and a shape in which the side surface is distorted in a state where the fθ lens is assembled to the optical device. . An fθ lens having a long direction and a short direction perpendicular to the optical axis direction, having a concave shape or a convex shape with respect to the optical axis direction, and assembled to an optical device,
When a line connecting the lowest point of the concave shape or the highest point of the convex shape along the longitudinal direction is a bus,
In a state where it is not assembled to the optical device, the bus bar is distorted,
The fθ lens that is closer to the design shape than the unassembled state in which the distortion of the busbar is corrected by the stress at the time of assembly when assembled in the optical apparatus. The fθ lens according to claim 12, wherein the side surface in the short side direction is not distorted in a state where the stress is not received, and the side surface in the short side direction is distorted when assembled in the optical apparatus. An fθ lens having a long direction and a short direction perpendicular to the optical axis direction, having a concave shape or a convex shape with respect to the optical axis direction, and assembled to an optical device,
When a line connecting the lowest point of the concave shape or the highest point of the convex shape along the longitudinal direction is a bus,
In a state where it is not assembled to the optical device, the bus bar is distorted,
In the state assembled to the optical instrument, due to the stress at the time of assembly, distortion of the busbar is corrected , and closer to the design shape than the state where the fθ lens is not assembled,
f θ lens. The fθ lens according to claim 14 , wherein the side surface in the short side direction is not distorted in a state where the stress is not received, and the side surface is distorted in a state where the side surface is assembled to the optical apparatus. The distortion of the fθ lens according to fθ lens or claim 14 or 15 according to claim 12 or 13 is modified, the fθ lens is assembled to be close to the designed shape than when no assembled An optical device equipped with an optical system. The fθ lens according to claim 14 or 15 ,
The distortion of the fθ lens is corrected, and an exposure device is provided so that the fθ lens is closer to the design shape than the unassembled state , and an image is formed on a sheet by electrophotography. An image forming apparatus to perform. The image forming apparatus according to claim 17 , further comprising an image reading device that reads an image of a document, and performing the image formation based on image data read by the image reading device.

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