CN118424154B - Spherical curvature radius measuring device and method based on computer-aided adjustment - Google Patents
Spherical curvature radius measuring device and method based on computer-aided adjustment Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 64
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- 239000004579 marble Substances 0.000 claims abstract description 16
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
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Abstract
The invention provides a spherical curvature radius measuring device and a method based on computer-aided adjustment, wherein a phase-shifting interferometer is arranged in the center of a marble Dan Ji; the measuring platform consisting of the detecting tool and the four-dimensional electric control adjusting frame is arranged on the lifting device connected with the marble base, and the positions of the measured piece in confocal and cat eyes are adjusted through the four-dimensional electric control adjusting frame and the air floatation guide rail; the laser range finder is fixed on the marble base beam; the computer system is connected with the phase-shift interferometer, the laser range finder and the four-dimensional electric control adjusting frame, and is used for collecting interference pattern information and recording displacement; and analyzing the collected surface shape information near the cat eye position and the collected surface shape information near the confocal position respectively to obtain required adjustment quantity, quantitatively adjusting the measured piece through the four-dimensional electric control adjusting frame, and realizing accurate adjustment of the two fixed focus positions.
Description
Technical Field
The invention relates to the field of optical detection, in particular to a spherical curvature radius measuring device and method based on computer-aided adjustment.
Background
As spherical optical elements are widely used in the fields of optical metrology, optical communications, medical devices, and the like. The curvature radius of the spherical optical element is one of key parameters for determining imaging performance, influences the imaging quality of the whole system, and is particularly important for high-precision detection of the curvature radius of the spherical optical element.
The current spherical curvature radius measuring method mainly comprises a template method, a sphere diameter meter method, a three-coordinate measuring method and an interferometry method, wherein the interferometry method is simple in measuring principle, traceable in result and high in precision, and is one of the most widely-used high-precision spherical curvature radius measuring methods at present. In a patent, a computer-aided adjustment device and a method (publication number 114252023B) for aspheric surface calculation holographic detection, the detection light path is accurately adjusted by analyzing collected surface shape information to obtain the adjustment amount required by the aspheric surface to be detected; in a method for detecting the curvature radius of an optical spherical surface (publication number CN 102168955B), the relative positions of a target ball, a spherical mirror and an interferometer are adjusted by observing interference fringes, and the curvature center coordinate of the target ball and the position coordinates of multiple points on the spherical mirror to be detected are measured by adopting a laser tracker to obtain the curvature radius of the spherical mirror to be detected; in a method and a system for measuring curvature radius (publication number is CN 115790453A), defocusing wave front is collected through a phase interferometer, a Zernike fitting is carried out to obtain a defocusing coefficient, then a test light path is modeled in optical design software, the defocusing coefficient is used as an optimization target, and the curvature radius of a measured mirror is used as an optimization variable to obtain the curvature radius. The computer-aided adjustment technology is mainly used for detecting the surface shape of the free curved surface in the aspect of optical element detection, and is less applied in the aspect of spherical curvature radius measurement. In the existing spherical curvature radius interferometry, the cat eye and confocal positions are mostly positioned by a detector according to interference fringes, the positioning precision and the measuring efficiency are affected by subjective factors, and the curvature radius measuring precision and efficiency cannot be guaranteed.
Disclosure of Invention
In order to solve the problem that automatic measurement of spherical curvature radius is difficult to position a cat eye and a confocal position, the invention provides a spherical curvature radius measuring device and method based on computer-aided adjustment.
The invention adopts the technical scheme that: the device comprises a marble Dan Ji, a phase interferometer, a laser range finder, an air floatation guide rail, a four-dimensional electric control adjusting frame, a detection tool, a detected mirror, a reference mirror and a computer; wherein:
The phase-shifting interferometer is arranged in the center of the marble Dan Ji and is used for collecting interference fringes near a measuring position; the laser range finder is positioned on the beam above the marble base and is used for recording accurate axial displacement from the cat eye to the confocal position; the air-float guide rail is fixed on the marble base and used for driving the axial displacement of the measured mirror; the four-dimensional electric control adjusting frame is used for adjusting the translation and inclination of the measured mirror along the X, Y direction, and the detection tool is used for fixing the measured mirror;
The computer system is connected with the phase-shifting interferometer, the laser range finder, the air floatation guide rail and the four-dimensional electric control adjusting frame, and is used for collecting, analyzing and processing interference surface shape data collected by the phase-shifting interferometer, recording relative displacement and inclination quantity collected by the laser range finder and the four-dimensional electric control adjusting frame, and driving the measured mirror to move to a specific position through the air floatation guide rail and the four-dimensional electric control adjusting frame to achieve spherical curvature radius measurement.
Further, the device is used for realizing rapid and automatic measurement of the spherical curvature radius.
The invention further provides a spherical curvature radius measuring method based on computer-aided adjustment, which comprises the following steps of:
Step a: inputting the F number of a reference mirror, the light transmission aperture D and the nominal radius R of the measured piece, and defining the repeated scanning times K;
Step b: moving the detected mirror to the vicinity of the cat eye position along the optical axis, and recording axial displacement by a laser range finder;
Step c: obtaining measured wave front in a phase interferometer, performing Zernike fitting to obtain surface shape data, and obtaining offset according to the mutual corresponding relation between fitting wave aberration and offset-introduced wave aberration 、、And、Readjusting the attitude of the mirror under test, wherein the offset is：
Step d: if it isReturning to the previous step, otherwise, proceeding to the next step, whereinAn adjustment threshold value set for the position of the cat eye;
Step e: moving the measured lens to the vicinity of the confocal position along the optical axis, recording axial displacement by a laser range finder, and obtaining defocused wavefront in a phase interferometer;
step f: obtaining the offset according to the mutual corresponding relation between the fitting wave aberration and the offset-introduced wave aberration 、、And、Readjusting the attitude of the objective lens 7, wherein the offset is；
Step g: if it isReturning to the previous step ifAnd k +.0, returning to step b, ending the measurement when k=0,An adjustment amount threshold set for the confocal position;
Step h: because focusing and initial adjustment of the measured piece are mainly realized in the first measurement, the error is large, and the measurement result needs to be deleted. And finally, finishing k times of repeated measurement, and ending the measurement.
Further, the offset is obtained by establishing a relation between the offset and the aberration and according to the mutual corresponding relation between the fitting wave aberration and the offset-introduced wave aberration, namely, the surface shape data set acquired by the phase-shift interferometer is transmitted to a computer system for processing to obtain the required adjustment quantity of the measured mirror, and the specific analysis process is as follows:
First by the formula The approximate position of the cat eye position is calculated,The method is a theoretical curvature radius of a standard mirror, the measured mirror is pushed to the vicinity of the cat eye position along the optical axis, and Zernike fitting is carried out on defocused wave fronts acquired by the phase interferometer 1.
During the measurement, the resulting interferogram wave aberration can be expressed by the following formula:
；
In the method, in the process of the invention, Due to aberration caused by internal errors of the interferometer and errors of the mirror shape of the measured object,Indicating wave aberration caused by the offset at the measurement position. Light is incident to a focus O from a standard spherical lens TS, and the light in the propagation process meets the following conditions:
；
in the light ray Indicating the direction of the ith light ray along the ithIs propagated in the direction of (a) and passes through the point。The distance that light propagates in the ith section light path, light propagates to a point (namely focus O) on the sphere of the measured mirror and is reflected, and as the measured mirror has a trace adjustment amount, the actual light propagates to the point O' and is reflected, and the propagation direction is as follows:
；
wherein H (x, y) represents the propagation direction of the light after reflection at the spherical surface O'; is the surface normal of the sphere of the measured mirror at O'.
；
Establishing a rectangular coordinate system by taking an O point as an origin, wherein in the adjustment process, the measured spherical mirror accords with the rigid body rotation theorem, and has 6 degrees of freedom, namely translation along x, y and z axes respectively、、And rotation about x, y, z axes、、. The curvature center of the measured mirror moves from point Q (0, -R) to pointThe following equation sets with O, Q and Q' as the centers of spheres are obtained, wherein the points are [ (], , )，(,,)，(,,) Any point on the sphere with O, Q and Q' as the sphere center;
；
the wave aberration caused by the offset amount at the cat eye position is:
；
Wherein, As for wavelength, light AO is incident from the standard spherical lens TS to the focus O for reflection, and the actual light propagates to the point O' for reflection due to the trace adjustment of the measured mirror, the propagation direction after reflection is changed from OB to ；
The measured spherical mirror imbalance at the cat eye position mainly generates three items of inclination, defocus and astigmatism, and a Seidel aberration polynomial is adopted as a base fitting to obtain the measured spherical mirror imbalance induced wave aberration, so that the first 6 items of Seidel polynomials are selected to represent main aberration:
；
according to least squares theory, i.e. The following least squares matrix can be obtained:
；
In the method, in the process of the invention, 、、、、And。For wave aberration coefficients introduced by adjustment errors, the pair coefficients、、、、AndAnd solving. Obtaining the offset according to the mutual corresponding relation between the fitting wave aberration and the offset-introduced wave aberration、、And、Is a numerical value of (2). Judging whether the obtained adjustment parameters of the spherical mirror to be measured meet the angle and displacement threshold value:
；
Wherein the angle threshold And a displacement thresholdThe minimum angle and displacement adjustment quantity of the four-dimensional electric control platform and the air floatation guide rail can be selected as the judgment threshold value. If the measured spherical mirror adjustment quantity is not smaller than the threshold value, the optical path is readjusted according to the obtained approximate solution, then the optical path is solved and readjusted until the measured spherical mirror adjustment quantity is smaller than the threshold value.
Next, the measured mirror is pushed along the optical axis to the vicinity of the confocal position by the known nominal radius, and Zernike fitting is performed on the surface shape information acquired by the phase interferometer 1.
In the adjusting process, the measured spherical mirror accords with the rigid rotation theorem, and has 6 degrees of freedom, namely translation along x, y and z axes、、And rotation about x, y, z axes、、. Set the coordinates of any point on the mirror surface to be measured asAnd the coordinates of the point after the adjustment is introducedThe relation between the two is:
；
Since the angle is small, to simplify the calculation, let ，. The surface to be measured of the measured spherical mirror is a rotationally symmetrical surface, soCan be ignored. To sum up, the displacement vector from P to PExpressed as:
；
The spherical equation can be expressed by the following formula:
；
Wherein c represents a central curvature; r represents the positions of each point of the mirror surface, wherein 。
Measuring light entering along the normal direction of the inspected mirror surface at confocal position, so the adjustment error can approximate the position vectorThe projection in the normal direction thereof indicates that since the mirror surface is a reflecting surface, the introduced wave aberration is 2 times the wave aberration caused by the adjustment error:
；
Wherein, The unit normal vector, which is a sphere, can be expressed by the following formula:
；
Because the measured spherical lens is out of focus in the confocal position mainly generating two terms of inclination and defocus, the measured spherical lens is obtained by adopting a Seidel aberration polynomial as a base fitting, so that the first 4 terms of Seidel polynomials are selected to represent main aberration:
；
according to least squares theory, i.e. The following least squares matrix can be obtained:
；
In the method, in the process of the invention, 、、And. Coefficient of pair、、、And solving.Obtaining the offset according to the correlation between the fitting wave aberration and the offset-introduced wave aberration for the wave aberration coefficient introduced by the adjustment error、、And、Is a numerical value of (2). Judging whether the obtained adjustment parameters of the spherical mirror to be measured meet the displacement threshold value or not:
；
if the measured spherical mirror adjustment quantity is not smaller than the threshold value, the optical path is readjusted according to the obtained approximate solution, then the optical path is solved and readjusted until the measured spherical mirror adjustment quantity is smaller than the threshold value.
Compared with the prior art, the invention has the advantages that:
according to the invention, the offset is obtained by establishing a mathematical model between the offset and the aberration and fitting the mutual corresponding relation between the wave aberration and the offset-induced wave aberration, so that the adjustment error of the measured mirror at the cat eye position and the confocal position can be rapidly and accurately solved, and the position of the measured mirror is adjusted.
The spherical curvature radius measuring method based on computer-aided adjustment forms a closed loop in the light path adjusting process, dynamically adjusts the gesture of the measured mirror in real time, and improves the adjusting efficiency.
The spherical curvature radius measuring method based on computer-aided adjustment provided by the invention is also applicable to a horizontal type spherical curvature radius interferometry device, can be used for measuring spherical surfaces with various calibers and different curvature radiuses, and has good universality.
The invention can accurately measure the spherical curvature radius value by calculating and analyzing the relative adjustment quantity of the laser range finder and the four-dimensional electric control adjusting frame at two fixed focus positions.
The device provided by the invention is simple to operate, avoids human errors caused by manual measurement of detection personnel, is high in adjustment speed, improves the measurement efficiency, and provides a new automatic measurement mode for spherical curvature radius measurement.
Drawings
Fig. 1 is a spherical curvature radius measuring device based on computer-aided adjustment, wherein a marble base is 1, a phase interferometer is 2, a laser range finder is 3, an air floatation guide rail is 4, a four-dimensional electric control adjusting frame is 5, a detection tool is 6, a measured mirror is 7, a reference mirror is 8, and a computer system is 9;
FIG. 2 is a flow chart of the automatic repeat measurement of the radius of curvature of a sphere according to the present invention;
FIG. 3 is a schematic view of a spherical interferometry optical path at a cat eye position according to an embodiment of the present invention;
FIG. 4 is an interferogram collected near the cat eye position and collected after the measured mirror is adjusted according to the invention;
FIG. 5 is an interferogram acquired near the confocal position according to the present invention, after the measured mirror is adjusted by a computer-aided adjustment technique.
Detailed Description
To further illustrate the features of the present invention, the following description is provided in connection with specific examples thereof, and with the accompanying drawings.
Fig. 1 shows a spherical curvature radius measuring device based on computer-aided adjustment, which comprises a marble base 1, a phase interferometer 2, a laser range finder 3, an air floatation guide rail 4, a four-dimensional electric control adjusting frame 5, a detection tool 6, a measured mirror 7, a reference mirror 8 and a computer system 9; wherein:
The phase-shifting interferometer 2 is arranged at the center of the marble base 1 and is used for collecting interference fringes near a measuring position; the laser range finder 3 is positioned on the beam above the marble base 1 and is used for recording accurate axial displacement from the cat eye to the confocal position; the air-float guide rail 4 is fixed on the marble base 1 and is used for driving the axial displacement of the measured mirror 7; the measuring platform composed of the four-dimensional electric control adjusting frame 5 and the detecting tool 6 is connected with the air floatation guide rail 4, the four-dimensional electric control adjusting frame 5 is used for adjusting the translation and inclination of the detected mirror 7 along the X, Y direction, and the detecting tool 6 is used for fixing the detected mirror 7.
The computer system 9 is connected with the phase-shifting interferometer 2, the laser range finder 3, the air-float guide rail 4 and the four-dimensional electric control adjusting frame 5, and is used for collecting, analyzing and processing interference surface shape data collected by the phase-shifting interferometer 2, recording relative displacement and inclination collected by the laser range finder 3 and the four-dimensional electric control adjusting frame, and driving the measured mirror 7 to move to a specific position through the air-float guide rail 4 and the four-dimensional electric control adjusting frame 5 to realize spherical curvature radius measurement.
The device is used for realizing rapid and automatic measurement of the spherical curvature radius.
As shown in fig. 2, a spherical curvature radius measuring method based on computer-aided adjustment comprises the following steps:
Step a: inputting the F number of a reference mirror, the light transmission aperture D and the nominal radius R of the measured piece, and defining the repeated scanning times K;
Step b: moving the measured mirror 7 along the optical axis to the vicinity of the cat eye position, and recording axial displacement by the laser range finder 3;
Step c: obtaining measured wave front in the phase interferometer 2, performing Zernike fitting to obtain surface shape data, and obtaining offset according to the mutual corresponding relation between the fitting wave aberration and offset-introduced wave aberration 、、And、Readjusting the attitude of the objective lens 7, wherein the offset is：
Step d: if it isReturning to the previous step, otherwise, proceeding to the next step, whereinAn adjustment threshold value set for the position of the cat eye;
Step e: moving the measured mirror 7 along the optical axis to the vicinity of the confocal position, recording axial displacement by the laser range finder 3, and obtaining defocused wavefront in the phase interferometer 2;
step f: obtaining the offset according to the mutual corresponding relation between the fitting wave aberration and the offset-introduced wave aberration 、、And、Readjusting the attitude of the objective lens 7, wherein the offset is；
Step g: if it isReturning to the previous step ifAnd k +.0, returning to step b, ending the measurement when k=0,An adjustment amount threshold set for the confocal position;
Step h: because focusing and initial adjustment of the measured piece are mainly realized in the first measurement, the error is large, and the measurement result needs to be deleted. And finally, finishing k times of repeated measurement, and ending the measurement.
The offset is obtained by establishing the relation between the offset and the aberration and according to the mutual corresponding relation between the fitting wave aberration and the offset-induced wave aberration, namely, the surface shape data set acquired by the phase-shift interferometer 2 is transmitted to a computer system to be processed to obtain the required adjustment quantity of the measured mirror, and the specific analysis process is as follows:
First by the formula The approximate position of the cat eye position is calculated,In order to push the measured mirror 7 to the vicinity of the cat eye position along the optical axis for the wave aberration coefficient introduced by the adjustment error, zernike fitting is performed on the defocused wavefront acquired by the phase interferometer 1.
During the measurement, the resulting interferogram wave aberration can be expressed by the following formula:
；
In the method, in the process of the invention, Due to aberration caused by internal errors of the interferometer and errors of the mirror shape of the measured object,Indicating wave aberration caused by the offset at the measurement position. Light is incident to a focus O from a standard spherical lens TS, and the light in the propagation process meets the following conditions:
；
in the light ray Indicating the direction of the ith light ray along the ithIs propagated in the direction of (a) and passes through the point。The distance that light propagates in the ith section light path, light propagates to a point (namely focus O) on the sphere of the measured mirror and is reflected, and as the measured mirror has a trace adjustment amount, the actual light propagates to the point O' and is reflected, and the propagation direction is as follows:
；
wherein H (x, y) represents the propagation direction of the light after reflection at the spherical surface O'; Is the surface normal of the sphere of the measured mirror at O':
；
Establishing a rectangular coordinate system by taking an O point as an origin, wherein in the adjustment process, the measured spherical mirror accords with the rigid body rotation theorem, and has 6 degrees of freedom, namely translation along x, y and z axes respectively 、、And rotation about x, y, z axes、、. The curvature center of the measured mirror moves from point Q (0, -R) to pointThe following equation sets with O, Q and Q' as the centers of spheres are obtained, wherein the points are [ (], , )，(,,)，(,,) Any point on the sphere with O, Q and Q' as the sphere center;
；
the wave aberration caused by the offset amount at the cat eye position is:
；
Wherein, As for wavelength, light AO is incident from the standard spherical lens TS to the focus O for reflection, and the actual light propagates to the point O' for reflection due to the trace adjustment of the measured mirror, the propagation direction after reflection is changed from OB to。
The measured spherical mirror imbalance at the cat eye position mainly generates three items of inclination, defocus and astigmatism, and a Seidel aberration polynomial is adopted as a base fitting to obtain the measured spherical mirror imbalance induced wave aberration, so that the first 6 items of Seidel polynomials are selected to represent main aberration:
；
according to least squares theory, i.e. The following least squares matrix can be obtained:
；
In the method, in the process of the invention, For the wave aberration coefficients introduced by the adjustment errors,、、、、And. Coefficients c 0、c1、c2、c3、c4 and c 5 are solved. Obtaining the offset according to the mutual corresponding relation between the fitting wave aberration and the offset-introduced wave aberration、、And、Is a numerical value of (2). Judging whether the obtained adjustment parameters of the spherical mirror to be measured meet the angle and displacement threshold value:
；
Wherein the angle threshold And a displacement thresholdThe minimum angle and displacement adjustment quantity of the four-dimensional electric control platform and the air floatation guide rail can be selected as the judgment threshold value. If the measured spherical mirror adjustment quantity is not smaller than the threshold value, the optical path is readjusted according to the obtained approximate solution, then the optical path is solved and readjusted until the measured spherical mirror adjustment quantity is smaller than the threshold value.
Next, the measured mirror 7 is pushed along the optical axis to the vicinity of the confocal position by the known nominal radius, and Zernike fitting is performed on the surface shape information acquired by the phase interferometer 1.
In the adjusting process, the measured spherical mirror accords with the rigid rotation theorem, and has 6 degrees of freedom, namely translation along x, y and z axes、、And rotation about x, y, z axes、、. Set the coordinates of any point on the mirror surface to be measured asAnd the coordinates of the point after the adjustment is introducedThe relation between the two is:
；
Since the angle is small, to simplify the calculation, let ，. The surface to be measured of the measured spherical mirror is a rotationally symmetrical surface, soCan be ignored. To sum up, the displacement vector from P to PExpressed as:
；
The spherical equation can be expressed by the following formula:
；
Wherein c represents a central curvature; r represents the positions of each point of the mirror surface, wherein 。
Measuring light entering along the normal direction of the inspected mirror surface at confocal position, so the adjustment error can approximate the position vectorThe projection in the normal direction thereof indicates that since the mirror surface is a reflecting surface, the introduced wave aberration is 2 times the wave aberration caused by the adjustment error:
；
Wherein, The unit normal vector, which is a sphere, can be expressed by the following formula:
；
Because the measured spherical lens is out of focus in the confocal position mainly generating two terms of inclination and defocus, the measured spherical lens is obtained by adopting a Seidel aberration polynomial as a base fitting, so that the first 4 terms of Seidel polynomials are selected to represent main aberration:
；
according to least squares theory, i.e. The following least squares matrix can be obtained:
；
In the method, in the process of the invention, 、、And. The coefficient c 0、c1、c2、c3 is solved.Obtaining the offset according to the correlation between the fitting wave aberration and the offset-introduced wave aberration for the wave aberration coefficient introduced by the adjustment error、、And、Is a numerical value of (2). Judging whether the obtained adjustment parameters of the spherical mirror to be measured meet the displacement threshold value or not:
；
if the measured spherical mirror adjustment quantity is not smaller than the threshold value, the optical path is readjusted according to the obtained approximate solution, then the optical path is solved and readjusted until the measured spherical mirror adjustment quantity is smaller than the threshold value.
The curvature radius measured by the method can be calculated by the relative adjustment amounts of the laser range finder 3 and the four-dimensional electric control adjusting frame 5 at two fixed focus positions.
Fig. 3 is a schematic view of a spherical interferometry optical path at a cat eye position according to an embodiment of the present invention. In the figure, light AO is incident from a standard spherical lens TS to a focus O for reflection, and the actual light propagates to the point O' for reflection due to the trace adjustment of a measured mirror, and the propagation direction after reflection is changed from OB to. Where ri (x, y, p) is the direction vector of the incident ray, and hi (x, y, p) is the direction vector of the outgoing ray after the incident ray is reflected by O'.
Fig. 4 shows an interferogram collected near the cat eye position and an interferogram collected after the measured mirror is adjusted. The left image is an interference fringe image collected near the cat eye position, a large defocusing error exists, the interference fringe image in the right image is obtained after adjustment, adjustment errors such as defocusing and inclination in the image are reduced, and coma aberration mainly exists due to the internal error of the interferometer.
FIG. 5 is an interferogram acquired near the confocal position according to the present invention, after the measured mirror is adjusted by a computer-aided adjustment technique. The left image is an interference fringe image collected near the confocal position, has larger defocusing and tilting errors, and is adjusted to obtain the interference fringe image in the right image, wherein the adjustment errors such as defocusing and tilting in the image are reduced, and only a trace amount of adjustment errors exist.
While the invention has been described with respect to specific embodiments thereof, it will be appreciated that the invention is not limited thereto, but rather encompasses modifications and substitutions within the scope of the present invention as will be appreciated by those skilled in the art.
Claims (2)
1. The spherical curvature radius measuring method based on the computer-aided adjustment comprises a marble Dan Ji (1), a phase interferometer (2), a laser range finder (3), an air floatation guide rail (4), a four-dimensional electric control adjusting frame (5), a detection tool (6), a measured mirror (7), a reference mirror (8) and a computer system (9); wherein:
The phase interferometer (2) is arranged in the center of the marble Dan Ji (1) and is used for collecting interference fringes near a measuring position; the laser range finder (3) is positioned on the cross beam above the marble Dan Ji (1) and is used for recording the axial displacement from the cat eye to the confocal position; the air floatation guide rail (4) is fixed on the marble Dan Ji (1) and is used for driving the axial displacement of the tested mirror (7); the four-dimensional electric control adjusting frame (5) is used for adjusting the translation and inclination of the detected mirror (7) along the X, Y direction, and the detection tool (6) is used for fixing the detected mirror (7);
The computer system (9) is connected with the phase interferometer (2), the laser range finder (3), the air-float guide rail (4) and the four-dimensional electric control adjusting frame (5) and is used for collecting, analyzing and processing interference surface shape data collected by the phase interferometer (2), recording relative displacement and inclination collected by the laser range finder (3) and the four-dimensional electric control adjusting frame (5), and driving the measured mirror (7) to move to a specific position through the air-float guide rail (4) and the four-dimensional electric control adjusting frame (5) to realize spherical curvature radius measurement; characterized in that the method comprises the steps of:
step a: inputting the F number of a reference mirror, the light transmission aperture D and the nominal radius R of a measured mirror, and defining the repeated scanning times K;
Step b: moving a tested mirror (7) along an optical axis to the vicinity of the position of the cat eye, and recording axial displacement by a laser range finder (3);
step c: obtaining a measured wavefront in a phase interferometer (2) and performing Zernike fitting to obtain surface shape data, and obtaining a first offset according to the mutual corresponding relation between the fitting wave aberration and offset-introduced wave aberration 、、And、Re-adjusting the attitude of the mirror (7) under test, wherein the first adjustment is；
Step d: if it isReturning to the previous step, otherwise, proceeding to the next step, whereinA first adjustment threshold value set for the cat eye position;
step e: moving a measured mirror (7) along an optical axis to the vicinity of a confocal position, recording axial displacement by a laser range finder (3), and obtaining a defocused wavefront in a phase interferometer (2);
Step f: obtaining a second offset according to the mutual corresponding relation of the fitting wave aberration and the offset-introduced wave aberration 、、And、Re-adjusting the attitude of the mirror (7) under test, wherein the second adjustment is；
Step g: if it isReturning to the previous step ifAnd k is not equal to 0, returning to step b, ending the measurement when k=0, where k is the set number of measurements,A second adjustment amount threshold set for the confocal position;
Step h: finally, k times of repeated measurement are completed, and the measurement is finished;
wherein, an orthogonal coordinate system is established by taking an O point as an origin, and in the adjustment process, the measured mirror accords with the rigid body rotation theorem, and has 6 degrees of freedom, namely translational first offset along x, y and z axes respectively 、、And a first amount of misalignment of rotation about the x, y, z axes、、The curvature center of the measured mirror moves from point Q (0, -R) to pointThe following equation sets with O, Q and Q' as the centers of spheres are obtained, wherein the points are [ (], , )，(,,)，(,,) Any point on the sphere with O, Q and Q' as the sphere center;
；
the wave aberration caused by the offset amount at the cat eye position is:
；
Wherein, As for wavelength, light AO is incident from the standard spherical lens TS to the focus O for reflection, and the actual light propagates to the point O' for reflection due to the trace adjustment of the measured mirror, the propagation direction after reflection is changed from OB to；
Wherein, in the adjustment process, the measured mirror accords with the rigid body rotation theorem, and has 6 degrees of freedom, namely translational first offset along x, y and z axes respectively、、And a first amount of misalignment of rotation about the x, y, z axes、、Setting the coordinates of any point on the mirror surface to be measured asAnd the coordinates of the point after the adjustment is introducedThe relation between the two is:
；
Order the ，And ignoreTo sum up, the displacement vector from P to PExpressed as:
；
the spherical equation is represented by the following formula:
；
In the method, in the process of the invention, Representing the central curvature; Representing the positions of points of the mirror surface, wherein ；
Measuring light incident in the normal direction of the inspected mirror surface at the confocal position, so that the error is adjusted to take the position vectorThe projection in the normal direction thereof indicates that since the mirror surface is a reflecting surface, the introduced wave aberration is 2 times the wave aberration caused by the adjustment error:
；
Wherein, The unit normal vector of the sphere is expressed by the following formula:
；
The curvature radius measured by the method is calculated by the relative adjustment quantity of the laser range finder (3) and the four-dimensional electric control adjusting frame (5) at two fixed focus positions.
2. The method according to claim 1, wherein the offset is obtained by establishing a relation between the offset and the aberration and according to a mutual correspondence between the fitting wave aberration and the offset-induced wave aberration, that is, the adjustment amount required by the measured mirror is obtained by transmitting the surface shape data set acquired by the phase interferometer (2) to the computer system (9) for processing, and the specific analysis process is as follows:
First by the formula The position of the cat eye is calculated,The method is characterized in that the method comprises the steps of pushing a measured mirror (7) to the vicinity of a cat eye position along an optical axis by using a standard mirror theoretical curvature radius, and performing Zernike fitting on defocused wave fronts acquired by a phase interferometer (2);
During the measurement, the resulting interferogram wave aberration is expressed by the following formula:
；
In the method, in the process of the invention, Due to aberrations generated by interferometer internal errors and measured mirror shape errors,Indicating wave aberration caused by offset at the measurement position, light rays are incident to a focus O from a standard spherical lens TS selected, and the light rays in the propagation process satisfy the following conditions:
；
in the light ray Indicating the direction of the ith light ray along the ithIs propagated in the direction of (a) and passes through the point，The distance that light propagates in the ith section light path, light propagates to the spherical focus O of the measured mirror and reflects, and because the measured mirror has a trace adjustment quantity, the actual light propagates to the point O' and reflects, and the propagation direction is:
；
In the method, in the process of the invention, Representing the propagation direction of the light after reflection at the spherical surface O'; is the surface normal of the spherical surface of the measured mirror at the position O';
；
The measured mirror imbalance at the cat eye position generates three terms of inclination, defocus and astigmatism, and the measured mirror imbalance is obtained by adopting a Sedel aberration polynomial as a base fitting, so that the first 6 terms of Sedel polynomial expression aberration are selected here:
；
in the formula, the physical meaning of each aberration fitting coefficient is as follows: Is translation; Is inclined in the x direction; Is inclined in the y direction; is defocused; Is the astigmatism in the x direction; Is astigmatism in the y direction;
according to least squares theory, i.e. The following least squares matrix is obtained:
；
In the method, in the process of the invention, 、、、、And，For wave aberration coefficients introduced by adjustment errors, the pair coefficients、、、、AndSolving, and obtaining the offset according to the mutual correspondence between the fitting wave aberration and the offset-introduced wave aberration、、And、Judging whether the obtained adjustment parameters of the measured mirror meet the angle and displacement threshold values:
；
Wherein the angle threshold And a displacement thresholdSelecting the minimum angle and displacement adjustment quantity of the four-dimensional electric control platform and the air floatation guide rail as a judgment threshold value, if the minimum angle and displacement adjustment quantity do not meet the judgment threshold value, re-adjusting the light path according to the obtained approximate solution, then solving and re-adjusting the light path until the adjustment quantity of the measured mirror is smaller than the threshold value;
Secondly, pushing a measured mirror (7) to the vicinity of a confocal position along an optical axis by a known nominal radius, and performing Zernike fitting on surface shape information acquired by a phase interferometer (2);
because the measured lens generates two terms of inclination and defocus at the confocal position disorder, the measured lens disorder induced wave aberration is obtained by adopting a Sedel aberration polynomial as a base fitting, so that the first 4 terms of Sedel polynomial expression aberration are selected here:
；
according to least squares theory, i.e. The following least squares matrix is obtained:
；
In the method, in the process of the invention, 、、AndFor coefficient of、、、The solution is carried out,Obtaining a second offset according to the mutual correspondence between the fitting wave aberration and the offset-introduced wave aberration for the wave aberration coefficient introduced by the adjustment error、、And、Judging whether the obtained adjustment parameters of the spherical mirror to be measured meet the displacement threshold value:
；
if the measured mirror adjustment quantity is not smaller than the threshold value, the optical path is readjusted according to the obtained approximate solution, then the optical path is solved and readjusted until the measured mirror adjustment quantity is smaller than the threshold value.
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| CN108426699A (en) * | 2018-01-29 | 2018-08-21 | 中国科学院长春光学精密机械与物理研究所 | A kind of detection method of optical system image planes defocusing amount |
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| CN108426699A (en) * | 2018-01-29 | 2018-08-21 | 中国科学院长春光学精密机械与物理研究所 | A kind of detection method of optical system image planes defocusing amount |
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