JP3330274B2 - Optimization method in automatic design - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an automatic design of a lens system, in which variable values of constituent elements constituting the lens system are adjusted so that a plurality of predetermined characteristics of a desired lens system each approach a predetermined target value. More specifically, the present invention relates to a method for obtaining a variable value of the component at a point closest to the predetermined target value by using a quasi-Newton method.

[0002]

2. Description of the Related Art Lens design is basically to evaluate the performance of a plurality of lens systems having different variable values, to estimate the optimal variable values based on the results of the evaluation, and to gradually determine the image forming state of the luminous flux. It can be said that this is an operation to improve

By the way, in the automatic design of a lens system using a computer, each characteristic value f _i representing the current imaging state is used.
And their target values t _i ,

(Equation 3) Is formulated to find the minimum point of. Φ in the above equation is called a merit function, and w _i is a load (always positive) indicating the relative importance of each aberration.

The above variables (hereinafter referred to as parameters)
Is a variable that determines the components of the lens system, and includes, for example, the center curvature of the refractive surface, the surface interval, the type of glass, and the like. The above characteristics are also generally referred to as targets, and are characteristics calculated from the configuration of the lens system, and include, for example, paraxial trace values, ray trace values, shapes, and the like. In the automatic design, a mapping from a parameter space in which such parameters exist to a target space in which such targets exist is handled.

[0005] Finally, the last object of automatic design parameters that minimize the value of the merit function φ indicating the proximity of the values f _i and the target value t _i of the target (x _1, x _2,
.., X _m ).

The merit function φ is determined by the above characteristic values f _i
Is generally non-linear and cannot be solved by a simple least squares method, and in this respect there is difficulty in automatic design.
By the way, conventionally, a method using the quasi-Newton method is known as a method of obtaining the parameters x ₁ , x ₂ ,..., X _m corresponding to the minimum points of the merit function described above.

Hereinafter, an outline of the quasi-Newton method will be described with reference to a flowchart of FIG. First, a predetermined initial matrix H is set to set one point in the parameter space as an initial value (S1). This matrix H has the property of estimating the behavior of the merit function φ around the minimum point, and is referred to as an estimated inverse matrix.

Next,

(Equation 4) Is calculated (S2). Note that ∇ (vector ∇; the same applies hereinafter) f _i is the inclination of f _i at the current position x. However, ∇
f _i can be approximated by a value at a representative point near the current position x.

Next, from the gradient g (vector g; the same applies hereinafter) of the merit function φ at the current search position x (vector x; the same applies hereinafter), the direction d in which the minimum point will exist is calculated as follows:

(Equation 5) Ask for. Next, the minimum point x '(vector x'; the same applies hereinafter) of the merit function φ in the one-dimensional space {x + λd | λ is a real number} is obtained. This is called a one-dimensional search (S
3).

Next, the gradient g 'of the merit function φ at x'
(Vector g '; the same applies hereinafter) is calculated (S4), and it is determined whether or not the value of the gradient g' is 0 (minimum point) (S5). If the value is 0, optimization is performed If the value is not 0, H is determined according to the value of the gradient g '.
Is corrected to H ′ (S6) so that the behavior of the merit function φ is more appropriately reflected.

Thereafter, the flow returns to step S3, and the direction of the minimum point is

(Equation 6) , And the processing of steps S3 to S6 is repeated.

[0012]

In the above method, when the minimum point x 'of the merit function φ is obtained by the one-dimensional search in the process of step S3, the values of a plurality of sample points are compared for comparison. Each must be calculated. Conventionally, the target value f _i (i = 1,..., N) at that time has been obtained by actual ray tracing. Therefore, although it is a calculation process using a computer, an optimum solution can always be obtained in a short time. I could not say that.

The present invention has been made in view of such circumstances, and when obtaining each parameter value corresponding to a target value of each target using the quasi-Newton method, the efficiency of calculation is improved and optimization processing is performed. It is an object of the present invention to provide an optimization method in automatic design that can be accelerated.

[0014]

According to the present invention, there is provided an optimization method in an automatic design, wherein a lens system is designed such that a plurality of characteristics of the lens system have predetermined target values when designing the lens system. In an optimization method in automatic design for optimizing a plurality of variable values of constituent elements using a quasi-Newton method, in the step of performing an optimization process using the quasi-Newton method, the plurality of It is characterized by repeatedly executing a processing operation obtained by a one-dimensional search method by approximation and a processing operation of updating an estimated inverse matrix. Preferably, the two processing operations are performed during or before a processing operation for obtaining the variable value based on an actual value of the characteristic.

The one-dimensional search by the linear approximation is as follows:
The plurality of characteristic values,

(Equation 7) It is desirable to perform the approximation with the value obtained by the following.

Further, the processing operation for updating the estimated inverse matrix includes the merit function according to a value of a vector g indicating a gradient of a merit function indicating a proximity between a current value of the characteristic and the predetermined target value. Can be a processing operation for updating a matrix (estimated inverse matrix) H that estimates the behavior of the merit function near the minimum point of.

Further, a vector d indicating the direction in which the closest point to the predetermined target value exists is:

(Equation 8) Can be represented by

Further, the processing operation for obtaining the variable values by a one-dimensional search method based on linear approximation and the processing operation for updating the matrix H are repeated a predetermined number of times. As a result, the current position of the search is changed from the vector x to the vector x ’
If the matrix is updated from H to H ', it is desirable to return the current position of the search to the vector x, and obtain the variable value based on the actual characteristic value while keeping the matrix at H'.

[0019]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 3 is a schematic diagram showing an example of a lens system model to be used in the method according to one embodiment of the present invention. That is, in this method, each parameter of the lens system as shown in FIG. 3 including _four lenses L _{1 to} L ₄ arranged on the common optical axis X is adjusted, and each target (characteristic) is set to a desired target. The optimization process is performed so as to approach the value.

Then, in the target space represented by the multivariable function of the above parameter, predetermined coordinate values (f ₁ ,
f ₂ ,..., f _n ) and a predetermined coordinate value (t) in the target space.
The proximity (distance in the weighted target space) with the target position T (vector T; the same applies hereinafter) having ₁ , t ₂ ,..., T _n ) is represented by the following merit function φ.

[0021]

(Equation 9)

Note that w _i represents the value of the weight in each target. Therefore, in order to bring the current position F in the target space closer to the target position T, the parameters x ₁ ,
x ₂ , x ₃ ,..., x _m are set.

In this embodiment, the parameters to be handled are the lens surface curvature radii R _{1 to} R ₇ (seven), the lens thickness (and the lens surface interval) D _{1 of} each of the lenses L _{1 to} L ₄ as shown in FIG. to D ₆ (6 pieces), the refractive index N ₁ to N ₄ (4 pieces) and Abbe number ν ₁ ~ν _{4 (4} pieces) may also focal length (1) obtained from the ray tracing value as the target
(In FIG. 3, it is represented as a distance _Af between the principal plane (broken line) and the focal position P), and the lateral aberration (1
6), field curvature (4), spherical aberration (2), lateral chromatic aberration (10), and axial chromatic aberration (4).

The reason why there are a plurality of targets for each aberration is that the targets are set for each predetermined value of the incident height, and the total number of targets including the focal length is 37. The total number of parameters is 21.
Table 1 below shows the configuration of this parameter and the configuration of the target.
It is described in.

The values of the weights for each type of target are described in Table 1. These values indicate the relative importance of each target required when considering a merit function φ described later. It is a load. Further, in Table 1, the term "target" indicates a target value for each target. The target values are set to 0 for each aberration and 50 mm for the focal length.

[0026]

[Table 1] Parameter configuration type Number curvature 7 Surface spacing 6 Refractive index 4 Dispersion 4 Target configuration type Number Weight Target lateral aberration 16 550 Field curvature 4 10 Spherical aberration 2 10 Magnification chromatic aberration 10 5 0 On-axis chromatic aberration 4 5 0 Focal length 1 0.3 50

By the way, since the merit function φ represents the proximity (distance) from the current position to the target value, if the merit function φ proceeds in the direction in which it decreases most, there may be an optimum point ahead. It is possible, but not really. Considering this, for example, as shown in FIG. 6, considering a two-dimensional model of the contour surface of the merit function φ, the point T ′ where the minimum value of the merit function φ exists from the current position Jo set as the initial value is generally The case of obtaining using the quasi-Newton method will be described.

First, since there is no information on the contour surface 1 of the actual merit function φ at the current position Jo, a circle passing through this position Jo is considered as a pseudo contour surface, and the normal direction g of this circle is Search direction. The estimated inverse matrix H is set to a constant multiple of the unit matrix. Next, a plurality of sample points are selected on the straight line in the direction d (in a one-dimensional space),
Ray tracing is actually performed at each of these points, and the value of the merit function φ at those points is obtained.

On this straight line, the value of the merit function φ at the position of J ₁ is determined by the other vectors P ₁ , P ₂ ,
Vector P _3, when smaller than the value of the merit function φ at each position vector P _4, J ₁ minimum position on the straight line (minimum point), and in turn, to the position J ₁ and the current position, The estimated inverse matrix H is updated to H ', and the direction d' of the minimum position T 'is

(Equation 10) Ask for.

Then, the value of the merit function φ is calculated for a plurality of sample points on the straight line in the direction of d ′, and the position of the minimum value (the minimum point) is changed to the current position, and the estimated inverse matrix H is calculated. 'Is further updated. However, in the above operation, a plurality of sample points are selected on a straight line, and the value of the merit function φ is obtained for each point. In order to obtain the value of the merit function φ, each target value (lens performance Is extremely time-consuming.

Therefore, in the present embodiment, in order to reduce the total number of sample points to be selected, one-dimensional search by the above-described search method is repeatedly performed while linear approximation is performed.
The method of dimension search is adopted.

This will be conceptually described with reference to FIG. When starting from the current position Jo and searching by actual aberrations without searching by linear approximation, the search direction is the direction 1 which is the center direction of the first approximate contour surface (dashed line).
On the other hand, in the case of performing the search by the linear approximation and then performing the search by the actual aberration as in the present embodiment, the search direction is the second approximation close to the shape of the actual contour plane (solid line). The direction 2 is the center direction of the contour plane (two-dot chain line). That is, in the present embodiment, the search direction is not the direction 1 as in the prior art, but the direction 2 close to the direction in which the minimum value of the merit function φ exists. Time can be shortened.

Hereinafter, the search method of this embodiment including the one-dimensional search by the linear approximation will be described with reference to the flowchart shown in FIG. As described above, in the one-dimensional search, the value of the merit function φ is obtained at a plurality of sample points x + λd. At this time, an approximate value f _i + (か ら f _i ) ^T λd is used instead of calculating the target value from the configuration of the lens system. This is called a one-dimensional search by linear approximation.

First, the current position of the search is set to Jo, and an initial value H of the estimated inverse matrix is set (S1). The initial value H of the estimated inverse matrix is

[Equation 11] And Here, I is a unit matrix.

Next, the current position Jo of this search is stored in a predetermined data storage area (S2). Next, a one-dimensional search by linear approximation is performed using the above-described approximate expression as an expression of f _i + (∇f _i ) ^T λd (S3). Next, the estimated inverse matrix H is updated by the following equation (S4).

[0036]

(Equation 12)

Thereafter, a one-dimensional search (S
3) and updating of the estimated inverse matrix (S4) are repeated p times (p ≧
0) (S5). The number of repetitions p of the one-dimensional search by the linear approximation is set to a predetermined number of times set in advance, or the repetition operation is terminated when the moving distance becomes equal to or more than a predetermined value. As a result, the value of the merit function φ is not necessarily small at the current position J ₁ after the search, but H ′ appropriately reflects the behavior of the merit function φ more than H. The calculation time for a one-dimensional search by linear approximation is much shorter than the calculation time for finding an accurate target value.

Thereafter, the current position of the search is returned to Jo (S
6), the estimated inverse matrix is one-dimensional search using the correct target value using H '(S7), and the estimated inverse matrix is updated (S9).
Perform Thereafter, the one-dimensional search processing (S2) to (S5) by the linear approximation and the one-dimensional search processing (S6) to (S9) by the accurate target are repeated.

If the gradient g of the merit function φ at the position obtained in step S7 is 0 and the value of the merit function φ is a minimum point, the position x in the parameter space at that time is The solution becomes a solution and the optimization process ends (S8). The number of repetitions p may not be the same every time. As described above, the most characteristic of the above method is that the quasi-Newton method is used for the optimization processing, and that the one-dimensional search processing by linear approximation and the update processing of the estimated inverse matrix are interposed in the processing.

FIG. 4 shows the present embodiment and the prior art.
It is a graph which shows the calculation time required for the optimization process when performing the above-mentioned automatic design of a lens system. Here, the prior art here refers to the one based on linear approximation using the quasi-Newton method.
This is an optimization process that does not use dimension search. In this process, the number of loops p in step S5 in FIG. 1 is uniformly set to 4. As shown in FIG.
Both the present embodiment and the prior art approach the minimum value as the number of steps increases, but the time to reach the minimum value is greatly different from each other, and the calculation time in the prior art is t ₂ . The calculation time in this embodiment is significantly shorter than t _{1, which} is about ６ of t ₂ or less.

An information processing apparatus for implementing the method of the above embodiment will be briefly described below with reference to the block diagram of FIG. That is, in this information processing apparatus, the computer main body 11 and the peripheral device 12 are connected by the communication path 13. The computer main unit 12 includes a central processing unit 16 including a control unit 14 for controlling the operation of each unit of the device and various signals transmitted and received between the units, and a computing unit 15 for calculating various data. A main storage device 17 in which programs, data, and the like are stored is provided. The peripheral devices 12 are classified into a file device 18 and an input / output device 19. In FIG. 5, thick arrows indicate the flow of data, and dotted arrows indicate the relationship between observation and control between members.

In addition to the program described with reference to the flowchart of FIG. 1, various programs for automatic lens design are read from the main storage device 17, and various processes such as the above-described optimization process are performed based on the read programs. It will be. Each data obtained by the various processes is stored in the main storage device 17. It should be noted that the method of the present invention is not necessarily limited to the above-described embodiment, and various modifications can be made. For example, the initial value H of the above estimated inverse matrix can be set to another initial value as follows.

[0043]

(Equation 13)

In the present embodiment, the above-mentioned method of correcting H to H 'is based on the BFGS method (Broyden-Fletcher-Goldfab).
-Shanno method), which is an example of the quasi-Newton method, but the method applicable as the quasi-Newton method in the method of the present invention is not limited to this, and each method of other quasi-Newton methods, for example, The DFP method shown below (David
on-Fletcher-Powell) can be applied.

That is, when the DFP method is used,

[Equation 14] Is set in the same manner as in the above-described embodiment, but the equation for changing the estimated inverse matrix H to the estimated inverse matrix H ′ is expressed by the following calculation equation.

[0046]

(Equation 15)

Although the method of the present invention shows an optimization method for lens system design, it can be applied to the design of other optical systems using prisms and filters other than the lens system.

[0048]

As described above, according to the optimization method based on the automatic design described in the present description, when each parameter value corresponding to a value approaching the target value of each target is obtained using the quasi-Newton method. And a method of repeatedly performing a one-dimensional search process by linear approximation and a process of updating the estimated inverse matrix, thereby reducing the number of sample points for calculating the target value. The time can be significantly reduced. Therefore, the time required for the automatic design of the lens system can be shortened, in other words, the performance of the lens system can be improved within a limited design time compared to the related art.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining an embodiment of the method of the present invention.

FIG. 2 is a diagram conceptually showing the embodiment shown in FIG. 1;

FIG. 3 is a lens system to which the embodiment shown in FIG. 1 is applied;

FIG. 4 is a graph showing the effect of the embodiment shown in FIG. 1;

FIG. 5 is a block diagram showing an example of an information processing apparatus for implementing the embodiment shown in FIG. 1;

FIG. 6 is a diagram conceptually showing a conventional technique.

FIG. 7 is a flowchart for explaining a conventional technique.

[Explanation of symbols]

11 computer main body 12 peripheral devices 13 channel 14 control device 15 calculation device 16 the central processing unit 17 main storage 18 file system 19 input and output devices L ₁ ~L ₄ lens R ₁ to R ₇ radius of curvature D ₁ to D ₆ lens thickness (Spacing) N _{1 to} N ₄ Refractive index ν _{1 to} ν ₄ Abbe number (dispersion)

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G02B 13/00 G02B 9/00

Claims (6)

(57) [Claims] When designing a lens system, a plurality of variable values of components of the lens system are determined using a quasi-Newton method so that a plurality of characteristics of the lens system become predetermined target values. An optimization method in an automatic design that performs optimization by using the quasi-Newton method, in which the plurality of variable values are obtained by a one-dimensional search method based on linear approximation, and an estimated inverse matrix. Optimizing method in automatic design, characterized by repeatedly executing a processing operation for updating the data. 2. The optimization method according to claim 1, wherein the two processing operations are performed during or before a processing operation for obtaining the variable value based on an actual value of the characteristic. . 3. The one-dimensional search according to the linear approximation, wherein the plurality of characteristics are expressed by: 3. The optimization method in automatic design according to claim 1, wherein the optimization is performed by approximation with a value obtained by: 4. The processing operation for updating the estimated inverse matrix includes:
A matrix estimating the behavior of the merit function near the minimum point of the merit function according to the value of the vector g indicating the slope of the merit function representing the proximity between the current value of the characteristic and the predetermined target value. The optimization method according to any one of claims 1 to 3, wherein the processing operation is a processing operation for updating H. 5. A vector d indicating a direction in which the closest point to the predetermined target value exists is given by: 5. The optimization method in automatic design according to claim 4, wherein: 6. A processing operation for obtaining the variable value by a one-dimensional search method based on linear approximation and a processing operation for updating the matrix H are repeatedly performed a predetermined number of times. As a result, the current position of the search is changed from a vector x to a vector x ′, And if the matrix is updated from H to H ′, the current position of the search is returned to the vector x, and the variable value is determined based on the actual characteristic value while the matrix is set to H ′. 6. The optimization method in automatic design according to claim 5, wherein