JPH0894489A - Method and equipment for optimizing objective system and method apparatus for designing lens system by use thereof - Google Patents

Abstract

PURPOSE: To design a lens system quickly with minimum amount of calculation by providing means for calculating an eigenvalue based on a specific column vector comprising the variation amounts of respective characteristics for the micro variation of a plurality of components as the elements thereof. CONSTITUTION: A CPU 200 controls the entire lens design system and a memory 202 stores a program, components of lens, variables for optimization design, an evaluation function, etc. Optimal component values can be attained by locally modifying the value of component such that a lens system represented by a plurality of components has desired characteristics. In other words, an eigenvalue calculating means calculates the eigenvalue of the product of a submatrix having, as the base thereof, the column vector of Jacobian A comprising the variation amounts of respective characteristics for the micro variation of a plurality of components as the elements thereof and the transposed matrix thereof. If the absolute value of the product of eigenvalues is smaller than a predetermined value, a predetermined micro value is added to the micro variation of corresponding component to obtain a new micro variation.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention locally modifies a plurality of constituent elements so that a target system composed of the plurality of constituent elements has desired characteristics, and the optimum design value of the system is obtained. The present invention relates to an optimization processing method and a device for obtaining the same. Further, the present invention relates to a lens designing method and its apparatus using this optimization processing method and its apparatus, an optimal pattern designing method and its apparatus of LSI, a building designing method and its apparatus.

[0002]

2. Description of the Related Art Constituent elements constituting a target system are variable vectors consisting of n elements, X = [x ₁ ,. ． ． , X _n ] ^T (1) An evaluation function vector made up of m elements for evaluating the characteristic of the target,

[0003]

[Equation 2]

It is represented by. However,

[0005]

[Equation 3]

[0006] Here, f _k (X), f _{k, tar} are the value of the evaluation function representing each characteristic value and its target value, respectively. Note that these evaluation functions may include constraint condition values in addition to characteristic values intended to have desired values. In the least-squares method, a solution is generally obtained so that the amount of deviation (error) of each evaluation function value from the target value is minimized. For that purpose, an objective function represented by the following equation is used as a single evaluation scale.

[0007]

[Equation 4]

The objective function given by equation (4) is called a merit function in the field of lens design, for example. When the linear approximation of the evaluation function is applied to the equation (4), the necessary condition of X to obtain the local minimum value is

[0009]

[Equation 5]

Can be expressed as Here, X ₀ is the initial value of the variable vector. Also, A is Jacobian of F (X)
bian)

[0011]

[Equation 6]

[0012] In Expression (6), Fi means the i-th element Fi (X) of the evaluation function vector (Expression (2)). Further, ΔX is a solution vector representing the variation of the variable vector to the next step, and can be represented as follows.

[0013]

[Equation 7]

In general, since the relationship between the evaluation function and the variable is non-linear, instead of solving the equation (5) as it is, the non-linear component of the second derivative or higher is corrected. For example, D.I. S. In the orthogonalization method devised by Gray,
The following processing is performed. First, Equation (5) is transformed into a matrix A by Gram-Schmidt QR decomposition.

[0015]

[Equation 8]

Applying

[0017]

[Equation 9]

Is converted to Where Q is an orthonormal matrix,
R is an upper triangular matrix. In equation (9),

[0019]

[Equation 10]

In other words, U can be regarded as mutually independent orthogonal variables, and each orthogonal variable can be processed individually. The orthogonalization method utilizes such a property, and U
For each element, the vector length is lengthened or shortened depending on the strength of linearity to correct for non-linearity. In addition, K. Lebenberg and D.C. W. Invented by Marquardt, Levenberg-Marquardt (DLS: Damped)
Least Squares method introduces a scalar quantity ρ called a damping factor to correct the nonlinearity,
Instead of equation (5),

[0021]

[Equation 11]

The optimum solution is obtained by solving In Expression (11), I represents an identity matrix. On the other hand, in the actual numerical calculation, each element aij of A is an exact differential system numerical value as shown in the equation (6).

[0023]

[Equation 12]

Not the difference value;

[0025]

[Equation 13]

Is calculated using

[0027]

However, in this case, if the preset variable difference amount δx _j is not appropriate, a bad condition in numerical calculation will occur, and many iterative calculations will be required, resulting in efficient optimization. There was a problem that could not be solved. The present invention has been made in view of the above-described conventional example, and provides an optimization calculation method and a device for always performing efficient optimization calculation by performing appropriate / inappropriate evaluation of a difference amount setting value of a variable in advance. The purpose is to do.

It is another object of the present invention to provide a lens system designing method and a device therefor which can design a lens system at high speed with a minimum amount of calculation by using the optimizing calculation method and the apparatus.

[0029]

In order to achieve the above object, an object system optimizing method and apparatus, and a lens system designing method and apparatus using the same according to the present invention have the following configurations. That is, a lens system design that locally obtains the optimum component value by locally changing the values of the plurality of components so that the lens system represented by the plurality of components has desired characteristics. A device based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the amount of change in each characteristic with respect to a minute amount of change in the plurality of constituent elements each 'and eigenvalue calculation means for calculating the eigenvalue of the calculated by the eigenvalue calculation unit a' ^T a 'matrix product a with ^T' rolling value matrix a of the matrix a 'and its partial matrix a' ^T a ' If the absolute value of the product between the eigenvalues is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues to obtain a new minute change amount of the component. Generated by the constituent element minute change amount correcting means and the constituent element minute change amount correcting means. Based on the new minute change amount, the optimum constituent element that obtains the optimum constituent element value by locally changing the values of the plurality of constituent elements so that the lens system has desired characteristics. Value acquisition means.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A device for obtaining an element value, the column vector a _i (i = i = i
1 ... n) to a base portion matrix A 'and its partial matrix A''determinant of | A' ^T A 'matrix product A with ^T' rolling value matrix A ^T A '| calculate the matrix If the absolute value of | ^A'T A '| calculated by the formula calculation means and the eigenvalue calculation means is smaller than a predetermined value, the predetermined minute value is added to the minute change amount of the corresponding component to construct Based on the component minute change amount correction means for setting a new minute change amount of the element and the new minute change amount generated by the component element minute change amount correction means, the lens system is set to have desired characteristics. Optimal component value acquisition means for acquiring the optimum component value by locally changing the values of the plurality of components.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A device for obtaining an element value, the column vector a _i (i = i = i
If the absolute value of the product of the singular value calculating means for calculating the singular value of the submatrix A ′ based on 1 ... n) and the singular value calculating means is smaller than a predetermined value, the correspondence is obtained. Component minute change amount correction means for adding a predetermined minute value to the minute change amount of the component element to obtain a new minute change amount of the component element, and a new component minute change amount correction means generated by the component element minute change amount correction means. Based on such a minute change amount, the values of the plurality of constituent elements are locally changed so that the lens system has a desired characteristic, thereby obtaining the optimum constituent element values. And means.

Another aspect of the present invention is to optimize the values of the plurality of constituent elements locally so that the target system expressed by the plurality of constituent elements has desired characteristics. A device for acquiring component values, wherein a column vector a _i (i = i = i = _i ) of a Jacobian A whose component is the amount of change in each characteristic with respect to a minute amount of change in the plurality of components.
1 ... n) 'and its partial matrix A' partial matrix A of a base and eigenvalue calculation means for calculating the eigenvalues of ^T A '' matrix product A with ^T 'rolling value matrix A, the eigenvalue calculation means Calculated by A ' ^T
If the absolute value of the product between the eigenvalues for each A'is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues to obtain a new minute value of the component. A component minute change amount correction means for the change amount,
Optimum by locally changing the values of the plurality of constituent elements so that the lens system has desired characteristics based on the new minute change amount generated by the constituent minute change amount correction means. Optimal component value acquisition means for acquiring the values of various components.

Another aspect of the invention is to optimize the values of the plurality of constituent elements locally so that the target system expressed by the plurality of constituent elements has desired characteristics. A device for acquiring component values, wherein a column vector a _i (i = i = i = _i ) of a Jacobian A whose component is the amount of change in each characteristic with respect to a minute amount of change in the plurality of components.
1 ... n) to a base portion matrix A 'and its partial matrix A''determinant of | A' ^T A 'matrix product A with ^T' rolling value matrix A ^T A '| calculate the matrix If the absolute value of | ^A'T A '| calculated by the formula calculation means and the eigenvalue calculation means is smaller than a predetermined value, the predetermined minute value is added to the minute change amount of the corresponding component to construct Based on the component minute change amount correction means for setting a new minute change amount of the element and the new minute change amount generated by the component element minute change amount correction means, the lens system is set to have desired characteristics. Optimal component value acquisition means for acquiring the optimum component value by locally changing the values of the plurality of components.

Another aspect of the invention is to optimize the values of the plurality of constituent elements locally so that the target system expressed by the plurality of constituent elements has desired characteristics. A device for acquiring component values, wherein a column vector a _i (i = i = i = _i ) of a Jacobian A whose component is the amount of change in each characteristic with respect to a minute amount of change in the plurality of components.
If the absolute value of the product of the singular value calculating means for calculating the singular value of the submatrix A ′ based on 1 ... n) and the singular value calculating means is smaller than a predetermined value, the correspondence is obtained. Component minute change amount correction means for adding a predetermined minute value to the minute change amount of the component element to obtain a new minute change amount of the component element, and a new component minute change amount correction means generated by the component element minute change amount correction means. Based on such a minute change amount, the values of the plurality of constituent elements are locally changed so that the lens system has a desired characteristic, thereby obtaining the optimum constituent element values. And means.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A method for designing a lens system for obtaining an element value, wherein a column vector a _i (i = 1 ..) of Jacobian A whose element is the variation of each characteristic with respect to a minute variation of the plurality of constituent elements. .n) as a basis, and the eigenvalue calculation step of calculating the eigenvalue of the matrix product A ′ ^T A ′ of the transversion matrix A ′ ^T of the submatrix A ′ and the eigenvalue calculation step. If the absolute value of the product between the eigenvalues for each of A ′ ^T A ′ is smaller than a predetermined value, the predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues, and the component And a step of correcting the minute change amount of the component, which is a new minute change amount of Based on the new minute change amount generated in the change amount correction step, the values of the plurality of constituent elements are locally changed so that the lens system has desired characteristics, and thus the optimum constituent element An optimal component value acquisition step of acquiring a value.

Another aspect of the invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A method of obtaining an element value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose element is a variation of each characteristic with respect to a minute variation of the plurality of constituent elements
1 ... n) to a base portion matrix A 'and its partial matrix A''determinant of | A' ^T A 'matrix product A with ^T' rolling value matrix A ^T A '| calculate the matrix If the absolute value of | ^A'T A '| calculated in the formula calculation step and the eigenvalue calculation step is smaller than a predetermined value, the predetermined minute value is added to the minute change amount of the corresponding component to obtain the above-mentioned configuration. Based on the component minute change amount correction step of setting a new minute change amount of the element and the new minute change amount generated in the component element minute change amount correction step, the lens system is set to have desired characteristics. An optimum component value acquisition step of acquiring an optimum component value by locally changing the values of a plurality of components.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A method of obtaining an element value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose element is a variation of each characteristic with respect to a minute variation of the plurality of constituent elements
If the absolute value of the product of the singular value calculation step for calculating the singular value of the submatrix A ′ based on 1 ... n) and the singular value calculation step is smaller than a predetermined value, the corresponding The component minute change amount correction step of adding a predetermined minute value to the component minute change amount to obtain a new minute change amount of the component element, and a new component generated by the component element minute change amount correction step. Based on such a minute change amount, the values of the plurality of constituent elements are locally changed so that the lens system has a desired characteristic, thereby obtaining the optimum constituent element values. And a process.

Another aspect of the invention is to optimize the values of the plurality of constituent elements locally so that the target system represented by the plurality of constituent elements has desired characteristics. A method for obtaining a component value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose component is a variation amount of each characteristic with respect to a minute variation amount of the plurality of components.
1 ... n) 'and its partial matrix A' partial matrix A of the base and the eigenvalue calculation step of calculating the eigenvalues of ^T A '' matrix product A with ^T 'rolling value matrix A, the eigenvalue calculation step Calculated by A ' ^T
If the absolute value of the product between the eigenvalues for each A'is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues to obtain a new minute value of the component. A component minute change amount correction process for the change amount,
Optimizing by locally changing the values of the plurality of constituent elements so that the lens system has the desired characteristics based on the new minute change amount generated in the constituent minute change amount correction step. An optimal component value acquisition step of acquiring the values of various components. Another invention is to optimize the values of the constituent elements by locally changing the values of the constituent elements so that the target system represented by the constituent elements has desired characteristics. And a column vector a _i (i = 1 ... n) of a Jacobian A whose element is a variation amount of each characteristic with respect to a minute variation amount of the plurality of constituent elements. to the partial matrix a 'and its partial matrix a' ^T a 'matrix product a with ^T' rolling value matrix a 'determinant of | a'
^If the absolute value of | A ′ ^T A ′ | calculated in the determinant calculation step of calculating ^T A ′ | and the eigenvalue calculation step is smaller than a predetermined value, a small change amount of the corresponding component is set to a predetermined small amount. The lens system is desired based on the component minute change amount correction step of adding the values to obtain a new minute change amount of the component element and the new minute change amount generated in the component element minute change amount correction step. To obtain the optimum constituent element value by locally changing the values of the plurality of constituent elements so as to obtain the characteristic of 1.

Another aspect of the invention is to optimize the values of the plurality of constituent elements locally so that the target system represented by the plurality of constituent elements has desired characteristics. A method for obtaining a component value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose component is a variation amount of each characteristic with respect to a minute variation amount of the plurality of components.
If the absolute value of the product of the singular value calculation step for calculating the singular value of the submatrix A ′ based on 1 ... n) and the singular value calculation step is smaller than a predetermined value, the corresponding The component minute change amount correction step of adding a predetermined minute value to the component minute change amount to obtain a new minute change amount of the component element, and a new component generated by the component element minute change amount correction step. Based on such a minute change amount, the values of the plurality of constituent elements are locally changed so that the lens system has a desired characteristic, thereby obtaining the optimum constituent element values. And a process.

[0040]

In the above construction, the values of the plurality of constituent elements are locally changed so that the lens system represented by the plurality of constituent elements has desired characteristics, and thus the optimum constituent element values are obtained. In the lens system design apparatus, the eigenvalue calculation means uses the amount of change in each of the characteristics with respect to the amount of minute change in the plurality of constituent elements as an element.
the eigenvalues of an) column vector a _i of A (i = 1 ... n) the ^T A 'matrix product A with ^T' section as a base matrix A 'and its partial matrix A' rolling value matrix A ' calculated, components small variation correction means is, if the absolute value of the product between the eigenvalues for each calculated by the eigenvalue calculating unit a ^'T a' is smaller than the predetermined value, the absolute value of the product between the eigenvalues The predetermined minute value is added to the minute change amount of the component corresponding to to obtain a new minute change amount of the component, and the optimum component value obtaining means is generated by the component minute change amount correcting means. Based on the new minute change amount, the optimum values of the constituent elements are obtained by locally changing the values of the plurality of constituent elements so that the lens system has desired characteristics.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A device for obtaining an element value, wherein the determinant calculation means has a column vector a _i (i = 1) of Jacobian A whose element is the variation of each characteristic with respect to a minute variation of a plurality of constituent elements. ... submatrices a 'and its partial matrix a''determinant of | a' ^T a 'matrix product a with ^T' rolling value matrix a to base the n) ^T a '| is calculated and configuration If the absolute value of | A ′ ^T A ′ | calculated by the eigenvalue calculation means is smaller than the predetermined value, the element small change amount correction means adds the predetermined small value to the small change amount of the corresponding constituent element. , A new minute change amount of the constituent element, and the optimum constituent element value obtaining means is generated by the constituent element small change amount correcting means. Based on the new minute change amount, the optimum values of the constituent elements are obtained by locally changing the values of the plurality of constituent elements so that the lens system has desired characteristics.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A device for acquiring element values, wherein the singular value calculating means has a column vector a _i (i = i = i = i = _i ) of Jacobian A whose element is the amount of change in each characteristic with respect to minute changes in the plurality of constituent elements. 1 ... n) is used as the basis to calculate the singular value of the submatrix A ′, and the component small change amount correction means determines that the absolute value of the product of the singular values calculated by the singular value calculation means is greater than a predetermined value. If it is small, a predetermined minute value is added to the minute change amount of the corresponding component to obtain a new minute change amount of the component, and the optimum component value acquisition means is generated by the component minute change amount correction means. Based on the new minute change amount
Optimum component values are obtained by locally changing the values of the plurality of components so that the lens system has desired characteristics.

Another aspect of the invention is to optimize the values of the plurality of constituent elements locally so that the target system expressed by the plurality of constituent elements has desired characteristics. A device for acquiring component values, wherein a column vector a _i (i = i = i = _i ) of a Jacobian A whose component is the amount of change in each characteristic with respect to a minute amount of change in the plurality of components.
1 ... n) 'and its partial matrix A' partial matrix A of a base and eigenvalue calculation means for calculating the eigenvalues of ^T A '' matrix product A with ^T 'rolling value matrix A, the eigenvalue calculation means Calculated by A ' ^T
If the product between the eigenvalues for each of A'is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the absolute value of the product between the eigenvalues to obtain a new minute value of the component. A component minute change amount correction means for the change amount,
Optimum by locally changing the values of the plurality of constituent elements so that the lens system has desired characteristics based on the new minute change amount generated by the constituent minute change amount correction means. Optimal component value acquisition means for acquiring the values of various components.

Another aspect of the invention is to optimize the values of the plurality of constituent elements locally so that the target system represented by the plurality of constituent elements has desired characteristics. A device for acquiring component values, wherein a column vector a _i (i = i = i = _i ) of a Jacobian A whose component is the amount of change in each characteristic with respect to a minute amount of change in the plurality of components.
1 ... n) to a base portion matrix A 'and its partial matrix A''determinant of | A' ^T A 'matrix product A with ^T' rolling value matrix A ^T A '| calculate the matrix If the absolute value of | ^A'T A '| calculated by the formula calculation means and the eigenvalue calculation means is smaller than a predetermined value, the predetermined minute value is added to the minute change amount of the corresponding component to construct Based on the component minute change amount correction means for setting a new minute change amount of the element and the new minute change amount generated by the component element minute change amount correction means, the lens system is set to have desired characteristics. Optimal component value acquisition means for acquiring the optimum component value by locally changing the values of the plurality of components.

Another aspect of the present invention is to optimize the values of the plurality of constituent elements locally so that the target system expressed by the plurality of constituent elements has desired characteristics. A device for acquiring component values, wherein a column vector a _i (i = i = i = _i ) of a Jacobian A whose component is the amount of change in each characteristic with respect to a minute amount of change in the plurality of components.
If the absolute value of the product of the singular value calculating means for calculating the singular value of the submatrix A ′ based on 1 ... n) and the singular value calculating means is smaller than a predetermined value, the correspondence is obtained. Component minute change amount correction means for adding a predetermined minute value to the minute change amount of the component element to obtain a new minute change amount of the component element, and a new component minute change amount correction means generated by the component element minute change amount correction means. Based on such a minute change amount, the values of the plurality of constituent elements are locally changed so that the lens system has a desired characteristic, thereby obtaining the optimum constituent element values. And means.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A method for designing a lens system for obtaining an element value, wherein a column vector a _i (i = 1 ..) of Jacobian A whose element is the variation of each characteristic with respect to a minute variation of the plurality of constituent elements. .n) as a basis, and the eigenvalue calculation step of calculating the eigenvalue of the matrix product A ′ ^T A ′ of the transversion matrix A ′ ^T of the submatrix A ′ and the eigenvalue calculation step. If the absolute value of the product between the eigenvalues for each of A ′ ^T A ′ is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the absolute value of the product between the eigenvalues, A component minute change amount correction step for setting a new minute change amount of the component; Based on the new small change amount generated in the element small change amount correction process, the values of the plurality of constituent elements are locally changed so that the lens system has desired characteristics, thereby obtaining an optimum configuration. An optimum component element value acquisition step of acquiring an element value.

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A method of obtaining an element value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose element is a variation of each characteristic with respect to a minute variation of the plurality of constituent elements
Compute the determinant | A ′ ^T A ′ | of the matrix product A ′ ^T A ′ of the submatrix A ′ based on 1 ... n) and the transversion matrix A ′ ^T of the submatrix A ′, If the calculated absolute value of | A ′ ^T A ′ | is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the corresponding component to obtain a new minute change amount of the component. Based on the newly generated small amount of change, the values of the plurality of constituent elements are locally changed so that the lens system has desired characteristics, thereby obtaining optimum values of the constituent elements. .

Another aspect of the present invention is to locally change the values of the plurality of constituent elements so that the lens system represented by the plurality of constituent elements has desired characteristics. A method of obtaining an element value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose element is a variation of each characteristic with respect to a minute variation of the plurality of constituent elements
The singular value of the submatrix A ′ based on 1 ... n) is calculated, and if the absolute value of the product of the calculated singular values is smaller than a predetermined value, a predetermined small change amount of the corresponding constituent element is calculated. A minute value is added to obtain a new minute change amount of the constituent element, and the values of the plurality of constituent elements are locally changed based on the generated new minute change amount so that the lens system has desired characteristics. To obtain the optimum component value.

Another aspect of the present invention is to optimize the values of the plurality of constituent elements locally so that the target system represented by the plurality of constituent elements has desired characteristics. A method for obtaining a component value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose component is a variation amount of each characteristic with respect to a minute variation amount of the plurality of components.
The eigenvalue of the matrix product A ′ ^T A ′ of the submatrix A ′ based on 1 ... n) and the transversion matrix A ′ ^T of the submatrix A ′ is calculated, and calculated in the eigenvalue calculation step. If the absolute value of the product between the eigenvalues for each of A ′ ^T A ′ is smaller than the predetermined value, the predetermined minute value is added to the minute change amount of the component corresponding to the absolute value of the product between the eigenvalues, and Based on the new minute change amount of the component, based on the new minute change amount generated in the component minute change amount correction step, the values of the plurality of component elements are locally adjusted so that the lens system has desired characteristics. To obtain the optimum component value. Another invention is to optimize the values of the constituent elements by locally changing the values of the constituent elements so that the target system represented by the constituent elements has desired characteristics. And a column vector a _i (i = 1 ... n) of a Jacobian A whose element is a variation amount of each characteristic with respect to a minute variation amount of the plurality of constituent elements. The determinant | A ′ ^T A ′ | of the matrix product A ′ ^T A ′ of the submatrix A ′ and the transversion matrix A ′ ^T of the submatrix A ′ is calculated and calculated in the eigenvalue calculation step. If the absolute value of | ^A'T A '| is smaller than a predetermined value, a predetermined small value is added to the minute change amount of the corresponding component to obtain a new minute change amount of the component, The values of the plurality of constituent elements are adjusted so that the lens system has desired characteristics based on the new minute change amount generated in the change amount correction process. By locally changing, the optimum component value is obtained.

Another aspect of the invention is to optimize the values of the plurality of constituent elements locally so that the target system expressed by the plurality of constituent elements has desired characteristics. A method for obtaining a component value, wherein a column vector a _i (i = i = i = i = i = _{i i} ) of a Jacobian A whose component is a variation amount of each characteristic with respect to a minute variation amount of the plurality of components.
The singular value of the submatrix A ′ based on 1 ... n) is calculated, and if the absolute value of the product of the calculated singular values is smaller than a predetermined value, a predetermined small change amount of the corresponding constituent element is calculated. A minute value is added to obtain a new minute change amount of the constituent element, and the values of the plurality of constituent elements are locally changed based on the generated new minute change amount so that the lens system has desired characteristics. To obtain the optimum component value.

[0051]

【Example】

(Embodiment 1) With respect to an optimization calculation method and an apparatus thereof according to an embodiment of the present invention, first, the variable difference amount δx described above.
_The method of determining whether _j is appropriate will be described below. First, consider A by dividing it into column vectors a _i as follows.

[0052]

[Equation 14]

Here, each of the n column vectors corresponds to n variables and represents the contribution amount of each variable to each evaluation function. Here, the contribution amount is, for example, if δx _j is too small, the value of each element of the n column vectors is generally small, that is, the contribution amount is small, and conversely, δ
If x _j is large, it means that the value of each element of the n column vectors is large, that is, the contribution amount is large.

When the variable difference amount set value is inappropriate, for example, the contribution amount of the variable to each evaluation function becomes 0, and each element of the corresponding column vector becomes 0. In that case,

[0055]

(Equation 15)

It becomes On the other hand, the hypervolume Vn of the n-dimensional space spanned by the n column vectors in the equation (14) (here, the hypervolume means the case of n> 3 in the gram determinant) is as follows. Define to.

[0057]

[Equation 16]

Here, “·” represents the inner product of the vectors.
The ultrasonic volume Vn _{is, V n = [abs | A} T A |] expressed also ^1/2 (17). Therefore, for any variable from 1 to n (1
By investigating the expression (5) or whether the relationship of Vk = 0 occurs, it is possible to identify an inappropriate variable of the difference amount set value. For this purpose, for all subspaces to base the column vector a _i constituting the A, the product of the partial matrix of the A giving subspace A 'and its transposed matrix A' and ^T (A ^'T You can check the determinant of A ').

Here, the submatrix A'is

[0060]

(Equation 18)

Can be represented as n column vectors of A

[0062]

[Formula 19]

Means a matrix made up of any number of column vectors. The specific method is as follows. [1.] Each column vector a _i is normalized and expressed as s _i .

[0064]

[Equation 20]

Here, ‖ ... ‖ represents the norm of the vector. [2.] From i = 1 to n, a hypervolume Vi of a parallel polyhedron stretched by column vectors corresponding to respective variables is obtained. At that time, the column vectors are rearranged as follows. [2-1.] The first column vector s1 is arbitrarily selected. At this time, V1 is V ₁ = [abs | S ₁ · S ₁ |] ^1/2 = 1.0. [2-2.] V ₂ among the remaining (n−1) column vectors
Choose the one that maximizes

[0066]

[Equation 22]

Find [2-3.] After that, the super volume V _k is sequentially calculated in the same manner. [2-4.] When all the n column vectors are calculated completed, the column vectors are re newly arranged in descending variable order contribution amount, s _1, s _2, ..., and s _n, super volume corresponding The value 1.0 = V ₁ ≧ V ₂ ... ≧ V _n is obtained. [3.] A small positive value ε is set as a criterion for the hypervolume value obtained in 2, and when ε ≧ Vj, the variables j, j + 1, ... Determined to be inappropriate.

Next, a processing method for designing a lens using the above-described steps will be described below. FIG. 1 shows a double-sided aspherical CD objective lens used in the lens designing method of the present embodiment. For this lens system, a total of 32 variables such as aspherical coefficients on both sides and a total of 43 evaluation functions such as ray aberration amount were set. The expression of the aspherical shape on both surfaces (first and second surfaces) of the lens system is given below.

[0069]

[Equation 23]

Here, X and h are distances in the directions parallel and perpendicular to the optical axis, k _i is a conic constant, and A ′ _i to H _i (i = 1, 2) are aspherical coefficients. In this embodiment,
First, in order to check the variable difference amount setting value in the initial state, the determinant | A ^T A | or the supervolume value is used. As described above, in the present embodiment, in the optimization method in which the plurality of constituent elements are locally changed so that the target system including the plurality of constituent elements has desired characteristics, determinant of a matrix consisting of the product of Jacobian a and its transposed matrix a ^T with the variation of the respective characteristics for small changes in variables made that element | a ^T a | value, or column vector a _i of the a Is a method of evaluating a variable difference amount by a determinant in an optimization method, which is characterized in that a variable difference amount is evaluated using a value of a hypervolume constituted by.

In order to find out how many variables are inappropriate for the setting value of the difference amount, in this embodiment, the determinant or the supervolume of all the subspaces of the column vector a _i corresponding to each variable is calculated. Calculate the value. As described above, in this embodiment, in all subspaces based on the column vector a _i in A, the submatrix A ′ of A and the transposed matrix A ′ ^T thereof by the column vectors constituting the subspace are determinant of consisting of product matrix (a ^'T a) or, seeking super volume of subspace, the determinant in the optimization process, characterized in that the evaluation of the variable differential amount using these values Is an evaluation method of the variable difference amount by.

In order to perform the processing efficiently, in this embodiment, the variables are rearranged according to the determinant or the hypervolume value obtained thereby. As described above, in the method of the present embodiment, in all the subspaces based on the column vector a _i in A, the submatrix A ′ of A and the transposed matrix A ′ thereof by the column vectors forming the subspace. ^{Determinant of} matrix (A ' ^T A') consisting of product with ^T , or
The supervolume of the subspace is obtained, the column vectors a _i are rearranged according to their values, and the variable difference amount is evaluated using the value of the determinant or the value of the supervolume. This is a method for evaluating a variable difference amount by a determinant in the optimization method characterized by the above.

Further, in order to be able to determine the appropriateness of the variable difference amount set value by a common value in all cases, each column vector is normalized by its length (norm) and the norm of each vector is determined. It is desirable to unify "1". The difference amount setting value (increment) for each variable in the initial state of the present embodiment, and using them, the above [1.]
From the process [2.] to [2.], the ultravolume | A ^T A | ^1/2 value (volume) was calculated, and the result is as shown in FIG. Figure 2
As is clear from the above, after the 10th variable, the above | ^AT
Since the value of A | ^1/2 is 0, it can be determined that the difference amount setting value of the subsequent variables is inappropriate. In the field of lens design, [abs | A ^T A |] ^1/2 ≦ 10 ⁻⁵ (20) or abs | A ^T A | It is known that the difference value setting value of the variable after ≦ 10 ⁻¹⁰ (21) can be regarded as inappropriate. As described above, in the present embodiment, all the column vectors a _i are normalized by their respective norms, and then, in all subspaces having the column vector a _i as a basis, the column vectors forming the subspace are used. determinant of the a submatrix a 'and its transposed matrix a' matrix of the product of the ^T (a ^'T a') or, seeking super volume of subspace, the column according to the values The vectors a _i are rearranged, and the difference amount setting value of the variable corresponding to the column vector whose absolute value of the determinant is approximately 10 ⁻¹⁰ or less or the value of the supervolume is approximately 10 ⁻⁵ or less is set. This is an evaluation method of a variable difference amount by a determinant in an optimization method, which is characterized by determining that it is inappropriate.

On the other hand, resetting the variable difference amount in FIG. 2,
FIG. 3 shows the calculation of the super volume value by the processing method of [1.] and [2.]. As is clear from a comparison between FIG. 2 and FIG. 3, the value of the supervolume in the case of FIG.
The number of variables whose value is 0 or 10 ^-5 or less is small. Therefore, according to the method of the present embodiment, the variable difference amount set value of FIG. 3 is more appropriate than the case of FIG.

In order to show the effect of the present invention, FIG. 4 shows the result of the optimization calculation by the orthogonalization method in the case of FIG. 2 (initial increment) and the case of FIG. 3 (reset increment) in order to show the effect of the present invention. Show. In FIG. 4, the horizontal axis represents the number of calculation iterations, and the vertical axis represents the logarithmic value of the merit function value normalized by the value at the starting point. From this result, in the case of the variable difference amount set value determined to be more appropriate by the method of the present embodiment,
A solution that efficiently and has a smaller merit function value is detected, and the effect of the method according to the present embodiment is shown. (Second Embodiment) Next, a second embodiment will be described.

FIG. 5 shows a camera lens used in the second embodiment. For this lens system, a total of 20 variables such as a radius of curvature, a lens thickness surface spacing, and an aspherical coefficient, and a total of 40 evaluation functions such as a ray aberration amount were set. The second surface (9th surface) from the final surface of the lens system is an aspherical surface, and its expression is as follows.

[0077]

(Equation 26)

In the method of the second embodiment, first, the determinant | A ^T A | or the supervolume value is used in order to check the appropriateness of the variable difference amount set value in the initial state. As described above, in the present embodiment, in the optimization method in which the plurality of constituent elements are locally changed so that the target system including the plurality of constituent elements has desired characteristics, The value of the determinant | A ^T A | of the matrix consisting of the product of Jacobian A and its transposed matrix A ^T , which have the amount of change of each characteristic with respect to a slight change of the variable, or the column vector a _i of A This is a method for evaluating a variable difference amount by a determinant in an optimization method, which is characterized in that a variable difference amount is evaluated by using a value of a constructed supervolume.

In order to identify a variable whose variable difference amount set value is inappropriate, in the method of this embodiment, variables are rearranged and the determinant or supervolume value for each variable is calculated. Thus, in the method of the present embodiment, in all the subspaces based on the column vector a _i in the A, the A based on the column vectors forming the subspace is used.
Matrix (A ′ ^T A ′) determinant consisting of the product of the submatrix A ′ and its transposed matrix A ′ ^T , or the hypervolume of the subspace, and using these values to evaluate the variable difference amount Is a method of evaluating a variable difference amount by a determinant in an optimization method characterized by performing

In order to perform the processing efficiently, in the method of this embodiment, the variables are rearranged according to the determinant or the hypervolume value obtained thereby. As described above, in the method of the present embodiment, in all the subspaces based on the column vector a _i in A, the submatrix A ′ of A and the transposed matrix A thereof by the column vectors forming the subspace determinant of 'matrix of the product of the ^T (a' ^T a ') or, seeking super volume of subspace, performs sorting of the column vector a _i in accordance with their values, the matrix A method for evaluating a variable difference amount by a determinant in an optimization method, characterized in that the value of the formula or the value of the supervolume is used to evaluate the variable difference amount.

In addition, in order to be able to determine the appropriateness of the variable difference amount set value by a common value in all cases, each column vector is normalized by its length (norm), and the norm of each vector is determined. It is desirable to unify "1". By using the difference amount set value (increment) for each variable in the initial state of the second embodiment, and the processing of the above [1.] to [2.] using the value, the super volume | A ^T A
When the value (volume) of | ^1/2 was calculated, it became as shown in FIG. As is clear from FIG. 6, the value of | A ^T A | ^1/2 of the 20th variable is 0, and it can be determined that the difference amount set value of this variable is inappropriate. In the field of lens design, [abs | A ^T A |] ^1/2 ≦ 10 ⁻⁵ (22) or abs | A ^T A | It has been found that when ≦ 10 ⁻¹⁰ (23), the difference amount setting value of the following variables can be regarded as inappropriate. As described above, the method of the present embodiment normalizes all the column vectors a _i with their respective norms, and then, in all subspaces having the column vector a _i as a base, the columns forming the subspace determinant of consisting product 'and its transpose matrix a' partial matrix a of the a by vector and ^T matrix (a ^'T a') or to seek a super volume of subspace, depending on their values The column vector a _i
And the absolute value of the determinant is approximately 10
^-10 or less, or the variable by the determinant in the optimization method, which is characterized by determining the difference amount set value of the variable corresponding to the column vector whose supervolume value is approximately 10 ^-5 or less This is an evaluation method of the difference amount.

On the other hand, by resetting the variable difference amount in FIG.
FIG. 7 shows the recalculation of the supervolume value by the processing of [1.] and [2.]. As is clear from comparison between FIG. 6 and FIG. 7, the number of variables in which the ^supervolume value is 0 or 10 ⁻⁵ or less is smaller in the case of FIG. According to this, the variable difference amount set value in the case of FIG. 7 is more appropriate than that in the case of FIG. In order to show the effect of this embodiment, in the second embodiment, the case of FIG. 6 (initial increment) and the case of FIG. 7 (reset increment
FIG. 8 shows the result of performing the optimization calculation by the orthogonalization method with t). In the figure, the horizontal axis represents the number of calculation iterations, and the vertical axis represents the logarithmic value of the merit function value normalized by the value at the starting point. From this result, in the case of the variable difference amount setting value determined to be better by the method of the present embodiment, a solution with a small merit function value is detected efficiently, and the method of the present embodiment Showing the effect.

As described above, according to this embodiment,
The optimization method has the effect of efficiently searching for an optimal solution with a small number of iterations. (Embodiment 3) In the third embodiment, the points of another determination method of the difference amount set value will be shown first, and then an embodiment applied to the lens design will be shown.

As defined by the equation (14) in the first embodiment,
The matrix A constitutes a column vector. If the variable difference amount set value is inappropriate, as described in the first embodiment, (1
Equation 5) holds. Here, when the expression (15) is expressed by using the column vector of the matrix A as in the expression (14), the expression is as follows.

[0085]

[Equation 30]

(24) Here, “·” represents the inner product of the vectors. On the other hand, (A ^T
The eigenvalue decomposition of A) is as follows. A ^T A = VEV ^T (25) Here, V is an orthonormal matrix, E is a matrix with diagonal elements A ^T A
Is an eigenvalue matrix having eigenvalues corresponding to the rank of, and the rank of A ^T A is n,

[0087]

[Equation 31]

[0088] Can be written. Then, in the case of (26), there is a relationship of | A ^T A | = e ₁ · e ₂ ... E _n (27). Therefore, by investigating which variable of k = 1 to n causes the relationship of | A ^T A | = e ₁ · e ₂ ... E _k = 0 (28), an inappropriate variable of the difference amount set value is identified. can do. For that purpose, A
For all subspaces whose basis is the column vector a _i that composes, the eigenvalues of the product (A ′ ^T A ′) of the submatrix A ′ of A giving the subspace and its transposed matrix A ′ ^T are You can look it up.

Here, the submatrix A'is already (1
8), which means a matrix created by an arbitrary number of column vectors among the _n column vectors a ₁ , a ₂ , ..., An of A. The specific method is as follows. [10.] to normalize each column vector a _i, represent them with s _i.

[0090]

[Equation 20]

Here, ‖ ... ‖ represents the norm of the vector. [20.] From i = 1 to n, the product of the eigenvalues of (A ^T A) by the matrix A composed of column vectors corresponding to the respective variables is obtained. At that time, the column vectors are rearranged as follows. [20-1.] The first column vector s ₁ is arbitrarily selected. The absolute value of the time e ₁ becomes e ₁ = 1.0. [20-2.] Among the remaining (n-1) column vectors, the _one having the maximum absolute value of e ₁ · e ₂ is selected to obtain e ₁ · e ₂ . [20-3.] Thereafter, the product of eigenvalues e ₁ ·
to calculate the absolute value of e ₂ ... e _k. [20-4.] When the n calculated for all column vectors is completed, the column vectors are re newly arranged in order of the amount of contribution is large variable, s _1, s _2, ..., and s _n, the eigenvalues and the corresponding Absolute value of product 1.0 = abs [e ₁ ] ≧ abs [e ₁ · e ₂ ] ≧ ... ≧ abs [e ₁ · e ₂
... E _n ] is obtained. [30.] A small positive value ε is set as a criterion for the eigenvalue obtained in [20.], and when ε ≧ abs [e ₁ · e ₂ ... E _j ], j, j + 1, .., n are determined to be inappropriate for the difference amount setting value.

Next, a processing method for designing a lens using the steps described above will be described below. The same objective as that shown in FIG. 1 is used for the CD objective lens having aspherical surfaces on both sides used in the lens designing method of the present embodiment. For this lens system, a total of 32 variables such as aspherical coefficients on both sides and a total of 43 evaluation functions such as ray aberration amount were set. The expression of the aspherical shape on both surfaces (first and second surfaces) of the lens system is
It is the same as the equation (23).

In this embodiment, first, the product of the eigenvalues of the matrix (A ^T A) is used to check the variable difference amount setting value in the initial state. As described above, in the present embodiment, in the optimization method in which the plurality of constituent elements are locally changed so that the target system including the plurality of constituent elements has desired characteristics,
The variable difference is calculated by using the eigenvalue of (A ^T A) of the matrix formed by the product of Jacobian A and its transposed matrix A ^T , each element having the amount of change in each characteristic with respect to a minute change in the variable consisting of the plurality of constituent elements. This is an evaluation method of a variable difference amount by an eigenvalue in an optimization method characterized by evaluating a quantity.

In order to find out how many unsuitable variables of the difference amount set value exist, in this embodiment, the eigenvalues are calculated for all the subspaces of the column vector a _i corresponding to each variable. As described above, in this embodiment,
In all the subspaces based on the column vector a _i in, the matrix (A ′ ^T A that is the product of the submatrix A ′ of A and the transposed matrix A ′ ^T of the column vectors forming the subspace ) Is used to evaluate the variable difference amount, and the variable difference amount is evaluated by the eigenvalue in the optimization method.

In order to perform the processing efficiently, in this embodiment, the variables are rearranged according to the value of the product of the eigenvalues obtained thereby. As described above, in the method of the present embodiment, in all subspaces based on the column vector a _i in A, the submatrix A ′ of A and its transposed matrix A by the column vectors forming the subspace The column vector a _i is rearranged according to the eigenvalues of the matrix (A ′ ^T A ′) formed by the product of ' ^T and the variable difference amount is evaluated using the eigenvalues. This is an evaluation method of the variable difference amount by the eigenvalue in the optimization method.

Further, in order to be able to determine the appropriateness of the variable difference amount set value by a common value in all cases, each column vector is normalized by its length (norm), and the norm of each vector is determined. It is desirable to unify "1". The difference amount setting value (increment) for each variable in the initial state of the present embodiment, and using them, the above-mentioned [1
When the absolute value (productofeigenvalues) of the product of the eigenvalues of (A ^T A) is calculated by the processing from 0.] to [20.], it becomes as shown in FIG. As is clear from FIG. 9, 1
After the 0th variable, the absolute value of the product of the eigenvalues is 0, and it can be determined that the difference amount setting value of the subsequent variables is inappropriate. In the field of lens design, when the _{abs [e 1 · e 2 ...} e j] ≦ 10 ^-10, after variables have been found to be regarded as a dependent. As described above, in the present embodiment, all the column vectors a _i are normalized by their respective norms, and then, in all subspaces having the column vector a _i as a basis, the column vectors forming the subspace are used. wherein a submatrix a 'and its transposed matrix a' consisting of the product of the ^T matrix (a '
^The column vector a _i is rearranged according to the eigenvalue of ^T A ′), and the difference amount setting value of the variable corresponding to the column vector whose absolute value of the product of the eigenvalues is about 10 ⁻¹⁰ or less This is an evaluation method of a variable difference amount by an eigenvalue in an optimization method, which is characterized by determining appropriateness.

On the other hand, resetting the variable difference amount in FIG. 9,
FIG. 10 shows the eigenvalues calculated by the processing methods [10.] and [20.]. As is clear from a comparison between FIG. 9 and FIG. 10, in the case of FIG. 10, the absolute value (product of eigenvalues) of the eigenvalues is 0 or 10.
The number of variables equal to or less than ^-10 is small, and therefore, according to the method of this embodiment, the variable difference amount setting value in FIG. 10 is more appropriate than in the case of FIG.

In order to show the effect of the present embodiment, in this embodiment, the result of performing the optimization calculation by the orthogonalization method in the case of FIG. 9 (initial increment) and the case of FIG. 10 (reset increment) is shown in FIG. Shown in. In FIG. 11, the horizontal axis represents the number of iterations and the vertical axis represents the logarithmic value of the merit function value normalized by the value at the starting point. From this result, in the case of the variable difference amount set value determined to be more appropriate by the method of the present embodiment, a solution with a smaller merit function value is detected more efficiently, and according to the present embodiment, Shows the effect of the method. (Embodiment 4) Next, an optimum lens designing method according to a fourth embodiment will be described with reference to the camera lens design shown in FIG.

For this lens system, a total of 20 variables such as the radius of curvature, the lens thickness surface spacing, and the aspherical coefficient, and a total of 40 evaluation functions such as the amount of ray aberration were set. The second surface (9th surface) from the final surface of the lens system is an aspherical surface, and the expression thereof is the same as the expression (26). In the method of the present embodiment, first, the value of the product of the eigenvalues of the matrix (A ^T A) is used in order to check the adequacy of the variable difference amount setting value in the initial state. As described above, in this embodiment, in the optimization method in which the plurality of constituent elements are locally changed so that the target system including the plurality of constituent elements has desired characteristics,
Variables using the eigenvalues of a matrix (A ^T A) of a matrix formed by a product of Jacobian A and its transposed matrix A ^T , each element having the amount of change of each characteristic with respect to a minute change of a variable composed of the plurality of constituent This is an evaluation method of a variable difference amount by an eigenvalue in an optimization method characterized by evaluating a difference amount.

In order to identify a variable whose variable difference amount setting value is inappropriate, the method of the present embodiment calculates the eigenvalues for all subspaces of the column vector a _i corresponding to each variable. As described above, in the method of the present embodiment, in all the subspaces based on the column vector a _i in A, the submatrix A ′ of A and the transposed matrix A thereof by the column vectors forming the subspace This is a method for evaluating a variable difference amount by an eigenvalue in an optimization method, which is characterized in that the variable difference amount is evaluated using an eigenvalue of a matrix ( ^A'T A ') formed by a product with' ^T.

In order to perform the processing efficiently, in the method of this embodiment, the variables are rearranged according to the value of the product of the eigenvalues obtained thereby. As described above, in the method of the present embodiment, in all the subspaces based on the column vector a _i in A, the submatrix A ′ of A and the transposed matrix A thereof by the column vectors forming the subspace The column vector a _i is rearranged according to the eigenvalues of the matrix (A ′ ^T A ′) formed by the product of ' ^T and the variable difference amount is evaluated using the eigenvalues. This is an evaluation method of the variable difference amount by the eigenvalue in the optimization method.

Further, in order to be able to determine the appropriateness of the variable difference amount setting value by a common value in all cases, each column vector is normalized by its length (norm) and the norm of each vector is determined. It is desirable to unify "1". The difference amount setting value (increment) for each variable in the initial state of the fourth embodiment, and the absolute value (product) of the product of the eigenvalues by the processing of [1.] to [2.] using the value. ofeigenvalues)
It became like. As is clear from FIG. 12, the value of the product of the eigenvalues of (A ^T A) of the 20th variable is 0, and it can be determined that the difference amount setting value of this variable is inappropriate. In the field of lens design, it has been known that when abs [e ₁ · e ₂ ... E _k ] ≦ ¹⁰⁻¹⁰ , the difference amount setting value of the following variables can be regarded as inappropriate. As described above, the method of the present embodiment normalizes all the column vectors a _i with their respective norms, and then, in all subspaces having the column vector a _i as a base, the columns forming the subspace The column vector a _i is rearranged according to the eigenvalue of a matrix (A ′ ^T A ′) formed by the product of the partial matrix A ′ of A and its transposed matrix A ′ ^T by a vector, and the product of the eigenvalues It is a method of evaluating a variable difference amount based on an eigenvalue in an optimization method, characterized in that a difference amount set value of a variable corresponding to the column vector whose absolute value is approximately 10 ⁻¹⁰ or less is determined to be inappropriate.

On the other hand, FIG. 13 shows that the eigenvalues are calculated by resetting the variable difference amount of FIG. 12 and performing the processing of [1.] [2.]. As is apparent from a comparison between FIG. 12 and FIG. 13, the absolute value of the product of the eigenvalues is 0 or 1
The number of variables that are 0 ^-10 or less is smaller in the case of FIG. 13. Therefore, according to the method of this embodiment, the variable difference amount setting value in the case of FIG. 13 is more appropriate than that in the case of FIG. It turns out that.

In order to show the effect of this embodiment, the case of FIG. 12 (initial increment) and the case of FIG. 13 (reset incre
FIG. 14 shows the result of the optimization calculation by the orthogonalization method with the In FIG. 14, the horizontal axis represents the number of calculation iterations, and the vertical axis represents the logarithmic value of the merit function value normalized by the value at the starting point. From this result, in the case of the variable difference amount setting value determined to be better by the method of the present embodiment, a solution with a small merit function value is detected efficiently, and the method of the present embodiment Showing the effect.

As described above, according to this embodiment,
The optimization method has the effect of efficiently searching for an optimal solution with a small number of iterations. (Fifth Embodiment) In a fifth embodiment, the points of another method for determining the difference amount set value will be shown first, and then an embodiment applied to lens design will be shown.

As defined by the equation (14) in the first embodiment,
The matrix A constitutes a column vector. If the variable difference amount set value is inappropriate, as described in the first embodiment, (1
Equation 5) holds. Here, when the expression (15) is expressed using the column vector of the matrix A as in the expression (14), (30)
It becomes as shown in the formula.

On the other hand, when A is singularly decomposed such that A = USV ^T , (A ^T A) can be written as follows. A ^T A = VS ^T SV ^T Here, U and V are orthonormal matrices, S is a diagonal matrix whose diagonal elements have singular values corresponding to the rank of the matrix A, and when the rank of A is n. ,

[0108]

[Equation 32]

Can be written as At this time, there is a relationship of | A ^T A | ^1/2 = s ₁ · s ₂ ... s _n . Therefore, by investigating which of _k = 1 to _n causes the relationship of | A ^T A | ^1/2 = s ₁ · s ₂ ... s _k = 0, an inappropriate variable of the difference amount setting value can be identified. can do. For that purpose, A
The singular value of the submatrix A ′ of A that gives the subspace may be examined for all the subspaces based on the column vector a _i forming the subspace.

Here, the submatrix A'is already (1
8), which means a matrix created by an arbitrary number of column vectors among the _n column vectors a ₁ , a ₂ , ..., An of A. The specific method is as follows. [100.] Normalize each column vector a _i and make them b _i
Express.

B _i = a _i / ‖a _i ‖ where ‖ ... ‖ represents the norm of the vector. [200.] From i = 1 to n, the product of the singular values of the matrix A composed of the column vectors corresponding to the respective variables is obtained. At that time, the column vectors are rearranged as follows. [200-1.] The first column vector b ₁ is arbitrarily selected. At this time, abs [s ₁ ] = 1.0. [200-2.] Among the remaining (n-1) column vectors, the _one having the maximum absolute value of s ₁ s ₂ is selected to obtain s ₁ s ₂ . [200-3.] From then on, the product s _{1 of} singular values is sequentially repeated in the same manner.
The absolute value of the · s ₂ ... s _k is calculated. [200-4.] When the calculation is completed for all the n column vectors, the column vectors b ₁ , b ₂ , ..., B _n newly rearranged in the order of large contribution amount and the corresponding singular values Absolute value of product 1.0 = abs [s ₁ ] ≧ abs [s ₁ · s ₂ ] ≧ ... ≧ abs [s ₁ · s ₂
... s _n ] is obtained. [300.] Set a small positive value ε as a criterion for the product of the singular values obtained in [200.], and if ε ≧ abs [s ₁ · s ₂ ... s _j ], then j , J + 1, ..., N, the difference amount setting value is determined to be inappropriate.

Next, a processing method for designing a lens using the above-described steps will be described below. The same objective as that shown in FIG. 1 is used for the CD objective lens having aspherical surfaces on both sides used in the lens designing method of the present embodiment. For this lens system, a total of 32 variables such as aspherical coefficients on both sides and a total of 43 evaluation functions such as ray aberration amount were set. The expression of the aspherical shape on both surfaces (first and second surfaces) of the lens system is
It is the same as the equation (23).

In the present embodiment, first, the product of the singular values of the matrix A is used to check the variable difference amount setting value in the initial state. As described above, in the present embodiment, in the optimization method in which the plurality of constituent elements are locally changed so that the target system including the plurality of constituent elements has desired characteristics, Method for evaluating a variable difference amount by a singular value in an optimization method, which is characterized by using a singular value of Jacobian A having the amount of change of each characteristic with respect to a minute change of a variable Is.

In order to find out how many unsuitable variables of the difference amount set value exist, in the present embodiment, the singular value is calculated for all the subspaces of the column vector a _i corresponding to each variable. As described above, in this embodiment,
In all subspaces based on the column vector a _i in, the variable difference amount is evaluated by using the singular value of the submatrix A ′ of A by the column vectors forming the subspace. This is an evaluation method of the variable difference amount by the singular value in the optimization method.

In order to perform the processing efficiently, in this embodiment
Is a variable depending on the product of the singular values obtained thereby
Rearrange. Thus, the method of the present embodiment is
The column vector a at_iAll subspaces based on
Between the column vectors that make up the subspace
The column vector a according to the singular value of the submatrix A'of A
_iAnd the singular values are used to sort the variables
In the optimization method characterized by evaluating the amount of difference
This is an evaluation method of a variable difference amount by a singular value.

Further, in order to be able to determine the appropriateness of the variable difference amount setting value by a common value in all cases, each column vector is normalized by its length (norm), and the norm of each vector is set. It is desirable to unify "1". The difference amount setting value (increment) for each variable in the initial state of the present embodiment, and using them, the above-mentioned [1
When the product of singular values of the singular value of A is calculated by the processing from 0.] to [20.], the result is as shown in FIG. As is clear from FIG. 15, after the 10th variable, the value of the product of the singular values is 0, and it can be determined that the difference amount setting value of the subsequent variables is inappropriate. In the field of lens design, it has been found that the following variables can be considered dependent when abs [s ₁ · s ₂ ... S _j ] ≦ 10 ⁻⁵ . As described above, in the present embodiment, all the column vectors a _i are normalized by their respective norms, and then, in all subspaces having the column vector a _i as a basis, the column vectors forming the subspace are used. The column vector a _i is rearranged according to the singular value of the submatrix A ′ of A, and the difference between the variables corresponding to the column vector whose absolute value of the product of the singular values is approximately 10 ⁻⁵ or less. This is a method for evaluating a variable difference amount by a singular value in an optimization method, which is characterized by determining a quantity setting value as inappropriate.

On the other hand, FIG. 16 shows that the eigenvalues are calculated by the processing methods of [100] and [200.] by resetting the variable difference amounts of FIG. As is clear from a comparison between FIG. 15 and FIG. 16, in the case of FIG. 16, the absolute value (product of singular values) of the singular values is 0.
Alternatively, the number of variables of 10 ⁻⁵ or less is small, and therefore according to the method of the present embodiment, the variable difference amount setting value of FIG. 16 is more appropriate than the case of FIG.

In order to show the effect of this embodiment, the case of FIG. 15 (initial increment) and the case of FIG. 16 (reset incre
ment) and the result of performing the optimization operation by the orthogonalization method are shown in FIG. In FIG. 17, the horizontal axis represents the number of calculation iterations, and the vertical axis represents the logarithmic value of the merit function value normalized by the value at the starting point. From this result, in the case of the variable difference amount set value determined to be more appropriate by the method of the present embodiment, a solution with a smaller merit function value is detected more efficiently, and according to the present embodiment, Shows the effect of the method. (Embodiment 6) Next, an optimum lens designing method according to a sixth embodiment will be described with reference to the camera lens design shown in FIG.

For this lens system, a total of 20 variables such as a radius of curvature, a lens thickness surface spacing, and an aspherical coefficient, and a total of 40 evaluation functions such as a ray aberration amount were set. The second surface (9th surface) from the final surface of the lens system is an aspherical surface, and the expression thereof is the same as the expression (26). In the method of the present embodiment, first, the value of the product of the singular values of the matrix A is used to check the adequacy of the variable difference amount setting value in the initial state.

As described above, according to the present embodiment, in the optimization method in which the plurality of constituent elements are locally changed so that the target system composed of the plurality of constituent elements has desired characteristics, Of the variable difference amount by the singular value in the optimization method, which is characterized in that the singular value of Jacobian A having the change amount of each characteristic for the minute change of the variable composed of the constituent elements as its element is evaluated. This is an evaluation method.

In order to specify a variable whose variable difference amount setting value is inappropriate, the method of this embodiment calculates the singular value for all subspaces of the column vector a _i corresponding to each variable. . As described above, the method of the present embodiment uses the singular value of the submatrix A ′ of A by the column vectors forming the subspace in all subspaces based on the column vector a _i in A. This is a method for evaluating a variable difference amount by a singular value in an optimization method, which is characterized in that the variable difference amount is evaluated.

In order to perform the processing efficiently, in the method of this embodiment, the variables are rearranged according to the value of the product of the singular values obtained thereby. As described above, the method according to the present embodiment, in all subspaces of the A based on the column vector a _i , depends on the singular value of the submatrix A ′ of A by the column vectors forming the subspace. The column vector a _i is rearranged by using the singular value and the variable difference amount is evaluated using the singular value.

In addition, in order to be able to determine the appropriateness of the variable difference amount set value by a value common to all cases, each column vector is normalized by its length (norm), and the norm of each vector is determined. It is desirable to unify "1". Using the difference amount setting value (increment) for each variable in the initial state of this embodiment and the value thereof,
When the product of singular values of the singular values is calculated by the processing from [100.] to [200.], the result is as shown in FIG. As is clear from FIG. 18, the value of the product of the singular values of A is 0 for the 20th variable, and it can be determined that the difference amount setting value of this variable is inappropriate. In the field of lens design, it has been known that when abs [s ₁ · s ₂ ... s _k ] ≦ 10 ⁻⁵ , the difference amount setting value of the following variables can be regarded as inappropriate.

As described above, the method of this embodiment normalizes all the column vectors a _i by their respective norms, and then, in all the subspaces having the column vectors a _i as the basis, The column vectors a _i are rearranged according to the singular values of the submatrix A ′ of A according to the constituent column vectors, and the absolute value of the product of the singular values is approximately 10 ^−5.
It is a method of evaluating a variable difference amount based on a singular value in an optimization method, which is characterized by determining a variable difference amount set value of a variable corresponding to the following column vector as inappropriate.

On the other hand, FIG. 19 shows the calculation of the eigenvalue by resetting the variable difference amount of FIG. 18 and by the processing of [100.] [200.]. As is clear from a comparison between FIG. 18 and FIG. 19, the number of variables in which the absolute value of the product of the singular values is 0 or 10 ⁻⁵ or less is smaller in the case of FIG. According to the example method, the variable difference amount set value in the case of FIG. 19 is more appropriate than that in the case of FIG.

In order to show the effect of this embodiment, the case of FIG. 18 (initial increment) and the case of FIG. 19 (reset incre
20) shows the result of the optimization calculation by the orthogonalization method with the In FIG. 20, the horizontal axis represents the number of calculation iterations, and the vertical axis represents the logarithmic value of the merit function value normalized by the value at the starting point. From this result, in the case of the variable difference amount setting value determined to be better by the method of the present embodiment, a solution with a small merit function value is detected efficiently, and the method of the present embodiment Showing the effect.

The present invention may be applied to a system composed of a plurality of devices or an apparatus composed of one device. Further, it goes without saying that the present invention can be applied to the case where it is achieved by supplying a program to a system or an apparatus. As described above, according to this embodiment, there is an effect that the optimization method can efficiently search for an optimum solution with a small number of iterations. (Embodiment 7) In Embodiments 1 to 6 above, a method for processing a high-speed optimization problem and a lens designing method using the same have been described. Next, an example of a lens designing apparatus implementing the lens designing method Will be described.

FIG. 21 is a diagram showing an example of the hardware configuration of the lens design apparatus. Referring to FIG. 21, 200
Is a CPU that controls the entire lens design apparatus. 20
Reference numeral 2 stores a program corresponding to the method described in the first to sixth embodiments, a component of the lens, a design variable for optimal design of the lens, an evaluation function, and the like, and a work area for executing the program. Is a memory. 201 is
It is a display monitor that displays the configuration of the lens to be designed, the calculated design values of the lens, and various commands and data input from the keyboard 203 and pointing device 204.

Further, FIG. 22 shows an example of a processing flow chart of the above-described lens design. An execution program corresponding to this flowchart is stored in the memory 202 in advance, accessed by the CPU 200, interpreted, and executed. Hereinafter, the processing will be described for each step based on the flowchart of FIG.

In step S1, various target values of the lens system, constraints, etc. are input by the keyboard 203 or the like. In step S2, the target value of the lens such as the optical focal length of the lens is input using the keyboard 203 or the like. In step S3, the initial value of each variable for determining the lens shape is input using the keyboard 203 or the like.

In step S4, variables and evaluation functions for the optimization design of the lens are determined. FIG.
An example of variables and evaluation functions corresponding to the lenses shown in FIGS. 1 and 5 is shown in FIG. First, in the case of the lens of FIG. 1,
As variables, a total of 32 variables including aspherical coefficients on both surfaces of a plurality of types of lenses, the curvature of the second surface of the lens, and the lens thickness are set. Here, as the aspherical surface coefficients of both surfaces of the lens, 15 kinds of coefficients are set for each surface, and 30 kinds of aspherical surface coefficients are set for both surfaces.

The evaluation function for optimization design is 1
6 types of axial ray aberration (spherical aberration), 16 types of off-axis (image height 0.1 mm) meridional ray aberrations, 8 types of off-axis sagittal ray aberrations, off-axis Mary-Saj field curvature, Set off-axis sagittal field curvature and lens back. In the case of the lens of FIG. 5, a total of 20 variables of 6 types of surface curvatures, 9 types of lens thickness, and 5 types of aspherical coefficients are set as variables. Also, as evaluation functions, four types of ray aberration (spherical aberration) on the axis,
Axial chromatic aberration amount, 16 types of off-axis (image height 2 points: 21.6
35mm, 15.0mm) meridional ray aberration amount, 4
Two types of off-axis sagittal ray aberration, two types of off-axis Mary-sag field curvature, two types of off-axis lateral chromatic aberration, two types of off-axis distortion, and four types of lens meat as mechanical constraints A total of 40 lens thicknesses, which are five types of mechanical constraint conditions, are set.

In step S5, the Jacobian is calculated based on the evaluation function set in step S4. In step S6, the method of each embodiment described above, that is, | A ^T A
| Performing calculation using ^1/2 of the ultrasonic volume value, the eigenvalues of A ^T A, or any of the calculation method based on the singular values of A. It is assumed that the selection of this method is designated in advance by using the keyboard 203, for example.

If the method based on the hypervolume value of | A ^T A | ^1/2 is specified, [1.], [2.], [2-1.], [2-2 of Example 1] .], [2-3.], And [2-4.]. If a method based on the eigenvalue of A ^T A is specified, [10.], [20.], [20-1.], [20-2.],
The processing of [20-3.] And [20-4.] Is performed.

Further, if the method based on the singular value of A is designated, [100.], [200.], [200-1.], [2.
00-2.], [200-3.], And [200-4.]. In step S7, based on the selection of the method specified in step S6, a hypervolume value, an eigenvalue, or a singular value is used for comparison with a predetermined threshold value, and for a corresponding variable smaller than that, the difference amount is calculated. Judge that the set value is inappropriate.

That is, if the method based on the hypervolume value of | A ^T A | ^1/2 is specified, the process [3.] of the first embodiment is performed. If the method based on the eigenvalue of A ^T A is specified, the process of [30.] is performed. If the method based on the singular value of A is specified, the process of [300.] is performed.

Here, a predetermined minute value is added to the difference amount set value of the variable determined to be inappropriate. And step 5
Return to processing from. If appropriate, step S
Proceed to 8. In step S8, based on the difference amount setting value of each obtained variable that is determined to be appropriate, an optimization calculation method, for example, the above-described orthogonalization method or Marquard
t) method etc. is used to calculate the optimum value of each variable.

In step S9, it is checked whether or not the obtained optimum solution satisfies the various target values and constraint conditions input in step S1 and step S2. If they do not, the variables and evaluation function are reviewed again. Then, the process from step S4 is performed. If so, the lens optimization design process ends. Note that, in FIG. 24, the elements of the constraint conditions forming a part of the evaluation function in the second lens for which the optimization design is performed are shown. That is, there are five types of lens edge thickness and four types of wall thickness as the constraint condition elements.

As described above, according to the present embodiment, when the lens optimization design processing is performed, the optimal lens design value is calculated by setting the variable difference amount setting value to an appropriate value. You can get it fast with a number. Further, in the present embodiment, the method described above is used for the design of the lens system, but this is applicable to other optimization designs such as LSI layout design and pattern design, and architectural structure design. It is needless to say that it is effective even in the scene where the phase space search process with variables is required.

[0140]

As described above, according to the present invention, the optimization calculation of the target system can always be efficiently performed by previously performing the appropriateness / ineligibility evaluation on the difference amount setting value of the variable. In addition, the lens system can be designed at high speed with a minimum amount of calculation.

[Brief description of drawings]

FIG. 1 is a cross-sectional view of a first lens having an optimized design.

FIG. 2 is a diagram showing a difference amount (increment) set value and a super volume value (volume) of each variable in the first embodiment.

FIG. 3 is a difference amount (in) of each variable reset in the first embodiment.
It is a figure which shows crement) and a super-volume value (volume).

FIG. 4 is a diagram showing an effect of the method of the first embodiment.

FIG. 5 is a cross-sectional view of a second lens having an optimized design.

FIG. 6 is a diagram showing a difference amount (increment) set value and a super volume value (volume) of each variable in the second embodiment.

FIG. 7 is a diagram illustrating a difference amount (in) of each variable reset in the second embodiment.
It is a figure which shows crement) and a super-volume value (volume).

FIG. 8 is a diagram showing an effect of the method of the second embodiment.

FIG. 9 is a diagram showing a product value of a difference amount (increment) set value of each variable and an eigenvalue according to the third embodiment.

FIG. 10 is a diagram showing a product value of a difference amount (increment) of each variable and an eigenvalue reset in the third embodiment.

FIG. 11 is a diagram showing an effect of the method of the third embodiment.

FIG. 12 is a difference amount (increment) of each variable in the fourth embodiment.
It is a figure which shows the value of the product of a setting value and an eigenvalue.

FIG. 13 is a diagram showing a product value of a difference amount (increment) of each variable and an eigenvalue reset in the fourth embodiment.

FIG. 14 is a diagram showing an effect of the method of the fourth embodiment.

FIG. 15 is a difference amount (increment) of each variable in the fifth embodiment.
It is a figure which shows the value of the product of a setting value and a singular value.

FIG. 16 is a difference amount (incr) of each variable reset in the fifth example.
ement) and a singular value.

FIG. 17 is a diagram showing an effect of the method of the fifth embodiment.

FIG. 18 is a difference amount (increment) of each variable in the sixth embodiment.
It is a figure which shows the value of the product of a setting value and a singular value.

FIG. 19 is a diagram showing a value of a product of a difference amount (increment) of each variable and a singular value reset in the sixth embodiment.

FIG. 20 is a diagram showing the effect of the method of the sixth embodiment.

FIG. 21 is a diagram showing a hardware configuration of an optimum component acquisition device and a lens system design device in each embodiment.

FIG. 22 is a diagram showing a flowchart of lens system design processing of the seventh embodiment.

FIG. 23 is a diagram showing variables and evaluation functions in lens system design processing.

FIG. 24 is a diagram showing a second lens to be optimized and its constraint condition elements.

Claims (54)

[Claims] 1. An optimum component value is obtained by locally changing the values of the plurality of components so that a lens system represented by the plurality of components has desired characteristics. In a lens system designing device, a column vector a _i (i = 1 ... n) of a Jacobian A whose element is a variation amount of each of the characteristics with respect to a minute variation amount of the plurality of constituent elements is a basis. 'and eigenvalue calculation means for calculating the eigenvalue of the calculated by the eigenvalue calculation unit a' ^T a 'matrix product a with ^T' partial matrix a 'and its partial matrix a' rolling value matrix a ^T a 'of If the absolute value of the product between the eigenvalues for each is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues to obtain a new minute change amount of the component. Component minute variation amount correcting means, and the component element minute variation amount correcting means Optimum to obtain the optimum component value by locally changing the values of the plurality of components so that the lens system has the desired characteristics based on the new minute change amount generated. A lens system designing device, comprising: a component value acquiring means. 2. The lens system designing apparatus according to claim 1, wherein the lens system can evaluate the desired characteristic by a value of an evaluation function having the plurality of constituent elements as variables. 3. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 1
The lens system design device described in. 4. The lens system design device according to claim 1, wherein the predetermined value is approximately 10 ⁻¹⁰ . 5. The plurality of constituent elements include an aspherical coefficient of each lens and a ray aberration amount.
The lens system design device described in. 6. An optimum component value is obtained by locally changing the values of the plurality of components so that the lens system represented by the plurality of components has desired characteristics. In the device, a column vector a of a Jacobian A whose element is the variation of each of the characteristics with respect to the minute variation of the plurality of constituent elements
_{i (i} = 1 ... n) to a base portion matrix A 'and its partial matrix A''determinant of | A' ^T A 'matrix product A with ^T' rolling value matrix A ^T
If the absolute value of | ^A'T A '| calculated by the eigenvalue calculation means is smaller than a predetermined value, a determinant calculation means for calculating A' | Is added to obtain a new minute change amount of the constituent element, and the component minute change amount correcting means and the new minute change amount generated by the component minute change amount correcting means are used to determine the desired lens system. A lens system design characterized by comprising an optimum component value acquisition means for acquiring the optimum component value by locally changing the values of the plurality of components so as to obtain characteristics. apparatus. 7. The lens system designing apparatus according to claim 6, wherein the desired characteristic of the lens system can be evaluated by a value of an evaluation function having the plurality of constituent elements as variables. 8. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 6. The lens system designing device according to item 6. 9. The lens system designing apparatus according to claim 6, wherein the predetermined value is approximately 10 ⁻¹⁰ . 10. The lens system design apparatus according to claim 6, wherein the plurality of constituent elements include an aspherical coefficient of each lens and a ray aberration amount. 11. An optimum component value is obtained by locally changing the values of the plurality of components so that the lens system represented by the plurality of components has desired characteristics. In the device, a submatrix A based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the amount of change of each characteristic with respect to a minute change amount of the plurality of constituent elements Singular value calculating means for calculating the singular value of ', if the absolute value of the product of the singular values calculated by the singular value calculating means is smaller than a predetermined value, a predetermined minute value to the minute change amount of the corresponding component The lens system has a desired characteristic based on the component minute change amount correction means that adds the two components to obtain a new minute change amount of the component and the new minute change amount generated by the component minute change amount correction means. So that the values of the multiple components are locally By going to change, the lens system design device characterized by comprising an optimum component values acquiring means for acquiring the value of the optimal components. 12. The lens system designing device according to claim 11, wherein the desired characteristic of the lens system can be evaluated by a value of an evaluation function having the plurality of constituent elements as variables. 13. The Jacobian A column vector a _i (i = 1 ... n) is normalized by the norm of each vector a _i. 11. The lens system designing device according to item 11. 14. The lens system design apparatus according to claim 11, wherein the predetermined value is approximately 10 ⁻⁵ . 15. The lens system design apparatus according to claim 11, wherein the plurality of constituent elements include an aspherical coefficient of each lens and a ray aberration amount. 16. An optimum constituent element value is obtained by locally changing the values of the plural constituent elements so that a target system represented by the plural constituent elements has desired characteristics. In the device, a submatrix based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the amount of change in each characteristic with respect to a minute amount of change in the plurality of constituent elements for each of a 'and its partial matrix a''and eigenvalue calculation means for calculating the eigenvalue of, calculated by the eigenvalue calculating unit a' ^T a 'matrix product a with ^T' rolling value matrix a ^T a ' If the absolute value of the product between the eigenvalues is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues to obtain a new minute change amount of the component. An element minute change amount correction means, and the component element minute change amount correction means. The optimum component value that obtains the optimum component value by locally changing the values of the plurality of components so that the lens system has the desired characteristics based on the new minute change amount. An optimization design apparatus for a target system, comprising: acquisition means. 17. The optimization system for target system according to claim 16, wherein the target system is capable of evaluating the desired characteristic by a value of an evaluation function having the plurality of constituent elements as variables. . 18. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 16. The optimization design device for the target system according to item 16. 19. The optimization system for a target system according to claim 16, wherein the predetermined value is approximately 10 ⁻¹⁰ . 20. An optimum component element value is obtained by locally changing the values of the plurality of component elements so that the target system represented by the plurality of component elements has desired characteristics. In the device, a submatrix based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the amount of change in each characteristic with respect to a minute amount of change in the plurality of constituent elements a 'and its partial matrix a''determinant of | a' ^T a 'matrix product a with ^T' rolling value matrix a ^T a '| and determinant calculation means for calculating, is calculated in the eigenvalue calculation means If the absolute value of | A ′ ^T A ′ | is smaller than a predetermined value, a predetermined small value is added to the small change amount of the corresponding constituent element to obtain a new minute change amount of the constituent element. Based on the change amount correcting means and the new minute change amount generated by the component minute change amount correcting means, And an optimum component value acquisition means for acquiring the optimum component value by locally changing the values of the plurality of components so that the desired characteristic is obtained. Target system optimization design equipment. 21. The optimization system for a target system according to claim 16, wherein the target system can evaluate the desired characteristic by a value of an evaluation function having the plurality of constituent elements as variables. . 22. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 20. An optimization design device for a target system according to item 20. 23. The target system optimization design apparatus according to claim 20, wherein the predetermined value is approximately 10 ⁻¹⁰ . 24. An optimum component value is obtained by locally changing the values of the plurality of components so that the target system represented by the plurality of components has desired characteristics. In the device, a submatrix based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the amount of change in each characteristic with respect to a minute amount of change in the plurality of constituent elements If the absolute value of the product of the singular value calculating means for calculating the singular value of A ′ and the singular value calculated by the singular value calculating means is smaller than a predetermined value, a predetermined minute value is set for the minute change amount of the corresponding component. Is added to obtain a new minute change amount of the constituent element, and the component minute change amount correcting means and the new minute change amount generated by the component minute change amount correcting means are used to determine the desired lens system. Localize the values of the multiple components to By going to change and optimize the design device of the target system, characterized in that it comprises a optimum component values acquiring means for acquiring the value of the optimal components. 25. The optimization system for a target system according to claim 24, wherein the target system can evaluate the desired characteristic by a value of an evaluation function having the plurality of constituent elements as variables. . 26. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 24. An optimization design device for a target system according to 24. 27. The optimization system for a target system according to claim 24, wherein the predetermined value is approximately 10 ⁻⁵ . 28. Optimum constituent element values are obtained by locally changing the values of the plural constituent elements so that the lens system represented by the plural constituent elements has desired characteristics. In a lens system designing method, a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the amount of change in each characteristic with respect to a minute amount of change in the plurality of constituent elements is a basis. 'and eigenvalue calculation step of calculating the eigenvalues of the calculated eigenvalue calculation step a' ^T a 'matrix product a with ^T' partial matrix a 'and its partial matrix a' rolling value matrix a ^T a 'of If the absolute value of the product between the eigenvalues for each is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues to obtain a new minute change amount of the component. And a component minute change amount correction process, The values of the plurality of constituent elements are locally changed so that the lens system has a desired characteristic based on the new minute change amount generated in step 1, thereby obtaining the optimum constituent element values. A method of designing a lens system, comprising: obtaining an optimum component value. 29. The lens system designing method according to claim 28, wherein the lens system can evaluate the desired characteristic by a value of an evaluation function having the plurality of constituent elements as variables. 30. Each column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 28. A lens system designing method according to item 28. 31. The lens system designing method according to claim 28, wherein the predetermined value is approximately 10 ⁻¹⁰ . 32. The lens system designing method according to claim 28, wherein the plurality of constituent elements include an aspherical coefficient and a ray aberration amount of each lens. 33. Optimum constituent element values are obtained by locally changing the values of the plural constituent elements so that the lens system represented by the plural constituent elements has desired characteristics. In the method, a submatrix A based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the variation of each characteristic with respect to a minute variation of the plurality of constituent elements 'and its partial matrix a''determinant of | a' ^T a 'matrix product a with ^T' rolling value matrix a ^T a '| and determinant calculation step of calculating, calculated by the eigenvalue calculation step If the absolute value of | ^A'T A '| is smaller than a predetermined value, a predetermined small value is added to the minute change amount of the corresponding constituent element to obtain a new minute change amount of the constituent element. Based on the amount correction step and the new minute change amount generated in the component minute change amount correction step. So as to have a desired characteristic, by locally changing the values of the plurality of constituent elements to obtain the optimum constituent element value. Lens system design method. 34. The lens system designing method according to claim 33, wherein the desired characteristic of the lens system can be evaluated by a value of an evaluation function having the plurality of constituent elements as variables. 35. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 33. The lens system design method according to 33. 36. The lens system designing method according to claim 33, wherein the predetermined value is approximately 10 ⁻¹⁰ . 37. The lens system designing method according to claim 33, wherein the plurality of constituent elements include an aspherical coefficient and a ray aberration amount of each lens. 38. Optimum constituent element values are obtained by locally changing the values of the plural constituent elements so that the lens system represented by the plural constituent elements has desired characteristics. In the method, a submatrix A based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the variation of each characteristic with respect to a minute variation of the plurality of constituent elements Singular value calculation step of calculating the singular value of ', if the absolute value of the product of the singular value calculated in the singular value calculation step is smaller than a predetermined value, a predetermined minute value to the minute change amount of the corresponding component The lens system has a desired characteristic based on the component minute change amount correction step of adding the components to obtain a new minute change amount of the component and the new minute change amount generated in the component element minute change amount correction step. So that the values of the multiple components are locally By going to change, the lens system design method characterized by comprising the optimum component values acquired step of acquiring the value of the optimal components. 39. The lens system designing method according to claim 38, wherein the desired characteristic of the lens system can be evaluated by a value of an evaluation function having the plurality of constituent elements as variables. 40. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 38. The lens system designing method according to item 38. 41. The lens system designing method according to claim 38, wherein the predetermined value is approximately 10 ⁻⁵ . 42. The lens system designing method according to claim 38, wherein the plurality of constituent elements include an aspherical coefficient and a ray aberration amount of each lens. 43. An optimum component value is obtained by locally changing the values of the plurality of components so that the target system represented by the plurality of components has desired characteristics. In the method, a submatrix based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the variation of each characteristic with respect to a minute variation of the plurality of constituent elements for each of a 'and its partial matrix a''and eigenvalue calculation step of calculating the eigenvalues of, calculated by the eigenvalue calculation step a' ^T a 'matrix product a with ^T' rolling value matrix a ^T a ' If the absolute value of the product between the eigenvalues is smaller than a predetermined value, a predetermined minute value is added to the minute change amount of the component corresponding to the product between the eigenvalues to obtain a new minute change amount of the component. The element minute change amount correction step and the component element minute change amount correction step are generated. The optimum component value that obtains the optimum component value by locally changing the values of the plurality of components so that the lens system has the desired characteristics based on the new minute change amount. An optimization design method for a target system, comprising: an acquisition step. 44. The optimization design method for a target system according to claim 43, wherein the desired characteristic can be evaluated by the value of an evaluation function having the plurality of components as variables. . 45. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 43. The optimization design method of the object system described in 43. 46. The optimization design method for a target system according to claim 43, wherein the predetermined value is approximately 10 ⁻¹⁰ . 47. An optimum component value is obtained by locally changing the values of the plurality of components so that the target system represented by the plurality of components has desired characteristics. In the method, a submatrix based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the variation of each characteristic with respect to a minute variation of the plurality of constituent elements A determinant calculation step of calculating the determinant | A ′ ^T A ′ | of the matrix product A ′ ^T A ′ of A ′ and the transversion matrix A ′ ^T of its submatrix A ′, and the eigenvalue calculation step If the absolute value of | A ′ ^T A ′ | is smaller than a predetermined value, a predetermined small value is added to the small change amount of the corresponding constituent element to obtain a new minute change amount of the constituent element. Based on the change amount correction step and the new minute change amount generated in the component minute change amount correction step, the lens So as to have a desired characteristic, by locally changing the values of the plurality of constituent elements to obtain the optimum constituent element value. Target system optimization design method. 48. The optimization design method for a target system according to claim 47, wherein the target system can evaluate the desired characteristic by a value of an evaluation function having the plurality of constituent elements as variables. . 49. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 47. The optimization design method of the object system according to 47. 50. The optimization design method for a target system according to claim 47, wherein the predetermined value is approximately 10 ⁻¹⁰ . 51. An optimum constituent element value is obtained by locally changing the values of the plural constituent elements so that a target system represented by the plural constituent elements has desired characteristics. In the method, a submatrix based on a column vector a _i (i = 1 ... n) of a Jacobian A whose element is the variation of each characteristic with respect to a minute variation of the plurality of constituent elements If the absolute value of the product of the singular values calculated in the singular value calculation step for calculating the singular value of A ′ is smaller than a predetermined value, a predetermined small value is set for the minute change amount of the corresponding component. Based on the new minute change amount generated in the component minute change amount correction step and the component minute change amount correction step to obtain a new minute change amount of the component, Localize the values of the multiple components to By going to change and optimize the design method of the target system, characterized in that it comprises a optimum component values acquired step of acquiring the value of the optimal components. 52. The optimization design method for a target system according to claim 51, wherein the target system can evaluate the desired characteristic by a value of an evaluation function having the plurality of constituent elements as variables. . 53. The column vector a _i (i = 1 ... n) of the Jacobian A is normalized by the norm of each vector a _i. 51. The optimization design method of the object system described in 51. 54. The optimization design method for a target system according to claim 51, wherein the predetermined value is approximately 10 ⁻⁵ .