JPH08152556A - Device and method for evaluating optical performance - Google Patents

Abstract

PURPOSE: To predict the optical performance of a heterogeneous glass material which is actually manufactured through more accurate simulation calculation by representing refractive index information in the form of a series of dots, approximating the curve passing the series of dots with a spline function, and finding a refractive index distribution function. CONSTITUTION: Lens data on the curvature, thickness, refractive index, incident light beam angle of an optical element to be evaluated are inputted to a CPU2 from a keyboard 1 or hard disk 4. Further, a sampling quantity and a sampling pitch on a coordinate system where a refractive index distribution is generated, and lens data, such as a refractive index which is actually measured in measurement point coordinates are inputted to the CPU2 as refractive index of the specified glass material. The CPU 2 performs the spline interpolation of two-dimensional data on the basis of the refractive index information to find the refractive index distribution function. And, the CPU 2 performs light beam tracking by a Sharma method, etc., to perform aberration calculation. The calculated aberrations are displayed on a CRT 3.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical performance evaluation device in optical design.

[0002]

2. Description of the Related Art Inhomogeneous glass materials, that is, lenses having a refractive index distribution, give optical designers a new degree of freedom, and they are used in copiers, facsimile machines and the like. There are mainly three types of this inhomogeneous glass material, one having a refractive index distribution in the radial direction, one having a refractive index distribution in the optical axis direction, and one having a refractive index distribution in the spherical center direction. Each can be expressed by a clear mathematical formula, ray tracing on a computer,
Aberration calculation simulations are being performed. Commercially available optical design software such as OPTALGE of Minolta Co., Inc. and codeV of ORA Inc. of the United States prepares several functions for expressing the refractive index distribution, and theoretically gives the refractive index distribution in the form of setting a coefficient therefor. The optical performance of can be evaluated. However, for the actual processing of inhomogeneous glass materials, although research on processing techniques such as the PC method and ion exchange method is progressing,
It is still difficult and the optical performance such as the theoretical value obtained by the above simulation has not been realized in the inhomogeneous glass material actually made. There is a gap between the inhomogeneous glass material that can be actually manufactured and the inhomogeneous glass material expressed by a mathematical formula, and this simulation method has a problem in accuracy.

[0003]

SUMMARY OF THE INVENTION In the present invention, the refractive index distribution function is obtained by approximating them by a spline function using the refractive index measured by the heterodyne method or the like from an actually manufactured inhomogeneous glass material as a point sequence. An optical performance evaluation device and an evaluation method capable of predicting the optical performance of a heterogeneous glass material actually manufactured by the present processing technology by performing a more accurate simulation calculation by performing an optical performance simulation by And

[0004]

Means for Solving the Problems The above-mentioned problems are solved,
In order to achieve the object, the optical performance evaluation device of the present invention,
An optical performance evaluation device comprising an input device, a display device, and an external storage device, and an information processing device capable of setting a plurality of functional means in a processor based on information from the input device or the external storage device, The functional means includes an optical system information setting means for setting optical system information such as lens data according to input information from the input device or information from the external storage device, and a refractive index according to input from the input device or information from the external storage device. Refractive index information setting means for setting the refractive index information for setting the distribution function, the refractive index information as a point sequence, a calculating means for approximating a curve passing through this point sequence by a spline function to obtain a refractive index distribution function, Ray tracing based on the optical system information and the refractive index distribution information, calculating the optical performance such as aberration calculation, point spread,
A means for displaying or analyzing the results is provided, and the performance of the optical system is evaluated by giving the refractive index as a sequence of points.

Further, in the optical performance evaluation apparatus according to the present invention, the optical system includes an optical element made of a heterogeneous glass material.

Further, the optical performance evaluation method of the present invention comprises a measuring step of measuring the refractive index of a plurality of points of an optical element, and the refractive index of the plurality of points as a point sequence, and a curve passing through the point sequence by a spline function. A function setting step of approximating and calculating a refractive index distribution function, and a calculation step of calculating optical performance such as ray tracing, aberration calculation, point spread, etc. based on the refractive index distribution function obtained by the function setting step. It is characterized by having.

Further, in the optical performance evaluation method according to the present invention, the optical element is made of a heterogeneous glass material.

[0008]

The spline function is a kind of the best approximation function, and the refractive index distribution function based on the spline approximation makes it possible to easily perform a highly accurate simulation of the actually manufactured inhomogeneous glass material.

[0009]

Embodiments of the present invention will be described below.

FIG. 1 is a block diagram showing the outline of an optical performance evaluation apparatus of the present invention. 1 is an input device such as a keyboard, 2 is a CPU, 3 is a display device such as a CRT, and 4 is an external storage such as a hard disk. Shows the device.

The keyboard 1 and the hard disk 4 are CPUs
2, the CPU 2 controls the CRT 3 based on the input.

The operation of this optical performance evaluation apparatus will be described with reference to the block diagram shown in FIG. 1 and the process flow chart shown in FIG.

First, before performing the operation of this flowchart, the refractive index at a plurality of points of an optical element made of a heterogeneous glass material to be subjected to performance evaluation is measured in advance by a known method such as the heterodyne method.

Next, when the power is turned on and a preparatory operation is performed, a program is read from the external storage device 4 into the CPU 2, and an optical system setting program, a refractive index information setting program, a refractive index distribution function calculation program are executed by software. An optical performance evaluation program and the like are formed.

From the keyboard 1 or the hard disk 4, lens data such as curvature, wall pressure, refractive index, incident light ray angle of an optical element to be evaluated are input into the CPU 2 (step S1). The number of samplings in the coordinate system (optical axis direction x, optical axis vertical direction h) that generates the refractive index distribution from the keyboard 1 or the hard disk 4, the sampling pitch (Δx, Δh), and the refractive index N ( x, h) is input into the CPU 2 as the refractive index information of the designated glass material of the lens data. Details of the refractive index information input are shown in FIG. 3, and an example of data input is shown in FIG. 4 (step S2). The refractive index at each point is measured in advance by a known method as already described.

The CPU 2 performs spline interpolation of the two-dimensional data N (x, h) based on the above refractive index information to obtain a refractive index distribution function (step S3).

The two-dimensional data spline interpolation method used here will be briefly described. A fourth-order or third-order normalized B-spline for two-dimensional data is defined as follows.

[0018]

[Equation 1]

The coordinate value (x, h) given here and the refractive index N (x, h) there are set as a point sequence, and (x _i , h _j , N _{i, j} ),
It is considered that i = 1, 2, ..., M and j = 1, 2, ..., N are interpolated as m × n point sequence data.

First, m-4 internal nodes ξ _i (i
= 1, ..., m-4), n-4 internal nodes ζ _{j in the} h direction
(J = 1, ..., n-4) is the Schoenberg-Whitney condition, x ₁ <ξ ₁ <x ₅ h ₁ <ζ ₁ <h ₅ x ₂ <ξ ₂ <x ₆ h ₂ <ζ ₂ <h ₆ ……… To satisfy x _m <ξ _m <x _{m + 4} h _n <ζ _n <hn ₊₄ ,

[0021]

[Equation 2]

, And 8 additional nodes in the x direction, ξ _-3 = ξ _-2 = ... = ξ ₀ = a ξ _m-3 = ξ _m-2 = ... = ξ _m = b h , Ζ _-3 = ζ _-2 = ... = ζ ₀ = c ζ _n-3 = ζ _n-2 = ... = ζ _n = d. Further, P _i-4,4 and P _j-4,4 can be obtained from the following recurrence formula by the difference quotient formula regarding the product of Leipniz.

[0023]

(Equation 3)

Here, the point sequence data (x, h, N) is (1)
Substituting into the equation, the simultaneous linear equations regarding the coefficient αi, j are established. By solving this simultaneous linear equation, a cubic spline can be obtained.

The CPU 2 performs ray tracing such as the Sharma method (ray tracing method of an optical system including an inhomogeneous medium) based on the lens data and the refractive index distribution function to calculate aberration.
The calculated aberration is displayed on the CRT 3. An example of this display is shown in FIG. (Step S4) Ray tracing method in the inhomogeneous medium used here (A.Shar
ma, et al., "Tracingrays through gradeindex media:
a new method ", Appl. Opt. 21 984 (1982)). x: ray vector, N: refractive index distribution, ds:
It is the minute optical path length at the time of line integration.

The optical path in a medium is expressed by the following optical equation

[0027]

[Equation 4]

It can be determined by solving
here,

[0029]

(Equation 5)

If we define

[0031]

(Equation 6)

This differential equation is solved using the Runge-Kutta method.

[0033]

(Equation 7)

However,

[0035]

(Equation 8)

The procedure is as follows. i) Obtaining the intersection of the ray and the surface The convergence method is used so that F (x) ≡x−f (y, z) = 0. The starting point is x ₀ = (x ₀ , y ₀ , z ₀ ). (F
_{(X 0) = x 0 -f} (y 0, z 0)

[0037]

[Equation 9]

However,

[0039]

[Equation 10]

Where

[0041]

[Equation 11]

Transfer is performed again with the pitch set as. The above procedure is repeated until | F | ≦ ε, and the intersection point (x, y,
z) is calculated. ii) Find the optical path length

[0043]

(Equation 12)

If the optical path length between t = t ₀ and t = t _m is L _m ,

[0045]

(Equation 13)

However, t '= t-t _m , Δt _m = t _{m + 1} -t _m where n ² (t') is Taylar expanded and discontinued in the fourth term,

[0047]

[Equation 14]

However,

[0049]

(Equation 15)

Also, during ray tracing, Δt is constant except in the area where the intersection with the surface is obtained, but in that case, t = t0 to t.
= Optical path length L _M to the t _M is

[0051]

[Equation 16]

That is, except for the first step in which the light ray enters the optical element surface and the final step in which the light ray exits from the optical element, it is sufficient to obtain the square of the refractive index and add them sequentially.

It should be noted that the present invention can be applied to modifications and variations of the above embodiments without departing from the spirit of the present invention.

[0054]

The spline function is a kind of best approximation function, and the refractive index distribution function based on this spline approximation makes it possible to easily perform a highly accurate simulation of an actually manufactured inhomogeneous glass material.

[0055]

[Brief description of drawings]

FIG. 1 is a block diagram of an embodiment of an optical performance evaluation apparatus of the present invention.

2 is an optical system setting by the optical performance evaluation device of FIG.
It is a flowchart which shows a refractive index information setting, a refractive index distribution function calculation, and an optical performance evaluation process.

FIG. 3 is a detailed explanatory diagram of refractive index information.

FIG. 4 is an example of data input.

FIG. 5 is a display example of an aberration diagram.

[Explanation of symbols]

 1 keyboard 2 CPU 3 CRT 4 hard disk

Claims (4)

[Claims] 1. An optical performance including an information processing device, which is connected to an input device, a display device, and an external storage device, and can set a plurality of functional means in a processor based on information from the input device or the external storage device. In the evaluation device, the functional means includes optical system information setting means for setting optical system information such as lens data according to input information from the input device or information from the external storage device, and input from the input device or from the external storage device. The refractive index information setting means for setting the refractive index information for setting the refractive index distribution function by the information of, and the refractive index information as a point sequence, a curve passing through this point sequence is approximated by a spline function to obtain the refractive index distribution function. Based on the calculating means to obtain, the optical system information and the refractive index distribution information, the optical performance such as ray tracing, aberration calculation, point image distribution, etc. is calculated, and the result And means for displaying or analyzing the optical performance evaluation device, characterized in that it has to perform the performance evaluation of the given optical system a refractive index as a point sequence. 2. The optical performance evaluation apparatus according to claim 1, wherein the optical system includes an optical element made of a heterogeneous glass material. 3. A measuring step of measuring a refractive index at a plurality of points of an optical element, and a refractive index distribution function is obtained by approximating a curve passing through the point series with the refractive index at the plurality of points as a point sequence by a spline function. Optical performance characterized by comprising a function setting step and a calculation step for calculating optical performance such as ray tracing, aberration calculation, point spread distribution, etc., based on the refractive index distribution function obtained by the function setting step. Evaluation methods. 4. The optical performance evaluation method according to claim 3, wherein the optical element is made of a heterogeneous glass material.