JPH10104508A - Method for determining shape of lens - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make it possible to effectively determine the shape of the lens in a thick system in designing of an optical system by applying the fundamental data of the lens and specific thickness characteristic coeffts. inputted at the time of designing the optical system and determining the shape by an arithmetic means. SOLUTION: At the time of expressing the thickness characteristic coefft. Wk of the single lens in the form of Wk =fk (r1 <-1> , Ψ1 , Ψ2 , (n), (d)); K=1 to 6 by using a five variables r1 <-1> , Ψ1 , Ψ2 , (n) and (d), wherein (m) pieces among these five variables and (5-m) pieces of the thickness characteristic coeffts. are given as coeffts. by an input means 13. The shape of the single lens is determined by solving the remaining (5-m) pieces of the variables by simultaneous equations using (5-m) pieces of the equations expressing the thickness characteristic coeffts. previously given as the constants by the arithmetic means 121 at this time. In the equations, r1 <-1> denotes the curvature of the first face, Ψa denotes the quartic aspherical face quantity of the (a) plane; d denotes the thickness of the single lens; W1 to W6 respectively denote the respective characteristic coeffts. of a spherical aberration, coma aberration, astigmatism, Petzval's sum, distortion aberration and the spherical aberration of the pupil.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of designing an optical system used in a photographic camera, a video camera, and an illumination system copier, for example, by utilizing an aberration coefficient or tracing a ray to each lens surface. The present invention relates to a method for determining a shape of a lens which is suitable for determining the optimum shape of a lens by evaluating the optical characteristics by performing a simulation or the like.

[0002]

2. Description of the Related Art Conventionally, there is a method of using an aberration coefficient as a method of designing an optical system, for example, setting an optical system such as a photographic lens or a lens for a video camera.

As a method used to determine the shape of a lens by correcting a low-order aberration region of an optical system, there is a method using a thin intrinsic coefficient. Here, the intrinsic coefficient is defined irrespective of the detailed structure of the optical system, normalizes the refracting power of a certain member to 1 and places an entrance pupil on the first principal plane to allow the entrance of paraxial rays. It is an aberration coefficient calculated by setting the height to 1 and the incident tilt angle of the paraxial chief ray to -1.

[0004] Assuming that an eigencoefficient in an mth-order aberration region is represented by a vector _S0 ^(m) and an aberration coefficient is S ^(m) in a certain constituent member, both of them are structural characteristics T ^(m) in the aberration region. Are combined by the first order transformation.

S ^(m) = T ^(m) · S ₀ ^(m) (m = 3,5, ‥‥) (9) If a certain member i is used as the i-th member of the synthesis system, When the aberration coefficient of the whole synthesis system is

[0006]

[Outside 2] S _i ^(m) = T _i ^(m) · S _0i ^(m) (11)

Here, T ^(m) does not depend on detailed structures such as r, (radius of curvature), d (thickness), and n (refractive index of material ⁾ in the optical system. A matrix representing the characteristic of the aberration configuration in the region, and is called a characteristic matrix.

[0008] In each order region of the aberration, the characteristic coefficient S ₀
Is used in a state represented by the characteristic matrix T, resulting in an operation characteristic of S = T · S ₀ (that is, an apparent aberration coefficient). Of particular note as the intrinsic coefficients of the optical system in the third-order aberration region are spherical aberration I ₀ , coma II ₀ , astigmatism III ₀ , Petzval sum P ₀ , distortion V ₀ , and pupil spherical aberration I ^s _0. 6 in total.

In thin-walled systems, the intrinsic coefficients III ₀ , P ₀ ,
Since the values of V ₀ and I ^s ₀ have constant values, the eigen coefficient I
Only ₀ and II ₀ are degrees of freedom. The characteristic coefficients I ₀ and II ₀
Is expressed as a function of the refractive index of the material, the radius of curvature of the first surface, the aspheric coefficient, and the like. For example, for a thin single lens,
By giving the paraxial ray incidence initial condition at the time of calculating the aberration coefficient as shown in the equation (12), the thin intrinsic coefficient becomes the following (1)
It is expressed as in equations 3) and (14).

[0010]

[Outside 3] FIG. 6 shows a graph of the existence range of the intrinsic coefficient of the thin single lens derived from the equations (13) and (14).

[0011] In the figure, "Sph." Indicates an existence curve in a spherical system. BB has a relationship of aspheric coefficient b and 8BB = b. From this figure, in the thin-walled system, the existence curve of the characteristic coefficient shows a parabola. When an aspherical surface is introduced, it can be seen that the existence curve moves up and down in parallel. In other words, if an aspherical surface is used, the intrinsic coefficients I ₀ and II ₀ can be freely controlled, and it can be said that aberration correction is versatile in a third-order region. Therefore, if the thin intrinsic coefficients I ₀ , II ₀ and the refractive index n are given, the shape of the single lens (the first lens) can be obtained from the equations (13) and (14).
It is possible to analytically determine the surface curvature r ₁ ^-1 and the amount of aspheric surface ψ).

[0012]

A method of treating a lens system as a thin-walled system and determining its initial shape using an aberration coefficient is effective at an early stage of design.

However, the actual lens system is a thick system, and it is necessary to consider the thickness of the lens, the air gap, and the like.
In particular, in recent years, there is a tendency to further reduce the size of the optical system by shortening the focal length of each group. Accordingly, the thickness of the lens with respect to the focal length of each lens group is further increased, and this is an area that cannot be handled by a thin system.

The difference in the existence range of the intrinsic coefficient between the thick-walled system and the thin-walled system is described in 1993. The present inventor reports at the 18th Optical Symposium Preprints of the Lectures, P65.

FIGS. 7 and 8 show the existence range of the thick intrinsic coefficient of the single lens when the thickness d = 0.2 (the value when the focal length of the group is normalized to 1). FIG. 7 shows the case where the aspherical surface is introduced on the first surface, and FIG. 8 shows the case where the aspherical surface is introduced on the second surface.

When FIG. 6 is compared with these figures, it can be seen that the condition of the existence area is considerably different between the thin-walled system and the thick-walled system. Further, in FIG. 6, the characteristic coefficient value (point P) in FIG.
It can be seen that while the lens shape corresponding to (1) can be obtained by the equations (13) and (14), there is no satisfactory shape in the case of FIG.

As described above, the method of determining the shape of the lens using the thin-wall intrinsic coefficient is not practical when the condition deviates from the thin-walled system (d is larger). Furthermore, in the case of thick-walled systems, the effect differs depending on the introduction of an aspherical surface.
The aspect is significantly different from the case of a thin-walled system in which the effect is the same regardless of which surface is introduced.

Conventionally, therefore, the thick-walled shapes are (13), (1)
4) It could not be obtained analytically by the formula. For this reason, first, in a thin state, the shape of the lens is obtained by Equations (13) and (14), and then the thickness is gradually given to correct the deviation of the focal length by the curvature of the lens surface, or the like. A lens shape that satisfies a desired characteristic coefficient has been determined using an optimization technique.

However, obtaining the initial value of the lens design by such a method results in a long time. Further, it is difficult to analytically determine a plurality of different effective lens shapes at an early stage of design.

Further, in a thin state, it is difficult to determine on which surface the aspherical surface should be introduced.

Conventionally, an expression for the characteristic coefficient of a thick-walled system corresponding to the expressions (13) and (14) has not been obtained.

According to the present invention, when designing an optical system, a part of basic data relating to a lens and a thick-wall specific coefficient based on a radius of curvature of a lens surface, a lens thickness, a refractive index of a material, etc., input from input means. Is given by the predetermined arithmetic means,
It is an object of the present invention to provide a lens shape determining method capable of analytically determining initial shapes of a plurality of effective lenses in a thick-walled system.

[0023]

According to the present invention, there is provided a method for determining the shape of a lens, comprising: (1-1) a method for determining a shape of a lens using an intrinsic coefficient in a third-order aberration region;
_{k (k = 1,2, ‥‥,} 6) the five variables r ₁ ^-1 (or ^{_{r 2 -1), ψ 1,}} ψ 2, n, by using the _{d W k = f k (r} 1 - ^{_{1, ψ 1, ψ 2,}} n, d); k = 1,2, ‥‥, 6 (1) where, r ₁ ^-1: single lens first Menkyokuritsu r ₂ ^-1: single lens second Menkyokuritsu ψ _a : a-th surface fourth-order aspherical amount (ψ _a = (na′−na) b,
b: 4th order aspherical coefficient) na, na ′: refractive index before and after the a-th surface d: single lens thickness n: single lens refractive index W ₁ : intrinsic coefficient of spherical aberration (= I ₀ ) W ₂ : coma aberration specific coefficient (= II ₀₎ W _3: the intrinsic coefficient of astigmatism (= III ₀₎ W _4: intrinsic coefficient (= P ₀₎ of the Petzval sum W _5: intrinsic coefficient distortion (= V ₀₎ W ₆ : Eigencoefficient of spherical aberration of pupil (= I ^s ₀ ) When expressed in the form:
And (5-m) thick natural coefficient values as constants, the remaining (5-m) variables represent the thick natural coefficient previously given as a constant by the arithmetic means. (5-
It is characterized in that the shape of a single lens is determined by assembling and solving simultaneous equations using m) equations.

In particular, (1-1-1) the thick wall specific coefficient W ₁ (=
It is characterized in that r ₁ ^-1 (or r ₂ ^-1 ), ψ ₁ is obtained by giving each value of I ₀ ), W ₂ (= II ₀ ) and d, n, ψ ₂ .

(1-1-2) Thickness specific coefficient W from the input means
It is characterized in that r ₁ ^-1 (or r ₂ ^-1 ) and ψ ₂ are obtained by giving each value of ₁ (= I ₀ ), W ₂ (= II ₀ ), d, n and ψ ₁ .

(1-1-3) The solution of the simultaneous equations by the variables r ₁ ^-1 and ψ ₁ calculated by the calculation means is represented by the variable r ₁ ^-1
The characteristic is that it is derived as a real number solution of a quartic equation related to

(1-1-4) The solution of the simultaneous equations by the variables r ₁ ^-1 and ψ ₂ calculated by the calculation means is represented by the variable r ₁ ^-1
Is derived as a real solution of an eighth-order equation.

(1-1-5) Thickness specific coefficient W from the input means
By giving each value of ₁ (= I ₀ ), W ₂ (= II ₀ ), W ₃ (= III ₀ ), and d and n, r ₁ ^-1 (or r ₂
^-1 ), ψ ₁ , ψ ₂ .

The method of displaying the intrinsic coefficient of the thick single lens of the present invention is as follows: (2-1) The thick intrinsic coefficient W of the single lens in the third-order aberration region
_{k (k = 1,2, ‥‥,} 6) the five variables r ₁ ^-1 (or ^{_{r 2 -1), ψ 1,}} ψ 2, n, by using the _{d W k = f k (r} 1 - ^{_{1, ψ 1, ψ 2,}} n, d); k = 1,2, ‥‥, 6 (1) where, r ₁ ^-1: single lens first Menkyokuritsu r ₂ ^-1: single lens second Menkyokuritsu ψ _a : a-th surface fourth-order aspherical amount (ψ _a = (na′−na) b,
b: 4th order aspherical coefficient) na, na ′: refractive index before and after the a-th surface d: single lens thickness n: single lens refractive index W ₁ : intrinsic coefficient of spherical aberration (= I ₀ ) W ₂ : coma aberration specific coefficient (= II ₀₎ W _3: the intrinsic coefficient of astigmatism (= III ₀₎ W _4: intrinsic coefficient (= P ₀₎ of the Petzval sum W _5: intrinsic coefficient distortion (= V ₀₎ W ₆ : A characteristic having a characteristic coefficient of pupil spherical aberration (= I ^s ₀ ), and the characteristic is displayed on display means.

(2-1-2) The display means displays the thick wall intrinsic coefficient.

[0031]

[Outside 4] (However, A _i to F _i is a coefficient represented by the refractive index n, thickness d, the i-th surface aspherical amount [psi _i) is characterized in that expressed as.

The lens shape determining method of the present invention is as follows: (3-1) A lens shape determining method using an intrinsic coefficient in a third-order aberration region for a lens system represented by a plurality of constituent elements (groups). Lens shape calculation means for calculating a plurality of thick lens shapes of each group by numerical calculation from the intrinsic coefficient values given to each group and several variable values constituting the lens shape, It is characterized by having aberration coefficient calculating means for calculating an aberration coefficient for each lens shape, and lens system forming means for forming an optical system by combining the calculated lens shapes of the respective groups.

(3-2) For a lens system represented by a plurality of constituent elements (groups), in a method of determining the shape of a lens using an intrinsic coefficient in the third-order aberration region, a plurality of eigenvalues required for each group are determined. Eigen coefficient value obtaining means for obtaining a coefficient value; lens shape calculating means for calculating a plurality of thick lens shapes of each group by numerical calculation from the eigen coefficient value and several variable values constituting the lens shape; It is characterized by having an aberration coefficient calculating means for calculating an aberration coefficient for each lens shape of each group, and a lens system forming means for forming an optical system by combining each lens shape of each group.

In particular, among the constituent requirements (3-1) and (3-2), (3-2-1) a lens shape which does not satisfy a predetermined condition is selected from the lens shapes calculated by the lens shape calculating means. It is characterized in that it has a lens shape exclusion means for exclusion of the lens.

(3-2-2) The lens system constituting means is characterized in that it comprises an optical system exclusion means for selectively excluding those which do not satisfy a predetermined condition among the combined optical systems.

[0036]

FIG. 1 is a block diagram of a main part of a first embodiment of the present invention, showing a configuration of information processing for realizing a method for determining a shape of a lens of an optical system. In FIG. 1, 1
Reference numeral 3 denotes an input unit, which includes, for example, a keyboard and the like, to which various numerical values relating to the optical system and aberration drawing control data for displaying the amount of aberration of the optical system are input. Numeral 11 denotes an arithmetic unit, which calculates the shape of the single lens of the optical system, the intrinsic coefficient, and the like based on data from the input unit 13 and data from the storage unit 12 and the external storage unit 15 described later.

Reference numeral 12 denotes storage means, and reference numeral 15 denotes external storage means, which store various data calculated by the calculation means 11 and lens data given in advance. Reference numeral 14 denotes display means (drawing means),
Calculating means 1 for calculating the lens shape, the intrinsic coefficient, etc.
The display is based on the data from No. 1.

FIG. 2 is a flowchart of the first embodiment of the present invention. In the present invention, first, the thick intrinsic coefficient of a single lens is represented by a refractive index n, a first surface curvature r ₁ ^-1 , a first surface aspherical amount ψ ₁ , a second surface aspherical amount ψ ₂ , and a wall thickness d. .

For a thick single lens, the paraxial ray tracing initial value takes the following value (however, the focal length of the single lens is normalized to 1).

[0040]

[Outside 5] The surface refractive power Φ ₁ of the first surface and the surface refractive power Φ ₂ of the second surface can be expressed as follows.

Φ ₁ = (n−1) / r ₁ , Φ ₂ = n (1−Φ ₁ ) / (n−dΦ ₁ ) (18) According to the above equation, the third-order thick wall natural coefficient is as follows. Can be expressed as

[0042]

[Outside 6] The following Table 1 shows the coefficients A _{i to} F _{i in the} equations (2) to (7).
Is shown. These coefficients A _{i to} F _i are the refractive index n, the thickness d, the first surface aspherical amount ψ ₁ , the second surface aspherical amount ψ
Represented by ₂ . The expressions in the above equations (2) to (8) are independently derived by the inventor, and are not present in the related art.

In the present embodiment, when the thick intrinsic coefficient is expressed by several parameters as described above, for example, the intrinsic coefficient, the refractive index, and the thickness are given, and (2) to
By solving several equations of (7) simultaneously, the shape of the single lens is analytically determined. Then, these calculation results are displayed on the display means.

Next, the determination of the shape of the single lens when the thick intrinsic coefficients I ₀ and II ₀ are given in this embodiment will be described with reference to the flowchart of FIG. In this embodiment,
A method of determining a shape when an aspheric surface is introduced into either the first surface or the second surface of a single lens is shown.

First, when the thick intrinsic coefficients I ₀ and II ₀ are given (step 401), the following equations are derived from the equations (2) and (3) depending on the difference in the aspherical introduction surface. (1
Equation (9) is obtained when an aspherical surface is introduced as the first surface (step 4).
02 → 403), and the thickness and refractive index of the single lens are constants, which is a quartic equation of the first surface curvature. Incidentally, described later (Table 2) shows the contents of the zeta _i.

[0046]

[Outside 7] Expression (20) is a case where an aspheric surface is introduced into the second surface (step 402 → 405), and becomes an eighth-order equation of the first surface curvature with the thickness and refractive index of the single lens as constants. In addition,
Table 3 shows the contents of η _i .

[0047]

[Outside 8] By solving the above equations, the thick-wall specific coefficients I ₀ , II
_The curvature of the first surface and the amount of aspherical surface satisfying the value of ₀ can be obtained analytically with respect to the difference between the introduction surfaces of the aspherical surfaces. Then, the aspherical amount can be obtained by substituting the obtained first surface curvature value into the expression (2) or (3) (steps 404 and 406).

Next, the shape of the single lens is specifically determined. Here, the shape of a single lens having a negative refractive power is determined. First, a refractive index n, a thickness d, and a thick intrinsic coefficient I ₀ , II
Give a value of ₀ as follows:

N = 1.8052, d = −0.0295, I ₀ = 199.09, II ₀ = 2.99 (21) However, since the focal length of the single lens is normalized to 1,
When the single lens has a negative refractive power, the wall thickness takes a negative value.

By substituting the values of the expression (21) into the expressions (19) and (20) and solving them, the shapes can be obtained by the differences in the introduction surfaces of the aspherical surfaces as follows. However, a shape solution and an imaginary solution having a curvature of 50 or more in absolute value when the focal length of the single lens is 1 were excluded. To return the first surface curvature and the aspherical amount obtained below to the actual scale, the following is performed. First, the curvature of the first surface may be divided by the focal length f _i of the group constituted by the single lens. Also, the amount of asphericity may be divided by the cube of f _i.

[0051] As described above, when a plurality of real number solutions are obtained and displayed on the display means, the designer selects from among the solutions that actually comply.

As described above, by providing two sets of eigen coefficients, the shape of a single lens satisfying the given desired eigen coefficient value can be instantaneously determined for each difference in the aspherical introduction surface. It is possible. Here, the set of unique coefficients to be applied does not need to be limited to the thick natural coefficients I ₀ and II ₀ , and may be another thick natural coefficient set. In that case, (1
Equations (9) and (20) change correspondingly. In the present embodiment, the variables are the first surface curvature and the amount of aspherical surface.
Other parameters may be variables. Also,
Equations (2) to (3) are expressed as a function of the curvature of the first surface, but may be expressed as a function of the curvature of the second surface. In this case, equations (19) and (20) are It changes with it.

In the present embodiment, when obtaining the aspherical amount of the first surface (steps 402, 403, 404),
Although the amount of aspherical surface on the second surface is solved as 0, the amount of aspherical surface on the second surface can be similarly calculated as long as the value is a constant. This is important when calculating the aspherical amount of the second surface (step 4).
02, 405, 406), which can be calculated by setting the amount of aspherical surface of the first surface as a constant.

Further, in the present embodiment, two eigenvalues are given, but it is also possible to determine the shape by giving three eigenvalues. In this case, assuming that the aspheric surface is introduced on both surfaces of the single lens, the amount of aspheric surface is calculated on both surfaces. Therefore, in this case, the variable is the first surface curvature r
₁ ⁻¹ , and three aspherical amounts ψ ₁ and な る₂ .

FIG. 3 is a flowchart according to the second embodiment of the present invention. In the present embodiment, a case is described in which a shape (initial shape) in a third-order aberration region of a zoom lens having a three-group configuration in which each group includes a single lens is obtained.

In this embodiment, it is assumed that the paraxial power arrangement of the three-unit zoom lens is known. First, in step 501, a target aberration coefficient value of the entire optical system is set.

In this embodiment, the spherical aberration coefficient I at the wide-angle end is
_W, coma aberration coefficient II _W, astigmatism coefficient III _W, spherical aberration coefficients of the telephoto end I _t, coma aberration coefficient II _t, astigmatism coefficient
Six values of III _t were used as target aberration coefficients. This is because each group has the thick intrinsic coefficients I ₀ and II ₀ as variables, so there are six variables. If a total of six target aberration coefficients at the wide-angle end and the telephoto end are given, the intrinsic coefficient values required for each group are given. Is uniquely determined.

FIG. 4 shows an example of a flow for determining the group-specific coefficient values in steps 501 and 502. As shown in the figure, the aberration coefficient of the entire system is represented by the product of the characteristic matrix and the eigen coefficient. Note that the four eigen coefficients other than I ₀ and II ₀ in each group are treated as constants here to form a constant matrix. The value of the characteristic matrix is
In the third order aberration region, it can be obtained from the paraxial power arrangement.

Accordingly, by calculating the inverse matrix, the aberration coefficient of the entire system is given, and the characteristic coefficient I of each group is given.
₀ and II ₀ can be determined. By the above procedure, the unique coefficient values I ₀ and II ₀ of each group can be calculated.

As the next stage, steps 503 and 50
In 4,505, the intrinsic coefficient value calculated for each group
For I ₀ and II ₀ , the shape of each group is calculated by equation (19) or equation (20). In this case, it is assumed that the thickness d and the refractive index n are given for each group.

In the zoom lens having a small number of components as in the present embodiment, some combinations of glass materials constituting the lens system can be determined from the viewpoint of chromatic aberration correction by the given paraxial power arrangement. Therefore, by providing one set of glass materials, the refractive index of each group can be given.

In this embodiment, an aspherical surface is introduced on one surface of the single lens constituting each group. Therefore,
When an aspherical surface is introduced into the first surface, the calculation is performed with the amount of aspherical surface ψ ₂ of the second surface set to 0.

Similarly, in the case of the second surface, the calculation is performed with the aspherical amount ψ ₁ of the first surface set to 0. Then, equation (19),
In general, there are a plurality of shapes solved by the equation (20) (however, there is a case where there is no solution in a region where no shape solution exists).

The first group will be described as an example. When the aspherical surface is first introduced into the first surface based on the eigencoefficient values I ₀ and II ₀ calculated for the first group, the expressions 1a to 1a are obtained from Expression (19).
The shape solution of 1c is obtained (however, an impractical shape and an imaginary solution are excluded).

Next, when an aspherical surface is introduced as the second surface,
The shape solutions 1d to 1f are obtained from the equation (20). Therefore, in the first group, six shapes 1a to 1f are analytically obtained. Similarly, for the second group and the third group, a plurality of shape solutions are obtained for each characteristic coefficient value.

In step 506, for the shapes of the respective groups obtained as described above, other unique coefficient values other than I ₀ and II ₀ are calculated according to the equations (4) to (8).

This is because in the present embodiment, the characteristic coefficient III
_0, so P _0, V _0, the I ^s ₀ was treated as constant as shown in FIG. 4, is the re-calculated anew in this step. By this step 506, all the intrinsic coefficient values for each shape of each group are known. Step 50
In step 7, the aberration coefficient is calculated by multiplying the characteristic matrix of each group by the set of eigen coefficient values for each shape of each group.

Further, in step 508, a plurality of shapes obtained for each group are combined in a brute force manner so as to constitute an optical system. As an example, the optical system shown by 509 has a shape of the first group 1a, a shape of the second group 2c, and a third shape.
This is the result of selecting and combining 3a as the group shape.

At this time, the aberration coefficient of the entire optical system is obtained as the sum of the aberration coefficient values of each group. In this embodiment, 60 × 5 × 2 = 60 optical systems are obtained. Actually, of the 60 optical systems, only the shape solutions of the combination satisfying the required optical performance are selected and output (step 509).

It should be noted that the eigen coefficient value given in step 502 is not only given by the means in step 501, but a value may be given directly to step 502, for example. Further, the unique coefficient value required by each group may be obtained by another method.

Further, in this embodiment, one set (six) of the target aberration coefficients is given in step 501, but each value of the aberration coefficients is changed to a certain pitch to obtain a desired optical performance. It is also possible to search for a shape solution having the same.

The type and number of target aberration coefficients may be selected in any manner. It is also possible to search for a shape solution having desired optical performance by changing the values of the intrinsic coefficients I ₀ and II ₀ given to each group at a certain pitch.

When optimization is performed by ordinary automatic design using the result obtained in step 509 as a starting point, it is possible to perform design with excellent performance in a short time. Further, the present invention is effective for an automatic design tool in which the above-described lens design technique is automated and adopted.

FIG. 5 is a flowchart according to the third embodiment of the present invention. In the present embodiment, a method of calculating the existence range of the thick intrinsic coefficient when introducing an aspheric surface to the first surface in a single lens is shown.

First, in step 701, the calculation of the existence range of the unique coefficient is started. However, in the present embodiment, the thickness and refractive index of the single lens are given, and the first lens
Aspherical surface is set. In step 702, the value BB of the aspherical amount of the first surface given as a parameter and the first value
The initial values of the surface curvature values AA are Bs and As, respectively.

In step 703, the aspherical amount of the first surface 面
Set the BB value to ₁ . And in step 704,
An initial value AA at the time of bending is given as the first surface curvature r.

Next, in step 705, six unique coefficient values (or only necessary unique coefficient values) are calculated. The calculation method follows equations (2) to (8). The calculated data is stored in the data storage device 711.

When the specific coefficient is calculated as described above, in step 706, it is determined whether or not the curvature r of the first surface matches the curvature value Ae set for terminating the bending. If not the end value, step 708
The calculation is repeated until the first surface curvature value becomes equal to the bending end value. If it matches the end value, the bending is ended and the process proceeds to step 707.

Then, at step 707, the aspherical amount ψ
_{If 1} does not match the final change amount Be of the aspheric surface, the process returns to step 703 by step 709, and the same procedure is repeated. If, at step 707, if the aspherical amount [psi ₁ agrees to the final variation Be aspherical proceeds to step 710 to end the calculation, and outputs the result.

FIG. 7 shows an example of the existence range of the thick intrinsic coefficient of the single lens, which is created based on the data calculated using the above method. By using such a method, it is possible to calculate the existence range of the thick-wall specific coefficient in a very short time.

In the present embodiment, the specific coefficients I ₀ , II
_{Although the} existence range for ₀ is shown, it goes without saying that the same applies to the existence ranges of various combinations regarding other unique coefficients.

Further, when an aspherical surface is introduced as the second surface, it can be obtained in the same manner as in the present embodiment. In the present embodiment, one aspherical surface amount is used as a parameter. However, by providing two aspherical surface amounts, it is also possible to calculate and display the existence range of the intrinsic coefficient for a double-sided aspherical surface in a single lens.

[0083]

[Outside 9]

[0084]

[Outside 10]

[0085]

[Outside 11]

[0086]

As described above, according to the present invention, a part of basic data relating to a lens is obtained based on the radius of curvature of the lens surface, the thickness of the lens, the refractive index of the material, and the like input from the input means when designing the optical system. By giving the characteristic coefficient of thick and the thick wall, it is possible to achieve a method of determining the shape of the lens in which the calculating means can effectively determine the shape of the lens analytically in the thick wall system. If this is set as a starting point of the automatic design, an effective design can be performed in a short time.

[Brief description of the drawings]

FIG. 1 is a main block diagram of a first embodiment of the present invention.

FIG. 2 is a flowchart according to the first embodiment of the present invention.

FIG. 3 is a flowchart according to a second embodiment of the present invention.

FIG. 4 is an explanatory diagram for calculating a unique coefficient value according to the second embodiment of the present invention.

FIG. 5 is a flowchart according to a third embodiment of the present invention.

FIG. 6 is a diagram showing a range where characteristic coefficients I ₀ and II ₀ exist in a thin-walled system.

FIG. 7 is a diagram showing a range in which characteristic coefficients I ₀ and II ₀ exist in a thick-walled system when an aspheric surface is introduced into a first surface;

FIG. 8 is a diagram showing a range where natural coefficients I ₀ and II ₀ exist in a thick-walled system when an aspheric surface is introduced on a second surface.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 11 Operation means 12 Storage means 13 Input means 14 Display means 15 External storage means

Claims (12)

[Claims] In a method for determining a shape of a lens using an intrinsic coefficient in a third-order aberration region, a thick intrinsic coefficient W _k (k = 1, 2, ‥‥, 6) of a single lens is set to five variables r ₁ ^{−. 1}
(Or r ₂ ⁻¹ ), ψ ₁ , ψ ₂ , n, d, and W _k = f _k (r ₁ ⁻¹ , ψ ₁ , ψ ₂ , n, d); k = 1, 2, ‥‥ , 6 (1) where r ₁ ^-1 : curvature of the first surface of the single lens r ₂ ^-1 : curvature of the second surface of the single lens ψ _a : quaternary aspherical surface of the a surface (ψ _a = (na′−na) b,
b: fourth-order aspherical surface coefficient) na, na ′: refractive index before and after the a-th surface d: single lens thickness n: single lens refractive index W ₁ : intrinsic coefficient of spherical aberration (= I ₀ ) W ₂ : coma aberration specific coefficient (= II ₀₎ W _3: the intrinsic coefficient of astigmatism (= III ₀₎ W _4: intrinsic coefficient (= P ₀₎ of the Petzval sum W _5: intrinsic coefficient distortion (= V ₀₎ W ₆ : Eigencoefficient of spherical aberration of pupil (= I ^s ₀ ) When expressed in the form:
And (5-m) thick natural coefficient values as constants, the remaining (5-m) variables represent the thick natural coefficient previously given as a constant by the arithmetic means. (5-
m) A method of determining a shape of a lens, comprising determining a shape of a single lens by assembling and solving simultaneous equations using the equations. 2. The thick-wall specific coefficient W ₁ (=
_2. The method according to claim 1, wherein r ₁ ^-1 (or r ₂ ^-1 ), ψ ₁ is obtained by giving each value of I ₀ ), W ₂ (= II ₀ ) and d, n, ψ _2. The method for determining the shape of the lens. 3. A thick wall specific coefficient W ₁ (= 3)
_{2. The method} according to claim ₁ , wherein r ₁ ^-1 (or r ₂ ^-1 ), ψ ₂ is obtained by giving each value of I ₀ ), W ₂ (= II ₀ ) and d, n, ψ _1. The method for determining the shape of the lens. 4. A variable r calculated by said calculating means.
3. The method according to claim 2, wherein the solution of the simultaneous equations by ₁ ^-1 and ψ ₁ is derived as a real solution of a quartic equation relating to the variable r ₁ ^-1 . 5. A variable r calculated by said calculating means.
4. The method according to claim 3, wherein the solution of the simultaneous equations by ₁ ^-1 and ψ ₂ is derived as a real solution of an eighth-order equation relating to the variable r ₁ ^-1 . 6. The thick-wall specific coefficient W ₁ (=
By giving each value of I ₀ ), W ₂ (= II ₀ ), W ₃ (= III ₀ ), and d and n, r ₁ ^-1 (or r ₂ ^-1 ), ψ
_{2. The} method for determining the shape of a lens according to claim ₁ , wherein ₁ and ψ2 are obtained. 7. The thick natural coefficient W _k (k = 1, 2, ‥‥, 6) of a single lens in a third-order aberration region is set to five variables r ₁ ^-1.
(Or r ₂ ⁻¹ ), ψ ₁ , ψ ₂ , n, d, and W _k = f _k (r ₁ ⁻¹ , ψ ₁ , ψ ₂ , n, d); k = 1, 2, ‥‥ , 6 (1) where r ₁ ^-1 : curvature of the first surface of the single lens r ₂ ^-1 : curvature of the second surface of the single lens ψ _a : quaternary aspherical surface of the a-th surface (ψ _a = (na′-na) b,
b: 4th order aspherical coefficient) na, na ′: refractive index before and after the a-th surface d: single lens thickness n: single lens refractive index W ₁ : intrinsic coefficient of spherical aberration (= I ₀ ) W ₂ : coma aberration specific coefficient (= II ₀₎ W _3: the intrinsic coefficient of astigmatism (= III ₀₎ W _4: intrinsic coefficient (= P ₀₎ of the Petzval sum W _5: intrinsic coefficient distortion (= V ₀₎ W ₆ : A method of displaying the characteristic coefficient of a thick single lens, characterized in that the form is represented by a characteristic coefficient (= I ^s ₀ ) of spherical aberration of a pupil, and the form is displayed on display means. 8. The display means displays the thick intrinsic coefficient as (However, A _i to F _i is the refractive index n, thickness d, the i-th surface coefficient represented by the aspherical amount [psi _i) thick single lens according to claim 7, characterized in that expressed as How to display the unique coefficient of 9. A method for determining a lens shape using a characteristic coefficient in a third-order aberration region for a lens system represented by a plurality of constituent elements (groups) and a characteristic coefficient value and a lens given to each group. Lens shape calculating means for calculating a plurality of thick lens shapes of each group by numerical calculation from several variable values constituting the shape, and aberration calculating an aberration coefficient for each calculated lens shape of each group A lens shape determining method comprising: a coefficient calculating means; and a lens system forming means for forming an optical system by combining the calculated lens shapes of the respective groups. 10. For a lens system represented by a plurality of constituent elements (groups), in a lens shape determination method using eigen coefficients in a third-order aberration region, a plurality of eigen coefficient values required for each group are determined. Eigen coefficient value obtaining means for obtaining, lens shape calculation means for calculating a plurality of thick lens shapes of each group by numerical calculation from the eigen coefficient values and some variable values constituting the lens shape, and each calculated group A lens coefficient calculating means for calculating an aberration coefficient for each lens shape, and a lens system forming means for forming an optical system by combining each lens shape of each group. Method. 11. A lens shape excluding means for selectively excluding a lens shape calculated by said lens shape calculating means that does not satisfy a predetermined condition. The method for determining the shape of the lens described in the above. 12. The lens system constituting means according to claim 9, wherein said lens system constituting means has an optical system excluding means for selectively excluding an optical system which does not satisfy a predetermined condition among the combined optical systems. The method for determining the shape of the lens.