Patent Application
20230115346
The present invention relates to a lens evaluation method, a lens designing method, a spectacle lens production method, and a lens evaluation program.
In order to provide a spectacle lens that favorably matches the spectacle wearer's demands, a technique has been proposed in which, when designing or producing a spectacle lens, a wavefront shape relating to the spectacle lens is specified and an individual eye model of the spectacle wearer is also defined, and the surface shape of the spectacle lens is optimized based on the wavefront shape and the individual eye model (for example, see Patent Document 1).
Patent Document 1: Japanese Patent No. 6209722
For example, a wavefront formed by a spectacle lens can be evaluated by numerically calculating the optical path lengths of a sufficient number of light beams, and also subsequently fitting the wavefront to Zernike polynomials. However, if this requires a large calculation load, long processing time, high-performance hardware resources, etc., are required, which is unfavorable for quick and easy spectacle lens evaluation.
An aim of the present invention is to provide a technique for optimizing spectacle lens evaluation while realizing quick and easy processing.
The present invention has been conceived to achieve the above-described aim.
A first aspect of the present invention is a lens evaluation method in which
an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount is adopted as an evaluation index of the spectacle lens.
A second aspect of the present invention is the lens evaluation method according to the first aspect,
wherein the predetermined vector amount is a Fourier transform of a pseudo-inverse matrix that is for obtaining, for a local evaluation region of the spectacle lens, expansion coefficients for predetermined terms of predetermined polynomials.
A third aspect of the present invention is the lens evaluation method according to the first aspect,
wherein the predetermined vector amount is a Fourier transform of a pseudo-inverse matrix that is for obtaining, for a local evaluation region of the spectacle lens, expansion coefficients for predetermined terms of predetermined orthogonal polynomials.
A fourth aspect of the present invention is the lens evaluation method according to the second or third aspect,
wherein the predetermined terms are predetermined terms of Zemike polynomials.
A fifth aspect of the present invention is the lens evaluation method according to the second or third aspect,
wherein the predetermined terms are a weighted sum of a plurality of predetermined terms of Zemike polynomials.
A sixth aspect of the present invention is the lens evaluation method according to any one of the second to fifth aspects,
wherein, in regard to the expansion coefficients, 1 is applied as a weight to each rotationally symmetric component when expansion using Zemike polynomials is performed.
A seventh aspect of the present invention is a lens designing method including:
a step for determining an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount as an evaluation index of the spectacle lens; and
a step for designing a spectacle lens using the evaluation index.
An eighth aspect of the present invention is a lens manufacturing method including:
a step for determining an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount as an evaluation index of the spectacle lens; and
a step for determining whether or not an optical characteristic of the spectacle lens is appropriate using the evaluation index.
A ninth aspect of the present invention is a lens evaluation program for causing a computer to execute
a step for adopting an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount as an evaluation index of the spectacle lens.
According to the present invention, spectacle lens evaluation can be optimized while realizing quick and easy processing.
An embodiment of the present invention will be described below with reference to the drawings.
Findings made by the inventor will be described first, before describing the present embodiment in detail.
There are cases in which preferences relating to the visual perception of the outer world as perceived by a spectacle wearer are reflected in the optical characteristics of a spectacle lens to be used by the spectacle wearer. For example, there are spectacle wearers who prefer visual perception with priority placed on brightness (PSF and good low-frequency contrast), spectacle wearers who prefer visual perception with priority placed on resolution (good high-frequency contrast), etc., and it is thus desirable to be able to provide spectacle lenses having optical characteristics matching the preferences of spectacle wearers.
Specifically, there are spectacle wearers who prefer the visual perception at a focus position with the smallest point spread function (PSF) variance, as illustrated in
It is known that the focus position (image forming position) of a spectacle lens is dependent not only on power but also on the amount of aberration (especially spherical aberration) and object spatial frequency. Accordingly, in order to correctly estimate the focus position of a spectacle lens, aberration amount, object spatial frequency, etc., need to be taken into consideration.
Thus, it is conceivable to use Zemike polynomials and the wavefront of a spectacle lens in the evaluation of visual perception through a spectacle lens (in other words, the optical characteristics of the spectacle lens), as mentioned above, so as to be able to obtain results in which not only power but also aberration amount, object spatial frequency, etc., are taken into consideration.
The wavefront of a spectacle lens is the wavefront of a luminous flux passing through the spectacle lens and having a diameter defined by the pupil.
Zemike polynomials are functions (orthogonal polynomials) defined within unit circles having a radius of 1. Specifically, Zemike polynomials are represented by formula (1) below.
In formula (1), W(x, y) is the wavefront at coordinates x, y, Zj(x, y) is the jth Zemike polynomial, cj is the Zemike coefficient corresponding to the jth Zemike polynomial, and J is the number of Zemike polynomials used for expansion.
According to such Zemike polynomials, all surface shapes can be (approximately) expressed by adding Zemike polynomials together.
Specifically, for example, a given surface shape can be broken up into the 0th-order to nth-order (where n is a natural number) aberrations using Zemike polynomials, as illustrated in
Note that, in the drawing, the components enclosed by the box near the center indicate rotationally symmetric components, and the rest of the components indicate non-rotationally symmetric components. Furthermore, in the drawing, the 2nd-order aberration component belonging to the rotationally symmetric components is commonly referred to as a power error (defocus), and the coefficient of this aberration corresponds to the focus position with the smallest wavefront aberration. The 4th-order aberration component belonging to the rotationally symmetric components is a component corresponding to spherical aberration. The sum of the coefficients of the components belonging to the rotationally symmetric components corresponds to the focus position with the smallest PSF.
By using Zemike polynomials and the wavefront of a spectacle lens as described above, the evaluation of visual perception through a spectacle lens can be optimized. However, if this requires a large calculation load, long processing time, high-performance hardware resources, etc., are required, which is unfavorable for quick and easy spectacle lens evaluation. In particular, if the spectacle lens is a progressive multifocal lens, the increase in load becomes highly prominent because calculation needs to be performed separately for each measurement point over the entire effective diameter.
Having conducted diligent investigation based on the circumstances described above, the present inventor conceived of a technique for optimizing spectacle lens evaluation (especially the evaluation of defocus, spherical aberration, PSF, etc., that significantly affect visual perception through spectacle lenses) while realizing quick and easy processing using high-speed computation. Such a technique will be described in detail below in the present embodiment.
As mentioned above, Zemike polynomials are represented by formula (1). In order to determine wavefront aberration for each coordinate point of an evaluation-target spectacle lens based on formula (1), the Zemike coefficients cj (the magnitudes thereof) need to be known.
In order to determine the Zemike coefficients cj, it is conceivable to adopt the following method: the Zemike coefficients cj are treated as unknown coefficients; each Zemike polynomial Zj(x, y) (i.e., function f) is multiplied by an unknown coefficient, and the Zemike polynomials Zj(x, y) are added up; and an operation (the least squares method, etc.) for fitting the results to a measured shape is performed to calculate the Zemike coefficients cj. A pseudo-inverse matrix is used for the formulation of this method. Pseudo-inverse matrices are matrices similar to inverse matrices that are obtained by performing mathematical operations on matrices that cannot have inverse matrices. Pseudo-inverse matrices are also called generalized inverses, and inverse matrices extended to non-square and singular matrices correspond thereto, for example.
Here, in order to describe the pseudo-inverse matrix in more detail, the relationship between a local wavefront and Zemike coefficients will be investigated. For example, if the relationship represented by W=cZ holds true between a local wavefront W, Zemike polynomials Z, and Zemike coefficients c, the relationship c=(ZTZ)−1ZTW can be obtained by mathematically processing W=cZ, and one set of Zemike coefficients c can be calculated therefrom. The “T” on the right shoulder indicates matrix transposition. Furthermore, the “−1” indicates an inverse matrix. In the relationship c=(ZTZ)−1ZTW, the portion “(ZTZ)−1ZT” corresponds to the pseudo-inverse matrix. Such a pseudo-inverse matrix may also be simply indicated below by “M”.
Specifically, the relationship between Zemike coefficients and a local wavefront, or in other words the Zemike expansion, is given by formula (2) below.
[Math. 2]
C(x,y)=(ZTZ)−1ZTW(x,y) (2)
In formula (2), C is a vector amount obtained by arranging Zemike coefficients corresponding to the number of components, W(x, y) is obtained by extracting, as vectors, data corresponding to a number of local data items centering on x, y from W indicating the entirety of the wavefront data, and Z is a matrix representing the Zemike polynomials corresponding to the respective points and components that has a size of (the number of local data items×the number of components).
Suppose a case in which the calculation using formula (2) above is performed for every point of a spectacle lens.
In this case, when the pseudo-inverse matrix is defined as (ZTZ)−1ZT=M, formula (2) can be rewritten as formula (3) below by calculating the matrix M having a size of (the number of local data items×the number of components) in advance and reusing the matrix M.
[Math. 3]
C(x,y)=MW(x,y) (3)
According to formula (3), the calculation amount per point can be reduced by reusing the matrix M. However, a calculation amount corresponding to (the number of local data items×the number of components) is still required. Thus, if calculation is performed for every point of a spectacle lens, a calculation amount corresponding to (the number of data items of all points×the number of local data items×the number of components) will be required. Here, the number of data items of all points is the square of the number k of data items in one direction because the data is two dimensional. Furthermore, the number of local data items is proportional to the number of data items of all points because a local region is defined as an area corresponding to x % of the entire area. When such matters are taken into consideration, the calculation amount per component is proportional to the fourth power of the number k of data items in one direction.
In regard to this, in the present embodiment, the calculation amount is reduced using a method as described below.
The Zernike expansion at all points of a spectacle lens can be regarded as a convolution as shown in formula (4) below.
[Math. 4]
C=M*W (4)
In a Fourier space, a convolution can be represented as a product of functions. This feature is also used in the present embodiment. That is, as shown in formula (5) below, C can therefore be obtained be performing inverse-Fourier transform on the product of the Fourier transform of M and the Fourier transform of W.
[Math. 5]
C=
−1[(M)·
(W)] (5)
In formula (5), “F−1[ ]” indicates the inverse-Fourier transform of the function enclosed by the square brackets. F[W] is the Fourier transform of the wavefront W. F[M] is the Fourier transform of the matrix M, and corresponds to an example of the preset predetermined vector amount. The predetermined vector amount here indicates a vector amount obtained by Fourier transform of a pseudo-inverse matrix for obtaining expansion coefficients for predetermined terms of polynomials, and when expressed mathematically, corresponds to F[M], which is the Fourier transform of the matrix M, for example.
It is known that the calculation amount in Fourier transform is O(N log N) according to the Bachmann-Landau O notation. Accordingly, the calculation amount in high-speed Zernike expansion in which Fourier transform is used, such as that in formula (5), is proportional to n2 log n, and a significant reduction in the calculation amount can be realized in comparison with, for example, a case in which Zernike expansion is performed using the least squares method or the like.
That is, in the present embodiment, upon evaluating a spectacle lens, an amount obtained by multiplying the Fourier transform F[W] of the wavefront W of the spectacle lens by the Fourier transform F[M] of the matrix M, which is a preset predetermined vector amount, is determined, and the evaluation is performed using the determined amount. Accordingly, the present embodiment is highly favorable for performing evaluation quickly and easily because a significant reduction in the calculation amount can be realized, and an increase in the calculation load for the evaluation can thus be suppressed.
Next, an example of steps for evaluating a spectacle lens using the high-speed computation according to the above-described method, or that is, steps in the lens evaluation method according to the present embodiment, will be described.
The steps of the lens evaluation method described below are executed using a computer device. That is, lens evaluation according to the steps described below is performed while using a computer device comprising hardware resources such as a computation unit including a central processing unit (CPU) or the like, a memory such as a flash memory or a hard disk drive (HDD), and an input/output interface, and by causing the computation unit to execute a predetermined program that is pre-installed in the memory.
As shown in the illustrated example, the steps of the lens evaluation method according to the present embodiment are divided into preprocessing (step 10; “step” is hereinafter abbreviated as “S”), and repetitive processing (S20).
In the preprocessing (S10), first, for a spectacle wearer who is to wear the evaluation-target spectacle lens, the spectacle wearer's preferences regarding visual perception are ascertained (S11). Specifically, for example, it is ascertained, inter alia, whether the spectacle wearer: prefers the visual perception at a focus position where the variance of PSF is the smallest; prefers the visual perception at a focus position where wavefront aberration is the smallest; or prefers the visual perception at a focus position where the contrast for the 30 CPD spatial frequency is the highest. For example, the spectacle wearer's preferences regarding visual perception can be ascertained by outputting images such as those illustrated in
Upon ascertaining the spectacle wearer's preferences regarding visual perception, the degree of spherical power to be added to the power of the spectacle lens is determined for the spectacle lens that the spectacle wearer is to wear (S12). Specifically, weighting amounts to be applied to the Zernike coefficients cj of the respective terms in the weighted sum evaluation of Zernike polynomials relating to the surface shape of the spectacle lens wavefront are determined based on the ascertained results of the spectacle wearer's preferences regarding visual perception. By determining the weighting amounts to be applied to the Zernike coefficients cj, the spectacle wearer's preferences regarding visual perception are reflected in the surface shape specified by the Zernike polynomials.
Then, once the weighting amounts to be applied to the Zernike coefficients cj have been determined, the results of the determination are stored in the memory for later use (S13). Specifically, the matrix M obtained by determining the weighting amounts to be applied to the Zernike coefficients cj is calculated in advance and stored in a predetermined storage area in the memory. Thus, the matrix M having a size of (the number of local data items×the number of components) can be read from the memory and reused.
Note that multiple types of the matrix M having different weighting amounts may be stored in the memory.
The repetitive processing (S20) is performed after the aforementioned preprocessing (S10) is complete. In the repetitive processing (S20), first, the wavefront of the evaluation-target spectacle lens is specified (S21). The method to be adopted for wavefront specification is not particularly limited, and wavefront specification can be performed through simulation processing in which a wave-optical calculation is used, for example.
Following the specification of the wavefront of the evaluation-target spectacle lens, Zernike expansion is performed with respect to the specified wavefront of the spectacle lens (S22).
Specifically, first, the matrix M for solving local Zernike expansions is read from the memory. The matrix M corresponds to a pseudo-inverse matrix for integrating the number of terms of Zernike polynomials into one. Thus, reading and reusing the matrix M here makes it unnecessary to consider each Zernike polynomial term.
Once the matrix M has been read, Fourier transform is performed on the specified wavefront of the spectacle lens, and Fourier transform is performed on the read matrix M. Furthermore, in a Fourier space, the Fourier transform of the wavefront and the Fourier transform of the matrix M are multiplied, and inverse-Fourier transform is performed on the product, as shown in formula (5). Thus, a result equivalent to a result that would be obtained by convolution (see formula (4)) of the wavefront W and the matrix M, i.e., Zemike expansion results at all points of the evaluation-target spectacle lens, can be obtained. Here, because calculation processing in which a Fourier space is used is performed instead of actually performing convolution, calculation equivalent to loops of convolution can be completed through a single iteration of the calculation processing, and a significant reduction in the calculation amount can be realized compared to a case in which convolution is performed.
Subsequently, based on the Zemike expansion results, a power distribution of the evaluation-target spectacle lens in which the spectacle wearer's preferences are taken into consideration is evaluated (S23). Here, the Zemike expansion result for the spectacle lens wavefront is used as an evaluation index. That is, an amount obtained by multiplying the Fourier transform of the spectacle lens wavefront (i.e., a vector amount obtained by Fourier transform of a wavefront of a spectacle lens) by the Fourier transform of the matrix M, which is an example of the preset predetermined vector amount, or more specifically, an amount obtained by performing inverse-Fourier transform on the product, is used as an evaluation index.
Specifically, with respect to the evaluation-target spectacle lens, a determination is made as to whether or not the power distribution of the evaluation-target spectacle lens, which is one optical characteristic of the evaluation-target spectacle lens, is appropriate using the result obtained by the Zemike expansion as an evaluation index. It suffices to make the determination as to whether or not the power distribution is appropriate according to whether or not the power distribution matches a preset determination criterion. For example, the power distribution is determined as being appropriate if the power distribution matches the determination criterion, and the power distribution is determined as being inappropriate if the power distribution does not match the determination criterion. Because the result obtained by the Zemike expansion is used as an evaluation index with respect to the power distribution subjected to determination here, not only power but also aberration amount, object spatial frequency, etc., are taken into consideration in the focus position (image forming position) of the spectacle lens. Accordingly, the spectacle wearer's preferences regarding visual perception are reflected in the determination result, and the evaluation of the spectacle lens can thus be optimized.
Note that, if lens evaluation is to be newly performed for a spectacle lens having a different surface shape, it suffices to perform the above-described repetitive processing (S20) again.
In the present embodiment, lens evaluation of a spectacle lens is performed through the above-described steps. That is, it can be said that the lens evaluation method according to the present embodiment is a “lens evaluation method in which an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount is adopted as an evaluation index of the spectacle lens”.
Furthermore, as already mentioned above, the steps of the lens evaluation method according to the present embodiment are executed using a computer device. In this case, the predetermined program for causing the computer device to execute the steps of the lens evaluation method may be provided in a state in which the program is stored in a recording medium (for example, a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, or the like) that can be read by the computer device, or may be provided from the outside via a network such as the Internet or a dedicated line, as long as the program can be installed to the computer device. It can be said that the predetermined program installed to the computer device in such a manner is a “lens evaluation program that causes a computer to execute a step for adopting an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount as an evaluation index of the spectacle lens”.
The lens evaluation method involving the above-described steps can be applied to a spectacle lens designing method. In other words, a spectacle lens may be designed using the evaluation index determined through the above-described steps. This allows a spectacle lens in which the spectacle wearer's preferences regarding visual perception are reflected to be designed. That is, in the present embodiment, a spectacle lens may be designed using a “lens designing method including: a step for determining an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount as an evaluation index of the spectacle lens; and a step for designing a spectacle lens using the evaluation index”.
According to such a lens designing method, processing such as that described below can be realized. For example, assume Zernike coefficient and the matrix for the spherical aberration term of Zernike polynomials are CSA and MSA, respectively, and assume Zernike coefficient and the matrix for the defocus term of Zernike polynomials are Cdefocus and Mdefocus, respectively (see
Furthermore, the lens evaluation method involving the above-described steps can be applied to a spectacle lens production method. In other words, in the production of a spectacle lens, determination as to whether or not an optical characteristic of the spectacle lens is appropriate may be performed using the evaluation index determined through the above-described steps. This enables production of a spectacle lens in which the spectacle wearer's preferences regarding visual perception are reflected. That is, in the present embodiment, a spectacle lens may be produced using a “spectacle lens production method including: a step for determining an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount as an evaluation index of the spectacle lens; and a step for judging whether an optical characteristic of the spectacle lens is appropriate or not using the evaluation index”.
According to the present embodiment, one or more of the effects described below can be obtained.
In the present embodiment, an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount is adopted as an evaluation index of the spectacle lens. Furthermore, a result obtained by Zemike expansion is used as the evaluation index. Thus, in the evaluation using the evaluation index, not only power but also aberration amount, object spatial frequency, etc., are taken into consideration for the focus position (image forming position) of the spectacle lens. Accordingly, the spectacle wearer's preferences regarding visual perception are reflected in the evaluation of a spectacle lens in the present embodiment, and the evaluation of the spectacle lens can thus be optimized.
Moreover, in the present embodiment, an amount obtained by multiplying a vector amount obtained by Fourier transform of a wavefront of a spectacle lens by a preset predetermined vector amount is determined when Zemike expansion is performed. Furthermore, a Fourier transform of a pseudo-inverse matrix is used as the predetermined vector amount. That is, calculation processing in which a Fourier space is used is performed instead of actually performing convolution. Accordingly, a significant reduction in the calculation amount can be realized, and an increase in the calculation load for the evaluation can thus be suppressed. If a large calculation load is not required, neither are a long processing time, high-performance hardware resources, etc., which is highly favorable for quick and easy spectacle lens evaluation.
As described above, according to the present embodiment, spectacle lens evaluation can be optimized while realizing quick and easy processing.
An embodiment of the present invention has been described above. However, the content disclosed above indicates an example embodiment of the present invention. That is, the technical scope of the present invention is not limited to the example embodiment described above, and various modifications can be made within the spirit and scope of the present invention.
In the above-described embodiment, the Fourier transform of the matrix M is described as an example of a predetermined vector amount by which a vector amount obtained by Fourier transform of a wavefront of a spectacle lens is multiplied. However, the predetermined vector amount may be a vector amount as described below. For example, the predetermined vector amount may be a Fourier transform of a pseudo-inverse matrix that is for obtaining, for a local evaluation region of a spectacle lens, expansion coefficients for predetermined terms of predetermined polynomials. Furthermore, for example, the vector amount may be a Fourier transform of a pseudo-inverse matrix that is for obtaining, for a local evaluation region of a spectacle lens, expansion coefficients for predetermined terms of predetermined orthogonal functions. For example, polynomials that are orthogonal in a weighted circular region in which the Stiles-Crawford effect is taken into consideration may be used.
Furthermore, for example, the predetermined terms of the above-described polynomials or orthogonal polynomials may be predetermined terms of Zernike polynomials, or may be a weighted sum of a plurality of predetermined terms of Zernike polynomials.
Furthermore, for example, in regard to the expansion coefficients in the above-described polynomials or orthogonal polynomials, 1 may be applied as a weight to each rotationally symmetric component (see
Furthermore, for example, the expansion coefficients in the above-described polynomials or orthogonal polynomials may be applied to the evaluation of astigmatic power. By applying 1 as the weight for each 2nd-order symmetric component, the deviation of the defocus position can be calculated using a cross-section based on the position with the smallest PSF. However, weights for components that do not have significant amounts may be omitted.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2020-051102 | Mar 2020 | JP | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/JP2021/000681 | 1/12/2021 | WO |
