Method for calculating curvature of optical element in any range, device for calculating curvature of optical element in any range, and recording medium

Abstract

This invention provides a method for calculating the curvature of an optical element within an arbitrary range, comprising: step (a), obtaining a row vector s with an element count n representing the local curvature distribution within an arbitrary range of the optical element; and step (b), when the average spherical degree within a specified beam range within the arbitrary range is set as the macroscopic curvature c, using c≈ws T The approximation holds for the weighted vector w, which does not use wavefront information of any arbitrary range to calculate the macroscopic curvature c.

Description

Technical Field

[0001] This invention relates to a method for calculating the curvature of an optical element within any range, a device for calculating the curvature of an optical element within any range, and a recording medium. Background Technology

[0002] For the evaluation of optical components such as lenses, there are surface measurements and transmission measurements. The former is useful for understanding the quality of the front and back surfaces, while the latter is useful for managing the quality of the lens. A representative method of transmission measurement is wavefront measurement using interferometers, etc. Wavefront measurement can directly obtain wavefront information including higher-order aberrations, but it is only applicable to lenses that are close to aberration-free. As a method that can be applied to lenses with large aberrations, there is degree distribution measurement, which involves passing a large number of tiny beams through and detecting the curvature of the wavefront of these tiny beams. The disadvantage of degree distribution measurement is that it can only obtain wavefront information in the form of a local curvature distribution.

[0003] In the case of spectacle lenses or contact lenses, if viewed as a whole, such lenses are structures that intentionally incorporate aberrations, such as astigmatism correction and added power. Furthermore, if viewed from the perspective of a beam unit with a diameter of approximately 4 mm passing through the pupil, the aberrations of interest are quantities directly corresponding to the wavefront curvature, such as spherical power error and astigmatism. Therefore, power distribution measurement is widely used. For example, the device described in Patent Document 1 measures the local power of each tiny beam with a diameter of 0.5 mm.

[0004] Existing technical documents

[0005] Patent documents

[0006] Patent document 1: Japanese Patent Application Publication No. 2004-205438. Summary of the Invention

[0007] The problem the invention aims to solve

[0008] However, eyeglass lenses (or contact lenses) that have emerged in recent years and have the effect of inhibiting the development of myopia are systems in which the areas that impart the prescription power and the areas that impart defocus are discretely distributed even when viewed within the range of a beam of light with a diameter of about 4 mm passing through the pupil, and contain ultra-high-order aberrations. Therefore, power distribution measurements may not be able to obtain sufficient information.

[0009] In optical elements, the location where the focus of each beam can form can be determined from the radius of curvature when approximating the wavefront of the beam's range (hereinafter referred to as the macroscopic wavefront) as a spherical surface. The refractive power (mean spherical power for ophthalmic lenses), which is the reciprocal of the focal length, can also be determined from the curvature. Hereinafter, the curvature corresponding to the macroscopic wavefront will be referred to as "macroscopic curvature." Furthermore, the approximation error corresponds to the degree of decrease in the peak intensity of the light spot. On the other hand, the location and pattern of caustic lines can be determined from the local curvature distribution of the wavefront. Power distribution measurement is equivalent to measuring the local curvature distribution of the wavefront; since the wavefront cannot be reproduced from its local curvature distribution, it can be said that it is unsuitable for obtaining information related to the focus (macroscopic curvature, etc.).

[0010] One embodiment of the present invention aims to provide a technique for calculating macroscopic curvature from local curvature distribution.

[0011] Technical solutions for solving technical problems

[0012] The first aspect of the present invention is a method for calculating the curvature of an optical element within an arbitrary range, comprising: step (a), obtaining a row vector s representing the local curvature distribution with an element count n within an arbitrary range of the optical element; and step (b), when the average spherical degree within a specified beam range within the aforementioned arbitrary range is set as the macroscopic curvature c, using c≈ws T The weighted vector w, for which the approximation holds, is used to calculate the macroscopic curvature c without using wavefront information within the aforementioned arbitrary range.

[0013] The second aspect of the present invention is a method for calculating the curvature of an optical element within any range according to the first aspect described above, wherein the sum of the elements of the weighted vector w is 1, and the cross section passing through the center of the two-dimensional graph of the weighted vector w has an upwardly convex shape.

[0014] The third aspect of the present invention is, according to the method for calculating the curvature of an optical element within an arbitrary range as described in the first aspect above, wherein, in step (b) above, the unknown wavefront aberration distribution within the arbitrary range is set as a row vector z with n elements, and c = mz T Let m be the row vector used to calculate the macroscopic curvature c from the aforementioned wavefront aberration distribution, and let m be the measuring device used to obtain the aforementioned local curvature distribution. T =Lz T The linear system of operations, according to wLL T =mL T The relational formula is used to calculate the weighted vector w mentioned above.

[0015] The fourth aspect of the present invention is, according to the method for calculating the curvature of an optical element within an arbitrary range as described in the first aspect above, wherein, in step (b) above, the weighted vector w is represented by a rotationally symmetric polynomial with k degrees of freedom, the unknown wavefront aberration distribution within the arbitrary range is set as a row vector z with n elements, and c = mz T Let m be the row vector used to calculate the macroscopic curvature c from the aforementioned wavefront aberration distribution, and let m be the measuring device used to obtain the aforementioned local curvature distribution. T =Lz T The linear system of operation defines the calculation range as the range after the diameter of the aforementioned beam range is reduced by the value of the tiny beam diameter φ1 when calculating the local curvature. The values ​​within the calculation range are composed of values ​​determined by the position coordinates of the p-th order rotational symmetry function at each measurement point; values ​​outside the calculation range are 0; and the row vector f has n elements and a sum of all elements of 0. p Let F be the matrix obtained by arranging k degrees of freedom vertically. Let a be the row vector a of the number of elements k of the rotationally symmetric polynomial. Let e ​​be the row vector of the number of elements n with values ​​of 1 within the calculation range and 0 outside the calculation range. Let a0 be the reciprocal of the number of measurement points included in the calculation range. T =(m-a0eL)(FL) T The relational formula is used to calculate the weighted vector w mentioned above.

[0016] The fifth aspect of the present invention is a method for calculating the curvature of an optical element within an arbitrary range, according to the fourth aspect described above, wherein, in step (b) above, when the generalized inverse matrix for calculating the local curvature at a location for z is set to l, the curvature is calculated using the two-dimensionalized f... p Compared to l after it has been 2Dized 2d The convolution operation computes FL without explicitly constructing L.

[0017] The sixth aspect of the present invention is a method for calculating the curvature of an optical element within any range according to the fourth aspect described above, wherein the weighting vector w is represented by a rotationally symmetric polynomial of an odd degree.

[0018] The seventh aspect of the present invention is a method for calculating the curvature of an optical element within an arbitrary range according to the first aspect described above, wherein the optical element has a periodic microstructure, and in step (b) above, the center position O of the beam range is set... i Within the periodic range of the aforementioned microstructure, the aforementioned center position O is varied. i The corresponding weighted vector w iThe average macroscopic curvature c' is calculated by summing the weighted vector w' obtained by aggregating the periodicity of the above microstructures.

[0019] The eighth aspect of the present invention is a method for calculating the curvature of an optical element within any range according to the first aspect described above, wherein, in step (a) above, the number of elements n of the row vector s is set to 10000 or more.

[0020] The ninth aspect of the present invention is a method for calculating the curvature of an optical element within any range according to the fourth aspect described above, wherein, in step (b) above, the degree of freedom k of the weighting vector w is set to 1 or more and 20 or less.

[0021] The tenth aspect of the present invention is a method for calculating the curvature of an optical element within any range according to the first aspect described above, wherein, in step (a) above, the diameter φ1 of the small beam when calculating the local curvature is set to 0.7 times or less than the diameter φ2 of the macroscopic curvature c.

[0022] The eleventh aspect of the present invention is a curvature calculation device for an optical element within an arbitrary range, comprising: a measurement unit that measures a local curvature distribution with a data quantity of n within an arbitrary range of the optical element; and a calculation unit that, when the local curvature distribution is set as a row vector s with an element quantity of n, and the average spherical measure within a specified beam range within the arbitrary range is set as the macroscopic curvature c, uses c≈ws T The weighted vector w, for which the approximation holds, is used to calculate the macroscopic curvature c without using wavefront information within the aforementioned specified range.

[0023] The twelfth aspect of the present invention is a curvature calculation device for an optical element of any range according to the eleventh aspect described above, wherein it further comprises: a recording unit that records the pre-calculated weighted vector w or polynomial coefficients for representing the weighted vector w, and the calculation unit calculates the macroscopic curvature c based on the recorded weighted vector w and the measured local curvature distribution.

[0024] The thirteenth aspect of the present invention is a computer-readable recording medium containing a program that causes a computer to execute the curvature calculation method described in any one of the first to tenth aspects.

[0025] Invention Effects

[0026] According to one embodiment of the present invention, macroscopic curvature can be calculated from local curvature distribution. Attached Figure Description

[0027] Figure 1 This is a diagram illustrating an example of the wavefront and local curvature distribution of a spectacle lens that has the effect of inhibiting the progression of myopia.

[0028] Figure 2 It is Figure 1 The local curvature distribution shown is plotted as a histogram.

[0029] Figure 3 This is a diagram illustrating an example of the wavefront and local curvature distribution of a contact lens that has the effect of inhibiting myopia progression.

[0030] Figure 4 It is Figure 3 The local curvature distribution shown is plotted as a histogram.

[0031] Figure 5 This diagram illustrates the case where only the wavefront gradient of the outer periphery of the beam is processed, while the wavefront inside the beam is completely ignored.

[0032] Figure 6 This is a diagram showing the case where the wavefront of the outer periphery of the beam has a gradient.

[0033] Figure 7 This is a diagram representing the filter used to calculate the local curvature distribution.

[0034] Figure 8 This is a diagram representing a specific example of a weighted vector.

[0035] Figure 9 This is a diagram illustrating an example of the wavefront of a spectacle lens that has the effect of inhibiting the progression of myopia.

[0036] Figure 10 This is a diagram showing the results of calculating the macroscopic curvature while changing the center of the beam.

[0037] Figure 11 It is a graph representing the local curvature distribution and composite weighted vector of eyeglass lenses that have the effect of inhibiting the development of myopia.

[0038] Figure 12 It represents the contour of the weighted function a.

[0039] Figure 13 This is a diagram illustrating an example of the weighted vector w oscillating in the periphery.

[0040] Figure 14 This is a diagram showing the wavefront and local curvature distribution of samples 1 to 7 involved in the embodiments of the present invention.

[0041] Figure 15 This is a graph showing the calculation results of the macroscopic curvature involved in the embodiments of the present invention. Detailed Implementation

[0042] <Insights gained by the inventor>

[0043] First, let's explain the inventor's insights. Measuring the degree distribution is equivalent to measuring the local curvature distribution of a wavefront, making it difficult to accurately determine the macroscopic curvature of the wavefront. Therefore, statistical values ​​of the local curvature distribution are often used as substitutes. One such method is the arithmetic mean of the local curvature distribution. This seems reasonable at first glance, considering that the local curvature is constant in the case of a perfect sphere. Furthermore, as another method, the arithmetic mean of only the most frequent data is used. This can be considered an improvement to reduce the influence of outliers in the aforementioned methods. However, the following examples demonstrate that these methods are not appropriate.

[0044] Figure 1 This diagram illustrates an example of the wavefront and local curvature distribution of a spectacle lens that has the effect of inhibiting myopia progression. For further details regarding spectacle lenses that have the effect of inhibiting myopia progression, please refer, for example, to U.S. Patent Application Publication No. 2017 / 0131567. Here, an example is shown where convex regions (defocus regions) with a defocus power of +4D and a diameter of 0.8mm are provided at 1.2mm intervals on a surface with a prescription power of 0D. Figure 1 The drawing in the upper left corner of the paper represents the wavefront, while the curve in the upper right corner is a cross-sectional view of the wavefront in the x-direction (lateral direction) passing through the center. Furthermore, Figure 1 The drawing at the lower left of the paper represents the local curvature distribution (the local curvature is calculated with a diameter φ1 = 0.5 mm), and the curve at the lower right of the paper is a cross-sectional view of the local curvature in the x-direction (lateral direction) passing through the center.

[0045] exist Figure 1 In the example shown, the average spherical degree within the range of beam diameter φ2=4mm is set as the macroscopic curvature c. The macroscopic curvature c is obtained from the wavefront and the result is -0.01D. Figure 2 It is Figure 1 The local curvature distribution is shown as a histogram. The arithmetic mean of this histogram is -0.2D, while the average value using only the high-frequency data is -1.8D. Therefore, there is a deviation between the average value calculated from the local curvature distribution and the macroscopic curvature c obtained from the wavefront, especially the deviation is relatively large when using only the average value of the high-frequency data.

[0046] Figure 3 This diagram illustrates an example of the wavefront and local curvature distribution of a contact lens that has the effect of inhibiting myopia progression. Here, an example is shown where, in a lens with a prescription power (average power at a beam diameter φ2 = 4 mm) of 0D, the local power at a distance of 1.25 mm from the lens center is set to produce +3D defocus relative to the lens center power. Figure 3 The drawing in the upper left corner of the paper represents the wavefront, while the curve in the upper right corner is a cross-sectional view of the wavefront in the x-direction (lateral direction) passing through the center. Furthermore, Figure 3The drawing at the lower left of the paper represents the local curvature distribution (the local curvature is calculated with a diameter φ1 = 0.5 mm), and the curve at the lower right of the paper is a cross-sectional view of the local curvature in the x-direction (lateral direction) passing through the center.

[0047] exist Figure 3 In the example shown, the macroscopic curvature c obtained from the wavefront within the range of beam diameter φ2=4mm is 0D. Figure 4 It is Figure 3 The local curvature distribution is shown as a histogram. The arithmetic mean of this histogram is +0.4D, while the average value using only the high-frequency data is +1.0D. Therefore, there is a deviation between the average value calculated from the local curvature distribution and the macroscopic curvature c obtained from the wavefront, especially the deviation is relatively large when using only the average value of the high-frequency data.

[0048] Next, we also investigate the case where the local curvature distribution is given as a continuous function. We define the unknown wavefront at coordinates (x, y) on the lens as w(x, y). Hereinafter, coordinates (x, y) are assumed to be continuous values, the local curvature calculation diameter is sufficiently small, and the local curvature s(x, y) is expressed as the second derivative of the wavefront, as shown in the following equation.

[0049] [Formula 1]

[0050]

[0051] Here, we assume that the macroscopic curvature c is obtained by simply averaging the local curvatures. The average local curvature s (underlined) of a beam with diameter φ and radius u (equivalent to the pupil diameter) is represented by the following formula.

[0052] [Formula 2]

[0053]

[0054] According to Green's theorem, the surface integral of the second differential of x above is replaced by a line integral. The same applies to the second differential of y. Therefore, the average value s of the local curvature (underlined) is expressed by the following equation.

[0055] [Formula 3]

[0056]

[0057] From the integral range of the above equations, it can be seen that the average local curvature s (underlined) is determined only by the wavefront gradient of the outer periphery of the beam. Therefore, as Figure 5 As shown, only the wavefront gradient of the outer periphery of the beam is processed, while the wavefront inside the beam is completely ignored. Therefore, when the outer periphery of the beam has discontinuities or near-discontinuities, the value of the macroscopic curvature c will vary significantly. For example, as... Figure 6As shown, in the case where the lens has spherical aberration ( Figure 6 (on the left side of the paper) or in the case where there are discontinuities in the beam ( Figure 6 When the wavefront of the outer periphery of the beam has a gradient (as shown on the right side of the paper), simply averaging the local curvature may over-evaluate the degree.

[0058] The inventors conducted in-depth research into problems such as those described above. As a result, they discovered a new method for calculating the macroscopic curvature *c* from the local curvature distribution, even when the wavefront information is unknown. This invention is particularly useful for calculating macroscopic curvatures that approximate the values ​​obtained from the wavefront, even for lenses with large aberrations, such as spectacle lenses designed to inhibit myopia progression.

[0059] [Details of embodiments of the present invention]

[0060] Next, refer to the appendix below. Figure 1 One embodiment of the invention will be described below. Furthermore, the invention is not limited to these examples, but is shown by way of the scope of the patent claims, and is intended to include the meaning equivalent to the scope of the patent claims and all modifications within that scope.

[0061] <First Embodiment of the Invention>

[0062] (1) Method for calculating the curvature of optical elements in any range

[0063] The method for calculating the curvature of an optical element within an arbitrary range according to this embodiment will be described. The method for calculating the curvature of an optical element within an arbitrary range according to this embodiment includes, for example, a local curvature distribution acquisition step S100 and a macroscopic curvature calculation step S200. In this embodiment, the case where the average spherical power, i.e., the macroscopic curvature c, of a specified beam range (e.g., beam diameter φ2 = 4 mm) within an arbitrary range of an optical element such as a lens is described without using wavefront information when the wavefront information is unknown.

[0064] (Step S100 for obtaining local curvature distribution)

[0065] The step S100 for obtaining the local curvature distribution is, for example, obtaining a row vector s with n elements representing the local curvature distribution within an arbitrary range of the optical element. The row vector s is a vector formed by rearranging the local curvature distribution on the surface in a one-dimensional form. The data of the local curvature distribution can be measured using a degree distribution measuring device or by using pre-prepared data. In this embodiment, the data of the local curvature distribution is set as a row vector x = (x1, x2...x...) with n elements, obtained by arranging the (x, y) coordinates of the measurement position within an arbitrary range of the optical element and the values ​​of n degrees (local curvature) in a column. n ), y = (y1, y2...y n ), s = (s1, s2...s n Composed of ) . In this specification, unless otherwise specified, vectors refer to row vectors.

[0066] In the step S100 of obtaining the local curvature distribution, it is preferable to set the number of elements n of s to 10000 or more. This allows for the calculation of a more accurate macroscopic curvature c.

[0067] In the step S100 of obtaining the local curvature distribution, it is preferable to set the small beam diameter φ1 used to calculate the local curvature to be less than 0.7 times the beam diameter φ2 of the macroscopic curvature c. This allows for a more accurate calculation of the macroscopic curvature c.

[0068] Before explaining the method for calculating the macroscopic curvature c from the local curvature distribution, we will explain the method for calculating the macroscopic curvature c when the wavefront information (e.g., a quantified wavefront or wavefront aberration distribution) within an arbitrary range of the optical element is known. Let the row vector representing the number of elements n of the wavefront aberration distribution within an arbitrary range of the optical element be z = (z1, z2...z...). n Furthermore, c = mz T Let m be the row vector used to calculate the macroscopic curvature c from the wavefront aberration distribution, where the relation holds. m is equivalent to, for example, the generalized inverse matrix based on the least squares spherical approximation (which is actually a row vector since it is a 1×n matrix), or the result of vectorizing the Defocus term of the normalized Zernike polynomial. Therefore, given the wavefront aberration distribution, the macroscopic curvature c can be easily calculated from z.

[0069] Furthermore, the method of constructing m is explained in more detail. Assume the center coordinates of the beam are o = (o... x o y If the beam radius is R, then the elements of the vector u with the number of elements n are represented by the following formula, where 1 represents the case where the measurement point is included within the beam range and 0 represents the case where the measurement point is not included within the beam range.

[0070] [Formula 4]

[0071]

[0072] Furthermore, the elements of a vector q with the number of elements n, which is a quadratic function within the beam range and zero outside the beam range, are represented by the following formula when using u.

[0073] [Formula 5]

[0074]

[0075] m can be constructed by orthogonalizing and normalizing q. Orthogonalization refers to the operation used to make the result of the calculation of the macroscopic curvature c independent of the constant term (0th degree term) or tilt term (1st degree term) of the entire wavefront. For example, the vector q' with n elements obtained by orthogonalizing q with the 0th degree term is represented by the following formula. In addition, in the case of quadratic functions, it is mostly automatically orthogonal with the tilt term, but orthogonalization can also be performed as needed.

[0076] [Formula 6]

[0077]

[0078] Furthermore, normalization refers to the operation of dividing by the scalar that is the denominator of c. Therefore, m is represented by the following formula when using q'.

[0079] [Formula 7]

[0080]

[0081] (Macro curvature calculation step S200)

[0082] The macroscopic curvature calculation step S200 is, for example, a step to calculate the macroscopic curvature c without using wavefront information when the wavefront information for any range of the optical element is unknown. Hereinafter, a method for calculating the macroscopic curvature c solely from s, which represents the local curvature distribution, without using z, which represents the wavefront aberration distribution.

[0083] The inventor discovered the use of c≈ws T The method for calculating the macroscopic curvature c is to use the row vector w (hereinafter referred to as the weighted vector w) that holds the approximation. That is, it can be said that the macroscopic curvature c is obtained by weighting the weighted vector w over the local curvature distribution s.

[0084] The sum of the elements of the weighted vector w is preferably 1. This is because, for example, in the case of a perfect spherical wave (constant curvature), the local curvature of all measurement points is equal to c. Furthermore, from the viewpoint of assigning higher weights closer to the center, the cross-section at the center of the two-dimensional plot of the weighted vector w is preferably convex, and more preferably, it takes a maximum value at the center. Moreover, the two-dimensional plot referred to here is a plot in which row vectors are rearranged according to two-dimensional coordinates representing positions on the surface.

[0085] The method for calculating the weighted vector w is explained in more detail below. This method allows for a more appropriate weighted vector w, thus enabling a more accurate calculation of the macroscopic curvature c.

[0086] (Method 1)

[0087] A measuring device for obtaining a local curvature distribution (degree distribution measuring device) can be considered as a linear system that outputs the wavefront aberration distribution (unknown to the measurer) imparted to the beam by optical elements as a local curvature distribution. That is, if an n×n matrix L is introduced, the degree distribution measuring device can be considered as performing s... T =Lz T Linear systems of operations.

[0088] More specifically, the local curvature distribution can be considered as a local quadratic approximation of the wavefront aberration distribution at various locations. For example, suppose the degree s at a certain location... i It is determined by the center coordinates o of the tiny beam of light i =(o ix o iy ), the radius of the tiny beam r i The matrix is ​​obtained by approximating the wavefront with a quadratic function. Then, following the same method as when constructing m, a generalized inverse matrix (actually a row vector) l can be constructed for the spherical approximation at that location. That is, l can be considered the generalized inverse matrix for calculating the local curvature of z at a given location. By preparing n matrices for all locations, an n×n matrix L can be constructed.

[0089] In reality, in most cases, the radius r of the tiny beam is... i For constant values, each location represents the center coordinate o of the tiny beam. i =(o ix o iy In this case, the generalized inverse matrix l is taken as... Figure 7 The filter l shown is formed by arranging row vectors of number n elements in two dimensions. 2d By l 2d z, which is formed by rearranging z in two dimensions 2d Perform convolution to obtain s. Figure 7The drawing on the left side of the paper is l 2d The two-dimensional diagram, the drawing on the right side of the paper is obtained through l 2d The drawing is of the cross-section at the center. However, at points where a second approximation is made across the ends of the measurement area, the local curvature will become an incorrect value, so care must be taken.

[0090] Furthermore, when using a degree distribution measuring device, if the small beam is not circular (e.g., rectangular), it is sufficient to construct l and L according to the given conditions. Moreover, if the degree distribution measuring device does not employ a quadratic function approximation (e.g., a device structure where measured values ​​are obtained internally as local gradients in each direction of the wavefront, and a degree distribution map is derived from their differences), it is sufficient to use l and L to represent the operation of obtaining the difference between two points using a linear function approximation. Hereinafter, the range of values ​​for l will be treated as the range of the small beam.

[0091] As described above, by considering the degree distribution measurement device as performing s T =Lz T For a linear system of operations, the relationship m = wL can be obtained. However, since the relationship s is calculated from a point z within a small beam range (e.g., a small beam diameter φ1 = 0.5 mm), the number of points in s is less than the number of measurement points in z. Therefore, it is impossible to solve the numerical expression m = wL, and it actually becomes a matter of finding an approximate solution that minimizes the absolute value of |wL - m|. Therefore, it is only necessary to calculate the expression satisfying wL using the Lagrange indeterminate multiplier method. T =mL T The relation w is sufficient.

[0092] By calculating the weighted vector w using method 1, the macroscopic curvature c can be accurately calculated from s, which represents the local curvature distribution. Since LL... T Since it is an n×n matrix, the computational complexity of method 1 is O(n×n). 6 Approximately 10000. Specifically, assuming n = 10000, the computational complexity of Method 1 is very large, approximately O(10^25). 24 Approximately 100,000,000 elements in the recording medium. Furthermore, storing and accessing a matrix L with 100,000,000 elements in the recording medium would also be a burden.

[0093] (Method 2)

[0094] Method 2 reduces the computational cost by representing the weighted vector w as a rotationally symmetric polynomial with k degrees of freedom. The degrees of freedom k correspond to the number of independent coefficients in the polynomial, preferably 1 or more and 20 or less, more preferably 2 or more and 10 or less. This allows for accurate calculation of the macroscopic curvature c while reducing computational cost.

[0095] Here, when measuring local curvature at the outer periphery of the beam range, to avoid including information outside the beam range due to a portion of the small beam range extending beyond the beam range, the range for determining the degree (local curvature) based solely on information about the beam range on the optical element is called the calculation range. That is, the calculation range refers to the range after reducing the diameter of the beam range by the value of the small beam diameter φ1 used in calculating the local curvature; its diameter is φ2 - φ1. Then, the following row vector f... p Let F be the matrix obtained by arranging k degrees of freedom vertically, that is, the row vector f p The values ​​within the computational range are determined by the coordinates of the p-th order rotationally symmetric function at each measurement point. Values ​​outside the computational range are 0, and the sum of all elements is 0 (n elements). Furthermore, the coefficient vector of the rotationally symmetric polynomial is set as a row vector a with k elements, the row vector e with n elements (1 within the computational range and 0 outside the range) is set as e, and the reciprocal of the number of measurement points included in the computational range (i.e., the number of elements with a value of 1 in row vector e) is set as a0. Furthermore, the relationship m = wL = (aF + a0e)L is obtained. That is, the approximate solution that minimizes the absolute value of |(aF + a0e)L - m| is found. Therefore, by using the Lagrange indeterminate multiplier method, according to a(FL)(FL)... T =(m-a0eL)(FL) T The relational expression can be used to calculate w.

[0096] By calculating the weighted vector w using Method 2, the macroscopic curvature c can be accurately calculated from s, which represents the local curvature distribution. Furthermore, since FL is a multiplication operation between k×n and n×n matrices, the computational complexity of Method 2 is O(kn×n). 2 This reduces the computational load by approximately 10^25 kJ / k. Specifically, assuming n = 10000 and k = 10, the computational load of method 2 is O(10^25 kJ / k). 9 It reduces the computational load by approximately 100%, compared to method 1.

[0097] In method 2, to reduce the cost of storing L in the recording medium, it is preferable to not explicitly construct L. Specifically, it is preferable to construct L by modifying the two-dimensional f... p Compared to l after 2D transformation 2d The convolution operation is used to compute FL without explicitly constructing L. In the convolution operation, reducing the computational cost through Fourier transform is effective, thus reducing the computational cost to O(kn·logn). Furthermore, eL is also preferably computed via convolution.

[0098] In Method 2, it is preferable to represent the weighted vector w using a rotationally symmetric polynomial of odd degree. This further reduces the computational load.

[0099] As a specific example, the result of calculating the weighted vector w under the following conditions is shown: beam diameter φ2 = 4 mm, local curvature calculation diameter (micro-beam diameter) φ1 = 0.5 mm, measurement spacing 0.05 mm (400 measurement points in a 1 mm square area), and the weighted vector w being a polynomial with odd-order degrees of freedom k = 7 (2nd to 8th order). Figure 8 In the middle. The diameter of the range where w has values ​​other than 0 is 3.5 mm, obtained by subtracting φ1 from φ2. Figure 8 The left side of the paper shows a two-dimensional graph of the weighted vector w, and the right side shows a plot of the cross-section passing through the center. Furthermore, the values ​​of a0 to a8 are shown in the table below.

[0100] [Table 1]

[0101]

[0102] (Method 3)

[0103] Method 3 is an effective method when the optical element has a periodic microstructure (e.g., spectacle lenses that have the effect of inhibiting myopia progression). First, the problems with optical elements having a periodic microstructure are explained.

[0104] Figure 9 This diagram illustrates an example of the wavefront of a spectacle lens that has the effect of inhibiting myopia progression. Here, an example is shown where convex regions (defocus regions) with a defocus power of +4D and a diameter of 0.8mm are arranged at 1.2mm intervals on a surface with a prescription power of 0D. In this case, when the optical element has a periodic microstructure, a slight change in the measurement position (the center position of the beam) will cause a change (vibration) in the calculated macroscopic curvature c. For example, Figure 10 The diagram shows the beam center being moved from... Figure 9 The location O1 was changed to a location O2 shifted 1.03 mm upwards from the plane of the paper, and the macroscopic curvature c within the range of beam diameter φ2 = 6 mm was calculated. Furthermore, in Figure 10 In this context, the macroscopic curvature c is calculated from the wavefront. For example... Figure 10 As shown, the macroscopic curvature c oscillates with an amplitude of approximately 0.04D (changing mirror-symmetrically after a position of 1.03 mm). In degree distribution measurements, the effects of vibration are easily apparent due to the difficulty in aligning the measurement position. Therefore, a robust evaluation method that eliminates the effects of vibration is needed. Furthermore, the values ​​after eliminating the effects of vibration are also important for the quality management of such optical components.

[0105] To eliminate the effects of vibration, it is sufficient to repeatedly calculate and sum the macroscopic curvature within the periodic range of the microstructure (since the beams do not interact with each other, simple addition is possible). However, repeatedly calculating the macroscopic curvature increases the computational load. Therefore, it is preferable to center the beam range at position O. i It varies within the periodic range of the microstructure and is preparing to move the central position O. i The corresponding weighted vector w i The composite weighted vector w', obtained by summing within the periodic range of the microstructure, is used to calculate the average macroscopic curvature c' by taking the weighted sum of w' relative to s. Thus, the average macroscopic curvature c' can be calculated in a single operation.

[0106] Figure 11 Specific examples are shown. Figure 11 The left side of the paper shows a drawing illustrating the local curvature distribution of a spectacle lens that has the effect of inhibiting myopia progression. The area enclosed by the dashed lines shown in this drawing (0mm ≤ x ≤ 0.6mm, 0mm ≤ y ≤ 1.03mm) is defined as the periodic range, and the center positions O1...O of 400 points divided into 20 equal parts in the x and y directions are set. 400 The weighted vector w corresponding to each position is calculated using either method 1 or method 2 described above. i The weighted vector w is calculated using the following formula. i By summing the results, we can obtain the composite weighted vector w'. Figure 11 The right side of the paper shows a two-dimensional graph of the composite weighted vector w'.

[0107] [Formula 8]

[0108]

[0109] Using the composite weighted vector w', through c' = w's T The formula can be used to calculate the average macroscopic curvature c'. Using this method, even when optical elements have periodic microstructures, the average macroscopic curvature c', after eliminating the effects of vibration, can be easily calculated.

[0110] Furthermore, by applying this method, the magnitude of the vibration (the difference in macroscopic curvature) can be calculated. Moreover, it is not limited to the average or difference, but can be applied to all linear calculations, thus enabling the evaluation of the amplitude and period of the vibration of macroscopic curvature in the manner of discrete Fourier transform.

[0111] (Method 4)

[0112] Method 4 is a method for obtaining the weighted vector w from the continuous weighted function a when the local curvature distribution is given as a continuous function or when the amount of data in the local curvature distribution is very large. The following explains the method for solving the weighted function a.

[0113] Assuming macroscopic curvature s macro It is represented by a weighted average using a weighted function a(x, y) as shown in the following equation. Furthermore, s(x, y) is the local curvature distribution, w(x, y) is the unknown wavefront, and u represents the radius of the beam.

[0114] [Formula 9]

[0115]

[0116] The following section examines the conditions required for the weighting function a.

[0117] (Condition 1)

[0118] Since the weighting function 'a' is a function used to calculate the average, the first condition is that the sum is 1, as shown in the following formula.

[0119] [Formula 10]

[0120]

[0121] (Condition 2)

[0122] Assuming macroscopic curvature s macro The result is equal to that of the spherical approximation of the unknown wavefront w(x, y) (hereinafter replaced by the orthogonal quadratic function approximation), as shown in the following formula.

[0123] [Formula 11]

[0124]

[0125] If we calculate the denominator of the above expression, we get the following expression.

[0126] [Formula 12]

[0127]

[0128] Furthermore, assume that the integral of the product of the second derivative of the weighting function a and the wavefront w, as shown in the following equation, is equal to the integral of the product of the second derivative of the wavefront w and the weighting function a.

[0129] [Formula 13]

[0130]

[0131] From the two equations above, we can see that the second condition for the weighted function a is to satisfy the following equation.

[0132] [Formula 14]

[0133]

[0134] (Condition 3)

[0135] Integrating the integral of the product of the second derivative of the weighting function a and the wavefront w described in condition 2 with respect to x (the integration range is from x0 to x1), and then rearranging, we obtain the following equation.

[0136] [Formula 15]

[0137]

[0138] To make the above equation hold for all wavefronts w, the following equation only needs to be satisfied.

[0139] [Formula 16]

[0140]

[0141] The same applies to y, so when extended to two variables, the third condition for the weighting function a is that the value of a and the gradient are 0 on the circumference of the beam, as shown in the following equation.

[0142] [Formula 17]

[0143]

[0144] The weighting function 'a' that satisfies the above three conditions is expressed by the following formula. Furthermore, Figure 12 The profile of the weighted function a is shown.

[0145] [Formula 18]

[0146]

[0147] In this method, by using such a continuous weighting function 'a', the computational load can be reduced even when the amount of data, for example, is very large due to local curvature distribution.

[0148] Using the calculation method described above, even when the wavefront information is unknown within any range of the optical element, the macroscopic curvature c can be calculated from the local curvature distribution without using the wavefront information.

[0149] In addition, depending on the calculation conditions, such as Figure 13As shown, the weighting vector w sometimes oscillates at the periphery. This is likely to occur in situations where the beam range cannot be smoothly depicted due to discrete measurement data, resulting in a jagged shape; or where the degree of the polynomial in the weighting vector w is inappropriately chosen. When the weighting vector w oscillates, the calculation of the macroscopic curvature c easily becomes unstable. Therefore, in such cases, it is preferable to reduce the weight of the periphery of the beam range when creating the generalized inverse matrix m of the spherical approximation, or to use odd-degree polynomials, Gaussian functions, etc., instead of high-degree polynomials.

[0150] Furthermore, in the macroscopic curvature calculation step S200, the macroscopic curvature c can be calculated using a pre-calculated weighted vector w, for example. In this case, since it is not necessary to calculate the weighted vector w every time, the macroscopic curvature c can be calculated easily. Alternatively, multiple pre-calculated weighted vectors w can be prepared in advance, and an appropriate weighted vector w can be selected based on the measurement conditions.

[0151] (2) Curvature calculation device for optical elements in any range

[0152] This invention can also be applied as a curvature calculation device for optical elements within any range. The curvature calculation device for optical elements within any range according to this embodiment includes, for example, a measurement unit that measures the local curvature distribution of a data quantity n within any range of the optical element; and a calculation unit that, when the local curvature distribution is set as a row vector s with n elements, and the average spherical curvature within a specified beam range within the arbitrary range is set as the macroscopic curvature c, uses c≈ws. T The weighted vector w, for which the approximation holds, is used to calculate the macroscopic curvature c without using wavefront information when the wavefront information within a specified range is unknown. As the measurement unit, a known degree distribution measurement device can be used. The calculation of the macroscopic curvature c performed by the calculation unit is as described in (1) the method for calculating the curvature of an optical element within an arbitrary range.

[0153] The curvature calculation device for any range of optical elements in this embodiment may, for example, include a recording unit that records a pre-calculated weighted vector w or polynomial coefficients representing the weighted vector w. The calculation unit can then calculate the macroscopic curvature c based on the recorded weighted vector w and the measured local curvature distribution. In this case, since the calculation unit does not need to calculate the weighted vector w every time, the macroscopic curvature c can be calculated easily.

[0154] (3) Recording medium

[0155] Furthermore, the present invention can also be used as a computer-readable recording medium containing a program that enables a computer to execute the curvature calculation method described in (1) the curvature calculation method for any range of optical elements.

[0156] <Other embodiments of the present invention>

[0157] The above describes the specific implementation of the present invention, but the present invention is not limited to the above implementation and various modifications can be made without departing from its spirit.

[0158] For example, the above embodiments illustrate the case of calculating macroscopic curvature from local curvature distribution, but the present invention can also calculate macroscopic x-direction degree from local x-direction degree distribution or obtain macroscopic astigmatism from local astigmatism distribution by following the same steps.

[0159] Furthermore, while the above embodiment describes the calculation of the curvature of a circular region corresponding to the beam, it can also be applied to regions where a portion of a circle is missing or to regions with a rectangular shape. However, in this case, due to the reduced symmetry, the required parameters increase when using a polynomial of the weighted vector w in Method 2, or it may be necessary to optimize the weighted vector w without using a polynomial, thus increasing the computational load.

[0160] Furthermore, while the above embodiments illustrate the calculation of the weighted vector w (or the synthesis of the weighted vector w') using methods 1 to 4, the method for obtaining the weighted vector w is not limited to these methods. For example, it is also possible to directly calculate, such as c≈ws, through machine learning. T The approximation of w holds true.

[0161] Example

[0162] Next, embodiments of the present invention will be described. These embodiments are examples of the present invention, and the present invention is not limited to these embodiments.

[0163] In this embodiment, wavefront aberration distribution data for samples 1 to 7 were created, and the values ​​of macroscopic curvature obtained by the following calculation methods (calculation methods 1 to 4) were compared. The common calculation conditions were: beam diameter φ2 = 2 mm, local curvature calculation diameter (micro beam diameter) φ1 = 0.5 mm, and measurement spacing 0.005 mm (40,000 measurement points in a 1 mm square area).

[0164] Figure 14 The wavefronts (above the paper) and local curvature distributions (below the paper) of samples 1–7 are shown. Figure 14 In the middle, starting from the left side of the paper, they are arranged as Sample 1, Sample 2, etc. For example... Figure 14As shown, samples 1-7 are depicted as wavefronts undulating in a sinusoidal pattern, with corresponding degree distributions. The undulation period of sample 1 is set to 0.6 mm, sample 2 to 1.2 mm, sample 3 to 1.9 mm, sample 4 to 2.6 mm, sample 5 to 3.2 mm, sample 6 to 3.8 mm, and sample 7 to 4.5 mm. Furthermore, in samples 1-7, the amplitude was normalized by a local curvature of -2D within a small area at the center.

[0165] In calculation method 1, the macroscopic curvature is calculated using a spherical approximation of the wavefront aberration distribution. In calculation method 2, the macroscopic curvature is calculated by averaging the local curvatures within a range. In calculation method 3, the macroscopic curvature is calculated by averaging the top 5% of the most frequent local curvatures from a histogram within a range. In calculation method 4, the macroscopic curvature is calculated using method 2 as described in the above embodiments. In calculation method 4, the weighting vector w is set as a polynomial with an odd number of degrees of freedom, k = 7 (2nd to 8th degree). Furthermore, in methods other than calculation method 1, calculations are performed only when the local curvature distribution is known and the wavefront aberration distribution is unknown.

[0166] Figure 15 The results of calculating the macroscopic curvature of samples 1-7 using methods 1-4 are shown. Figure 15 As shown, the result of calculation method 4 using method 2 described in the above embodiment is basically consistent with the value of calculation method 1, which approximates the spherical surface as the wavefront. On the other hand, calculation method 2, which calculates the average value of local curvature, and calculation method 3, which calculates the average value of high-frequency values ​​of local curvature, deviate significantly from calculation method 1.

[0167] As can be confirmed from the above, by using an appropriate weighting vector w, macroscopic curvature can be accurately calculated without using wavefront information, even when the wavefront information is unknown.

[0168] Symbol Explanation

[0169] Steps for obtaining the local curvature distribution of S100;

[0170] S200 Macroscopic Curvature Calculation Steps.

Claims

1. A method for calculating the curvature of an optical element within an arbitrary range, comprising: Step (a) involves obtaining a row vector s with n elements representing the local curvature distribution within an arbitrary range of the optical element; and Step (b), when setting the average spherical degree within the specified beam range of the arbitrary range as the macroscopic curvature c, uses c≈ws T The weighted vector w, for which the approximation holds, is used to calculate the macroscopic curvature c without using wavefront information of the arbitrary range.

2. The method for calculating the curvature of an optical element within any range according to claim 1, wherein, The sum of the elements of the weighted vector w is 1, and the cross section passing through the center of the two-dimensional graph of the weighted vector w has an upward convex shape.

3. The method for calculating the curvature of an optical element within any range according to claim 1, wherein, In step (b), Let the unknown wavefront aberration distribution within the arbitrary range be a row vector z with n elements. c = mz T Let m be the row vector used to calculate the macroscopic curvature c from the aberration distribution of the wavefront, which holds the relationship. The measuring device used to obtain the local curvature distribution is considered as performing s T =Lz T Linear systems of operations, According to wLL T =mL T The weighted vector w is calculated using the relational formula.

4. The method for calculating the curvature of an optical element within any range according to claim 1, wherein, In step (b), The weighted vector w is represented by a rotationally symmetric polynomial with k degrees of freedom. Let the unknown wavefront aberration distribution within the arbitrary range be a row vector z with n elements. c = mz T Let m be the row vector used to calculate the macroscopic curvature c from the aberration distribution of the wavefront, which holds the relationship. The measuring device used to obtain the local curvature distribution is considered as performing s T =Lz T For a linear system operating on this system, the calculation range is defined as the range after the diameter of the beam range is reduced by the value of the tiny beam diameter φ1 used to calculate the local curvature. The values ​​within the calculation range are determined by the position coordinates of the p-th order rotational symmetry function at each measurement point; values ​​outside the calculation range are 0; and the row vector f has n elements and the sum of all elements is 0. p Let F be the matrix obtained by arranging k degrees of freedom vertically. Let the coefficient vector of the rotationally symmetric polynomial be a row vector a with the number of elements k. Let e ​​be the row vector containing n elements with a value of 1 within the calculation range and a value of 0 outside the calculation range. Let a0 be the reciprocal of the number of measurement points included in the calculation range. According to a(FL)(FL) T =(m−a0eL)(FL) T The weighted vector w is calculated using the relational formula.

5. The method for calculating the curvature of an optical element within any range according to claim 4, wherein, In step (b), When the generalized inverse matrix for calculating the local curvature of a location with respect to z is set to l, the result is obtained by the two-dimensionalized f. p Compared to l after it has been 2Dized 2d The convolution operation computes FL without explicitly constructing L.

6. The method for calculating the curvature of an optical element within any range according to claim 4, wherein, The weighted vector w is represented by a rotationally symmetric polynomial of odd degree.

7. The method for calculating the curvature of an optical element within any range according to claim 1, wherein, The optical element has a periodic microstructure. In step (b), the center position O of the beam range is set. i The variation within the periodic range of the microstructure is used to determine the center position O. i The corresponding weighted vector w i The average macroscopic curvature c' is calculated by summing the weighted vector w' obtained by aggregating the values ​​within the periodic range of the microstructure.

8. The method for calculating the curvature of an optical element within any range according to claim 1, wherein, In step (a), the number of elements n of the row vector s is set to 10000 or more.

9. The method for calculating the curvature of an optical element within any range according to claim 4, wherein, In step (b), the degree of freedom k of the weighted vector w is set to be greater than 1 and less than 20.

10. The method for calculating the curvature of an optical element within any range according to claim 1, wherein, In step (a), the small beam diameter φ1 when calculating the local curvature is set to less than 0.7 times the beam diameter φ2 of the macro curvature c.

11. A device for calculating the curvature of an optical element within an arbitrary range, comprising: The measuring unit measures the local curvature distribution of the data quantity n within an arbitrary range of the optical element; and The computing unit, when defining the local curvature distribution as a row vector s with n elements and the average spherical degree within the specified beam range in the arbitrary range as the macroscopic curvature c, uses c≈ws. T The weighted vector w, for which the approximation holds, is used to calculate the macroscopic curvature c without using wavefront information within the specified range.

12. The curvature calculation device for any range of optical elements according to claim 11, wherein, It also includes a recording unit that records the pre-calculated weighted vector w, or the polynomial coefficients used to represent the weighted vector w. The calculation unit calculates the macroscopic curvature c based on the recorded weighted vector w and the measured local curvature distribution.

13. A computer-readable recording medium having a program that causes a computer to perform a method for calculating the curvature of any range of an optical element according to any one of claims 1 to 10.

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