Method for acquiring wavefront aberration of human eye and human eye aberration measuring device

Abstract

The application discloses a method for obtaining human eye wavefront aberration and a human eye aberration measuring device, and relates to the technical field of optical instruments. The method for obtaining human eye wavefront aberration is applied to a Hartmann sensor and comprises the following steps: calculating an actual slope matrix according to a wavefront light spot diagram obtained by the Hartmann sensor; multiplying a generalized inverse matrix of a standard slope matrix with the actual slope matrix to obtain a Zernike coefficient matrix; subtracting the product of the actual slope matrix, the standard slope matrix and the Zernike coefficient matrix to obtain a residual error matrix; and updating the Zernike coefficient matrix according to the residual error matrix until the residual error matrix of the updated Zernike coefficient matrix is less than or equal to a preset value. The standard slope matrix is a matrix formed by the slope of a wavefront with all Zernike polynomial terms superimposed. The technical scheme provided by the application can improve the accuracy of the obtained human eye wavefront aberration.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical instruments, in particular to a method for obtaining wavefront aberration of human eyes and a human eye aberration measuring device. BACKGROUND

[0002] After the reflection of the fundus passes through the pupil, light with the image information of the fundus of the human eye is formed. If the light is collected and the wavefront information of the light is obtained, the aberration information of the human eye can be calculated through the wavefront information. Specifically, the wavefront can be expanded by using Zernike polynomials to obtain a coefficient matrix of the Zernike polynomials when the wavefront is expanded. The coefficients of the Zernike polynomials represent the type and size of the aberration, so obtaining the coefficient matrix of the Zernike polynomials means obtaining the aberration information of the human eye. According to the aberration information of the human eye, the fundus topography can be mapped or objective refraction can be performed for ophthalmic detection.

[0003] The inventor finds that the coefficient matrix obtained by directly expanding the wavefront by using the Zernike polynomials often contains large errors, which cannot meet the needs of ophthalmic detection, and therefore can only be used for auxiliary measurement and cannot be directly used as the basis for the manufacture of vision correction devices such as lenses. However, in some cases, for example, the measurement of the defocus degree of the periphery of the fundus, it is difficult to determine the defocus degree of the periphery of the fundus through subjective refraction, and therefore objective refraction is needed to measure the specific information of the human eye. Therefore, a method for obtaining human eye wavefront aberration with higher accuracy is needed as an objective refraction method that can determine the defocus degree of the fundus. SUMMARY

[0004] The main purpose of the present application is to provide a method for obtaining wavefront aberration of human eyes and a human eye aberration measuring device, which aims to improve the accuracy of obtaining wavefront aberration of human eyes.

[0005] To achieve the above-mentioned purpose, the method for obtaining wavefront aberration of human eyes according to the present application is applied to a Hartmann sensor, and the method comprises the following steps: calculating an actual slope matrix according to a wavefront spot diagram obtained by the Hartmann sensor; multiplying a generalized inverse matrix of a standard slope matrix with the actual slope matrix to obtain a Zernike coefficient matrix; subtracting the product of the actual slope matrix and the standard slope matrix and the Zernike coefficient matrix from each other to obtain a residual matrix; and updating the Zernike coefficient matrix according to the residual matrix until the residual matrix of the updated Zernike coefficient matrix is less than or equal to a preset value. The standard slope matrix is a matrix formed by the slopes of the wavefront of the Zernike polynomials.

[0006] In some embodiments, the step of updating the Zernike coefficient matrix according to the residual matrix until the residual matrix of the updated Zernike coefficient matrix is less than a preset value comprises:

[0007] According to calculating an initial residual matrix, and letting ;

[0008] According to calculating a step size;

[0009] According to calculating a first updated Zernike coefficient matrix;

[0010] According to calculating a first updated residual matrix;

[0011] If is less than or equal to the preset value, output as the final solution of the Zernike coefficient matrix;

[0012] If is greater than the preset value, calculating a direction coefficient according to , and letting ;

[0013] According to calculating the step size, and updating the Zernike coefficient matrix until the residual matrix is less than or equal to the preset value;

[0014] wherein, is the initial residual matrix, is the actual slope matrix, is the standard slope matrix, is the Zernike coefficient matrix obtained by first calculation, is the direction matrix used by first update, is the step size used by first update, is the Zernike coefficient matrix obtained by first update, is the residual matrix obtained by first update, is the direction coefficient used by second update, is the direction matrix used by second update.

[0015] In some embodiments, the actual slope matrix obtained according to the wavefront spot diagram acquired by the Hartmann sensor comprises:

[0016] taking the spot closest to the center of the wavefront spot diagram as the center spot, and dividing a grid with the center of the center spot as the center, so that each of the spots is located in a unit cell of the grid, to obtain a first processed image;

[0017] According to the first processed image, an offset between the center of the light spot and the center of the unit cell is obtained to calculate the actual slope matrix.

[0018] In some embodiments, the obtaining, according to the first processed image, of the offset between the center of the light spot and the center of the unit cell to calculate the actual slope matrix comprises:

[0019] Bilinear interpolation is performed on the first processed image to make the number of pixels occupied by each unit cell an integer, to obtain a second processed image.

[0020] According to the second processed image, an offset between the center of the light spot and the center of the unit cell is obtained to calculate the actual slope matrix.

[0021] In some embodiments, the obtaining, according to the first processed image, of the offset between the center of the light spot and the center of the unit cell to calculate the actual slope matrix comprises:

[0022] In the first processed image, a gray scale threshold value corresponding to each unit cell is selected in each unit cell, and pixels with a gray scale lower than the gray scale threshold value in the unit cell are excluded to obtain a third processed image.

[0023] According to the third processed image, an offset between the center of the light spot and the center of the unit cell is obtained to calculate the actual slope matrix.

[0024] In some embodiments, the selecting, in the first processed image, of a gray scale threshold value corresponding to each unit cell in each unit cell and excluding pixels with a gray scale lower than the gray scale threshold value in the unit cell to obtain a third processed image comprises:

[0025] In the unit cell, a pixel with the maximum gray scale value is selected as an origin.

[0026] A preset path is formed from the origin as a starting point, and the gray scale of a pixel with an increasing gray scale on the preset path is selected as a first reference value.

[0027] The maximum value of the first reference values of all origins in the unit cell is taken as the gray scale threshold value of the current unit cell.

[0028] In some embodiments, the preset path extends outward along the radial direction of the origin, and a plurality of paths are arranged at intervals in the circumferential direction of the origin, and the forming of the preset path from the origin as a starting point and the selection of the gray scale of a pixel with an increasing gray scale on the preset path as a first reference value comprises:

[0029] On the preset path, the size change of the gray scale of the current pixel compared with the gray scale of the previous pixel is determined pixel by pixel in the radial outward direction of the origin;

[0030] When the gray scale of the current pixel is first increased compared with the gray scale of the previous pixel, the gray scale of the current pixel is selected as the second reference value;

[0031] The maximum value of the second reference values on all the preset paths is selected as the first reference value.

[0032] In some embodiments, the preset paths are provided with 8 straight lines, and the included angle between two adjacent preset paths is 45°.

[0033] In some embodiments, the preset value is less than or equal to .

[0034] The application further provides a human eye wavefront aberration measuring device, which comprises a Hartmann sensor, and the wavefront spot diagram obtained by the Hartmann sensor is used to obtain the aberration information of the human eye wavefront by using the method for obtaining the human eye wavefront aberration.

[0035] In actual measurement, the standard slope matrix is often not a full rank square matrix, and does not have an inverse matrix in the usual sense, so only the generalized inverse matrix of the standard slope matrix can be obtained, and the generalized inverse matrix is multiplied by the actual slope matrix, so as to obtain the Zernike coefficient matrix.

[0036] According to the principle of linear algebra, the generalized inverse matrix is not unique, and when the generalized inverse matrix of the standard slope matrix is obtained, only one of multiple (even infinite) generalized inverse matrices is selected, so the Zernike coefficient matrix obtained by the generalized inverse matrix is often not the coefficient matrix that can best reflect the human eye wavefront aberration.

[0037] However, the residual matrix obtained by subtracting the product of the actual slope matrix, the standard slope matrix and the Zernike coefficient matrix can represent the difference between the wavefront fitted by the Zernike polynomial and the human eye wavefront, so the coefficient matrix of the Zernike polynomial can be updated according to the residual matrix, so that the residual matrix of the updated Zernike coefficient matrix gradually decreases, and finally decreases to a preset value, and the Zernike polynomial corresponding to the coefficient matrix can have sufficient accuracy in fitting the human eye wavefront.

[0038] Since the coefficients of the Zernike polynomial represent the strength of various aberrations, the better the Zernike polynomial fits the human eye wavefront, the more accurately the coefficients of the Zernike polynomial can reflect the human eye aberration, so the technical scheme improves the accuracy of obtaining the human eye wavefront aberration. BRIEF DESCRIPTION OF DRAWINGS

[0039] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or the prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only show some embodiments of the present application, and for those skilled in the art, other drawings can be obtained from the structures shown in the drawings without any creative effort.

[0040] Figure 1 Flow chart of the first embodiment of the method for obtaining wavefront aberration of human eye provided by the present application;

[0041] Figure 2 Partial flow chart of the second embodiment of the method for obtaining wavefront aberration of human eye provided by the present application;

[0042] Figure 3 Partial flow chart of the third embodiment of the method for obtaining wavefront aberration of human eye provided by the present application;

[0043] Figure 4 Partial flow chart of the fourth embodiment of the method for obtaining wavefront aberration of human eye provided by the present application;

[0044] Figure 5 Partial flow chart of the fifth embodiment of the method for obtaining wavefront aberration of human eye provided by the present application;

[0045] Figure 6 Partial flow chart of the sixth embodiment of the method for obtaining wavefront aberration of human eye provided by the present application;

[0046] Figure 7 Partial flow chart of the seventh embodiment of the method for obtaining wavefront aberration of human eye provided by the present application;

[0047] Figure 8 Wavefront spot diagram;

[0048] Figure 9 First processed image;

[0049] Figure 10 Comparison chart of the first processed image and the second processed image;

[0050] Figure 11 Comparison chart of the first processed image and the third processed image;

[0051] Figure 12 Reference wavefront aberration distribution chart;

[0052] Figure 13 Comparison chart of the wavefront aberration distribution chart obtained by the conventional method and the wavefront aberration distribution chart obtained by the embodiments of the method for obtaining wavefront aberration of human eye provided by the present application;

[0053] Figure 14 For reference Zernike coefficient histogram and inversion error histogram;

[0054] Figure 15 In some embodiments of the method for obtaining wavefront aberration of human eye provided by the application, the preset path distribution diagram in a unit cell.

[0055] The implementation, functional features and advantages of the application will be further described in conjunction with the embodiments and with reference to the drawings. DETAILED DESCRIPTION

[0056] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the application.

[0057] It should be noted that if the embodiments of the application involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative positional relationship, movement condition, etc. between components in a certain posture, and if the certain posture changes, the directional indications also change accordingly.

[0058] In addition, if the embodiments of the application involve descriptions such as “first”, “second”, etc., the descriptions of “first”, “second”, etc. are only for description purposes, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features limited by “first” and “second” can explicitly or implicitly include at least one of the features. In addition, “and / or” or “and / or” appearing throughout the text means that the three parallel schemes are included, for example, “A and / or B” includes A scheme, or B scheme, or A and B simultaneously satisfy the scheme. In addition, the technical solutions of each embodiment can be combined with each other, but it must be based on the realization of a person skilled in the art, and when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist and is not within the protection scope required by the application.

[0059] The application provides a method for obtaining wavefront aberration of human eye.

[0060] Please refer to Figure 1 The method for obtaining wavefront aberration of human eye provided by the application is applied to a Hartmann sensor, and the method for obtaining wavefront aberration of human eye comprises the following steps.

[0061] S10, calculating an actual slope matrix according to the wavefront spot diagram obtained by the Hartmann sensor;

[0062] S20 multiplies the generalized inverse matrix of the standard slope matrix with the actual slope matrix to obtain a Zernike coefficient matrix;

[0063] S30 subtracts the product of the actual slope matrix and the standard slope matrix and the Zernike coefficient matrix from each other to obtain a residual matrix;

[0064] S40 updates the Zernike coefficient matrix according to the residual matrix until the residual matrix of the updated Zernike coefficient matrix is less than or equal to a preset value.

[0065] The standard slope matrix is a matrix formed by the slopes of a wavefront of a Zernike polynomial full-term superposition.

[0066] The Hartmann sensor refers to a Shack-Hartmann Wavefront Sensor (SHWFS). The sensor is provided with a microlens array, and each microlens of the microlens array forms a sub-aperture (the entire microlens array forms a complete light entrance aperture). When working, the wavefront to be detected is made to pass through the lens array, so that different parts of the wavefront pass through different microlenses. Since there is an aberration between different parts of the wavefront, the light axis of the wavefront passing through the microlenses is offset to different degrees. The method of deducing the wavefront shape through the offset is called wavefront reconstruction.

[0067] The above-mentioned offset is represented by a slope. The microlens array is often arranged in parallel with an image sensor (CCD or CMOS, etc.), and the image sensor is arranged on the back focal plane of the microlens array. Thus, the light passing through the sub-lens forms a spot projected onto the image sensor. Since the light passing through the sub-lens is offset from the optical axis of the sub-lens, the spot is not at the center of the mapping of the sub-lens to the image sensor (the mapping is also referred to as a sub-aperture in the wavefront spot diagram, and the mapping is not distinguished below in the case of no confusion). Therefore, the phase difference of each part of the wavefront can be determined by the degree of offset of the spot from the center of the sub-aperture, and the total wavefront phase distribution can be reconstructed.

[0068] The quotient of the above-mentioned offset and the focal length of the sub-lens is the slope. Since the focal lengths of the sub-lenses are consistent, the slope is determined by the above-mentioned offset.

[0069] The wavefront spot map is the image (or the image converted into a gray scale image but not processed further) taken by the image sensor of the Hartmann sensor. The image is formed by the wavefront actually measured, so the shift of the spot formed by the wavefront passing through the lens array from the center of the sub-aperture can be calculated from the image, and then the slope can be determined. The slopes of all the wavefronts passing through the lens array and forming the spots that can be taken form a slope data set, which is in the form of an array, i.e. an actual slope matrix.

[0070] Since the operations for processing such a data set are usually performed in the form of a matrix, the data set is represented in the form of a matrix in this application. This is convenient for description, but in some other embodiments, the data set can be represented in the form of a function space and processed in the form of a function. Different linear operations can be converted into each other, so the specific principles are not described herein.

[0071] Zernike polynomials are a set of polynomials orthogonal in a unit circle. Each term of the Zernike polynomial actually represents a type of wavefront surface, and accordingly represents a type of aberration (which can be the same type but in a different form). Therefore, when each term of the Zernike polynomial is multiplied by a different coefficient, the actual wavefront to be measured can be expanded within a certain accuracy. At this time, only the coefficients of each term of the Zernike polynomial need to be obtained, and the distribution intensity of the aberration represented by each term in the wavefront to be measured can be known.

[0072] An ideal wavefront is assumed, which is represented by the wavefront when the coefficients of each term of the Zernike polynomial are all 1 (i.e. the wavefront formed by superimposing all the terms). Such an ideal wavefront will also have the above-mentioned shift after passing through the lens array of the Hartmann sensor, and accordingly can form the corresponding slope data. The standard slope matrix is the slope data formed by the above-mentioned ideal wavefront passing through the lens array.

[0073] However, the standard slope matrix has a special point that it usually shows the slope caused by the wavefront represented by each term respectively. In an example, the Zernike polynomial has 36 terms, and the standard slope matrix has at least 36 times the number of effective sub-apertures, multiplied by 2 data (here, the data is the effective slope data, and of course, 0 elements can be inserted to make the standard slope matrix a sparse matrix for the convenience of operation; similarly, the actual slope matrix can also be a sparse matrix), wherein the number of effective sub-apertures is the number of effective spots formed by the wavefront to be measured (in actual measurement, not all sub-lenses will have a wavefront passing through, so the number of effective sub-apertures is generally not equal to the number of sub-apertures), and the multiplication by 2 is because the image is two-dimensional, and usually a spot has slope data in two directions.

[0074] Similarly, in an example, the number of effective slope data in the actual slope matrix can be the number of effective sub-apertures multiplied by 2.

[0075] Since in reality, there is usually no above-mentioned ideal wavefront, the data in the standard slope matrix is often calculated, that is, the wavefront represented by each term of the Zernike polynomial is simulated, the Fraunhofer diffraction spot formed on the Hartmann sensor after passing through the microlens array, and the offset of each wavefront distribution is solved under the same sub-aperture as the wavefront spot diagram to form the standard slope matrix. In an example, the following method can be used:

[0076] The wavefront represented by each term of the Zernike polynomial is generated with the same resolution as the wavefront spot diagram (in other embodiments, it can also be the second processed image, because the second processed image uses linear interpolation processing, and the resolution will be different from that of the wavefront spot diagram) to generate a standard wavefront aberration distribution of a preset number of terms, and then based on the mapping of the sub-aperture in the wavefront spot diagram (in other embodiments, it can also be the division of the grid in the first processed image), each local wavefront is transformed through the lens function and the Fraunhofer diffraction formula , and then discrete Fourier transform is performed to make the low-frequency part centered, so as to simulate the final point spread function (PSF). Based on the above-mentioned PSF, the centroid of the simulated spot is calculated to obtain the centroid coordinates of the simulated spot under each sub-aperture, and the offset of the centroid coordinates under each sub-aperture from the reference centroid divided by the focal length of the sub-lens of the microlens array is the slope of the simulated spot under the sub-aperture. The slopes of all sub-apertures are collected to form the standard slope matrix.

[0077] The above-mentioned preset number of terms is the number of terms of the Zernike polynomial selected in advance. In principle, the Zernike polynomial can be taken to an infinite term, but too high a number of terms cannot accurately expand the wavefront to be measured, but rather reduces the accuracy of the final aberration obtained. Therefore, the number of terms is often limited to a finite value, for example, the first 36 terms of the Zernike polynomial can be taken for accurate measurement. When fast calculation is required, the first 3 orders, the first 4 orders or the first 5 orders of the Zernike polynomial can be taken.

[0078] The above-mentioned centroid coordinate calculation method can be a weighted average of the horizontal index and the vertical index with gray scale as the weight in the gray scale image. Specifically, for a spot, the following formula can be used: , , wherein and are the horizontal index and the vertical index of the centroid, respectively, and L and M are the number of pixels in the horizontal and vertical directions of the mapping of a sub-lens on the image sensor or a unit cell in the first processed image (for the first processed image and the unit cell, refer to the embodiments below), , and are the index variables of the summation symbol, respectively. the gray scale of the pixel, denotes the horizontal index, denotes the vertical index, the subscript of the two indices is the same index variable of the summation symbol.

[0079] The above reference centroid is the center of the mapping of the sub-lens on the image sensor, or for the embodiment of obtaining the first processed image, it is the center of the unit cell. Generally, the center can be determined by the center of the horizontal index and the center of the vertical index, but it can also be calculated by the above centroid coordinate formula, just let all Take a constant (for example, take 1), and the calculation result is the horizontal index and the vertical index of the center.

[0080] The centroid of the light spot to be measured can also be calculated by the above formula. The calculation method of the coordinates of other centroids can also use the above formula, which will not be described here.

[0081] As can be seen from the above, in the ideal case, if the Zernike polynomial can completely expand the wavefront to be measured, that is, there is no error, the Zernike coefficient matrix (that is, the matrix formed by the coefficients of each term after the Zernike polynomial expands the wavefront to be measured), the standard slope matrix and the actual slope matrix should satisfy , wherein is the actual slope matrix, is the standard slope matrix, is the ideal Zernike coefficient matrix.

[0082] The Zernike polynomial coefficient matrix is often the quantity to be solved, because the actual slope matrix and the standard slope matrix can be obtained by measurement and simulation respectively (refer to the above). Therefore, generally, the generalized inverse matrix of the standard slope matrix is multiplied by the actual slope matrix, that is, , wherein is the generalized inverse matrix (also called pseudo-inverse matrix) of , and is the actual obtained Zernike coefficient matrix (that is, the Zernike coefficient matrix obtained by the initial calculation of the embodiment below).

[0083] Since is not unique, the actual slope wavefront cannot be ideally expanded, so there will be a residual error, which is in the form of a matrix, that is, , wherein is the initial residual error matrix. Generally, the generalized inverse matrix of can be calculated by the formula , and for the matrix with row full rank, the generalized inverse matrix can be calculated by the above formula after transposition.

[0084] As can be seen, the residual matrix represents the degree to which the Zernike coefficient matrix approximates the actual wavefront expansion. Therefore, based on the residual matrix, methods such as gradient descent, Gauss-Newton algorithm, or conjugate gradient method can be used to iteratively optimize the Zernike coefficient matrix to make the residual matrix as small as possible.

[0085] Because the Zernike coefficient matrix is ​​updated iteratively, each Zernike coefficient matrix yields a residual matrix. The residual matrix is ​​less than or equal to a preset value, which ensures that the Zernike coefficient matrix has sufficient expansion accuracy for the wavefront under test. Since the coefficients in the Zernike coefficient matrix represent wavefront aberrations, the more accurate the expansion of the Zernike coefficient matrix for the wavefront under test, the more accurate the actual aberration data obtained, thus improving the accuracy of obtaining human eye wavefront aberrations.

[0086] It should be noted that, in a typical sense, the residual matrix is ​​a matrix and cannot be directly assumed to be less than a single numerical value. However, the preset value can be a matrix with the same number of rows and columns as the residual matrix. Each element in the preset value matrix is ​​assigned a specific value. Thus, when every element in the residual matrix is ​​less than the corresponding element in the preset value matrix, the residual matrix can be considered less than the preset value. Of course, the residual matrix being less than the preset value can also mean that the inner product of the residual matrices is less than a preset numerical value. The comparison method can be selected according to actual needs to ensure that the residuals represented by the residual matrix are sufficiently small to meet sufficiently high measurement accuracy.

[0087] Please refer to Figure 2 In some implementations, updating the Zernike coefficient matrix based on the residual matrix until the residual matrix of the updated Zernike coefficient matrix is ​​less than a preset value includes:

[0088] S41 according to Calculate the initial residual matrix and let ;

[0089] S42 according to Calculate step size;

[0090] S43 according to Calculate the Zernike coefficient matrix for the first update;

[0091] S44 according to Calculate the residual matrix after the initial update;

[0092] S45 if If the value is less than or equal to the preset value, output As the final solution to the Zernike coefficient matrix;

[0093] S46 If If it is greater than the preset value, then according to Calculate the direction coefficient and let ;

[0094] S47 according to Calculate the step size and update the Zernike coefficient matrix until the residual matrix is ​​less than or equal to the preset value;

[0095] in, The initial residual matrix, This is the actual slope matrix. The standard slope matrix, This is the Zernike coefficient matrix obtained from the initial calculation. The direction matrix used for the initial update. For the first update, step-by-step growth. The Zernike coefficient matrix obtained from the initial update. The residual matrix obtained from the initial update. The directional coefficient used for the second update. The direction matrix used for the second update.

[0096] The direction matrix represents the direction of the update of the Zernike coefficient matrix; the direction refers to the direction in which the Zernike coefficient matrix is ​​updated. The direction in the vector space represented by the matrix or Zernike coefficient matrix corresponds to each element in the matrix. It specifies whether to increase or decrease the size of elements in the current update (elements can be positive or negative, so it is not the size of absolute values, but the size relationship on the real number line), and also specifies the proportional relationship between the changes of each element.

[0097] The step size ultimately defines the magnitude of the change in each element of the Zernike coefficient matrix during the current update. In the initial update, the step size is the quotient of the inner product of the initial residual matrix and the quadratic form of the initial residual matrix and the standard slope matrix; it is a scalar. In the second and subsequent updates, the step size is associated with the current residual matrix and the residual matrix of the previous update: that is, if we let... This represents updating the index; the first call is made for each variable. The second call And so on, the calculation of the step size satisfies .in, The update is related to the previous residual matrix, and the specific principle is described below.

[0098] During the initial update, Take the initial residual matrix, i.e. In the second and subsequent updates, It needs to be correlated with the current residual matrix and the previous residual matrix, which is achieved through the current residual matrix. is associated with the previous , and the calculation of the direction coefficient is associated with the previous residual matrix, that is, the same update index is used as the subscript, and the calculation of the direction coefficient satisfies , the calculation of the residual matrix satisfies . It can be seen that is associated with , and is associated with , so is associated with the current residual matrix and the previous residual matrix.

[0099] In this way, the step size and the direction matrix are associated with the previous update in each update, and the Zernike coefficient matrix can be updated according to the previous residual, so that the residual matrix can be quickly attenuated, and the efficiency of obtaining the coefficient can be improved.

[0100] Since the above residual matrix attenuation method can be a conditional loop algorithm (i.e., a loop algorithm that exits the loop when the residual matrix is less than or equal to a preset value), the recursive formula in the loop process is particularly given (the update index is the same as defined above, and is true for the second and subsequent loops. For the first update, refer to the above, and no recursive formula is needed):

[0101] the calculation of the Zernike coefficient matrix satisfies ;

[0102] the calculation of the residual matrix satisfies .

[0103] In the above loop, when is less than or equal to a preset value, the loop is stopped, and is output, that is, the Zernike coefficient matrix to be solved.

[0104] Please refer to Figure 3 , in some embodiments, the actual slope matrix is calculated based on the wavefront spot diagram obtained by the Hartmann sensor, including:

[0105] S11 takes the spot closest to the center of the wavefront spot diagram as the center spot, and divides the grid with the center of the center spot as the center, so that each spot is located in a unit cell of the grid, to obtain a first processed image;

[0106] S12 obtains the offset of the center of the spot from the center of the unit cell according to the first processed image, to calculate the actual slope matrix.

[0107] Please refer to Figure 8 , Figure 8The image shown is the wavefront spot diagram, that is, the initial image obtained by the image sensor of the Hartmann sensor, and the center of the wavefront spot diagram is the center pixel of the initial image obtained by the image sensor; the center of mass of the spot can be obtained according to the center of mass calculation formula proposed above, and the distance between the center of mass and the center is the pixel distance, which can be calculated by the following method:

[0108] Divide the maximum horizontal index and the maximum vertical index of the wavefront spot diagram by 2 (if it is not an integer, take the integer), to obtain the index coordinates of the center pixel of the wavefront spot diagram, defined as After extracting the feature map of the wavefront spot diagram, the center of mass of each spot is calculated, defined as ; and the Euclidean distance between and the center of mass of each spot is calculated , wherein represents the Euclidean distance.

[0109] Select the spot with the smallest as the center spot, and consider that the center of mass of the spot should be at the center of the corresponding cell (the center of the cell is the center pixel in the cell, and the confirmation method can be the same as that of the center of the wavefront spot diagram).

[0110] The shape of the grid should be the same as the shape of the lens array of the Hartmann sensor mapped onto the image sensor; that is, the number of pixels of the cell of the grid can be the ratio of the sub-lens aperture size to the image sensor pixel, and the number of cells of the grid can be the ratio of the resolution of the wavefront spot diagram to the number of pixels of the cell (or it can also be considered as the number of effective spots collected; although the effective spots are not necessarily distributed throughout the wavefront spot diagram, generally, the cells without spots are not included in the calculation and can be ignored; in the Figure 8 corner position, there are some areas without distributed spots).

[0111] As can be seen, although the shape of the above grid is highly related to the lens array, it is not directly mapped from the sub-lens boundary of the lens array to the image sensor, but is divided according to the center spot. In this way, the calculation amount of wavefront retrieval can be reduced.

[0112] Because the wavefront incident on the Hartmann sensor is not always normal incidence, but at a certain angle with the optical axis of the Hartmann sensor, each spot actually naturally has a shift, and each spot has the same shift caused by the non-normal incidence angle, which is irrelevant to the wavefront aberration. If not handled, it may affect the accuracy of the final wavefront retrieval, and if handled by algorithm, a large amount of calculation is required. Directly dividing the grid by the center spot can naturally exclude this shift, reduce the retrieval calculation amount, and ensure the measurement accuracy.

[0113] Please refer to Figure 9 , Figure 9 This is the wavefront spot image with a pre-divided grid, also known as the first processed image. It can be seen that, except for the central spot, most of the spots are offset from the center of the grid. The centroid of the spot can be obtained by summing the values ​​within the corresponding cell range using the centroid calculation formula described above. The lateral and vertical offsets of the spot can be calculated using the formulas... and The calculation yielded, where This represents the offset of the lateral index of the spot centroid relative to the lateral index of the grid center. This represents the offset of the vertical index of the spot centroid relative to the vertical index of the grid center. The actual size of the pixel. This is the focal length of the sub-lens.

[0114] Please refer to Figure 4 In some implementations, obtaining the offset between the centroid of the light spot and the center of the cell based on the first processed image to calculate the actual slope matrix includes:

[0115] S13 performs bilinear interpolation on the first processed image to make the number of pixels occupied by each cell an integer, so as to obtain the second processed image;

[0116] S14 obtains the offset between the centroid of the light spot and the center of the cell based on the second processed image, in order to calculate the actual slope matrix.

[0117] Bilinear interpolation is an image scaling algorithm that introduces new pixels into an image. In the initial wavefront flare image, the pixels occupied by a single cell of the grid may not be an integer because the grid is divided around the centroid of the central flare, and the centroid coordinates calculated using the centroid calculation formula may not be integers. However, it's impossible to perform calculations for non-integer pixels, which may cause the flare or grid to be offset in the first processed image.

[0118] By using bilinear interpolation to insert new pixels, the number of pixels occupied by a cell can be an integer. This can eliminate the spot offset caused by a cell occupying a non-integer number of pixels, making the acquisition of the spot offset more accurate.

[0119] Please refer to Figure 10 , Figure 10 Image (a) in the image is the first processed image. Figure 10 Figure (b) in the image is the second processed image, and some parts of both images are magnified. It can be seen that the light spot in the second processed image is displaced from the light spot at the same position in the first processed image. This shows that the effect of eliminating the light spot shift by bilinear interpolation is significant.

[0120] Please refer toFigure 5 In some embodiments, the step of obtaining the offset of the center of mass of the light spot from the center of the cell according to the first processed image to calculate the actual slope matrix comprises:

[0121] S15 selecting, in the first processed image, a gray scale threshold corresponding to each cell, and excluding pixels with a gray scale lower than the gray scale threshold in the cell to obtain a third processed image;

[0122] S16 obtaining the offset of the center of mass of the light spot from the center of the cell according to the third processed image to calculate the actual slope matrix.

[0123] Since the sub-lenses of the microlens array are small, a relatively obvious diffraction effect is likely to occur, i.e., Fresnel diffraction phenomenon may occur, so that the gray scale distribution in the cell is relatively discrete. The fringes formed by such diffraction phenomenon affect the calculation of the center of mass, except for the central Airy disk. Therefore, excluding pixels with a gray scale lower than the gray scale threshold can reduce the influence of the diffraction phenomenon on the calculation of the center of mass of the light spot, so that the final wavefront reconstruction structure is more accurate.

[0124] The selection of the gray scale threshold can select the median or mode of the gray scale of the pixels in the cell, because the peripheral diffraction fringes are generally dark, and can refer to Figure 11 FIG. 13 (a) is the first processed image (which can also be the second processed image, because in some embodiments, steps S15 and S16 can be performed after steps S13 and S14, at which time the first processed image has become the second processed image, so in these embodiments, the first processed image in S15 should be understood as the second processed image). It can be seen that there are weak Fresnel diffraction fringes. Selecting the median and mode can exclude the influence of some diffraction fringes.

[0125] Please refer to Figure 6 In some embodiments, the step of selecting, in the first processed image, a gray scale threshold corresponding to each cell, and excluding pixels with a gray scale lower than the gray scale threshold in the cell to obtain a third processed image comprises:

[0126] S151 selecting, in the cell, a pixel with the maximum gray scale value as the origin;

[0127] S152 forming a preset path starting from the origin, and selecting the gray scale of the pixel at the place where the gray scale increases along the preset path as the first reference value;

[0128] S153 taking the maximum value of the first reference values of all origins in a cell as the gray scale threshold of the current cell.

[0129] If the wavefront light spot image is overexposed, the gray scale of multiple pixels in the unit cell can reach the maximum value, i.e., the pixel with the maximum gray scale in the unit cell; after the wavefront light spot image is scaled by bilinear interpolation, multiple pixels in the unit cell can have the same gray scale, and the gray scale of these pixels is greater than that of other pixels in the unit cell, so multiple pixels can have the maximum gray scale. Of course, multiple pixels with the same gray scale and greater than that of other pixels in the unit cell can naturally exist in the image during image shooting.

[0130] Therefore, for a unit cell, the pixel with the maximum gray scale is not always one (in a special case, there can be only one, in which case only the following processing is performed on this pixel). Therefore, all pixels with the maximum gray scale in a unit cell can be selected as the origin, and therefore multiple first reference values can be obtained according to step S152 in the foregoing.

[0131] The preset path needs to extend from the origin and generally has a trend of extending radially outward from the origin. Therefore, the preset path can be linear, curved, or polygonal in the following embodiments. One preset path can be one or multiple (see below). However, the preset path starts from the origin, so the preset path can be set in the same way for each origin to obtain the first reference value for each origin.

[0132] Multiple pixels are distributed on the preset path. It can be understood that, because the pixel at the origin has the maximum gray scale, the gray scale of the pixel on the preset path needs to decrease first and then increase in the direction radially outward from the origin. In addition, the pixel with the maximum gray scale is generally in the center bright spot (Fraunhofer diffraction spot) in the unit cell, and there is a Fraunhofer diffraction ring around the center bright spot. The center bright spot and the Fraunhofer diffraction ring are relatively dark regions, so the preset path will have a pixel with an increased gray scale when it extends to the Fraunhofer diffraction ring.

[0133] However, generally, there is a pixel with an increased gray scale in the center bright spot, so generally, the pixel with the selected gray scale is in the center bright spot. This can be verified in Figure 11 The right third processed image (b) in FIG. 6 shows that, compared with the left first processed image (a), the center bright spot is removed to a greater extent in addition to the diffraction ring.

[0134] When the gray scale of a current pixel is greater than that of a previous pixel on the preset path, it can be considered that a position with an increased gray scale is present, and the gray scale of the current pixel can be taken as the first reference value, i.e., when the following condition is met, the gray scale of the n+1th pixel is taken as the first reference value, where the subscript represents the number of the pixel. This represents the gray level of the nth pixel.

[0135] Excluding pixels with a gray level below the gray level threshold within a cell can be done by either retaining pixels with a gray level equal to the gray level threshold (without performing any transformation on these pixels, i.e., retaining them) or by changing the gray level of pixels with a gray level equal to the gray level threshold to 0 (i.e., excluding these pixels).

[0136] As can be seen, by finding the grayscale threshold through a preset path, the final determined grayscale threshold can be adaptively adjusted for different cells. As mentioned above, if the uniformity of the central bright spot is high enough and the grayscale value dispersion is very low, then the Fraunhofer diffraction ring mainly affects the centroid calculation. In this case, the position where the grayscale rises is exactly at the Fraunhofer diffraction ring. Taking the grayscale value of the pixel at this position as the grayscale threshold can eliminate the interference of the Fraunhofer diffraction ring while retaining almost all the pixels of the central bright spot.

[0137] If the uniformity of the central bright spot is low and the grayscale value dispersion is high, then there will often be positions where the grayscale value increases within the central bright spot. Selecting the grayscale value of the pixel in this position as the grayscale threshold can also eliminate the part with greater interference within the central bright spot. At the same time, since the brightness of the central bright spot is generally greater than that of the Fraunhofer diffraction ring, its grayscale value is also greater than that of the Fraunhofer diffraction ring. Selecting the grayscale value of the pixel within the central bright spot as the grayscale threshold can also eliminate the influence of the Fraunhofer diffraction ring.

[0138] In summary, by finding the grayscale threshold through a preset path, the grayscale threshold can be adaptively adjusted according to the situation in different cells, resulting in higher accuracy in the final centroid calculation.

[0139] Please refer to Figure 11 , Figure 11 The middle (b) image is the third processed image. After excluding pixels with gray values ​​below the gray value threshold (i.e., setting the gray value of these pixels to 0), the diffraction fringes disappear, and the size of the central bright spot shrinks. This ensures that only the position where the light spot is most concentrated enters the final centroid calculation process, and at the same time reduces the dispersion of gray value distribution, thus improving the accuracy of the final wavefront inversion result.

[0140] Please refer to Figure 7 In some embodiments, the preset path extends radially outward from the origin, and multiple preset paths are spaced apart circumferentially around the origin. The preset path is formed with the origin as the starting point, and the grayscale of pixels at points of increased grayscale along the preset path is selected as the first reference value, including:

[0141] S1521 determines the change in grayscale value of the current pixel compared to the previous pixel in the radial outward direction from the origin along the preset path.

[0142] S1522 When the gray level of the current pixel increases for the first time compared to the gray level of the previous pixel, the gray level of the current pixel is selected as the second reference value.

[0143] S1523 selects the maximum value among all the second reference values ​​on the preset paths as the first reference value.

[0144] Since the sub-lenses of a microlens array are generally not circular but may be square, and there may be diffraction effects between different sub-lenses, the diffraction fringes are often not annular but have a certain degree of asymmetry. Selecting multiple preset paths allows sampling in multiple directions to ensure that the maximum gray value in the diffraction fringes can be reflected, thus guaranteeing the final effect of eliminating interference.

[0145] Please refer to Figure 15 In some implementations, there are 8 preset paths, all of which are straight lines; the angle between two adjacent preset paths is 45°.

[0146] Selecting too many preset paths increases the computational load; selecting too few preset paths makes it difficult to reflect the maximum grayscale value in different directions. Setting 8 preset paths, with an angle of 45° between adjacent preset paths, can maintain an appropriate computational load while reflecting the maximum grayscale value in all directions, ensuring the final interference elimination effect.

[0147] To clearly demonstrate the method for selecting the grayscale threshold, an additional example of grayscale threshold selection is provided here:

[0148] Please refer to Figure 15 , Figure 15 The square box R represents the boundary of a grid cell. For simplicity, the Fraunhofer diffraction rings within the cell are not shown; only the central bright spot, i.e., the area within the ring C1, is shown. The central position within C1 generally has the highest gray level, so a circle O represents the set of pixels with the highest gray level. However, it should be noted that in reality, the set of pixels with the highest gray level may not necessarily form a circle; it may also form multiple spaced-apart points. Figure 15 This is for illustrative purposes only and does not depict the actual situation.

[0149] Figure 15 In a circle O, multiple line segments L with arrows intersect at their unarrowed ends; the intersection point represents a pixel within circle O. Therefore... Figure 15 This is a schematic diagram for selecting the first reference value for a pixel with the largest grayscale value. For the sake of simplicity, this pixel will be referred to as the origin below (this pixel is specifically referred to below and should not be confused with the origin mentioned above).

[0150] The line segment L is the preset path, and the direction indicated by the arrow is the radial outward direction of the original point. The line segment is in a straight line shape, and there are multiple pixels on the preset path. In the figure, C2 represents the position of the gray level increase, that is, the gray level of the pixel on C2 is greater than the gray level of the pixel adjacent to C2 and inside C2. C2 is a set formed by the pixels of the gray level increase position. Please note that in practice, the set of pixels of the gray level increase position does not necessarily form a circle, or even a ring, but can form an intermittent line or a scattered point.

[0151] The point where L intersects C2 is D, and the gray level of the pixel at D is the second reference value. As L is provided with 8 lines and the included angle between adjacent L is 45°, there are 8 second reference values for the original point. The maximum of the 8 second reference values is the first reference value.

[0152] According to the above method, the first reference value can be selected for all pixels in O, and the maximum of all first reference values is taken as the gray level threshold in the unit cell R.

[0153] In some embodiments, the preset value is less than or equal to If the preset value is too large, the residual represented by the residual matrix is large, and it is difficult to meet the accuracy of the wavefront aberration. When the preset value is less than or equal to , sufficient accuracy can be obtained. In one example, the preset value can also be , or . The unit of the preset value changes according to the unit of the elements of the residual matrix. When the preset value directly corresponds to the elements in the residual matrix (i.e., each element in the residual matrix is less than the preset value), the unit of the preset value is the same as the unit of the elements of the residual matrix. When the inner product of the residual matrix is less than the preset value, the unit of the preset value is the square of the unit of the residual matrix.

[0154] For the accuracy of the embodiments of the present application, experiments are used for verification: Figure 12 , Figure 13 and Figure 14 .

[0155] Figure 14 In (a) of FIG. 1, the Zernike coefficient column chart of the reference wavefront incident on the Hartmann sensor is shown, that is, the wavefront incident on the Hartmann sensor with a known coefficient distribution of the Zernike polynomial, and then the wavefront is respectively inverted by the traditional method (mode method) and the method of the embodiment of the method for obtaining the wavefront aberration of the human eye proposed in the present application. The inverted wavefronts are compared to show the improvement in accuracy of the present application.

[0156] The incident wave front (i.e. the reference wave front) is red light with a wavelength of 635 nm, the size of the sub-lenses of the microlens array of the Hartmann sensor is 150 μm (square lens), the focal length is 5.2 mm, the size of the image element of the image sensor is 3.45 μm, and the aperture of the collected wave front is 5 mm.

[0157] Figure 12 The aberration distribution of the incident wave front is shown in the left part of Fig. 1, wherein the RMS (root mean square) of the wave front is 0.65 μm, and the PV (peak to valley) is 2.73 μm. Figure 13 The aberration distribution of the wave front obtained by the traditional mode method is shown in the left part of Fig. 1, wherein the RMS is 0.39 μm, and the PV is 1.7 μm. Figure 13 The aberration distribution of the wave front obtained by the method according to the embodiments of the present application is shown in the right part of Fig. 1, wherein the RMS is 0.65 μm, and the PV is 2.77 μm.

[0158] It can be seen that the wave front obtained by the method according to the embodiments of the present application is closer to the incident wave front, and thus has a more accurate fitting effect, thereby improving the accuracy of obtaining the wave front aberration of the human eye.

[0159] In addition to the reference RMS and PV, the difference between the coefficients of the Zernike polynomials of the obtained wave front and the coefficients of the Zernike polynomials of the reference wave front can also be referred to, i.e. (b) in Fig. 2. Figure 14 It can be seen that the coefficients of the Zernike polynomials of the wave front obtained by the traditional mode method differ greatly from those of the reference wave front, and the coefficients of the Zernike polynomials of the wave front obtained by the method according to the embodiments of the present application differ less from those of the reference wave front, and thus the accuracy is higher.

[0160] The method of using the RMS and PV values to judge the fitting effect is also an important method of judging the final fitting effect. It can be used to judge the measurement accuracy of the human eye aberration measuring device.

[0161] The present application also provides a human eye aberration measuring device, which comprises a Hartmann sensor, and obtains the aberration information of the wave front of the human eye by using the wave front spot diagram obtained by the Hartmann sensor and the method of obtaining the wave front aberration of the human eye. Since the human eye aberration measuring device adopts all the technical solutions of the above-mentioned embodiments, it has at least all the beneficial effects brought by the technical solutions of the above-mentioned embodiments, which will not be described herein.

[0162] The human eye aberration measuring device can be a topography instrument, a wide-angle optometry instrument or a window optometry instrument, etc. The wave front spot diagram can be obtained by the Hartmann sensor, and the wave front aberration distribution can be obtained by the method of obtaining the wave front aberration of the human eye, and then the defocus condition of the human eye can be determined, which can be used to draw a topography or simply used for macular area optometry.

[0163] The above merely describes exemplary embodiments of the present application, and is not intended to limit the protection scope of the present application, and any equivalent structural transformation made according to the technical concept of the present application, or direct / indirect application in other related technical fields, is included in the protection scope of the present application.

Claims

1. A method for obtaining wavefront aberration of the human eye, characterized in that, Applied to Hartmann sensors, the method for acquiring wavefront aberrations of the human eye includes: The actual slope matrix is ​​calculated based on the wavefront spot pattern obtained by the Hartmann sensor. Multiply the generalized inverse of the standard slope matrix by the actual slope matrix to obtain the Zernike coefficient matrix; Subtracting the product of the actual slope matrix and the standard slope matrix and the Zernike coefficient matrix yields the residual matrix; and The Zernike coefficient matrix is ​​updated based on the residual matrix until the residual matrix of the updated Zernike coefficient matrix is ​​less than or equal to a preset value; The standard slope matrix is ​​a matrix formed by the slopes of the wavefronts of the superposition of all Zernike polynomials. The step of updating the Zernike coefficient matrix based on the residual matrix until the residual matrix of the updated Zernike coefficient matrix is ​​less than a preset value includes: according to Calculate the initial residual matrix and let ; according to Calculate step size; according to Calculate the Zernike coefficient matrix for the first update; according to Calculate the residual matrix for the first update; like If the value is less than or equal to the preset value, output As the final solution of the Zernike coefficient matrix; like If it is greater than the preset value, then according to Calculate the direction coefficient and let ; according to Calculate the step size and update the Zernike coefficient matrix until the residual matrix is ​​less than or equal to the preset value; in, Let be the initial residual matrix. The actual slope matrix is... The standard slope matrix is... The Zernike coefficient matrix obtained in the initial calculation is shown below. The direction matrix used for the initial update. The steps described are for the initial update. The Zernike coefficient matrix obtained during the initial update, The residual matrix obtained during the initial update, The direction coefficients used for the second update. The direction matrix used for the second update.

2. The method for obtaining wavefront aberration of the human eye as described in claim 1, characterized in that, The calculation of the actual slope matrix based on the wavefront spot pattern obtained from the Hartmann sensor includes: The spot whose centroid is closest to the center of the wavefront spot pattern is taken as the center spot, and the grid is divided with the centroid of the center spot as the center, so that each spot is located in one cell of the grid to obtain the first processed image; Based on the first processed image, the offset between the centroid of the light spot and the center of the cell is obtained to calculate the actual slope matrix.

3. The method for obtaining wavefront aberration of the human eye as described in claim 2, characterized in that, The step of obtaining the offset between the centroid of the light spot and the center of the cell based on the first processed image, and calculating the actual slope matrix, includes: The first processed image is subjected to bilinear interpolation so that the number of pixels occupied by each cell is an integer, thereby obtaining the second processed image; Based on the second processed image, the offset between the centroid of the light spot and the center of the cell is obtained to calculate the actual slope matrix.

4. The method for obtaining wavefront aberration of the human eye as described in claim 2, characterized in that, The step of obtaining the offset between the centroid of the light spot and the center of the cell based on the first processed image, and calculating the actual slope matrix, includes: In the first processed image, within each cell, a grayscale threshold corresponding to each cell is selected, and pixels with a grayscale value lower than the grayscale threshold within the cell are excluded to obtain the third processed image. Based on the third processed image, the offset between the centroid of the light spot and the center of the cell is obtained to calculate the actual slope matrix.

5. The method for obtaining wavefront aberration of the human eye as described in claim 4, characterized in that, In the first processed image, within each cell, a grayscale threshold corresponding to that cell is selected, and pixels with a grayscale value lower than the grayscale threshold are excluded to obtain the third processed image. Within the cell, the pixel with the highest grayscale value is selected as the origin. A preset path is formed starting from the origin, and the gray level of the pixel at the gray level increase point along the preset path is selected as the first reference value. The maximum value among all the first reference values ​​of the origin within a cell is used as the grayscale threshold of the current cell.

6. The method for obtaining wavefront aberration of the human eye as described in claim 5, characterized in that, The preset path extends radially outward from the origin, and multiple paths are spaced apart circumferentially around the origin. The step of forming the preset path with the origin as the starting point and selecting the grayscale of pixels at points of increased grayscale along the preset path as the first reference value includes: Along the preset path, in the radial outward direction from the origin, the change in grayscale value of the current pixel compared to the grayscale value of the previous pixel is determined pixel by pixel. When the gray level of the current pixel increases for the first time compared to the gray level of the previous pixel, the gray level of the current pixel is selected as the second reference value. The maximum value among all the second reference values ​​on the preset paths is selected as the first reference value.

7. The method for obtaining wavefront aberration of the human eye as described in claim 6, characterized in that, There are 8 preset paths, all of which are straight lines; the angle between two adjacent preset paths is 45°.

8. The method for obtaining wavefront aberration of the human eye as described in claim 1, characterized in that, The preset value is less than or equal to .

9. A human eye aberration measuring device, characterized in that, The method includes a Hartmann sensor, and uses the wavefront spot pattern obtained by the Hartmann sensor to obtain wavefront aberration information of the human eye by applying the method for obtaining wavefront aberration of the human eye as described in any one of claims 1-8.

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