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

Abstract

The invention 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 the human eye wavefront aberration is applied to a Hartmann sensor and comprises the steps that an actual slope matrix is obtained through calculation according to a wavefront light spot diagram obtained by the Hartmann sensor; multiplying the generalized inverse matrix of the standard slope matrix by the actual slope matrix to obtain a Zernike coefficient matrix; subtracting the actual slope matrix from the product of the standard slope matrix and the Zernike coefficient matrix 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 smaller than or equal to a preset value. Wherein the standard slope matrix is a matrix formed by wavefront slope of Zernike polynomial full-term superposition. According to the technical scheme provided by the invention, the accuracy of obtaining the wavefront aberration of the human eye can be improved.

Description

Technical Field

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

[0002] After the light reflected from the fundus passes through the pupil, it forms light with the image information of the human eye's fundus. If this 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 using Zernike polynomials to obtain the coefficient matrix of the Zernike polynomials when the wavefront is expanded. The coefficients of the Zernike polynomials represent the type and size of the aberrations. Therefore, the coefficient matrix of the Zernike polynomials is obtained, which means the aberration information of the human eye is obtained. Based on the phase difference information of the human eye, the fundus refractive topography can be surveyed and mapped or ophthalmic tests such as objective optometry can be performed.

[0003] The inventors have discovered that the coefficient matrix obtained by directly expanding the wavefront using Zernike polynomials often contains large errors and is difficult to meet the needs of ophthalmic testing. Therefore, it can only be used for auxiliary measurement and cannot be directly used as a basis for the manufacture of vision correction devices such as lenses. However, in some cases, such as measuring the degree of defocus in the peripheral fundus, it is difficult to determine the degree of defocus in the peripheral fundus through subjective optometry. Therefore, objective optometry is required to measure specific human eye information. Therefore, a more accurate method for obtaining human eye wavefront aberrations is needed as an objective optometry method that can determine the degree of defocus at various locations in the fundus. Summary of the Invention

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

[0005] To achieve the above objectives, the present invention proposes a method for obtaining human eye wavefront aberrations, which is applied to a Hartmann sensor. The method comprises: calculating an actual slope matrix based on a wavefront spot pattern obtained by the Hartmann sensor; multiplying the actual slope matrix by the generalized inverse matrix of the standard slope matrix to obtain a Zernike coefficient matrix; subtracting the actual slope matrix from the product of the standard slope matrix and the Zernike coefficient matrix to obtain a residual matrix; and updating the Zernike coefficient matrix 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 slope of the wavefront superimposed by all Zernike polynomials.

[0006] In some embodiments, 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 includes: according to Calculate the initial residual matrix and let ; according to Calculate step length; according to Calculating the Zernike coefficient matrix for initial update; according to Calculating the residual matrix for initial update; like is less than or equal to the preset value, output as the final solution of the Zernike coefficient matrix; like is greater than the preset value, then according to Calculate the directional coefficient and let ; according to Calculating the step length and updating the Zernike coefficient matrix until the residual matrix is ​​less than or equal to the preset value; in, is the initial residual matrix, is the actual slope matrix, is the standard slope matrix, is the Zernike coefficient matrix obtained by the initial calculation, is the direction matrix used for the initial update, The step length used for the initial update is as follows, is the Zernike coefficient matrix obtained by the initial update, is the residual matrix obtained by the initial update, is the directional coefficient used for the second update, The direction matrix used for the second update.

[0007] In some embodiments, calculating and obtaining an actual slope matrix based on the wavefront spot pattern acquired by the Hartmann sensor includes: The spot whose centroid is closest to the center of the wavefront spot pattern is taken as the central spot, and a grid is divided with the centroid of the central spot as the center, so that each spot is located in a cell of the grid, to obtain a first processed image; According to 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.

[0008] In some embodiments, obtaining, based on the first processed image, an offset between the centroid of the light spot and the center of the cell to calculate the actual slope matrix includes: performing bilinear interpolation on the first processed image so that the number of pixels occupied by each cell is an integer, to obtain a second processed image; According to 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.

[0009] In some embodiments, obtaining, based on the first processed image, an offset between the centroid of the light spot and the center of the cell to calculate the actual slope matrix includes: In each of the cells in the first processed image, a grayscale threshold corresponding to the cell is selected, and pixels in the cell with a grayscale lower than the grayscale threshold are excluded to obtain a third processed image; According to 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.

[0010] In some embodiments, in each cell of the first processed image, selecting a grayscale threshold corresponding to the cell and excluding pixels in the cell having a grayscale lower than the grayscale threshold to obtain a third processed image includes: In the cell, the pixel with the largest gray value is selected as the origin; A preset path is formed with the origin as a starting point, and the grayscale of pixels at locations where the grayscale increases along the preset path is selected as a first reference value; The maximum value of the first reference values ​​of all the origins in a cell is used as the grayscale threshold of the current cell.

[0011] In some embodiments, the preset path extends radially outward from the origin, and a plurality of paths are spaced apart in a circumferential direction of the origin. Forming the preset path with the origin as the starting point and selecting the grayscale of pixels at locations along the preset path where the grayscale increases as the first reference value includes: On the preset path, in a radially outward direction from the origin, determining pixel by pixel a change in the grayscale of a current pixel compared to the grayscale of a previous pixel; When the grayscale of the current pixel increases for the first time compared to the grayscale of the previous pixel, selecting the grayscale of the current pixel as the second reference value; The maximum value of the second reference values ​​on all the preset paths is selected as the first reference value.

[0012] In some embodiments, there are 8 preset paths, all of which are straight lines; and the angle between two adjacent preset paths is 45°.

[0013] In some embodiments, the preset value is less than or equal to .

[0014] The present invention also proposes a human eye aberration measuring device, comprising a Hartmann sensor, and applying the above-mentioned method for obtaining human eye wavefront aberration to the wavefront spot diagram obtained by the Hartmann sensor to obtain aberration information of the human eye wavefront.

[0015] In actual measurements, the standard slope matrix is ​​often not a full-rank square matrix and does not have an inverse matrix in the usual sense. Therefore, we can only calculate the generalized inverse matrix of the standard slope matrix and multiply the generalized inverse matrix with the actual slope matrix to obtain the Zernike coefficient matrix.

[0016] According to the principles of linear algebra, the generalized inverse matrix is ​​not unique. When calculating the generalized inverse matrix of the standard slope matrix, only one of multiple (even infinite) generalized inverse matrices is selected. It can be seen that the Zernike coefficient matrix obtained by such a generalized inverse matrix is ​​often not the coefficient matrix that best reflects the wavefront aberration of the human eye.

[0017] However, the residual matrix obtained by subtracting the actual slope matrix from the product of the standard slope matrix and the Zernike coefficient matrix can characterize the difference between the wavefront fitted by the Zernike polynomial and the wavefront of the human eye. Therefore, 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 eventually decreases to a preset value. The Zernike polynomial corresponding to the coefficient matrix can have sufficient accuracy in fitting the wavefront of the human eye.

[0018] Since the coefficients of the Zernike polynomials represent the strength of various aberrations, the better the Zernike polynomials fit the wavefront of the human eye, the more accurately the coefficients of the Zernike polynomials can reflect the aberrations of the human eye. Therefore, the technical solution of the present application improves the accuracy of obtaining the wavefront aberrations of the human eye. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0020] Figure 1 A flowchart of a first embodiment of the method for obtaining wavefront aberration of a human eye provided by the present invention; Figure 2 A partial flow chart of a second embodiment of the method for obtaining wavefront aberration of the human eye provided by the present invention; Figure 3A partial flow chart of a third embodiment of the method for obtaining wavefront aberration of the human eye provided by the present invention; Figure 4 A partial flow chart of a fourth embodiment of the method for obtaining human eye wavefront aberration provided by the present invention; Figure 5 A partial flow chart of a fifth embodiment of the method for obtaining wavefront aberration of the human eye provided by the present invention; Figure 6 A partial flow chart of a sixth embodiment of the method for obtaining wavefront aberration of a human eye provided by the present invention; Figure 7 A partial flow chart of a seventh embodiment of the method for obtaining wavefront aberration of a human eye provided by the present invention; Figure 8 is the wavefront spot diagram; Figure 9 is the first processed image; Figure 10 A comparison diagram of the first processed image and the second processed image; Figure 11 A comparison diagram of the first processed image and the third processed image; Figure 12 is the reference wavefront aberration distribution diagram; Figure 13 A comparison diagram of a wavefront aberration distribution diagram obtained by a traditional method and a wavefront aberration distribution diagram obtained by an embodiment of the method for obtaining human eye wavefront aberrations of the present application; Figure 14 The reference Zernike coefficient histogram and the inversion error histogram; Figure 15 Schematic diagram of the distribution of preset paths within a cell in some embodiments of the method for obtaining human eye wavefront aberration provided by the present invention.

[0021] The realization of the objectives, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0023] It should be noted that if the implementation methods of the present invention involve directional indications (such as up, down, left, right, front, back, etc.), such directional indications are only used to explain the relative position relationship and movement status of the various components under a certain specific posture. If the specific posture changes, the directional indication will also change accordingly.

[0024] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features limited to "first" and "second" may explicitly or implicitly include at least one of such features. In addition, if "and / or" or "and / or" appears in the full text, its meaning includes three parallel schemes. Taking "A and / or B" as an example, it includes scheme A, or scheme B, or a scheme in which A and B are satisfied at the same time. In addition, the technical solutions between the various implementation methods can be combined with each other, but it must be based on the ability of ordinary technicians in this field to implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0025] The present invention provides a method for obtaining wavefront aberration of a human eye.

[0026] See also Figure 1 The method for obtaining the wavefront aberration of the human eye proposed in the present invention is applied to the Hartmann sensor. The method for obtaining the wavefront aberration of the human eye includes: S10 calculates the actual slope matrix based on the wavefront pattern obtained by the Hartmann sensor; S20 multiplies the generalized inverse matrix of the standard slope matrix by the actual slope matrix to obtain the Zernike coefficient matrix; S30 subtracts the actual slope matrix from the product of the standard slope matrix and the Zernike coefficient matrix to obtain a residual matrix; 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.

[0027] The standard slope matrix is ​​a matrix formed by the slope of the wavefront superimposed by all the Zernike polynomials.

[0028] A Hartmann sensor refers to a Shack-Hartmann Wavefront Sensor (SHWFS). This type of sensor is equipped with a microlens array, each of which forms a sub-aperture (the entire microlens array forms a complete light entrance aperture). During operation, the wavefront to be detected passes through the lens array, so different parts of the wavefront pass through different microlenses. Due to the aberrations between different parts of the wavefront, after passing through the microlenses, different parts of the wavefront have different degrees of offset relative to the optical axis of the microlenses. The method of inferring the wavefront morphology through this offset is called wavefront inversion.

[0029] This offset is represented by the slope. A microlens array is often placed in parallel with an image sensor (such as a CCD or CMOS), with the image sensor positioned on the back focal plane of the microlens array. This allows light passing through the sub-lenses to form a light spot projected onto the image sensor. Because the light passing through the sub-lenses is offset from their optical axes, the light spot is not centered on the sub-lens's projection onto the image sensor (this projection is also referred to as a sub-aperture in the wavefront spot diagram; to avoid confusion, this distinction will not be made below). Therefore, the degree of offset between the light spot and the sub-aperture center can be used to determine the phase difference between various components of the wavefront, thereby inverting the overall wavefront phase distribution.

[0030] The quotient of the above offset and the focal length of the sub-lens is the slope. Since the focal lengths of the sub-lenses are the same, the slope is determined by the above offset.

[0031] The wavefront spot diagram is the image captured by the Hartmann sensor's image sensor (it can also refer to the image converted from the image sensor to a grayscale image without any other processing). This image is formed by the actual measured wavefront. Therefore, based on this image, the offset between the light spot formed by the measured wavefront passing through the lens array and the subaperture center can be calculated, thereby determining the slope. The slopes of all light spots that pass through the lens array and form a detectable light spot form a slope data set, which is presented in array form as the actual slope matrix.

[0032] Since operations on such data sets are typically performed using matrix methods, this application uses matrices to represent data sets for ease of presentation. However, in other implementations, data can also be presented in the form of function spaces, and corresponding linear operations can be performed in the form of functions. Different linear operations can be converted into each other, so the specific principles are not detailed here.

[0033] Zernike polynomials are a set of orthogonal polynomials that lie within the unit circle. Each term in a Zernike polynomial represents a specific type of wavefront curve and, accordingly, a specific type of aberration (or even the same type but with different specific forms). Therefore, by multiplying each term in a Zernike polynomial by a different coefficient, the actual wavefront to be measured can be expanded to a certain degree of accuracy. Simply by knowing the coefficients of each term in the Zernike polynomial, we can determine the intensity of the aberration represented by each term within the wavefront to be measured.

[0034] Imagine an ideal wavefront, represented by the sum of all the terms in the Zernike polynomials, when all coefficients are 1. After passing through the lens array of the Hartmann sensor, this ideal wavefront will also exhibit the aforementioned offset, thus generating corresponding slope data. The standard slope matrix is ​​the slope data generated by this ideal wavefront passing through the lens array.

[0035] However, the standard slope matrix is ​​unique in that it typically displays the slope caused by the wavefront represented by each term separately. For example, if the Zernike polynomial has 36 terms, the standard slope matrix will contain at least 36 times the effective number of subapertures, multiplied by 2 data (the data here is the effective slope data. Of course, for ease of calculation, 0 elements may be inserted to make the standard slope matrix sparse; similarly, the actual slope matrix can also be sparse). The effective number of subapertures is the number of effective light spots formed by the wavefront to be measured (in actual measurements, not all sub-lenses will have wavefronts passing through them, so the effective number of subapertures is generally not equal to the number of subapertures). The reason for multiplication by 2 is that the image is two-dimensional, and typically a light spot will have slope data in two directions.

[0036] Similarly, in one example, the number of valid slope data in the actual slope matrix may be the number of valid subapertures multiplied by 2.

[0037] Since the ideal wavefront described above is usually not available in reality, the data in the standard slope matrix is ​​often calculated. This involves simulating the wavefront represented by each term of the Zernike polynomial, the Fraunhofer diffraction spot formed on the Hartmann sensor after passing through the microlens array, and solving for the offset of each wavefront distribution at the same sub-aperture as the wavefront spot diagram to form the standard slope matrix. In one example, the following method can be used: The wavefront represented by each term of the Zernike polynomial is used to generate a standard wavefront aberration distribution with a preset number of terms at 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). Then, based on the sub-aperture mapping in the wavefront spot diagram (in other embodiments, it can also be the grid division in the first processed image), each local wavefront is passed through the lens function and the Fraunhofer diffraction formula After the transformation, a discrete Fourier transform is performed on it to center its low-frequency portion, simulating the final point spread function (PSF). Based on the above PSF, the center of mass of the simulated light spot is calculated to obtain the center of mass coordinates of the simulated light spot under each sub-aperture. The offset between the center of mass coordinates of a sub-aperture and the reference center of mass is divided by the focal length of the sub-lens of the microlens array to obtain the slope of the simulated light spot under that sub-aperture. The sum of the slopes of all sub-apertures can form the standard slope matrix.

[0038] The preset number of terms above is the number of terms in the preselected Zernike polynomials. In principle, Zernike polynomials can have infinite terms. However, a high number of terms makes it impossible to accurately expand the measured wavefront, and in turn reduces the accuracy of the final aberrations. Therefore, the number of terms is often limited to a finite value. For example, for precise measurements, the first 36 terms of the Zernike polynomials can be used. For faster calculations, the first three, four, or five orders of the Zernike polynomials can be used.

[0039] The calculation method of the centroid coordinates can be to use the grayscale as the weight under the grayscale image to perform the weighted average of the horizontal index and the vertical index. Specifically, for a light spot, , ,in, and are the horizontal index and vertical index of the centroid, L and M are the mapping of a sub-lens on the image sensor or the number of pixels of a cell in the first processed image (for the first processed image and the cell, refer to the following embodiments) in the horizontal and vertical directions, respectively. The index variables representing the summation symbols are and The grayscale of the pixel, Represents a horizontal index, Represents the vertical index, and the subscripts of the two indexes are index variables that are also summation symbols.

[0040] The reference centroid is the center of the sub-lens's projection on the image sensor, or for embodiments where a first processed image is obtained, the center of the cell. Typically, this center can be determined by the center of the horizontal index and the center of the vertical index, but it can also be calculated using the centroid coordinate formula above, by setting all Take a constant (for example, 1), and the calculation result is the horizontal index and vertical index of the center.

[0041] The centroid of the light spot of the wavefront to be measured can also be calculated using the above formula. The calculation method of the coordinates of other centroids can also be calculated using the above formula, which will not be repeated here.

[0042] In summary, under ideal circumstances, if the Zernike polynomials can completely expand the measured wavefront, that is, if there is no error at all, the Zernike coefficient matrix (that is, the matrix formed by the coefficients of each term before and after the Zernike polynomials expand the measured wavefront), the standard slope matrix, and the actual slope matrix should satisfy ,in is the actual slope matrix, is the standard slope matrix, is the ideal Zernike coefficient matrix.

[0043] The coefficient matrix of the Zernike polynomial is often a quantity to be determined, because the actual slope matrix and the standard slope matrix can be obtained by measurement and simulation respectively (see above). Therefore, the generalized inverse matrix of the standard slope matrix is ​​usually multiplied by the actual slope matrix on the left, that is, ,in for The generalized inverse matrix (also called pseudo-inverse matrix) of is the Zernike coefficient matrix actually obtained (that is, the Zernike coefficient matrix obtained by the initial calculation in the implementation method below).

[0044] because is non-unique, so It is usually impossible to ideally unfold the actual slope wavefront, so there will be residuals, which are presented in the form of a matrix, that is, ,in This is the initial residual matrix. Usually, the formula can be used Calculate the full rank of the column The generalized inverse matrix of The matrix can usually be transposed and then the generalized inverse matrix can be calculated using the above formula.

[0045] It can be seen that the residual matrix characterizes the approximation degree of the Zernike coefficient matrix to the expansion of the actual wavefront. Therefore, based on the residual matrix, methods such as gradient descent method, 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.

[0046] Since the Zernike coefficient matrix is ​​updated in an iterative manner, a residual matrix can be obtained for each Zernike coefficient matrix. The residual matrix is ​​less than or equal to a preset value, so that the Zernike coefficient matrix can have sufficient expansion accuracy for the wavefront to be measured. Since the coefficients in the Zernike coefficient matrix represent the wavefront aberration, the more accurate the expansion of the Zernike coefficient matrix to be measured, the more accurate the aberration data actually obtained will be, thereby improving the accuracy of obtaining the wavefront aberration of the human eye.

[0047] It should be noted that, in the general sense, the residual matrix is ​​a matrix and cannot be directly considered to be less than a numerical value. However, the preset value can be a matrix with the same number of rows and columns as the residual matrix, and a value is defined for each element in the preset value matrix. In this way, when each element in the residual matrix is ​​less than the corresponding element in the preset value matrix, the residual matrix can be considered to be 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 matrix is ​​less than a preset numerical value. A comparison method can be selected according to actual needs so that the residual represented by the residual matrix is ​​small enough to meet sufficiently high measurement accuracy.

[0048] Please refer to Figure 2 In some embodiments, 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 includes: S41 according to Calculate the initial residual matrix and let ; S42 according to Calculate step length; S43 according to Calculate the initial updated Zernike coefficient matrix; S44 according to Calculate the residual matrix of the initial update; S45 Less than or equal to the preset value, output As the final solution of the Zernike coefficient matrix; S46 If it is greater than the preset value, Calculate the directional coefficient and let ; S47 according to Calculate the step length and update the Zernike coefficient matrix until the residual matrix is ​​less than or equal to the preset value; in, is the initial residual matrix, is the actual slope matrix, is the standard slope matrix, is the Zernike coefficient matrix obtained by the initial calculation, is the direction matrix used for the initial update, For the initial update, use the step length. is the Zernike coefficient matrix obtained by the initial update, is the residual matrix obtained by the initial update, is the direction coefficient used for the second update, The direction matrix used for the second update.

[0049] The direction matrix represented by represents the direction of updating the Zernike coefficient matrix. The direction refers to the direction of updating the Zernike coefficient matrix. 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 the element in the current update (the elements can be positive or negative, so it is not the absolute value, but the size relationship on the real number axis), and also specifies the proportional relationship between the changes of each element.

[0050] The step size ultimately determines the amount of change in each element of the Zernike coefficient matrix during the update. In the first 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, which is a scalar; in the second and subsequent updates, the step size is related to the current residual matrix and the previous residual matrix: that is, if we let Represents the update index, each variable is called for the first time , the second call , and so on, the calculation of step length satisfies .in, The update is associated with the previous residual matrix, and the specific principle is described as follows.

[0051] During the initial update, Take the initial residual matrix, that is ; In the second and subsequent updates, To be associated with the residual matrix of the current time and the residual matrix of the previous time, this is done by With the previous The directional coefficient is associated with the previous residual matrix, that is, the calculation of the directional coefficient satisfies the same update index as the subscript. , The calculation satisfies .visible and associated, and and associated, so It is associated with the current residual matrix and the previous residual matrix.

[0052] In this way, the step length and direction matrix are associated with the previous update in each update, and the Zernike coefficient matrix can be updated according to the previous residual situation, which can quickly decay the residual matrix and improve the efficiency of obtaining coefficients.

[0053] Since the attenuation method of the residual matrix can be a conditional loop algorithm (that is, a loop algorithm that jumps out of the loop when the residual matrix is ​​less than or equal to a preset value), the recursive formula in the loop process is given in particular (the update index is defined the same as above and is valid for the second and subsequent loops. For the initial update, refer to the above and no recursive formula is required): The calculation of the Zernike coefficient matrix satisfies ; The calculation of the residual matrix satisfies .

[0054] In the above cycle, when When it is less than or equal to the preset value, the loop stops and the output , which is the desired Zernike coefficient matrix.

[0055] Please refer to Figure 3 In some embodiments, calculating and obtaining the actual slope matrix according to the wavefront pattern obtained by the Hartmann sensor includes: S11 takes the spot whose centroid is closest to the center of the wavefront spot pattern as the central spot, and divides the grid around the centroid of the central spot so that each spot is located in a cell of the grid, thereby obtaining a first processed image; S12 obtains the offset between the centroid of the light spot and the center of the cell according to the first processed image to calculate the actual slope matrix.

[0056] Please refer to Figure 8 , Figure 8 The image shown is the wavefront spot diagram, which is the initial image acquired by the image sensor of the Hartmann sensor. The center of the wavefront spot diagram is the central pixel of the initial image acquired by the image sensor. The centroid of the spot can be obtained by referring to the centroid calculation formula proposed above. The distance between the centroid and the center is the pixel distance, which can be calculated as follows: Divide the maximum horizontal index and the maximum vertical index of the wavefront spot image by 2 (if they are non-integers, round them to integers) to obtain the index coordinates of the center pixel of the wavefront spot image, which is defined as After extracting the characteristic map of the wavefront spot map, the centroid of each spot is calculated and defined as ;calculate With each spot Euclidean distance ,in represents the Euclidean distance.

[0057] Select The smallest spot is taken as the central spot, and it is considered that the centroid of the spot should be at the center of its corresponding cell (the center of the cell is the central pixel within the cell, and the confirmation method can be the same as the confirmation method of the center of the wavefront spot diagram).

[0058] The shape of the grid should be the same as the shape of the boundary of the lens array of the Hartmann sensor mapped to the image sensor; that is, the number of pixels in the grid cell can be the ratio of the sub-lens aperture size to the image sensor pixel, and the number of cells in the grid can be the ratio of the resolution of the wavefront spot diagram to the number of pixels in the cell (or it can also be considered as the number of effective light spots collected; although the effective light spots are not necessarily all over the wavefront spot diagram, cells without light spots are generally not included in the calculation and can be ignored; in Figure 8 There are some areas without light spots at the four corners of the image.

[0059] As can be seen, although the shape of the above grid is highly correlated with the lens array, it is not formed by directly mapping the sub-lens boundaries of the lens array to the image sensor, but rather is divided according to the central spot. This can reduce the computational complexity of wavefront inversion.

[0060] Because the wavefront incident on a Hartmann sensor is often not normally incident, but rather at a certain angle to the sensor's optical axis, each spot naturally has an offset. This offset is the same for each spot due to the non-positive angle of incidence. This offset is unrelated to wavefront aberrations and, if left unaddressed, can affect the accuracy of the final wavefront inversion. Using algorithms to address this issue requires a significant amount of computation. Directly dividing the grid based on the central spot naturally eliminates this offset, reducing the inversion computational effort while ensuring measurement accuracy.

[0061] Please refer to Figure 9 , Figure 9 This is the wavefront spot diagram after the grid is divided, which is also the first processed image. It can be seen that except for the central spot, most of them have a certain offset from the center of the grid. The center of mass of the spot can be obtained by summing the cells corresponding to the spot using the above center of mass calculation formula. The horizontal and vertical offsets of the spot can be obtained by the formulas and Calculated, where is the offset of the lateral index of the spot centroid compared to the lateral index of the center of the grid, is the offset of the vertical index of the spot centroid compared to the vertical index of the center of the grid, is the actual size of the pixel, is the focal length of the sub-lens.

[0062] Please refer to Figure 4 In some embodiments, obtaining the offset between the center of mass of the light spot and the center of the cell according to the first processed image to calculate the actual slope matrix includes: S13 performs bilinear interpolation on the first processed image so that the number of pixels occupied by each cell is an integer, to obtain a second processed image; S14 obtains the offset between the centroid of the light spot and the center of the cell according to the second processed image to calculate the actual slope matrix.

[0063] Bilinear interpolation is an image scaling algorithm that introduces new pixels into the image. In the initial wavefront spot image, the number of pixels occupied by a grid cell may not be an integer. This is because the grid is divided around the center of mass of the central spot, and the center of mass coordinates calculated using the center of mass calculation formula may not be an integer. However, calculations for non-integer pixels are impossible, so the spot or grid may be offset in the first processed image.

[0064] After inserting new pixels using bilinear interpolation, the number of pixels occupied by the cell can be made an integer, which can eliminate the light spot offset caused by the non-integer number of pixels occupied by a cell, making the acquisition of the light spot offset more accurate.

[0065] Please refer to Figure 10 , Figure 10 Figure (a) is the first processed image. Figure 10 Figure (b) is the second processed image, and part of it is enlarged. It can be seen that the light spot in the second processed image has a certain displacement from the light spot at the same position in the first processed image. It can be seen that the effect of eliminating the light spot offset through bilinear interpolation is significant.

[0066] Please refer to Figure 5 In some embodiments, obtaining the offset between the center of mass of the light spot and the center of the cell according to the first processed image to calculate the actual slope matrix includes: S15: In each cell of the first processed image, selecting a grayscale threshold corresponding to each cell, and excluding pixels in the cell with a grayscale lower than the grayscale threshold, to obtain a third processed image; S16 obtains the offset between the centroid of the light spot and the center of the cell according to the third processed image to calculate the actual slope matrix.

[0067] Because the sub-lenses in a microlens array are small, they are prone to significant diffraction effects, known as Fraunhofer diffraction. This can lead to a more discrete grayscale distribution within each cell. This diffraction phenomenon creates fringes that affect the centroid calculation, in addition to the central Airy disk. Therefore, excluding pixels below the grayscale threshold can reduce the impact of diffraction on the spot centroid calculation, resulting in a more accurate final wavefront inversion structure.

[0068] The grayscale threshold can be selected by selecting the median or mode of the grayscale of the pixels in the cell, because the peripheral diffraction fringes are generally darker, you can refer to Figure 11Figure (a) in the middle is the first processed image (it can also be the second processed image, as in some embodiments, steps S15 and S16 can be performed after steps S13 and S14, at which point the first processed image becomes the second processed image. Therefore, in these embodiments, the first processed image in S15 should be understood as the second processed image). Weak Fraunhofer diffraction fringes can be seen. Selecting the median and mode can eliminate the influence of some diffraction fringes.

[0069] Please refer to Figure 6 In some embodiments, in each cell of the first processed image, selecting a grayscale threshold corresponding to the cell and excluding pixels in the cell with a grayscale lower than the grayscale threshold to obtain a third processed image includes: S151 selects the pixel with the largest gray value in the cell as the origin; S152 forms a preset path with the origin as the starting point, and selects the grayscale of pixels at locations where the grayscale increases along the preset path as a first reference value; S153 uses the maximum value of the first reference values ​​of all origins in a cell as the grayscale threshold of the current cell.

[0070] If the wavefront spot image is overexposed when it is captured, the grayscale of multiple pixels in the cell may reach the maximum grayscale, that is, the pixels with the largest grayscale in the cell; after the wavefront spot image is scaled by bilinear interpolation, multiple pixels in the cell may have the same grayscale, and the grayscale of these pixels are all greater than the grayscale of other pixels in the cell, so there may also be multiple pixels with the maximum grayscale; of course, it is also possible that during the image capture process, there are naturally multiple pixels with the same grayscale, and all of them are greater than the grayscale of other pixels in the cell.

[0071] Therefore, for a cell, there is often not only one pixel with the maximum grayscale value (in special cases, there may be only one, in which case only this one pixel needs to be processed below). All pixels with the maximum grayscale values ​​in a cell can be selected as the origin. Therefore, according to the above step S152, there will often be multiple first reference values.

[0072] The preset path needs to extend from the origin and generally tend to extend radially outward from the origin. Therefore, the preset path can be a straight line as described in the following embodiments, or it can be a curved or broken line. A single origin can have one or multiple preset paths (see below). However, since the preset path starts at the origin, the preset path can be set in the same manner for each origin to obtain the first reference value for each origin.

[0073] Multiple pixels are distributed along a preset path. It's understandable that, because the pixels at the origin already have the highest grayscale, the grayscale of the pixels along the preset path must decrease before increasing again as they move radially outward from the origin. Furthermore, the pixels with the highest grayscale are often located within the central bright spot (Fraunhofer diffraction spot) within a cell. Fraunhofer diffraction rings surround the spot within the cell, and a darker region exists between the central bright spot and the Fraunhofer diffraction rings. Therefore, the preset path only needs to extend as far as the Fraunhofer diffraction rings before pixels with increased grayscale appear.

[0074] However, there are usually pixels with increased grayscale in the central bright spot, so the pixels whose grayscale is selected as the first reference value are usually located in the central bright spot. Figure 11 This can be confirmed in the figure. It can be seen that in the third processed image on the right (Figure b), compared with the first processed image on the left (Figure a), in addition to the diffraction ring being removed, a large part of the central bright spot is also removed.

[0075] On the preset path, when the grayscale of the current pixel is greater than the grayscale of the previous pixel, it can be considered that a grayscale increase position has appeared, and the grayscale of the current pixel can be used as the first reference value, that is ... increase position can be considered When , the gray level of the n+1th pixel is taken as the first reference value, where the subscript represents the pixel number, Represents the grayscale of the nth pixel.

[0076] Excluding pixels in cells whose grayscale is lower than the grayscale threshold can be done by retaining pixels in cells whose grayscale is equal to the grayscale threshold (not performing any transformation on these pixels, i.e., retaining them), or by transforming the grayscale of pixels whose grayscale value is equal to the grayscale threshold to 0 (i.e., excluding these pixels).

[0077] It can be seen that by finding the grayscale threshold through the preset path, the final grayscale threshold can be adaptively adjusted for different cells. Referring to the above, it can be seen that if the uniformity of the central bright spot itself is high enough and the grayscale value dispersion is very low, then the main influence on the centroid calculation is the Fraunhofer diffraction ring. In this case, the position where the grayscale rises is exactly at the Fraunhofer diffraction ring. Taking the grayscale value of the pixel here as the grayscale threshold, the interference of the Fraunhofer diffraction ring can be eliminated while retaining almost all the pixels of the central bright spot.

[0078] However, if the central bright spot itself has low uniformity and a high degree of grayscale dispersion, then there will often be a location within the central bright spot where the grayscale value rises. Selecting the grayscale of the pixel here as the grayscale threshold can also exclude the part within the central light spot with greater interference. 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 exclude the influence of the Fraunhofer diffraction ring.

[0079] 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, making the final centroid calculation more accurate.

[0080] Please refer to Figure 11 , Figure 11 Figure (b) in the middle is the third processed image. After excluding pixels in the cells whose grayscale is lower than the grayscale threshold (that is, setting the grayscale value of these pixels to 0), the diffraction fringes disappear and the size of the central bright spot is reduced. This means that only the position where the light spot is most concentrated enters the final centroid calculation process, and the degree of grayscale distribution dispersion is reduced, thereby improving the accuracy of the final wavefront inversion result.

[0081] Please refer to Figure 7 In some embodiments, the preset path extends radially outward from the origin, and a plurality of paths are spaced apart in the circumferential direction of the origin, the preset path is formed with the origin as the starting point, and the grayscale of pixels at locations where the grayscale increases along the preset path is selected as the first reference value includes: S1521 determines, pixel by pixel, a change in the grayscale of a current pixel compared to the grayscale of a previous pixel in a radially outward direction from the origin along a preset path; S1522: when the grayscale of the current pixel increases for the first time compared to the grayscale of the previous pixel, selecting the grayscale of the current pixel as the second reference value; S1523 selects the maximum value of the second reference values ​​on all preset paths as the first reference value.

[0082] Because the sub-lenses in a microlens array are typically not circular but may be square, and because diffraction effects may occur between different sub-lenses, the diffraction fringes are often not circular but rather have a certain degree of asymmetry. Selecting multiple preset paths allows sampling in multiple directions, ensuring that the maximum grayscale value in the diffraction fringes is captured, ultimately eliminating interference.

[0083] Please refer to Figure 15 In some embodiments, there are 8 preset paths, all of which are straight lines; the angle between two adjacent preset paths is 45°.

[0084] Choosing too many preset paths increases the computational load, while choosing too few makes it difficult to reflect the grayscale maximum values ​​in different directions. However, setting eight preset paths and keeping the angles between adjacent preset paths at 45° allows for a moderate computational load while reflecting the grayscale maximum values ​​in all directions, ultimately ensuring interference elimination.

[0085] To clearly illustrate the grayscale threshold selection method, an additional example of grayscale threshold selection is given here: Please refer to Figure 15 , Figure 15 The box R represents the boundary of a cell in the grid. For simplicity, the Fraunhofer diffraction rings within the cell are not shown. Instead, only the central bright spot, i.e., the area within the ring C1, is shown. The center of C1 generally has the highest grayscale, so the circle O represents the set of pixels with the highest grayscale value. However, it should be noted that in practice, the set of pixels with the highest grayscale value does not necessarily form a circle; it may also form multiple, spaced points. Figure 15 It is for illustration only and does not depict the actual situation.

[0086] Figure 15 The ends of the multiple arrowed line segments L without arrows intersect within the circle O, and the intersection point represents a pixel within the circle O. Figure 15 This is a schematic diagram of selecting the first reference value for a pixel with the maximum grayscale value. To simplify the description, this pixel is referred to as the origin below (hereinafter specifically refers to this pixel, please do not confuse it with the origin above).

[0087] Line segment L is the preset path. The arrow points radially outward from the origin. The line segment is straight, and there are multiple pixels along the preset path. In the figure, C2 represents the location of increased grayscale. That is, the grayscale of the pixels on C2 will be higher than the grayscale of the pixels adjacent to and within C2. C2 is the set of pixels at the location of increased grayscale. Please note that in practice, the set of pixels at the location of increased grayscale does not necessarily form a circle or even a ring, but may form a discontinuous line or scattered points.

[0088] The point where L intersects C2 is D. The grayscale of the pixel at D is the second reference value. Since there are eight L lines and the angle between adjacent L lines is 45°, there are eight second reference values ​​for the origin. The largest of the eight second reference values ​​is the first reference value.

[0089] According to the above method, a first reference value may be selected for all pixels in cell O, and the maximum of all first reference values ​​may be used as the grayscale threshold in cell R.

[0090] 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 will be large, which makes it difficult to meet the accuracy of the aberration acquisition. In one example, the preset value can also be 、 or The units of the preset value vary depending on the units of the elements of the residual matrix. When the preset value corresponds directly to an element in the residual matrix (that is, every element in the residual matrix is ​​less than the preset value), the units of the preset value are the same as the units of the elements of the residual matrix. When the inner product of the residual matrix is ​​less than the preset value, the units of the preset value are the square of the units of the residual matrix.

[0091] Please refer to Figure 12 、 Figure 13 and Figure 14 To demonstrate the accuracy of the implementation of this application, an experimental verification is performed: Figure 14 Figure (a) in the middle is a histogram of the Zernike coefficients of the reference wavefront incident on the Hartmann sensor, that is, a wavefront with a coefficient distribution of a known Zernike polynomial is incident on the Hartmann sensor, and then the wavefront is inverted by the traditional method (model method) and the implementation method of the method for obtaining the wavefront aberration of the human eye proposed in this application. The inverted wavefronts are then compared, reflecting the improvement in accuracy achieved by this application.

[0092] The wavelength of the incident wavefront (i.e., the reference wavefront) is red light of 635 nm. The size of the sub-lens of the microlens array of the Hartmann sensor is 150 μm (square lens), the focal length is 5.2 mm, the pixel size of the image sensor is 3.45 μm, and the aperture of the collected wavefront is 5 mm.

[0093] Figure 12 : is the aberration distribution diagram of the incident wavefront, the RMS (root mean square value) of the wavefront is 0.65μm, and the PV (peak to valley value) is 2.73μm. Figure 13 The left figure is the wavefront aberration distribution diagram inverted using the traditional model method, with an RMS of 0.39μm and a PV of 1.7μm. Figure 13 The right figure in the figure is a wavefront phase difference distribution diagram inverted according to the method of the embodiment of the present application, whose RMS is 0.65μm and PV is 2.77μm.

[0094] It can be seen that the wavefront inverted by the method of the embodiment of the present application is closer to the incident wavefront, and therefore has a more accurate fitting effect, thereby improving the accuracy of obtaining the wavefront aberration of the human eye.

[0095] In addition to referring to RMS and PV, you can also refer to Figure 14(b), that is, the difference between the coefficients of the Zernike polynomials after direct reference inversion and the coefficients of the Zernike polynomials of the reference wavefront, it can be seen that the multiple Zernike polynomial coefficients of the wavefront inverted by the traditional model method are quite different from the reference wavefront. In contrast, the wavefront inverted using the implementation method of the present application is less different from the reference wavefront, which shows that the accuracy is higher.

[0096] The above-mentioned method of using RMS and PV values ​​to judge the fitting effect is also an important method for judging the final fitting effect and can be used to judge the measurement accuracy of the human eye aberration measurement device.

[0097] The present invention also provides a human eye aberration measurement device, comprising a Hartmann sensor. The device uses the wavefront spot pattern acquired by the Hartmann sensor and the aforementioned method for obtaining human eye wavefront aberrations to obtain aberration information of the human eye wavefront. Because this device incorporates all the technical solutions of all the aforementioned embodiments, it possesses at least all the beneficial effects of the technical solutions of the aforementioned embodiments, and therefore will not be further elaborated upon here.

[0098] The human eye aberration measuring device can be an instrument such as a refractive topographer, a wide-angle ophthalmometer or a window ophthalmometer. It can obtain the wavefront spot diagram through a Hartmann sensor, and then invert the wavefront aberration distribution through the above-mentioned method of obtaining the human eye wavefront aberration, and then determine the defocus condition of the human eye, which is used to draw a refractive topography map, or simply used for optometry in the macular area.

[0099] The above description is merely an exemplary embodiment of the present invention and does not limit the scope of protection of the present invention. Any equivalent structural transformation made by using the contents of the present invention description and drawings under the technical concept of the present invention, or directly / indirectly applied in other related technical fields, is included in the scope of protection of the present invention.

Claims

1. A method for obtaining wavefront aberration of a human eye, characterized in that: Applied to the Hartmann sensor, the method for obtaining the wavefront aberration of the human eye includes: An actual slope matrix is ​​obtained by calculating the wavefront spot pattern obtained by the Hartmann sensor; Multiplying the generalized inverse matrix of the standard slope matrix by the actual slope matrix to obtain a Zernike coefficient matrix; Subtracting the actual slope matrix from the product of the standard slope matrix and the Zernike coefficient matrix 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 slope of the wavefront superimposed by all the Zernike polynomials.

2. The method for obtaining the wavefront aberration of the human eye according to claim 1, wherein: 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 includes: according to Calculate the initial residual matrix and let ; according to Calculate step length; according to Calculating the Zernike coefficient matrix for initial update; according to Calculating the residual matrix for initial update; like is less than or equal to the preset value, output as the final solution of the Zernike coefficient matrix; like is greater than the preset value, then according to Calculate the directional coefficient and let ; according to Calculating the step length and updating the Zernike coefficient matrix until the residual matrix is ​​less than or equal to the preset value; in, is the initial residual matrix, is the actual slope matrix, is the standard slope matrix, is the Zernike coefficient matrix obtained by the initial calculation, is the direction matrix used for the initial update, The step length used for the initial update is as follows, is the Zernike coefficient matrix obtained by the initial update, is the residual matrix obtained by the initial update, is the directional coefficient used for the second update, The direction matrix used for the second update.

3. The method for obtaining the wavefront aberration of the human eye according to claim 1, wherein: The calculating and obtaining of the actual slope matrix according to the wavefront spot pattern obtained by the Hartmann sensor includes: The spot whose centroid is closest to the center of the wavefront spot pattern is taken as the central spot, and a grid is divided with the centroid of the central spot as the center, so that each spot is located in a cell of the grid, to obtain a first processed image; According to 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.

4. The method for obtaining the wavefront aberration of the human eye according to claim 3, wherein: The obtaining, according to the first processed image, an offset between the centroid of the light spot and the center of the cell to calculate the actual slope matrix includes: performing bilinear interpolation on the first processed image so that the number of pixels occupied by each cell is an integer, to obtain a second processed image; According to 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.

5. The method for obtaining the wavefront aberration of the human eye according to claim 3, wherein: The obtaining, according to the first processed image, an offset between the centroid of the light spot and the center of the cell to calculate the actual slope matrix includes: In each of the cells in the first processed image, a grayscale threshold corresponding to the cell is selected, and pixels in the cell with a grayscale lower than the grayscale threshold are excluded to obtain a third processed image; According to 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.

6. The method for obtaining the wavefront aberration of the human eye according to claim 5, wherein: In the first processed image, in each cell, selecting a grayscale threshold corresponding to the cell, and excluding pixels in the cell with a grayscale lower than the grayscale threshold to obtain a third processed image includes: In the cell, the pixel with the largest gray value is selected as the origin; A preset path is formed with the origin as a starting point, and the grayscale of pixels at locations where the grayscale increases along the preset path is selected as a first reference value; The maximum value of the first reference values ​​of all the origins in a cell is used as the grayscale threshold of the current cell.

7. The method for obtaining human eye wavefront aberration according to claim 6, wherein: The preset path extends radially outward from the origin, and a plurality of paths are spaced apart in a circumferential direction of the origin. The forming of the preset path with the origin as the starting point and selecting the grayscale of pixels at locations where the grayscale increases along the preset path as the first reference value includes: On the preset path, in a radially outward direction from the origin, determining pixel by pixel a change in the grayscale of a current pixel compared to the grayscale of a previous pixel; When the grayscale of the current pixel increases for the first time compared to the grayscale of the previous pixel, selecting the grayscale of the current pixel as the second reference value; The maximum value of the second reference values ​​on all the preset paths is selected as the first reference value.

8. The method for obtaining the wavefront aberration of the human eye according to claim 7, wherein: There are 8 preset paths, all of which are straight lines; the angle between two adjacent preset paths is 45°.

9. The method for obtaining wavefront aberration of a human eye according to claim 1, wherein: The preset value is less than or equal to .

10. A human eye aberration measurement device, characterized in that: A Hartmann sensor is included, and the wavefront spot diagram obtained by the Hartmann sensor is used to obtain the aberration information of the human eye wavefront by applying the method for obtaining the human eye wavefront aberration according to any one of claims 1 to 9.

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