System and method for measuring positioning accuracy of linear translation stage based on multi-longitudinal mode laser

Abstract

The present invention relates to the field of optical detection technology, and discloses a system and method for measuring the positioning accuracy of a linear displacement stage based on a multi-longitudinal mode laser, so as to realize high-precision detection of the positioning accuracy of the displacement stage. The present invention calculates the optical path difference between the initial state and the final state of the movement through the correspondence between a series of speckle images collected during the movement of the displacement stage and the speckle contrast period. Since the optical path difference is twice the linear displacement of the displacement stage, the actual linear displacement value of the displacement stage can be accurately measured to the micron level, and then the actual displacement value is compared with the stroke obtained by the displacement stage itself to calculate the linear positioning accuracy of the displacement stage, and the whole operation is simple and convenient.

Description

Technical Field

[0001] The present invention relates to the field of optical detection technology, and in particular to a system and method for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers. Background Art

[0002] Translation stages, especially electric translation stages, are widely used in high-precision manufacturing fields. Related application fields include but are not limited to: laser cutting for controlling optical phase information, optical anti-counterfeiting, and manufacturing of optical components such as wave plates.

[0003] At present, most of the high-precision translation stages used in China rely on imports. Among the domestic alternative translation stages, how to design a system that can perform high-precision detection of the positioning accuracy of the translation stage has become a technical problem that needs to be solved urgently. Summary of the invention

[0004] The present invention aims to disclose a system and method for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers, so as to achieve high-precision detection of the positioning accuracy of the translation stage.

[0005] To achieve the above-mentioned purpose, the present invention discloses a system for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode laser, comprising:

[0006] An interference generating device whose light source is a multi-longitudinal mode laser, wherein a displacement stage for changing the optical path is arranged in a beam of light waves where interference occurs, wherein the displacement stage is provided with a first, a second, a third and a fourth reflector, wherein the first reflector reflects the incident light beam to the second reflector, the second reflector reflects the incident light beam to the third reflector, and the third reflector reflects the incident light beam to the fourth reflector; wherein the normals of the first, the second, the third and the fourth reflectors are each at an angle of 45 degrees to the incident light beam, and the second reflector and the third reflector are synchronously displaced in a straight line with equal spacing between the first reflector and the fourth reflector under manual or electric drive;

[0007] A scattering sheet presenting the interference image generated by the interference generating device;

[0008] An image collector for taking pictures of the pattern presented by the scattering sheet, wherein the minimum frame rate of the image collector is at least greater than or equal to 3 times the ratio of the maximum movement rate of the translation stage divided by the interference period of the multi-longitudinal mode laser light source;

[0009] A host computer that performs data communication with the image collector is used to obtain the collected speckle images from the image collector, calculate the gray value curves under different pixel radii in each frame of the speckle image, determine the threshold range of the light intensity corresponding to the intercepted circular ring area according to the maximum gray value, and then determine the pixel radius sizes corresponding to the inner and outer rings of the circular ring area according to the threshold range; then calculate the speckle contrast of the intercepted circular ring area in each frame of the speckle image, calculate the measured optical path difference according to the correspondence between the series of image frames and the speckle contrast period during the movement of the displacement stage, and in the calculation process, equate the period of the speckle contrast with the interference period of the multi-longitudinal mode laser light source, and then calculate the positioning accuracy result according to the measured optical path difference and the stroke obtained by the displacement stage.

[0010] Corresponding to the above method, the present invention also discloses a method for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode laser, comprising:

[0011] Step S1: deploying a system for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers, the system comprising:

[0012] An interference generating device whose light source is a multi-longitudinal mode laser, wherein a displacement stage for changing the optical path is arranged in a beam of light waves where interference occurs, wherein the displacement stage is provided with a first, a second, a third and a fourth reflector, wherein the first reflector reflects the incident light beam to the second reflector, the second reflector reflects the incident light beam to the third reflector, and the third reflector reflects the incident light beam to the fourth reflector; wherein the normals of the first, the second, the third and the fourth reflectors are each at an angle of 45 degrees to the incident light beam, and the second reflector and the third reflector are synchronously displaced in a straight line with equal spacing between the first reflector and the fourth reflector under manual or electric drive;

[0013] A scattering sheet presenting the interference image generated by the interference generating device;

[0014] An image collector for taking pictures of the pattern presented by the scattering sheet, wherein the minimum frame rate of the image collector is at least greater than or equal to 3 times the ratio of the maximum movement rate of the translation stage divided by the interference period of the multi-longitudinal mode laser light source;

[0015] A host computer that performs data communication with the image collector, the method comprising:

[0016] The host obtains the collected speckle images from the image collector, calculates the gray value curves under different pixel radii in each frame of the speckle image, determines the threshold range of the light intensity corresponding to the intercepted circular ring area according to the maximum gray value, and then determines the pixel radius sizes corresponding to the outer rings in the circular ring area according to the threshold range; then calculates the speckle contrast of the intercepted circular ring area in each frame of the speckle image, calculates the measured optical path difference according to the correspondence between the series of image frames and the speckle contrast period during the movement of the displacement stage, and in the calculation process, equates the period of the speckle contrast with the interference period of the multi-longitudinal mode laser light source, and then calculates the positioning accuracy result according to the measured optical path difference and the stroke obtained by the displacement stage.

[0017] The present invention has the following beneficial effects:

[0018] 1. The optical path difference between the initial state and the final state of the movement is calculated through the correspondence between the series of speckle images collected during the movement of the displacement stage and the speckle contrast period. Since the optical path difference is twice the linear displacement of the displacement stage, the actual linear displacement value of the displacement stage can be accurately calculated to the micron level. The actual displacement value is then compared with the stroke obtained by the displacement stage itself to calculate the linear positioning accuracy of the displacement stage. The entire operation is simple and convenient.

[0019] 2. In the process of calculating the speckle contrast, the threshold range of the light intensity corresponding to the intercepted circular area and the corresponding inner and outer ring pixel radius are determined according to the maximum gray value, and the standard of area interception and calculation of the speckle contrast in a series of speckle images is ensured to be unified through automatic image recognition, thereby laying a foundation for accurately determining the corresponding relationship between the series of image frames and the speckle contrast period during the motion process.

[0020] The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0022] Figure 1 It is a system block diagram of measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers disclosed in an embodiment of the present invention.

[0023] Figure 2 It is a schematic diagram of gray value curves at different pixel radii in a single-frame speckle image disclosed in an embodiment of the present invention.

[0024] Figure 3 It is a schematic diagram of the coordinate mapping relationship of mapping a circular area to a square area disclosed in an embodiment of the present invention.

[0025] Figure 4 It is a schematic diagram of the wavelength distribution curve of a multi-longitudinal mode laser with 5 longitudinal modes disclosed in an embodiment of the present invention.

[0026] Figure 5 It is a schematic diagram of the periodic regular distribution between the speckle contrast and the optical path difference disclosed in the embodiment of the present invention.

[0027] Figure 6 It is a partially enlarged schematic diagram of a part of the speckle area disclosed in an embodiment of the present invention.

[0028] Figure 7 It is a schematic diagram of specific components of a system for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers disclosed in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0030] Example 1

[0031] This embodiment discloses a system for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers. Figure 1 As shown, including:

[0032] An interference generating device 1 whose light source is a multi-longitudinal mode laser, is provided with a displacement stage for changing the optical path in a beam of light waves where interference occurs, and the displacement stage is provided with a first, a second, a third and a fourth reflector, wherein the first reflector reflects the incident light beam to the second reflector, the second reflector reflects the incident light beam to the third reflector, and the third reflector reflects the incident light beam to the fourth reflector; wherein the normals of the first, the second, the third and the fourth reflectors are respectively at an angle of 45 degrees to the incident light beam, and the second reflector and the third reflector are synchronously displaced at equal intervals with the first reflector and the fourth reflector under manual or electric drive.

[0033] The system of this embodiment also includes a scattering sheet 2 that presents the interference image generated by the interference generating device. And also includes: an image collector 3 that takes pictures of the pattern presented by the scattering sheet, and the minimum frame rate of the image collector is at least greater than or equal to 3 times the ratio of the maximum motion rate of the translation stage divided by the interference period of the multi-longitudinal mode laser light source. Since three points consisting of two peaks and one valley can determine an interference period, for this reason, in an interference period caused by an optical path difference, at least three frames of spot images are used to accurately restore the periodicity of the speckle contrast.

[0034] Moreover, the system of this embodiment further comprises a host 4 for data communication with the image collector, which is used for acquiring the collected speckle images from the image collector, calculating the gray value curves under different pixel radii in each frame of the speckle image, determining the threshold range of the light intensity corresponding to the intercepted circular ring area according to the maximum gray value, and then determining the pixel radius sizes corresponding to the outer rings in the circular ring area according to the threshold range; then calculating the speckle contrast of the intercepted circular ring area in each frame of the speckle image, calculating the measured optical path difference according to the correspondence between the series of image frames and the speckle contrast period during the movement of the displacement stage, and in the calculation process, equating the period of the speckle contrast with the interference period of the multi-longitudinal mode laser light source, and then calculating the positioning accuracy result according to the measured optical path difference and the stroke obtained by the displacement stage.

[0035] In this embodiment, the characteristics of the speckle can be referred to as Figure 6 As shown, the image on the right is a schematic diagram of the local enlarged structure of the rectangular area on the left.

[0036] Specifically, in this embodiment, a region is selected on each frame of the speckle image to calculate the speckle contrast. The region can be selected by drawing gray value curves under different pixel radii. Figure 2 As shown in FIG. 1 , a preferred gray value curve is specifically as follows: the horizontal axis is the pixel radius of the pixel point, and the vertical axis is the gray value intensity. After finding the first maximum intensity point Imax, a threshold is taken. Preferably, the threshold = Imax*86.5%, as shown in FIG. Figure 2 As shown, the selected area is the pixel point range corresponding to the threshold. As a prerequisite, before calculating the gray value intensity of each pixel radius, the circular boundary between multiple light and dark ring stripes is first identified through the image to roughly calculate multiple potential center coordinates, and then the average value of the multiple potential center coordinates is taken to accurately locate the center coordinates. Afterwards, in the process of calculating the speckle contrast, the pixel information of the intercepted circular ring area is first converted into the pixel information of the rectangular area through polar coordinate transformation and interpolation algorithm, and then the speckle contrast corresponding to the rectangular area is calculated, and the calculation result of the speckle contrast corresponding to the rectangular area is equal to the speckle contrast result of the intercepted circular ring area. Specifically: The calculation formula of speckle contrast C is:

[0037] C=Std(I) / Mean(I)

[0038] Among them, I is the gray value intensity, Std(I) represents the standard deviation of the intensity on the image, and Mean(I) represents the average value of the intensity on the image.

[0039] Reference Figure 3 , the pixel information of the circular area is transformed into the pixel information of the rectangular area through polar coordinate transformation and interpolation algorithm, specifically including:

[0040] 1. In a two-dimensional coordinate system, the (x, y) value is used to describe the position of a point, while in a polar coordinate system, the distance ρ to the origin and the angle θ are used to describe the position of the point.

[0041] 2. First of all, normal images are in a rectangular coordinate system and can be regarded as a two-dimensional plane. If we want to transform the image coordinates, we must first convert the position to a new coordinate system and then assign the value to it. Here we need to determine the position and grayscale value, that is, the grayscale value and position of any pixel after the transformation, and the grayscale value after the transformation remains unchanged.

[0042] 3. Solve the positional relationship of the transformation. The key to polar coordinate transformation and its inverse transformation is to determine the pixel value of each pixel on the image after polar coordinate transformation based on the image before polar coordinate transformation. That is, find Figure 3 The correspondence between the geometric coordinates of the "circle diagram" on the left and the "square diagram" on the right.

[0043] like Figure 3 As shown, the key to realize polar coordinate transformation is to find the corresponding point p(m, n) on the square graph for any point P(i, j) on the circular graph, for example, P(0, 10), R=10, and then realize the assignment of all pixel points on the circular graph through interpolation algorithm.

[0044] On the square diagram, the number of rows and columns is M and N respectively. Each column on the square diagram corresponds to each radius on the circular diagram. There is a length scaling factor delta_r = M / R in the radial direction. If M is 10, then delta_r = 1. The circumference is divided into N equal parts, that is, the angle factor is delta_t = 2π / N. If N is 32, then delta_t = 2π / 32 = π / 16.

[0045] On the circular graph, the image coordinates (i, j) and the world coordinates (x, y) have the following transformation relationship: x = j-R, y = R-i; then the world coordinates corresponding to P (0, 10) are temporarily taken as (0, 10). Then, the radius length of point P in the figure is r = sqrt (xx + yy) = 10, and the angle theta = arctan (y / x) = π / 2; thus, the number of rows corresponding to point P on the circular graph on the square graph is r / delta_r = 10 / 1 = 10; the number of columns corresponding to point P on the circular graph on the square graph is n = thata / delta_t = 8. The above is the basic principle of polar coordinate transformation. Combined with the corresponding interpolation algorithm, the polar coordinate transformation of the image can be realized.

[0046] In this embodiment, the wavelength λ of the laser and the longitudinal mode wavelength interval △λ are known, and the coherence length Lc of the laser can be calculated in advance:

[0047] Lp=λ 2 / △λM

[0048] Lc=λ 2 / ((N-1)*△λ M )

[0049] Where N is the number of longitudinal modes, △λ M is the longitudinal mode spacing. If N is set to 5, Figure 4 The multi-longitudinal mode laser shown in FIG. 1 shows a periodic law of the spot contrast obtained based on the multi-longitudinal mode laser. Figure 5 shown.

[0050] Optical path difference OPD=s*Lp, where s is the correspondence between a series of speckle images and a speckle contrast period during the movement of the stage, that is, the number of interference periods covered during the linear motion of the stage corresponding to the first and last collected spot images, and the types of the number include integers (such as an integer of 5) and undotted fractions (such as a decimal point of 5.1).

[0051] The positioning accuracy result is then calculated based on the measured optical path difference and the stroke obtained by the displacement stage; for example: if the actual optical path difference is 100 microns, the corresponding actual displacement of the linear displacement stage is 50 microns. If the data obtained by the displacement stage itself is 48 microns, the positioning accuracy error is 4%.

[0052] Alternatively, if Figure 7 As shown, a system for measuring the positioning accuracy of a linear translation stage based on a multi-longitudinal mode laser specifically includes: the light emitted by the multi-longitudinal mode laser passes through the first polarizer 10 and the first half-wave plate (for rotating the polarization direction of the laser) 20 in sequence, and is then split into P light and S light by the first PBS (the transmitted light is P light, and the reflected light is S light), and then the P light passes through the translation stage 40 and the fifth reflector 60 in sequence to reach the second PBS, and the S light also reaches the second PBS after being reflected by the sixth reflector 50, and the two beams of light combined in the second PBS produce interference, and are imaged on the scattering plate 90 after the polarization direction is selected by the second polarizer 80, and then the fixed focus lens 100 of the image collector realizes the acquisition of the speckle image. Among them, the first reflector 41, the second reflector 43, the third reflector 44 and the fourth reflector 42 as described above are arranged on the translation stage 40; and during the test process, the positions of the first and fourth reflectors 41 and 42 are fixed, and the second and third reflectors 43 and 44 can be synchronously displaced with the first and fourth reflectors 41 and 42 in the direction of travel as shown by the dotted line in the figure.

[0053] Example 2

[0054] Corresponding to the above embodiment, this embodiment discloses a method for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode laser, comprising:

[0055] Step S1, deploying a system for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers.

[0056] The system of this embodiment is the same as that of embodiment 1, and specifically includes:

[0057] An interference generating device whose light source is a multi-longitudinal mode laser, in which a displacement stage for changing the optical path is arranged in a beam of light waves where interference occurs, the displacement stage is provided with a first, a second, a third and a fourth reflector, the first reflector reflects the incident light beam to the second reflector, the second reflector reflects the incident light beam to the third reflector, and the third reflector reflects the incident light beam to the fourth reflector; wherein the normals of the first, the second, the third and the fourth reflectors are each at an angle of 45 degrees to the incident light beam, and the second reflector and the third reflector are synchronously displaced at equal intervals between the first reflector and the fourth reflector under manual or electric drive.

[0058] A scattering sheet presenting the interference image generated by the interference generating device.

[0059] An image collector for photographing the pattern presented by the scattering sheet, wherein the minimum frame rate of the image collector is at least greater than or equal to 3 times the ratio of the maximum movement rate of the translation stage divided by the interference period of the multi-longitudinal mode laser light source.

[0060] A host computer that performs data communication with the image collector.

[0061] The method of this embodiment also includes:

[0062] Step S2, the host obtains the collected speckle images from the image collector, calculates the gray value curves under different pixel radii in each frame of the speckle image, determines the threshold range of the light intensity corresponding to the intercepted circular ring area according to the maximum gray value, and then determines the pixel radius sizes corresponding to the inner and outer rings of the circular ring area according to the threshold range; then calculates the speckle contrast of the intercepted circular ring area in each frame of the speckle image, calculates the measured optical path difference according to the correspondence between the series of image frames and the speckle contrast period during the movement of the translation stage, and in the calculation process, equates the period of the speckle contrast with the interference period of the multi-longitudinal mode laser light source, and then calculates the positioning accuracy result according to the measured optical path difference and the stroke obtained by the translation stage.

[0063] Preferably, the method of this embodiment further includes: in the process of calculating the speckle contrast, firstly transforming the pixel information of the intercepted circular area into the pixel information of the rectangular area through polar coordinate transformation and interpolation algorithm, and then calculating the speckle contrast corresponding to the rectangular area, and equating the calculation result of the speckle contrast corresponding to the rectangular area with the speckle contrast result of the intercepted circular area.

[0064] In summary, the method and method for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode laser disclosed in the embodiments of the present invention have the following beneficial effects:

[0065] 1. The optical path difference between the initial state and the final state of the movement is calculated through the correspondence between the series of speckle images collected during the movement of the displacement stage and the speckle contrast period. Since the optical path difference is twice the linear displacement of the displacement stage, the actual linear displacement value of the displacement stage can be accurately calculated to the micron level (the accuracy is usually limited by the half-width of the laser. For common semiconductor lasers, the longitudinal mode wavelength interval is less than 10 nanometers, so the minimum accuracy of one interference cycle is at the level of tens of microns. Taking into account the period division, such as 0.2 period, the optical path difference is twice the displacement, so that the minimum accuracy can reach several microns). Then, the actual displacement value is compared with the stroke obtained by the displacement stage itself to calculate the linear positioning accuracy of the displacement stage, and the whole operation is simple and convenient.

[0066] 2. In the process of calculating the speckle contrast, the threshold range of the light intensity corresponding to the intercepted circular area and the corresponding inner and outer ring pixel radius are determined according to the maximum gray value, and the standard of area interception and calculation of the speckle contrast in a series of speckle images is ensured to be unified through automatic image recognition, thereby laying a foundation for accurately determining the corresponding relationship between the series of image frames and the speckle contrast period during the motion process.

[0067] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A system for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode laser, characterized in that: include: An interference generating device whose light source is a multi-longitudinal mode laser, wherein a displacement stage for changing the optical path is arranged in a beam of light waves where interference occurs, wherein the displacement stage is provided with a first, a second, a third and a fourth reflector, wherein the first reflector reflects the incident light beam to the second reflector, the second reflector reflects the incident light beam to the third reflector, and the third reflector reflects the incident light beam to the fourth reflector; wherein the normals of the first, the second, the third and the fourth reflectors are each at an angle of 45 degrees to the incident light beam, and the second reflector and the third reflector are synchronously displaced in a straight line with equal spacing between the first reflector and the fourth reflector under manual or electric drive; A scattering sheet presenting the interference image generated by the interference generating device; An image collector for taking pictures of the pattern presented by the scattering sheet, wherein the minimum frame rate of the image collector is at least greater than or equal to 3 times the ratio of the maximum movement rate of the translation stage divided by the interference period of the multi-longitudinal mode laser light source; A host computer that performs data communication with the image collector is used to obtain the collected speckle images from the image collector, calculate the gray value curves under different pixel radii in each frame of the speckle image, determine the threshold range of the light intensity corresponding to the intercepted circular ring area according to the maximum gray value, and then determine the pixel radius sizes corresponding to the inner and outer rings of the circular ring area according to the threshold range; then calculate the speckle contrast of the intercepted circular ring area in each frame of the speckle image, calculate the measured optical path difference according to the correspondence between the series of image frames and the speckle contrast period during the movement of the displacement stage, and in the calculation process, equate the period of the speckle contrast with the interference period of the multi-longitudinal mode laser light source, and then calculate the positioning accuracy result according to the measured optical path difference and the stroke obtained by the displacement stage.

2. The system according to claim 1, characterized in that Also includes: In the process of speckle contrast calculation, the pixel information of the intercepted circular area is first converted into the pixel information of the rectangular area through polar coordinate transformation and interpolation algorithm, and then the speckle contrast corresponding to the rectangular area is calculated, and the calculation result of the speckle contrast corresponding to the rectangular area is equal to the speckle contrast result of the intercepted circular area.

3. A method for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode laser, characterized in that: include: Step S1: deploying a system for measuring the positioning accuracy of a linear translation stage based on multi-longitudinal mode lasers, the system comprising: An interference generating device whose light source is a multi-longitudinal mode laser, wherein a displacement stage for changing the optical path is arranged in a beam of light waves where interference occurs, wherein the displacement stage is provided with a first, a second, a third and a fourth reflector, wherein the first reflector reflects the incident light beam to the second reflector, the second reflector reflects the incident light beam to the third reflector, and the third reflector reflects the incident light beam to the fourth reflector; wherein the normals of the first, the second, the third and the fourth reflectors are each at an angle of 45 degrees to the incident light beam, and the second reflector and the third reflector are synchronously displaced in a straight line with equal spacing between the first reflector and the fourth reflector under manual or electric drive; A scattering sheet presenting the interference image generated by the interference generating device; An image collector for taking pictures of the pattern presented by the scattering sheet, wherein the minimum frame rate of the image collector is at least greater than or equal to 3 times the ratio of the maximum movement rate of the translation stage divided by the interference period of the multi-longitudinal mode laser light source; A host computer that performs data communication with the image collector, the method comprising: The host obtains the collected speckle images from the image collector, calculates the gray value curves under different pixel radii in each frame of the speckle image, determines the threshold range of the light intensity corresponding to the intercepted circular ring area according to the maximum gray value, and then determines the pixel radius sizes corresponding to the outer rings in the circular ring area according to the threshold range; then calculates the speckle contrast of the intercepted circular ring area in each frame of the speckle image, calculates the measured optical path difference according to the correspondence between the series of image frames and the speckle contrast period during the movement of the displacement stage, and in the calculation process, equates the period of the speckle contrast with the interference period of the multi-longitudinal mode laser light source, and then calculates the positioning accuracy result according to the measured optical path difference and the stroke obtained by the displacement stage.

4. The method according to claim 3, characterized in that Also includes: In the process of speckle contrast calculation, the pixel information of the intercepted circular area is first converted into the pixel information of the rectangular area through polar coordinate transformation and interpolation algorithm, and then the speckle contrast corresponding to the rectangular area is calculated, and the calculation result of the speckle contrast corresponding to the rectangular area is equal to the speckle contrast result of the intercepted circular area.

Images