A method of monitoring imaging position shift of a doppler differential interferometer

Abstract

The present application relates to interferometer, specifically relates to a kind of Doppler differential interferometer imaging position shift monitoring method, for solving the insufficient that Doppler differential interferometer is caused by thermal drift effect to lead to image plane shift.The Doppler differential interferometer imaging position shift monitoring method is by extracting and expanding interferogram signal, constructs groove distribution model D (x) And scale signal distribution model I (x), utilize multiple calibration interferogram optimization model parameter, generate simulation scale signal;Again in actual measurement, by minimizing the error of simulation scale signal and measured scale signal, optimize first pulse position a0, to realize the accurate monitoring of Doppler differential interferometer imaging position shift amount.

Description

TECHNICAL FIELD

[0001] The present application relates to an interferometer, in particular to a method for monitoring imaging position shift of Doppler differential interferometer. BACKGROUND

[0002] Doppler differential interferometer is an improved optical measurement device based on Michelson interferometer, which replaces the mirrors of two arms with blazed gratings, and the two arms are asymmetrically arranged relative to the beam splitter. After the incident light passes through the beam splitter, it is divided into two beams, which are diffracted by the blazed gratings and then converge at the beam splitter. The two beams with different optical path differences interfere to form Fizeau interference fringes, which are recorded by the detector after the imaging system. Doppler differential interferometer does not require precise scanning structure, and can rely on the detector to sample the interference signals at different optical path differences at the same time, so that two-dimensional interferograms can be obtained at one time, which has the advantages of high light flux, high phase sensitivity and multi-channel simultaneous measurement, and is applied to the field of atmospheric wind field measurement.

[0003] Doppler differential interferometer measures atmospheric wind speed by measuring the phase change of interferogram caused by the Doppler frequency shift of atmospheric airglow spectrum. The interferogram is measured by the detector, and in actual measurement, environmental temperature change, platform vibration, and change of interferometer structure will all cause the misalignment of Doppler differential interferometer relative to the interferometer, which is specifically manifested as the overall shift of the interferogram on the detector image plane. In phase inversion, the shift will introduce additional phase change, thereby affecting the wind speed measurement result. Therefore, how to accurately detect the shift of the interferogram becomes the key to improve the phase measurement accuracy. SUMMARY

[0004] The purpose of the present application is to solve the problem of image plane shift of Doppler differential interferometer due to thermal drift effect, and to provide a method for monitoring imaging position shift of Doppler differential interferometer.

[0005] In order to solve the above-mentioned problems of the prior art, the present application provides the following technical solutions:

[0006] A method for monitoring imaging position shift of Doppler differential interferometer, characterized in that it comprises the following steps:

[0007] Step 1: selecting two adjacent rows of data in the interferogram, one of which contains a scale signal, denoted as I real (n), n is the horizontal coordinate of the sampling point on the detector, n=1, 2, 3,..., N, N is the total number of sampling points, and the other is the interference signal close to the scale signal, denoted as I out (n);

[0008] Step 2: interpolating I real (n) and I out(n) extended to the original A times, respectively, I real (x) and I out (x), x is the horizontal coordinate of the sampling point after extension, A ∈ [100, 1000];

[0009] Step 3, generate a square wave function f(x) from the convolution of the comb function h(x) and the rectangular function, and then model the groove distribution through the convolution of the square wave function f(x) and the Gaussian kernel g(y) to obtain the groove distribution model

[0010] Where, rect() represents the rectangular function, x size is the number of sampling points, N notches is the number of pulses, * represents the convolution operator symbol, W notches represents the width of the rectangular function, a0 is the first pulse position of the comb function h(x), σ is the standard deviation, and y is the number of sampling points of the Gaussian kernel.

[0011] Step 4, identify all local minimum points in I real (x) obtained in step 2, and generate the lower envelope curve by fitting as the dark signal I in (x) corresponding to the groove region.

[0012] Step 5, according to I out (x) obtained in step 2, the groove distribution model D(x) obtained in step 3, and the dark signal I in (x) obtained in step 4, establish the scale signal distribution model I(x) = D(x)·I out (x) + (1-D(x))·I in (x).

[0013] Step 6, according to the method of steps 1-2, obtain I real (x) of multiple calibration interferograms at the same position, and use multiple I real (x) to calculate W notches , σ, N notches in the scale signal distribution model I(x), and then take the average of W notches , σ, N notches obtained from multiple calibration interferograms as the optimal W notches , σ, N notches , and use the scale signal distribution model I(x) to generate the simulation scale signal I(x, a0).

[0014] Step 7, after actual measurement, according to the method of steps 1-2, obtain the measured scale signal I′ real (x) of the measured interferogram, and construct the measured scale signal I′ real(x) and I (x, a0), find the optimal value of a0 to minimize the error function E(a0), use the optimal value of a0 to represent the position of the scale image on the detector image plane, and complete the monitoring of the imaging position offset of the Doppler differential interferometer.

[0015] Further, the step 2 is specifically:

[0016] The sampling points are expanded to A times of the original by interpolation, and the horizontal coordinates of the expanded sampling points are calculated Wherein k is the index of the expanded sampling point number, k = 1, 2, …, AN.

[0017] For the coordinate x of the expanded sampling point, the signal at the corresponding position is calculated using the Lagrange interpolation polynomial to generate I real (x) and I out (x).

[0018] Further, the step 3 is specifically:

[0019] Step 3.1, define the comb function h(x) as follows:

[0020]

[0021] Wherein, δ represents the impulse function, x size / N notches Indicates the distance between adjacent pulses;

[0022] Define the square wave function f(x) as follows:

[0023] f(x) = h(x) * rect(x·W notches )

[0024] Wherein, the square wave function f(x) changes in the range of 0 to 1, when h(x) = 1, it represents the non-groove area, and when h(x) = 0, it represents the groove area.

[0025] Step 3.2, define the Gaussian kernel g(y) as follows:

[0026]

[0027] Define the groove distribution model D(x) as follows:

[0028]

[0029] Further, the step 4 is specifically:

[0030] Step 4.1, set the local minimum point (x i , I real (x iThe following conditions need to be met:

[0031]

[0032] where x i is the position of the minimum point, I real (x i ) is the corresponding signal value; x i-1 and x i+1 represent the adjacent sampling points before and after x i , respectively; the threshold value Threshold = mean(I real (x i ));

[0033] Step 4.2, generate the lower envelope curve by interpolating the local minimum points (x real , I i ) identified in step 4.1, as the corresponding dark signal I in (x) of the groove region.

[0034] Further, the step 6 is specifically:

[0035] Step 6.1, collect multiple calibration interferograms, and obtain I real (x) at the same position of multiple calibration interferograms according to the method of steps 1-2;

[0036] Step 6.2, for each calibration interferogram, determine the number of pulses N real by performing autocorrelation analysis on I notches (x), and fit I real (x) using the scale signal distribution model I(x) established in step 5 to calculate the width W notches of the rectangular function, the standard deviation σ of the Gaussian kernel;

[0037] Finally, take the average of W notches , σ, N notches obtained from multiple calibration interferograms as the optimal W notches , σ, N notches ;

[0038] Step 6.3, set an initial estimate for the position a0 of the first pulse of the comb function h(x), use the optimal W notches , σ, N notches , and generate a simulated scale signal I(x, a0) using the scale signal distribution model I(x).

[0039] Further, in step 7, the error function E(a0) is as follows:

[0040]

[0041] Compared with the prior art, the present application has the following advantages

[0042] (1) The present application is a method for monitoring the imaging position shift of a Doppler differential interferometer. By extracting and expanding the interferogram signal, a groove distribution model D(x) and a scale signal distribution model I(x) are constructed. The model parameters are optimized using multiple calibration interferograms to generate a simulated scale signal. In actual measurement, the first pulse position a0 is optimized by minimizing the error between the simulated scale signal and the measured scale signal, thereby achieving accurate monitoring of the imaging position shift of the Doppler differential interferometer.

[0043] (2) The present application greatly improves the calculation speed and algorithm running efficiency by simplifying the scale signal model and reducing the fitting parameters.

[0044] (3) The present application improves the adaptability to noise and environmental changes through averaging processing and parameter design related to physical characteristics.

[0045] (4) The present application uses a global optimization mechanism and a clear signal separation strategy to significantly improve the accuracy of position shift detection. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 Figure 1 is a schematic diagram of the interferogram in step 1 of the present application;

[0047] Figure 2 Figure 2 is a schematic diagram of I real (n) and I out (n) in step 1 of the present application;

[0048] Figure 3 Figure 3 is a schematic diagram of the groove distribution model D(x) in step 3 of the present application;

[0049] Figure 4 Figure 4 is a schematic diagram of the dark signal I in (x) corresponding to the groove region in step 4 of the present application;

[0050] Figure 5 Figure 5 is a schematic diagram of the fitting effect of the measured scale signal I′ real (x) and the simulated scale signal I(x, a0) in step 7 of the present application. DETAILED DESCRIPTION

[0051] The present application will be further described below in conjunction with the drawings and exemplary embodiments.

[0052] The present application precisely etches periodic grooves along the diffraction direction on the grating of a Doppler differential interferometer; for example,Figure 1 As shown, outside the groove, the incident light is diffracted normally, forming interference fringes on the detector; inside the groove, due to the influence of laser processing, the grating surface and the substrate are damaged, causing the incident light to be unable to form diffraction on the arm grating, and the corresponding position of the detector only has the diffraction light of the other arm grating; therefore, the signal corresponding to the groove line on the interference pattern is the combination of the signals inside and outside the groove, which is called a ruler image; the ruler image is modeled by using signal parameters, and the offset of the interference pattern is determined by globally fitting the ruler signal.

[0053] Based on the above idea, the application provides a monitoring method for imaging position offset of a Doppler differential interferometer, comprising the following steps:

[0054] Step 1, referring to Figure 1 , two adjacent rows of data are selected in the interference pattern formed by the Doppler differential interferometer, one of which contains a ruler signal (such as the solid line in Figure 2 ), denoted as I real (n), n is the horizontal coordinate of the sampling point on the detector, n=1, 2, 3,..., N, N is the total number of sampling points on the detector, and the other row of data is an interference signal (such as the dashed line in Figure 2 ) close to the ruler signal, which is denoted as I out (n);

[0055] I out (n) can be considered as the data corresponding to the region outside the groove in the ruler signal, and it can be seen from Figure 2 that the upper envelope of I out (n) is basically consistent with that of I real (n); in an ideal case, the signal without a groove in I real (n) should conform to the same cosine distribution as any row of interference signals in the interference pattern, but due to instrument aberration or uneven response of the detector, there are differences in amplitude, phase and frequency between different rows of interference signals, so the distance between I out (n) and I real (n) should be as small as possible to reduce the difference; in addition, in order to ensure signal quality, a region with high signal-to-noise ratio should be selected;

[0056] Step 2, I real (n) and I out (n) are expanded to A times of the original by interpolation, respectively obtaining I real (x) and I out (x), x is the horizontal coordinate of the expanded sampling point, and A∈[100, 1000];

[0057] Specifically, the sampling points are expanded to A times of the original by interpolation, and the horizontal coordinate of the expanded sampling point is calculated Where k is the index of the extended sampling point number, k = 1, 2…, AN, A = 1000;

[0058] For the extended sampling point coordinate x, the signal at the corresponding position is calculated using the Lagrange interpolation polynomial to generate I real (x) and I out (x);

[0059] Take I real (n) as an example, n i , is the i'th sampling point horizontal coordinate, I(n i′ ) is the function value at n i′ , represents the sampling point vertical coordinate, and the interpolated scale signal is I real (x):

[0060]

[0061] In the formula, j represents an auxiliary index used when calculating the Lagrange basis function;

[0062] Here I real (x) is the extended data of I real (n), and each data point (n i′ , I(n i′ )) corresponds to a Lagrange basis function: The function of this basis function is to ensure that when x = n i′ , the value of the basis function is 1, and when all other sampling points, the value of the basis function is 0;

[0063] Similarly, I out (x) is the extended data of I out (n);

[0064] Step 3, generate square wave function f(x) from the convolution of comb function h(x) and rectangular function, and then model the groove distribution by the convolution of square wave function f(x) and Gaussian kernel g(y), to obtain the groove distribution model D(x);

[0065] Step 3.1, generate square wave function f(x) from the convolution of comb function h(x) and rectangular function;

[0066] The square wave function has clear high-low switching characteristics, which can accurately represent the alternating structure of the groove and non-groove area. This characteristic makes the square wave function exhibit obvious periodic signal changes in the switching of the groove position, thereby effectively reflecting the periodic distribution of the groove;

[0067] First, define the comb function h(x) as follows:

[0068]

[0069] where δ denotes the impulse function, x size is the number of sampling points, N notches is the number of pulses, representing the number of grooves, x size / N notches denotes the distance between adjacent pulses, also the distance between adjacent grooves; a0represents the position of the first pulse of the comb function h(x), used to adjust the starting position of the groove region;

[0070] The square wave function f(x) is redefined as follows:

[0071] f(x) = h(x) * rect(x·W notches )

[0072] where rect() denotes the rectangular function, * denotes the convolution operator, W notches denotes the width of the rectangular function, determining the width of the groove-free region, and the groove width is x size / N notches -W notches ; the square wave function f(x) varies from 0 to 1, indicating the groove-free region when h(x) = 1, and the groove region when h(x) = 0;

[0073] Step 3.2, model the groove distribution by the convolution of the square wave function f(x) and the Gaussian kernel g(y), obtaining the groove distribution model D(x);

[0074] The actual groove edge is usually not ideal sharp transition, but due to the limitation of manufacturing process, the microstructure of the material and other factors lead to the blur of the groove edge; in order to simulate this phenomenon, the Gaussian kernel is introduced to convolve the square wave function; the Gaussian kernel smooths the sharp transition of the square wave, simulates the actual edge characteristics of the groove, and can more accurately describe the actual distribution characteristics of the groove while maintaining the periodic distribution;

[0075] The Gaussian kernel g(y) is defined as follows:

[0076]

[0077] where σ is the standard deviation, determining the spread of the Gaussian kernel; y is the sampling point number of the Gaussian kernel, which is related to the period of the square wave function f(x); in general case, the sampling point number y is 1 to 2 times the sample point number in the period of the square wave function f(x), ensuring that the Gaussian kernel can fully smooth the square wave edge without significantly changing the overall structure of the square wave function f(x);

[0078] The groove distribution model D(x) is defined as follows:

[0079]

[0080] D(x) as shown in Figure 3 , which can reflect the blur characteristics of the groove edge more realistically;

[0081] Step 4, I real (x) is obtained from I in (x) in step 2, and all local minimum points are identified by fitting to generate a lower envelope curve as the corresponding dark signal I real (x) of the groove region;

[0082] Step 4.1, the signal of the groove region in the ruler signal is usually weaker than that of the non-groove region, which is manifested as a dark signal; in order to extract the dark signal, all local minimum points (x i , I real (x i )) can be identified by analyzing I real (x) obtained in step 2, as indicated by the asterisk in Figure 4 , where x i is the position of the minimum point, and I real (x i ) is the corresponding signal value; these local minimum points satisfy the following conditions:

[0083] I real (x i ) < I real (x i-1 ) and I real (x i ) < I real (x i+1 )

[0084] where x i-1 and x i+1 represent the adjacent sampling points before and after x i , respectively;

[0085] In addition, in order to avoid abnormal values, a threshold Threshold is set, Threshold = mean(I real (x));

[0086] I real (x i ) < Threshold is required;

[0087] Step 4.2, by interpolating and fitting the local minimum points (x i , I real (x i )) identified in step 4.1, a lower envelope curve is generated as the corresponding dark signal I in (x) of the groove region;

[0088] Step 5, I i (x) is obtained from I real (x) in step 2, and all local minimum points are identified by fitting to generate a lower envelope curve as the corresponding dark signal I real (x) of the groove region;out (x), the groove distribution model D(x) obtained in step 3, the dark signal I in (x) obtained in step 4

[0089] The scale image, as the core signal for monitoring the imaging position shift in the Doppler differential interferometer, is essentially a complex optical signal distribution formed by the mutual superposition of the signals of the groove area and the non-groove area. The scale image reflects the signal change caused by the micro displacement of the interferometer on the detector plane by combining the distribution characteristics of the interference fringes and the geometric characteristics of the groove structure. In order to accurately describe the scale image, the scale signal distribution model I(x) is established as,

[0090] I(x) = D(x) · I out (x) + (1-D(x)) · I in (x)

[0091] wherein, I out (x) represents the interference signal of the non-groove area, which represents the complete interference fringe structure formed after the light beam passes through the interferometer without structural damage, and has clear phase and amplitude characteristics.

[0092] For a given position, if D(x) is close to 1, it means that the position is mainly dominated by the interference signal I out (x) of the non-groove area; if D(x) is close to 0, it means that the position is mainly dominated by the signal I in (x) of the groove area; by adjusting the parameters of D(x), the overall morphology of the scale image can be simulated.

[0093] Step 6, calculate the parameters W notches , σ, N notches of the scale signal distribution model I(x);

[0094] The scale signal distribution model I(x) established in step 5 contains three key parameters, namely the width W notches of the rectangular function, the standard deviation σ of the Gaussian kernel, and the pulse number N notches in the comb function. These parameters are closely related to the physical characteristics of the interferometer and are not affected by environmental changes.

[0095] Step 6.1, under the condition of stable laboratory environment, a plurality of calibration interference images are collected, and I real (x) at the same position of the plurality of calibration interference images is obtained according to the method of steps 1-2;

[0096] Step 6.2, for each calibration interference image, the pulse number N is determined by performing autocorrelation analysis on I real (x)notches , and use the scale signal distribution model I(x) established in step 5 to fit I real (x), calculate the width W of the rectangular function notches , the standard deviation σ of the Gaussian kernel;

[0097] Finally, take the W obtained from multiple calibration interferograms notches ,σ,N notches The average value of W is the optimal notches ,σ,N notches ;

[0098] Step 6.3, set an initial estimate for the position a0 of the first pulse of the comb function h(x), using the optimal W notches ,σ,N notches , generate a simulated scale signal I(x, a0) according to the scale signal distribution model I(x);

[0099] Step 7: After the actual measurement, the measured scale signal I′ of the measured interference pattern is obtained according to the method of steps 1 to 2. real (x), construct the measured scale signal I′ real The error function E(a0) between (x) and the simulated scale signal I(x, a0):

[0100]

[0101] Using the gradient descent method, find the optimal value of a0 to minimize the error function E(a0), so that I(x, a0) is consistent with the measured scale signal I′ real (x) achieves the best fit;

[0102] The optimal value of a0 is used to characterize the position of the scale image on the detector image plane, and the Doppler differential interferometer imaging position offset is monitored.

[0103] The fitting effect is shown in the attached Figure 5 As shown, the solid line represents the measured scale signal I' real (x), the dotted line represents the simulated scale signal I(x, a0), and it can be seen that the two signals are basically consistent.

Claims

1. A method of monitoring imaging position shifts of a Doppler differential interferometer, characterized in that Comprising the following steps: Step 1, select two adjacent rows of data in the interferogram, one of which contains the scale signal, denoted as I real (n), n is the horizontal coordinate of the sampling point on the detector, n = 1, 2, 3,..., N, N is the total number of sampling points, and the other is the interference signal close to the scale signal, denoted as I out (n); Step 2, I real (n), I out (n) is extended to A times of the original, respectively, I real (x) and I out (x), x is the horizontal coordinate of the sampling point after expansion, A ∈ [100, 1000]; Step 3, generate the square wave function f(x) from the convolution of the comb function h(x) and the rectangular function, and then model the groove distribution by the convolution of the square wave function f(x) and the Gaussian kernel g(y) to obtain the groove distribution model where rect() denotes a rectangular function, x size is the number of sampling points, N notches is the number of pulses, * denotes a convolution operator, W notches denotes the width of the rectangular function, a0is the first pulse position of the comb function h(x), σ is the standard deviation, and y is the number of sampling points of the Gaussian kernel. Step 4, I from step 2 real (x) All local minimum points are identified and the lower envelope curve is generated by fitting as the corresponding dark signal I for the groove region in (x); Step 5, I according to step 2 out (x), the recess distribution model D(x) obtained in step 3, the dark signal I obtained in step 4 in (x), the scale signal distribution model I(x) = D(x) · I is established out (x) + (1 - D(x)) · I in (x); Step 6: Obtain the I values ​​of multiple calibration interference patterns at the same position according to the method of steps 1 and 2. real (x), using multiple I real (x) respectively calculate W in the scale signal distribution model I(x) notches ,σ,N notches , and then take the W obtained from multiple calibration interferograms notches ,σ,N notches The average values ​​of the optimal W notches ,σ,N notches , and use the scale signal distribution model I(x) to generate the simulated scale signal I(x, a0); Step 7, after the actual measurement, the actual measured scale signal I' of the actual measured interferogram is obtained according to the method of steps 1-2 real (x), the error function E(a0) of the actual measured scale signal I'(x) and the simulation scale signal I(x, a0), the optimal value of a0 is found to minimize the error function E(a0), the optimal value of a0 is used to represent the position of the scale image on the detector image plane, and the monitoring of the imaging position shift of the Doppler differential interferometer is completed. real (x), the error function E(a0) of the actual measured scale signal I'(x) and the simulation scale signal I(x, a0), the optimal value of a0 is found to minimize the error function E(a0), the optimal value of a0 is used to represent the position of the scale image on the detector image plane, and the monitoring of the imaging position shift of the Doppler differential interferometer is completed.

2. A method of monitoring position shift of a Doppler differential interferometer imaging according to claim 1, characterized in that, The step 2 is specifically as follows: The sampling points are expanded to A times of the original by interpolation, and the horizontal coordinates of the expanded sampling points are calculated wherein k is the index of the expanded sampling point number, k = 1, 2, …, AN. For the extended sampling point coordinates x, the signal at the corresponding position is calculated using Lagrange interpolation polynomials to generate I real (x) and I out (x).

3. A method of monitoring position drift in a Doppler differential interferometer imaging according to claim 1 or 2, characterized in that, The step 3 is specifically as follows: Step 3.1, define the comb function h(x) as follows: where δ denotes an impulse function, x size / N notches denotes the distance between adjacent pulses; Define the square wave function f(x) as follows: f(x) = h(x) * rect(x * W notches ) Wherein, the square wave function f(x) changes in the range of 0 to 1, when h(x)=1, it represents the no-groove area, when h(x)=0, it represents the groove area; Step 3.2, define the Gaussian kernel g(y) as follows: Define the groove distribution model D(x) as follows:

4. A method of monitoring position shift of a Doppler differential interferometer imaging according to claim 3, characterized in that, The step 4 is specifically as follows: Step 4.1, Set the local minimum point (x i , I real (x i )) to satisfy the following conditions: Among them, x i is the position of the minimum point, I real (x i ) is the corresponding signal value; x i-1 and x i+1 Represents x respectively i The adjacent sampling points before and after; Threshold Threshold = mean (I real (x)); Step 4.2: The local minimum point (x i , I real (x i )) performs interpolation fitting to generate the lower envelope curve as the dark signal I corresponding to the groove area in (x).

5. A method of monitoring position shift of a Doppler differential interferometer imaging according to claim 4, characterized in that, The step 6 is specifically as follows: Step 6.1, Collecting multiple calibration interferograms, obtain multiple calibration interferograms at the same position according to the method of steps 1-2, and obtain I real (x); Step 6.

2. For each calibration interferogram, determine the number of pulses N by performing an autocorrelation analysis of I real (x) and using the scale signal distribution model I(x) established in step 5 to fit I notches (x) and calculate the width W real of the rectangular function, the standard deviation σ of the Gaussian kernel. notches Step 7.

2. For each calibration interferogram, determine the number of pulses N by performing an autocorrelation analysis of I real (x) and using the scale signal distribution model I(x) established in step 5 to fit I notches (x) and calculate the width W real of the rectangular function, the standard deviation σ of the Gaussian kernel. notches Step 8.

2. For each calibration interfer Finally, the average of W notches , σ, N notches from multiple calibrated interferograms is taken as the optimal W notches , σ, N notches ; Step 6.3 Set an initial estimate for the position a0of the first pulse of the comb function h(x) using the optimal W notches , σ, N notches Generate a simulated scale signal I(x, a0) using the scale signal distribution model I(x).

6. A method of monitoring position shift of a Doppler differential interferometer imaging according to claim 5, characterized in that, In step 7, the error function E(a0) is as follows:

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