Method for monitoring imaging position offset of Doppler differential interferometer

Abstract

The invention relates to an interferometer, in particular to a method for monitoring imaging position deviation of a Doppler differential interferometer, which is used for overcoming the defect of image surface drift of the Doppler differential interferometer caused by a thermal drift effect. According to the Doppler differential interferometer imaging position offset monitoring method, interference pattern signals are extracted and expanded, a groove distribution model D (x) and a scale signal distribution model I (x) are constructed, model parameters are optimized through multiple calibration interference patterns, and simulation scale signals are generated; and in actual measurement, the first pulse position a0 is optimized by minimizing an error between a simulation scale signal and an actually measured scale signal, so that accurate monitoring of the imaging position offset of the Doppler differential interferometer is realized.

Description

Technical Field

[0001] The invention relates to an interferometer, and in particular to a method for monitoring imaging position deviation of a Doppler differential interferometer. Background Art

[0002] The Doppler differential interferometer is an improved optical measurement device based on the Michelson interferometer. It replaces the reflectors of the two arms with blazed gratings, and the two arms are asymmetric relative to the beam splitter. The incident light passes through the beam splitter and is divided into two beams. After being diffracted by the blazed grating, they are reconverged in the beam splitter. The two light wavefronts with different optical path differences interfere to form Fizeau interference fringes, which are recorded by the detector after passing through the imaging system. The Doppler differential interferometer does not require a precise scanning structure. It can rely on the detector to simultaneously sample the interference signals at different optical path differences, and obtain a two-dimensional interference pattern at one time. It has the advantages of high light flux, high phase sensitivity, and multi-channel simultaneous measurement, and is used in the field of atmospheric wind field measurement.

[0003] The Doppler differential interferometer measures atmospheric wind speed by measuring the phase change of the interference pattern caused by the Doppler frequency shift of the atmospheric airglow spectrum. The interference pattern is measured by the detector. In actual measurements, changes in ambient temperature, platform vibration, changes in the interferometer structure, etc. will cause the Doppler differential interferometer to be misaligned relative to the interferometer, which is specifically manifested as an overall shift of the interference pattern on the detector image plane. In phase inversion, this shift will introduce additional phase changes, thereby affecting the wind speed measurement results. Therefore, how to accurately detect the offset of the interference pattern becomes the key to improving the accuracy of phase measurement. Summary of the invention

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

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

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

[0007] Step 1: Select two adjacent rows of data in the interference pattern, 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 row of data is the interference signal close to the scale signal, denoted by I out (n);

[0008] Step 2: Interpolate I real (n), I out(n) is expanded to A times of the original value, and I is obtained respectively. real (x) and I out (x), x is the horizontal coordinate of the sampling point after expansion, A∈[100, 1000];

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

[0010] Among them, rect() represents the rectangle function, x size is the number of sampling points, N notches is the number of pulses, * represents the convolution operator, W notches Represents the width of the rectangular function, a 0 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: I obtained from step 2 real All local minimum points are identified in (x), and the lower envelope curve is generated by fitting as the dark signal I corresponding to the groove area. in (x);

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

[0013] Step 6: Obtain the I values ​​of multiple calibration interference patterns at the same position according to the method of steps 1 to 2. real (x), using multiple I real (x) respectively calculate the W in the scale signal distribution model I(x) notches ,σ,N notches , and then take the W obtained from multiple calibration interference patterns notches ,σ,N notches The average values ​​of notches ,σ,N notches , and use the scale signal distribution model I(x) to generate the simulated scale signal I(x, a 0 );

[0014] Step 7: After 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 (x) and the simulated scale signal I(x, a 0 )’s error function E(a 0 ), find a 0 The optimal value of the error function E(a 0 ) is the smallest, using a 0 The optimal value of represents the position of the scale image on the detector image plane, completing the monitoring of the Doppler differential interferometer imaging position offset.

[0015] Furthermore, the step 2 is specifically as follows:

[0016] The sampling points are expanded to A times of the original value through interpolation, and the horizontal coordinates of the expanded sampling points are calculated. Where k is the index of the number of sampling points after expansion, k = 1, 2…, AN;

[0017] For the sampling point coordinate x after expansion, the Lagrange interpolation polynomial is used to calculate the signal at the corresponding position to generate I real (x) and I out (x).

[0018] Furthermore, the step 3 is specifically as follows:

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

[0020]

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

[0022] The square wave function f(x) is defined as follows:

[0023] f(x)=h(x)*rect(x·W notches )

[0024] Wherein, the square wave function f(x) varies from 0 to 1. When h(x)=1, it indicates a non-grooved area, and when h(x)=0, it indicates a grooved area.

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

[0026]

[0027] The groove distribution model D(x) is defined as follows:

[0028]

[0029] Furthermore, the step 4 is specifically as follows:

[0030] Step 4.1, set the local minimum point (x i , I real (x i ))The following conditions must be met:

[0031]

[0032] 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 i The adjacent sampling points before and after; Threshold Threshold = mean (I real (x));

[0033] Step 4.2: By analyzing 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).

[0034] Furthermore, the step 6 is specifically as follows:

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

[0036] Step 6.2: For each calibration interferogram, real (x) Perform autocorrelation analysis to determine the number of pulses N 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;

[0037] Finally, take the W obtained from multiple calibration interference patterns notches ,σ,N notches The average value of notches ,σ,N notches ;

[0038] Step 6.3: The position a of the first pulse of the comb function h(x) 0 Set the initial estimate and use the optimal W notches ,σ,N notches, using the scale signal distribution model I(x) to generate the simulated scale signal I(x, a 0 ).

[0039] Furthermore, in step 7, the error function E(a 0 )as follows:

[0040]

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) The present invention is a Doppler differential interferometer imaging position deviation monitoring method, which extracts and expands the interference pattern signal, constructs a groove distribution model D(x) and a scale signal distribution model I(x), optimizes the model parameters using multiple calibration interference patterns, and generates a simulated scale signal; and in actual measurement, optimizes the first pulse position a by minimizing the error between the simulated scale signal and the measured scale signal. 0 , thereby achieving accurate monitoring of the Doppler differential interferometer imaging position offset.

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

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

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

[0046] Figure 1 It is a schematic diagram of the interference diagram in step 1 of an embodiment of a method for monitoring imaging position deviation of a Doppler differential interferometer of the present invention;

[0047] Figure 2 In step 1 of the embodiment of the present invention, real (n), I out (n) Schematic diagram;

[0048] Figure 3 Schematic diagram of the groove distribution model D(x) in step 3 of the embodiment of the present invention;

[0049] Figure 4 is the dark signal I corresponding to the groove area in step 4 of the embodiment of the present invention in (x) schematic diagram;

[0050] Figure 5 is the actual scale signal I′ in step 7 of the embodiment of the present invention real(x) and the simulated scale signal I(x, a 0 ) is a schematic diagram of the fitting effect. DETAILED DESCRIPTION

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

[0052] The present invention etches periodic grooves precisely along the diffraction direction on the grating of the Doppler differential interferometer; Figure 1 As shown in the figure, outside the groove, the incident light diffracts normally and forms interference fringes on the detector; inside the groove, due to the influence of laser processing, the grating surface and the substrate are damaged, resulting in the incident light being unable to diffract on the arm grating, and only the diffracted light of the other arm grating is present at the corresponding position of the detector; therefore, the signal corresponding to the groove row on the interference pattern is a combination of the signals inside and outside the groove, which is called a scale image; the scale image is modeled using signal parameters and the offset of the interference pattern is determined by global fitting of the scale signal.

[0053] Based on the above ideas, the present invention provides a method for monitoring the imaging position deviation of a Doppler differential interferometer, comprising the following steps:

[0054] Step 1. Reference Figure 1 , select two adjacent rows of data in the interference pattern formed by the Doppler differential interferometer, one of which contains the scale signal (such as Figure 2 The solid line in the figure), 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 the interference signal close to the scale signal (such as Figure 2 The dotted line in the figure shows that the interference signal of this line is not affected by the groove and is recorded as I out (n);

[0055] I out (n) can be considered as the data corresponding to the area outside the groove in the scale signal. Figure 2 It can be seen that I out (n) and I real The upper envelope of (n) is basically consistent; ideally, I real The signal without grooves in (n) should follow the same cosine distribution as the interference signal of any row in the interference pattern. However, due to the instrument aberration or the non-uniform detector response, the amplitude, phase and frequency of the interference signal between different rows are different. out (n) and I real (n) The distance between the two should be as small as possible to reduce the difference; in addition, to ensure the signal quality, an area with a high signal-to-noise ratio should be selected;

[0056] Step 2: Interpolate I real (n), Iout (n) is expanded to A times of the original value, and I is obtained respectively. real (x) and I out (x), x is the horizontal coordinate of the sampling point after expansion, A∈[100, 1000];

[0057] Specifically: expand the sampling points to A times the original ones through interpolation, and calculate the horizontal coordinates of the expanded sampling points Where k is the index of the number of sampling points after expansion, k = 1, 2..., AN, A = 1000;

[0058] For the sampling point coordinate x after expansion, the Lagrange interpolation polynomial is used to calculate the signal at the corresponding position to generate I real (x) and I out (x);

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

[0060]

[0061] Where j represents the auxiliary index used to calculate the Lagrangian basis function;

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

[0063] Likewise, I out (x) is 1 out (n) expanded data;

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

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

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

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

[0068]

[0069] Where δ represents the pulse 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 Represents the distance between adjacent pulses, and also the distance between adjacent grooves; a 0 Represents the position of the first pulse of the comb function h(x), which is used to adjust the starting position of the groove area;

[0070] Redefine the square wave function f(x) as follows:

[0071] f(x)=h(x)*rect(x·W notches )

[0072] Among them, rect() represents the rectangular function, * represents the convolution operator symbol, and W notches Represents the width of the rectangular function, which determines the width of the non-grooved area. The groove width is x size / N notches -W notches ; The square wave function f(x) varies from 0 to 1. When h(x) = 1, it indicates a non-grooved area, and when h(x) = 0, it indicates a grooved area;

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

[0074] The actual groove edge is usually not an ideal sharp transition, but is blurred due to factors such as manufacturing process limitations and material microstructure. In order to simulate this phenomenon, the Gaussian kernel is introduced to perform convolution processing on the square wave function. The Gaussian kernel smoothes the sharp transition of the square wave and simulates the actual edge characteristics of the groove. It 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] Among them, σ is the standard deviation, which determines the degree of broadening of the Gaussian kernel; y is the number of sampling points of the Gaussian kernel, which is related to the period of the square wave function f(x). Usually, the number of sampling points y is 1 to 2 times the number of sample points 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) Figure 3 As shown, it can more realistically reflect the fuzzy characteristics of the groove edge;

[0081] Step 4: I obtained from step 2 real All local minimum points are identified in (x), and the lower envelope curve is generated by fitting as the dark signal I corresponding to the groove area. in (x);

[0082] Step 4.1: In the scale signal, the signal in the groove area is usually weaker than the signal in the non-groove area, which appears as a dark signal. In order to extract the dark signal, the I obtained in step 2 can be analyzed. real (x) to identify all local minima (x i , I real (x i )),like Figure 4 As shown by the asterisk in i is the position of the minimum point, 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] Among them, x i-1 and x i+1 Represents x i The adjacent sampling points before and after;

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

[0086] Requirement I real (xi )<Threshold;

[0087] Step 4.2: By analyzing 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);

[0088] Step 5: I obtained from step 2 out (x), the groove distribution model D(x) obtained in step 3, and the dark signal I obtained in step 4 in (x), establish the scale signal distribution model I(x);

[0089] The ruler image is the core signal used to monitor the imaging position offset in the Doppler differential interferometer. In essence, it is a complex optical signal distribution formed by the superposition of the signals in the groove area and the non-groove area. The ruler image reflects the signal changes caused by the small displacement of the interferometer on the detector plane by combining the distribution characteristics of the interference fringes with the geometric characteristics of the groove structure. In order to accurately describe the ruler image, an overall model is built for it. The ruler signal distribution model I(x) is expressed as,

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

[0091] Among them, I out (x) indicates the interference signal in 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 composed of the interference signal I out (x) is dominant; if D(x) is close to 0, it means that the position is dominated by the signal I in the groove area. in (x) dominates; by adjusting the parameters of D(x), the overall shape of the ruler image can be simulated;

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

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

[0095] Step 6.1: Under the condition of stable laboratory environment, collect multiple calibration interferograms, and obtain the I values ​​of multiple calibration interferograms at the same position according to the method of steps 1 to 2. real (x);

[0096] Step 6.2: For each calibration interferogram, real (x) Perform autocorrelation analysis to determine the number of pulses N 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 interference patterns notches ,σ,N notches The average value of notches ,σ,N notches ;

[0098] Step 6.3: The position a of the first pulse of the comb function h(x) 0 Set the initial estimate and use the optimal W notches ,σ,N notches , according to the scale signal distribution model I(x), the simulated scale signal I(x, a 0 );

[0099] Step 7: After 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 (x) and the simulated scale signal I(x, a 0 )’s error function E(a 0 ):

[0100]

[0101] Using gradient descent, find a 0 The optimal value of the error function E(a 0 ) is the smallest, making I(x, a 0 ) and the measured scale signal I′ real (x) achieve the best fit;

[0102] Using a 0 The optimal value of represents the position of the scale image on the detector image plane, completing the monitoring of the Doppler differential interferometer imaging position offset;

[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, a 0 ), we can see that the two signals are basically consistent.

Claims

1. A method for monitoring the imaging position deviation of a Doppler differential interferometer, characterized in that: The steps include: Step 1: Select two adjacent rows of data in the interference pattern, 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 line of data is the interference signal close to the scale signal, denoted by I out (n); Step 2: Interpolate I real (n), I out (n) is expanded to A times of the original value, and I is obtained respectively. real (x) and Io ut (x), x is the horizontal coordinate of the sampling point after expansion, A∈[100,1000]; Step 3: Generate a square wave function f(x) by convolution of the comb function h(x) and the rectangular function, and then model the groove distribution by convolution of the square wave function f(x) and the Gaussian kernel g(y) to obtain the groove distribution model. Among them, rect() represents the rectangle function, x size is the number of sampling points, N notches is the number of pulses, * represents the convolution operator, 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; Step 4: I obtained from step 2 real All local minimum points are identified in (x), and the lower envelope curve is generated by fitting as the dark signal I corresponding to the groove area. in (x); Step 5: I obtained from step 2 out (x), the groove distribution model D(x) obtained in step 3, and the dark signal I obtained in step 4 in (x), establish the scale signal distribution model I(x) = D(x)·I 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 to 2. real (x), using multiple I real (x) respectively calculate the W in the scale signal distribution model I(x) notches ,σ,N notches , and then take the W obtained from multiple calibration interference patterns notches ,σ,N notches The average values ​​of notches ,σ,N notches , and use the scale signal distribution model I(x) to generate a simulated scale signal I(x, a0); Step 7: After 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 the simulated scale signal I(x, a0) and the simulated scale signal I(x, a0) is calculated, and the optimal value of a0 is found to minimize the error function E(a0). The optimal value of a0 is used to characterize the position of the scale image on the detector image plane, thus completing the monitoring of the Doppler differential interferometer imaging position offset.

2. The method for monitoring the imaging position deviation of a Doppler differential interferometer 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 value through interpolation, and the horizontal coordinates of the expanded sampling points are calculated. Where k is the index of the number of sampling points after expansion, k = 1, 2…, AN; For the sampling point coordinate x after expansion, the Lagrange interpolation polynomial is used to calculate the signal at the corresponding position to generate I real (x) and I out (x).

3. A method for monitoring the imaging position deviation of a Doppler differential interferometer 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 represents the pulse function, x size / N notches Indicates the distance between adjacent pulses; The square wave function f(x) is defined as follows: f(x)=h(x)*rect(x·W notches ) Wherein, the square wave function f(x) varies from 0 to 1. When h(x)=1, it indicates a non-grooved area, and when h(x)=0, it indicates a grooved area. Step 3.2, define the Gaussian kernel g(y) as follows: The groove distribution model D(x) is defined as follows:

4. The method for monitoring the imaging position deviation of a Doppler differential interferometer 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 ))The following conditions must be met: 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 i The adjacent sampling points before and after; Threshold Threshold = mean (I real (x)); Step 4.2: By analyzing 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. The method for monitoring the imaging position deviation of a Doppler differential interferometer according to claim 4, characterized in that: The step 6 is specifically as follows: Step 6.1, collect multiple calibration interferograms, and obtain the I of multiple calibration interferograms at the same position according to the method of steps 1 to 2. real (x); Step 6.2: For each calibration interferogram, real (x) Perform autocorrelation analysis to determine the number of pulses N 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; Finally, take the W obtained from multiple calibration interference patterns notches ,σ,N notches The average value of notches ,σ,N notches ; 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 , use the scale signal distribution model I(x) to generate a simulated scale signal I(x, a0).

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

Images