阅读说明：本技术 一种应用于波长调谐式移相干涉仪的自适应移相方法 (Self-adaptive phase shifting method applied to wavelength tuning type phase shifting interferometer ) 是由 祝沛 于 2021-04-16 设计创作，主要内容包括：发明公开了一种应用于波长调谐式移相干涉仪的自适应移相方法,对波长调谐式移相干涉仪的步进电压量与腔长之间的关系进行标定,通过标定得到步进电压与腔长的关系函数；输入腔长在设定范围内的值,根据所标定的步进电压与腔长的关系函数,得到该腔长值下的步进电压值；以该腔长值下的步进电压值进行移相,获取具有设定相位间隔的移相干涉图,再基于最小二乘原理和迭代法的解相位算法,实现自适应干涉腔长的波长调谐移相干涉。本发明基于波长调谐移相干涉技术原理的波长调谐移相干涉方法可实现自适应的移相操作,提高检测的精度和稳定性。(The invention discloses a self-adaptive phase shifting method applied to a wavelength tuning type phase shifting interferometer, which is characterized in that the relation between the stepping voltage quantity and the cavity length of the wavelength tuning type phase shifting interferometer is calibrated, and a relation function between the stepping voltage and the cavity length is obtained through calibration; inputting the value of the cavity length within a set range, and obtaining a stepping voltage value under the cavity length value according to the calibrated relation function of the stepping voltage and the cavity length; and performing phase shifting by using the stepping voltage value under the cavity length value to obtain a phase-shifting interference pattern with a set phase interval, and realizing the wavelength tuning phase-shifting interference of the self-adaptive interference cavity length based on a least square principle and a phase-resolving algorithm of an iterative method. The wavelength tuning phase-shifting interference method based on the wavelength tuning phase-shifting interference technical principle can realize self-adaptive phase-shifting operation and improve the detection precision and stability.)

1. An adaptive phase shifting method applied to a wavelength tuning type phase shifting interferometer is characterized by comprising the following steps:

calibrating the relation between the stepping voltage quantity and the cavity length of the wavelength tuning type phase-shifting interferometer, and obtaining a relation function between the stepping voltage and the cavity length through calibration;

inputting the value of the cavity length within a set range, and obtaining a stepping voltage value under the cavity length value according to the calibrated relation function of the stepping voltage and the cavity length;

and performing phase shifting by using the stepping voltage value under the cavity length value to obtain a phase-shifting interference pattern with a set phase interval, and realizing the wavelength tuning phase-shifting interference of the self-adaptive interference cavity length based on a least square principle and a phase-resolving algorithm of an iterative method.

2. The adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer of claim 1, wherein:

the process of calibrating the relation between the stepping voltage quantity and the cavity length of the wavelength tuning type phase-shifting interferometer and obtaining the relation function of the stepping voltage and the cavity length through calibration comprises the following steps:

firstly, masking the interference pattern, and extracting an area containing interference fringe information in the interference pattern to obtain the relationship between the interference light intensity of each pixel point and the background light intensity, the modulation light intensity, the wavefront phase and the stepping shift quantity;

secondly, obtaining an interference pattern sequence by phase shifting with equal step length, calculating by using adjacent interference pattern sequences, and independently calculating the phase shifting quantity of each pixel point during calibration to obtain the phase shifting quantity of all pixel points in the mask;

and finally, counting the number of pixels in different angle intervals to obtain a statistical histogram of the phase shift amount of a group of interferograms, wherein the peak value of the histogram is the initial calibration value of the phase shift amount of the group of interferograms.

3. The adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer according to claim 2, wherein:

the process of performing phase shift by using the stepping voltage value under the cavity length value to obtain a phase shift interference pattern with a set phase interval, and then realizing wavelength tuning phase shift interference of the self-adaptive interference cavity length based on a least square principle and a phase-solving algorithm of an iterative method comprises the following steps:

when the value of the cavity length is input in a set range, the step voltage quantity which enables the phase shift quantity to be a set threshold value under the cavity length condition can be determined according to the calibrated relation function of the step voltage and the cavity length, and the wave front phase is calculated through least square fitting under the condition that the phase shift quantity is known;

increasing contrast compensation amount to make the background light intensity and the modulated light intensity perform iterative compensation in the calculation process, and after adding compensation coefficient, considering that the contrast difference is mainly between different interferograms, and the background light intensity and the modulated light intensity between different pixels of the same interferogram are equal, so that the compensation coefficient is only related to the sequence number of the interferogram;

and setting a compensation coefficient as 1 during first iterative calculation, calculating a wavefront phase by using a phase shift amount estimated value obtained by calibration, solving the phase point by point, solving the phase shift amount through the same fitting process under the condition that the wavefront phase is known, and calculating and solving by taking each frame image as an object when solving the phase shift amount so that the phase shift amount is closer to a real value.

4. The adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer of claim 3, wherein:

when the wavefront phase is known, the phase shift quantity can be solved through the same fitting process, and when the phase shift quantity is solved, the solution is calculated by taking each frame image as an object, so that the flow of making the phase shift quantity closer to a real value further includes:

when the phase shift quantity is solved through the same fitting process, the background light intensity and the modulated light intensity can be simultaneously obtained, and the compensation coefficient in the next iteration process is calculated according to the background light intensity and the modulated light intensity;

the two processes are repeatedly carried out to form an iterative loop, and after repeated iteration, the wavefront phase and the phase shift amount are continuously close to the true value.

5. The adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer of claim 4, wherein:

the iterative iteration controls the iteration times by setting an iteration threshold, the difference between the phase shift quantity of different interference patterns after n iterations and the average phase shift quantity can be used as an index for measuring the fluctuation range of the calculation result, the difference between the result of the nth iteration and the result of the (n-1) th iteration is calculated to the iteration precision, and the iteration is finished when the iteration precision reaches the set threshold.

Technical Field

The invention relates to the technical field of optics, in particular to a self-adaptive phase shifting method applied to a wavelength tuning type phase shifting interferometer.

Background

Phase Shifting Interference (PSI) is an eye and a ruler in modern optical manufacturing industry, and is widely applied to the production and detection processes of various optical elements due to the characteristics of no contact in detection, high response speed, high detection precision and the like.

However, since the twentieth century, the phase-shifting interference technology has been applied to the field of optical metrology, and through continuous technological innovation, the short boards limiting the development of the technology have not only related hardware conditions, but also more importantly, the phase-shifting mode and the corresponding dephasing algorithm. The traditional laser interferometer generally uses piezoelectric ceramic PZT to bear a reference mirror for micro-displacement, thereby realizing the introduction of phase difference. However, with the development of various fields, the application of large-aperture optical elements in various large and medium-sized optical systems is becoming more and more extensive. In the face of the increase of the size and the mass of a detection object and the limitation of the load capacity of piezoelectric ceramics, the PZT phase shift technology is not good. During the phase shifting, vibrations are easily induced inside the detection system, thereby introducing mechanical errors. The error is introduced from the inside of the interferometer, belongs to the defect of the phase shift principle, and can hardly avoid the generation of the error.

The wavelength phase-shifting interference technology is widely concerned because the wavelength phase-shifting interference technology realizes the precise control and adjustment of the output wavelength of the light source through the input of an electrical signal without changing the length of an interference cavity so as to realize the phase adjustment, and solves the phase-shifting problem of a large-caliber optical element in principle. In addition, as the wavelength phase-shifting interference technology introduces phase shift through the emergent wavelength of the laser, the phase shift quantity is influenced by the wavelength tuning quantity of the laser and the cavity length, and the adopted related image processing algorithms are different. Therefore, it is important to research the relevant principle of the wavelength phase-shifting interference technology and find out the relevant processing algorithm suitable for the wavelength tuning phase-shifting technology.

The modern phase-shifting interferometry combines research results in multiple fields and combines various high-precision measurement technologies such as a laser technology, an image processing technology, an electronic measurement technology and a computer technology. The rapid development of devices such as piezoelectric crystals and the like provides a hardware basis for the development of the phase-shifting interference technology, and the phase-shifting interference technology can accurately obtain the wave front phase distribution by benefiting from the development of the hardware technology. The phase-shifting interference technology integrates various high-precision measurement technologies, and in the initial development stage of the phase-shifting interference technology, due to the limitation of hardware conditions, the development of the interference measurement technology is limited, and the measurement precision is difficult to improve.

In recent thirty years, related hardware technology is rapidly developed, pixel precision of a photoelectric detector and computer power are continuously improved, and the bottleneck of development of a phase-shifting interference technology is broken. The limit of hardware technology is broken through, and the measurement precision and stability of the phase-shifting interference technology are mainly determined by two aspects: (1) the phase shift mode. According to the phase-shifting interference technical principle, the optical path difference between the reference light and the test light needs to be changed in the measuring process, the equidirectional displacement of interference fringes is realized, and the precision and the stability of phase shifting determine the measuring precision. (2) And (4) solving the phase algorithm. After obtaining the interferogram sequence with orderly changed phase by the phase shift technology, the computer needs to obtain the wavefront distribution of the lateral surface through a series of phase-solving calculations. Therefore, the precision of the dephasing algorithm directly influences the measurement result, and the high-precision dephasing algorithm not only can improve the phase extraction precision, but also can play a strong role in inhibiting random errors caused by air disturbance, artificial vibration and the like.

In the prior art, the wavelength tuning phase-shifting algorithm generally adopts an equal-step least square method iterative algorithm to calculate and count the phase distribution of an interferogram. The least square method iterative algorithm is a recursive iterative algorithm with low requirements on phase shift precision, good stability and high calculation precision, and is widely applied to the wavelength tuning phase shift technology. However, in practical application, the algorithm still has the following three problems: 1) calibrating a phase shift quantity by using an accurate value of the length of the interference cavity as an iteration initial value; 2) when the phase shift amount is close to N pi (N is 0, 1, 2 · · s.), the phase extraction error is relatively large; 3) when there is a contrast difference between the multi-frame interferograms, the phase extraction accuracy is greatly affected.

Disclosure of Invention

Aiming at the problems in the prior art, the invention aims to provide a self-adaptive phase shifting method applied to a wavelength tuning type phase shifting interferometer, which can self-adaptively adjust the stepping phase shifting voltage according to the rough calibration value of the cavity length and effectively improve the phase shifting accuracy, thereby obtaining and screening a high-quality interferogram which meets the quality requirement and is less affected by interference, solving the defect that the current wavelength tuning phase shifting interferometer needs to be re-calibrated after the cavity length is changed every time, and greatly improving the intelligent degree of the detection process; and by combining with a designed phase-solving algorithm based on a least square principle and an iterative method, the wavelength tuning phase-shifting interference of the self-adaptive interference cavity length is realized, and a better detection effect is achieved.

In order to solve the technical problems, the invention adopts the following technical scheme:

an adaptive phase shifting method applied to a wavelength tuned phase shifting interferometer, the method comprising:

calibrating the relation between the stepping voltage quantity and the cavity length of the wavelength tuning type phase-shifting interferometer, and obtaining a relation function between the stepping voltage and the cavity length through calibration;

inputting the value of the cavity length within a set range, and obtaining a stepping voltage value under the cavity length value according to the calibrated relation function of the stepping voltage and the cavity length;

and performing phase shifting by using the stepping voltage value under the cavity length value to obtain a phase-shifting interference pattern with a set phase interval, and realizing the wavelength tuning phase-shifting interference of the self-adaptive interference cavity length based on a least square principle and a phase-resolving algorithm of an iterative method.

Preferably, in the adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer,

the process of calibrating the relation between the stepping voltage quantity and the cavity length of the wavelength tuning type phase-shifting interferometer and obtaining the relation function of the stepping voltage and the cavity length through calibration comprises the following steps:

firstly, masking the interference pattern, and extracting an area containing interference fringe information in the interference pattern to obtain the relationship between the interference light intensity of each pixel point and the background light intensity, the modulation light intensity, the wave front phase and the stepping shift quantity;

secondly, obtaining an interference pattern sequence by phase shifting with equal step length, calculating by using adjacent interference pattern sequences, and independently calculating the phase shifting quantity of each pixel point during calibration to obtain the phase shifting quantity of all pixel points in the mask;

and finally, counting the number of pixels in different angle intervals to obtain a statistical histogram of the phase shift amount of a group of interferograms, wherein the peak value of the histogram is the initial calibration value of the phase shift amount of the group of interferograms.

Preferably, in the adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer,

the phase shifting is carried out by the stepping voltage value under the cavity length value, a phase shifting interference pattern with a set phase interval is obtained, and then the flow of the wavelength tuning phase shifting interference for realizing the self-adaptive interference cavity length comprises the following steps of based on a least square principle and a phase-solving algorithm of an iterative method:

when the value of the cavity length is input in a set range, the step voltage quantity which enables the phase shift quantity to be a set threshold value under the cavity length condition can be determined according to the calibrated relation function of the step voltage and the cavity length, and the wave front phase is calculated through least-two fitting under the condition that the phase shift quantity is known;

increasing contrast compensation amount to make the background light intensity and the modulated light intensity perform iterative compensation in the calculation process, and after adding compensation coefficient, considering that the contrast difference is mainly between different interferograms, and the background light intensity and the modulated light intensity between different pixels of the same interferogram are equal, so that the compensation coefficient is only related to the sequence number of the interferogram;

and setting a compensation coefficient as 1 during first iterative calculation, calculating a wavefront phase by using a phase shift amount estimated value obtained by calibration, solving the phase point by point, solving the phase shift amount through the same fitting process under the condition that the wavefront phase is known, and calculating and solving by taking each frame image as an object when solving the phase shift amount so as to enable the phase shift amount to be closer to a real value.

Preferably, in the adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer,

when the wavefront phase is known, the phase shift quantity can be solved through the same fitting process, and when the phase shift quantity is solved, the solution is calculated by taking each frame image as an object, so that the flow of making the phase shift quantity closer to a real value further includes:

when the phase shift quantity is solved through the same fitting process, the background light intensity and the modulated light intensity can be simultaneously obtained, and the compensation coefficient in the next iteration process is calculated according to the background light intensity and the modulated light intensity;

the two processes are repeatedly carried out to form an iterative loop, and after repeated iteration, the wavefront phase and the phase shift amount are continuously close to the true value.

Preferably, in the adaptive phase shifting method applied to the wavelength-tuned phase shifting interferometer,

the iterative iteration controls the iteration times by setting an iteration threshold, the difference between the phase shift quantity of different interference patterns after n iterations and the average phase shift quantity can be used as an index for measuring the fluctuation range of the calculation result, the difference between the result of the nth iteration and the result of the (n-1) th iteration is calculated to the iteration precision, and the iteration is finished when the iteration precision reaches the set threshold.

Compared with the prior art, the self-adaptive phase shifting method applied to the wavelength tuning phase shifting interferometer provided by the invention is based on the laser wavelength tuning principle, according to the calibrated phase shifting voltage and cavity length curve, a user only needs to input rough numerical values of the cavity length, the algorithm can self-adaptively adjust the stepping voltage to complete phase shifting, further a high-quality interference diagram group with ideal phase shifting is obtained, and phase extraction work is carried out by combining with an anti-vibration algorithm based on the least square principle, so that a better detection result can be realized.

The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without inventive labor.

FIG. 1: the invention is applied to the self-adaptive phase-shifting method flow chart of the wavelength tuning type phase-shifting interferometer;

FIG. 2: the embodiment of the invention has 9 frames of phase-shifting interference fringe patterns with 90-degree phase-shifting intervals;

FIG. 3: the tuning schematic diagram of the Littman type grating structure in the embodiment of the invention;

FIG. 4: the embodiment of the invention is a schematic diagram of the linear relation between the cavity length and the wavelength tuning amount when the stepping phase shift amount is pi/2;

FIG. 5: according to the embodiment of the invention, a statistical histogram of the phase shift quantity is obtained by calculating the interference pattern with the phase shift quantity of 30 degrees;

FIG. 6: according to the embodiment of the invention, the statistical histogram of the phase shift quantity is calculated on the interference pattern with the phase shift quantity of 90 degrees;

FIG. 7: according to the embodiment of the invention, a statistical histogram of the phase shift quantity is obtained by calculating the interference pattern with the phase shift quantity of 140 degrees;

FIG. 8: the embodiment of the invention provides a schematic flow chart of an algorithm for solving the phase.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention clearer, the present invention will be described in further detail with reference to the accompanying drawings, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The embodiments of the present invention will be described in further detail with reference to the drawings attached hereto.

As shown in fig. 1, the present invention provides an adaptive phase shifting method applied to a wavelength-tuned phase shifting interferometer, which includes:

calibrating the relation between the stepping voltage quantity and the cavity length of the wavelength tuning type phase-shifting interferometer, and obtaining a relation function between the stepping voltage and the cavity length through calibration;

inputting the value of the cavity length within a set range, and obtaining a stepping voltage value under the cavity length value according to the calibrated relation function of the stepping voltage and the cavity length;

and performing phase shifting by using the stepping voltage value under the cavity length value to obtain a phase-shifting interference pattern with a set phase interval, and realizing the wavelength tuning phase-shifting interference of the self-adaptive interference cavity length based on a least square principle and a phase-resolving algorithm of an iterative method.

In the implementation, the phase-shifting interference technology in the embodiment of the invention is based on an interferometer, and two interference structures, namely a fizeau interference structure and a Taeman interference structure, are generally adopted. In the measuring process, laser is divided into two beams after being expanded by a beam expander, reference light is reflected by the upper surface of a reference surface, and measured light carries wave surface information of a measured side surface after being reflected by a measured side surface. The two beams of coherent light are converged at the CMOS target surface to form interference fringes, and the interference fringes are recorded and stored in a computer by a photoelectric detector. The wavefronts of the reference light and the measured light can be written as:

in the formula, (x, y) denotes a spatial coordinate of a pixel point, a_r(x, y) and a_t(x, y) is the wavefront amplitude, φ, of the two beams_r(x, y) and phi_r(x, y) is the wavefront phase of both.

On the surface of the imaging system, the light intensity of the two beams of light after superposition can be expressed as:

I(x，y)＝|W_r(x，y)+W_t(x，y)|²；

in the figure, I (x, y) is the gray value of the pixel point (x, y) in the interference pattern, and is the light intensity signal received by the CMOS, and the above formula is developed to be a trigonometric function form to obtain:

I(x，y)＝A(x，y)+B(x，y)cos[φ_t(x，y)-φ_r(x，y)]；

in the formula (I), the compound is shown in the specification,for average intensity or background intensity, B (x, y) is 2a_r(x，y)a_t(x, y) is the modulated intensity of the interference fringes.

Definition ofFitting a wave surface to be measured according to wave front phase distribution for the wave front phase of the interference light so as to obtain the appearance information of the wave surface to be measured, wherein the relation between the appearance information and the interference cavity length is as follows:

where h is the cavity length of the interferometer, λ₀The center wavelength of the emitted laser light.

Therefore, the conventional laser phase-shifting interferometer moves the position of the reference mirror by controlling the piezoelectric ceramic actuator (PZT), so that the optical path difference between the reference light and the test light is changed by changing the length of the interference cavity, and the interference fringes can be seen to perform corresponding displacement from the interference image, where fig. 2 is a 9-frame phase-shifting interference fringe image with a phase-shifting interval of 90 °.

Different from the traditional phase shifting mode, the wavelength tuning phase shifting interference technology realizes phase shifting by adjusting the central wavelength of laser emitted by a laser. Therefore, the wavelength tuning laser is a key component of the wavelength phase-shifting interferometer, and the output of a single longitudinal mode is realized in the semiconductor diode laser and an external resonant cavity containing a wavelength selection device, namely the semiconductor diode laser is called an external cavity semiconductor laser, so that the wavelength of the emitted light of the laser can be accurately tuned.

Fig. 3 shows a schematic tuning diagram of a Littman type grating structure. In the semiconductor laser of this structure, the first order diffracted light is reflected to the added mirror, reflected by the mirror back to the grating, and the second order diffracted light is returned to the laser tube, while the zero order light is output from the laser. When the angle between the incident light and the normal of the grating changes and the change amount is Δ θ (Δ θ is small enough), the wavelength change amount of the incident light is easily derived as:

Δλ＝Δθ·d·cosθ；

therefore, in the phase shifting process, only when the PZT pushes the reflector, the included angle between the plane of the reflector and the plane of the grating is changed, and accurate phase shifting can be realized. After obtaining a plurality of interferograms with fixed phase shift, the pixel data I of the interferogram group can be processed by a phase-resolving algorithm_i(x, y), can be calculatedAnd further obtain surface shape information P (x, y) to complete the detection work, and common dephasing algorithms include a four-step phase shifting method, a nine-step phase shifting method, and the like.

From the wavelength tuning phase-shifting interference principle, it can be seen that the phase change amount of the wavelength phase-shifting technique is related to both the cavity length and the wavelength tuning, so that when the wavelength tuning phase-shifting technique is researched, the wavelength tuning phase-shifting rule under the condition of different interference cavity lengths needs to be researched. As described above, in the laser according to the embodiment of the present invention, the PZT pushes the reflective mirror to tune the wavelength of the emitted laser, and since the displacement of the piezoelectric ceramic is proportional to the input voltage, the relationship between the laser wavelength tuning amount and the input voltage can be written as follows:

Δλ＝G·(Δv)^k；

in the formula, G and k are constants related to piezoelectric ceramics, and can be obtained by calibration, and the values of G and k are changed according to different lasers. The better the laser is linear, the closer the k value will be to 1.

It can be seen from the relationship between the laser wavelength tuning amount and the input voltage that, when the cavity length is constant, the phase change amount is related to both the laser center wavelength and the wavelength tuning amount. Taking G60U wavelength tuning phase-shifting interferometer as an example, the center wavelength of the laser is 638nm, the cavity length of the interferometer is changed within the range of 10-60cm, and by using the equal step phase-shifting technology, the relation between the phase-shifting quantity and the wavelength tuning quantity can be obtained as follows:

when the step phase shift amount is pi/2, the phase change amount can be obtained as follows:

it can be seen that with the stepped phase shift determination, the voltage tuning amount is inversely proportional to the interference cavity length, and the proportionality coefficient is linearly related to the laser wavelength tuning amount. Taking logarithm of two sides of the above formula to obtain:

therefore, the relationship between the voltage tuning amount and the interference cavity length can be calibrated according to the formula. In the embodiment of the invention, the relationship between the voltage tuning amount Δ v and the interference cavity length h in the cavity length change range using the interferometer is shown in fig. 4.

As can be seen from fig. 4, with a fixed amount of phase shift, as the cavity length increases, the amount of voltage tuning decreases, and the amount of wavelength tuning decreases, which means that a higher wavelength tuning resolution is required for the laser. When the length of the interference cavity is 60cm, the change of the wavelength of each step phase is required to be 8.5X 10^-5And (5) nm. By adopting the phase shifting mode adopted by the embodiment of the invention, the total phase change amount in the phase shifting process is 9 pi/2, and the maximum wavelength change amount of the laser is 0.0045nm within the cavity length adjustable range, so that the wavelength adjustable range of the laser can exceed 0.0045nm to meet the requirement of phase shifting.

In summary, the relation between the step voltage and the cavity length in the detection process is obtained through calibration, and the step voltage amount which makes the phase shift amount pi/2 under the cavity length can be obtained through the rough value of the cavity length.

Preferably, the embodiment of the present invention is applied to an adaptive phase shifting method for a wavelength-tuned phase-shifting interferometer, where the calibration is performed on the relationship between the step voltage amount and the cavity length of the wavelength-tuned phase-shifting interferometer, and the process of obtaining the relationship function between the step voltage and the cavity length by the calibration includes:

firstly, masking the interference pattern, and extracting an area containing interference fringe information in the interference pattern to obtain the relationship between the interference light intensity of each pixel point and the background light intensity, the modulation light intensity, the wave front phase and the stepping shift quantity;

secondly, obtaining an interference pattern sequence by phase shifting with equal step length, calculating by using adjacent interference pattern sequences, and independently calculating the phase shifting quantity of each pixel point during calibration to obtain the phase shifting quantity of all pixel points in the mask;

and finally, counting the number of pixels in different angle intervals to obtain a statistical histogram of the phase shift amount of a group of interferograms, wherein the peak value of the histogram is the initial calibration value of the phase shift amount of the group of interferograms.

In the implementation, after 5 frames of interferograms are obtained by shifting the phase with the stepping voltage as delta V, the interferograms are firstly subjected to mask processing, and areas containing interference fringe information in the interferograms are extracted. In the mask extracted from the kth frame of interferogram, the interference light intensity of each pixel point can be written as:

in the formula: i denotes the light intensity, A (x, y) is the background light intensity, B (x, y) is the modulated light intensity,for the wavefront phase of each point in the graph, δ (x, y) is the step phase shift. In the wavelength-tuned phase-shifting technique,and δ can be expressed as:

in the formula: h is the length of the interference cavity, lambda₀Δ λ is the amount of wavelength tuning per phase shift for the initial center wavelength of the laser. Obtaining an interferogram sequence by shifting the phase with equal step length, calculating by using adjacent 5 frames of interferograms, wherein the phase shift quantity of each pixel point can be expressed as:

during calibration, the phase shift amount of each point is independently calculated to obtain the phase shift amount of all pixel points in the mask, the number of the pixels falling in different angle intervals is counted to obtain a statistical histogram of the phase shift amount of a group of interferograms, and the peak value of the histogram is the initial calibration value of the phase shift amount of the group of interferograms. Fig. 5-7 show statistical histograms of phase shift amounts calculated from three sets of interferograms with different phase shift amounts.

The initial calibration value of the phase shift amount is obtained, the opening width and the peak height of the histogram directly reflect the phase shift accuracy of the interferograms, and the phase shift accuracy can be measured by the standard deviation of the histogram. The calibration accuracy is related to the quality of the interferogram and the magnitude of the phase shift. In order to investigate the effect of the magnitude of the phase shift on the accuracy, the standard deviation of the phase shift was measured using a G60U interferometer over the interval 0 to π, and the data is shown in the following table:

as can be seen from the table, when the phase shift amounts are all 6 or less in the range of 70 ° to 110 °, the values are within the acceptable range in consideration of the disturbance such as slight vibration in the actual shooting environment. Therefore, during calibration, it is necessary to measure the amount of step voltage that will result in a phase shift of π/2 at different chamber lengths. Setting the measured N sets of data, a least squares fit formula is used, according to the following formula:

the following results were obtained:

V＝a-bH；

wherein, V ═ log (Δ V), H ═ log (H),Where a is related to the center wavelength of the laser and the PZT elastic coefficient, and can be considered as a constant.

According to the principle of least squares, a least squares residual function can be established:

the solution of the residual function coefficient matrix is:

β＝(X^TX)^-1XV＝A^-1B；

wherein:

β＝[a b]^T，

it can be seen from the above formula that when N is greater than or equal to 2, the formula has a solution, but in order to ensure the accuracy of the calibrated function curve, it is generally required that the calibration data amount is not less than 15 groups, and the cavity length setting is uniformly distributed.

Preferably, the embodiment of the present invention is applied to an adaptive phase shifting method of a wavelength-tuned phase shifting interferometer, where the phase shifting is performed by using a step voltage value under the cavity length value to obtain a phase-shifting interferogram with a set phase interval, and then based on a least square principle and a phase-shifting algorithm of an iterative method, the process of implementing the wavelength-tuned phase-shifting interference of the adaptive interference cavity length includes:

when the value of the cavity length is input in a set range, the step voltage quantity which enables the phase shift quantity to be a set threshold value under the cavity length condition can be determined according to the calibrated relation function of the step voltage and the cavity length, and the wave front phase is calculated through least-two fitting under the condition that the phase shift quantity is known;

increasing contrast compensation amount to make the background light intensity and the modulated light intensity perform iterative compensation in the calculation process, and after adding compensation coefficient, considering that the contrast difference is mainly between different interferograms, and the background light intensity and the modulated light intensity between different pixels of the same interferogram are equal, so that the compensation coefficient is only related to the sequence number of the interferogram;

and setting a compensation coefficient as 1 during first iterative calculation, calculating a wavefront phase by using a phase shift amount estimated value obtained by calibration, solving the phase point by point, solving the phase shift amount through the same fitting process under the condition that the wavefront phase is known, and calculating and solving by taking each frame image as an object when solving the phase shift amount so as to enable the phase shift amount to be closer to a real value.

Preferably, the value of the input cavity length within the set range is estimated and read based on the current interference cavity adjustment state of the interferometer and an auxiliary scale provided by the interferometer, and the value is accurate one bit after the decimal point.

In the implementation of the invention, on the basis of the original least square algorithm, in order to solve the problem that the calculation precision is affected when the contrast difference exists between the same group of interferograms, the improved algorithm adds the contrast compensation amount, so that the background light intensity and the modulated light intensity are subjected to iterative compensation in the calculation process, and after the compensation coefficient is added, the following formula is adopted:

I(x，y)＝A(x，y)+B(x，y)cos[φ_t(x，y)-φ_r(x，y)]，

the rewrite is:

in the formula: i represents the serial numbers of different pixel points, j represents the serial number of the interference pattern, P_AjAnd P_BjAnd respectively representing the compensation coefficients of the background light intensity and the modulated light intensity of the interference image of the j frame relative to the interference image of the first frame, considering that the contrast difference is mainly between different interference images, and considering that the background light intensity and the modulated light intensity of different pixels of the same interference image are equal, so the compensation coefficients are only related to the sequence number of the interference image.

In implementation, the compensation coefficient is set to be 1 during the first iterative computation, the wavefront phase is computed by the phase shift amount estimated value obtained by calibration, and the phase is solved point by point. For the pixel with sequence number i, orderEstablishing a linear equation to obtain a theoretical value of light intensityComprises the following steps:

calculating theoretical valueWith the true value I_ijThe difference between them, the least squares residual function is established:

in the formula: n represents the number of frames, beta, of a set of interferogram sequences_iRepresenting a coefficient matrix containing wavefront phase information, and according to the minimum two-multiplication principle, when the frame number of the interferogram is more than or equal to 3 frames, the determinant has a solution, and the solution of a residual function coefficient matrix is as follows:

wherein:

β_i＝[a_i b_i c_i]^T，，

obtaining a coefficient matrix beta_iThen, the wavefront phase can be found as:

in the case that the wavefront phase is known, the phase shift amount can be solved by the same fitting process, so that the phase shift amount is closer to a real value. When the phase shift quantity is solved, the solution is calculated by taking each frame image as an object. Order:

a_j＝P_AjA_ij，b_j＝P_BjB_ijcos(δ_j)，c_j＝-P_BjB_ijsin(δ_j) Then the theoretical value of the light intensity is:

calculating theoretical valueWith the true value I_ijThe difference between the two, the least squares residual function is established:

in the formula: m represents the number of all pixel points in a picture, beta_jRepresenting a coefficient matrix containing phase shift amount information, and solving the coefficient matrix of the residual function according to a minimum two-multiplication principle as follows:

wherein:

β_j＝[a_j b_j c_j]^T，，

obtaining a coefficient matrix beta_iThen, the phase shift quantity can be obtained as follows:

δ_j＝arctan(-c_j/b_j)；

preferably, the embodiment of the present invention is applied to an adaptive phase shifting method of a wavelength-tuned phase shifting interferometer, where the phase of the wavefront is known, the same fitting process can be used to solve the phase shift quantity, and when the phase shift quantity is solved, the flow of calculating and solving the object with each frame diagram, so that the phase shift quantity is closer to the true value further includes:

when the phase shift quantity is solved through the same fitting process, the background light intensity and the modulated light intensity can be simultaneously obtained, and the compensation coefficient in the next iteration process is calculated according to the background light intensity and the modulated light intensity;

the two processes are repeatedly carried out to form an iterative loop, and after repeated iteration, the wavefront phase and the phase shift amount are continuously close to the true value.

In implementation, the embodiment of the present invention may calculate the phase shift amount and may calculate the background light intensity and the modulated light intensity from the coefficient matrix, so as to calculate the compensation coefficient in the next iteration process as follows:

the two processes are repeatedly carried out to form an iterative loop, after repeated iteration, the wavefront phase and the phase shift amount are continuously close to the true value, when the calculation result reaches a certain precision, the change of the result obtained by carrying out iterative calculation is very small, and the meaning of continuous calculation is not very large. In order to improve the efficiency of the algorithm, the iterative iteration in the embodiment of the invention controls the iteration times by setting an iteration threshold, the phase shift quantity of different interference patterns after n iterations is different from the average phase shift quantity, the value of the difference can be used as an index for measuring the fluctuation range of the calculation result, the result of the nth iteration is different from the result of the (n-1) th iteration to the iteration precision, and the iteration can be finished when the iteration precision reaches the set threshold.

Through the phase solving process, the wavefront phase can be solved by taking the phase shift amount calibration value as an iteration initial value, and the algorithm flow of phase solving in the embodiment of the invention is shown in fig. 8.

As can be seen from the principle of least squares fitting algorithm, the sequence of interferograms requires at least a solution to the 3-frame coefficient matrix. The minimum required 5 frames of interferograms are combined with a calibration algorithm, the phase-solving algorithm can solve by requiring 5 frames of interferograms, but in order to improve the accuracy of the iterative algorithm, the introduced data redundancy is considered to reduce errors caused by vibration, air disturbance and the like in the measurement process, so that 9 frames are generally taken as a group of shooting interferogram sequences during each measurement. In practice, after 6 to 8 iterations, the phase calculation value does not change much during the experiment, so 8 iterations are generally sufficient.

The invention provides a self-adaptive wavelength tuning phase-shifting method combining phase-shifting quantity calibration and de-phasing calculation, and when a wavelength tuning phase-shifting interferometer is used for the first time, the relation between the stepping voltage quantity and the cavity length of the interferometer needs to be calibrated. Firstly, a plurality of experiments are carried out under different interference cavity lengths, and the stepping voltage quantity when the phase shift quantity is pi/2 is obtained. The obtained data should be not less than 15 groups, and the distribution of the acquired cavity length data should be distributed over the whole cavity length adjustable interval as much as possible. And (3) shooting 5 interferograms in each group of experiment, taking pixel data with the central area size of 271 multiplied by 271 of each picture, taking the pixel data as a sample area, and calibrating the phase shift amount by utilizing the calibration principle. Every five frames of images in the interference image group are used as a phase shift amount calculation group, and the phase shift amount corresponding to each pixel point can be calculated according to a specific phase shift solving formulaWherein I_k(i，j)The gray value of the pixel at the ith row and the jth column of the image of the kth frame. Calculating the phase shift amount of each phase shift amountCounting, rounding up the phase shift amount corresponding to all the pixel points, and counting the number of pixel points corresponding to each integer value within 0-180 deg., wherein the integer value with the largest pixel point can be used as the phase shift value of the reorganized interference pattern groupAnd adjusting the stepping voltage amount to the phase shift amount of pi/2, wherein the stepping voltage amount is the ideal stepping voltage amount under the cavity length. And according to the data obtained in the last step, a relation function between the cavity length and the stepping voltage can be obtained by combining a least square algorithm. The functional relation of the two is linearly related to the wavelength change of the laser, the better the laser is linear, and the closer the relation function of the two is to the inverse proportion relation. And calibrating a curve according to the obtained phase shift amount, and recording the curve in a program. After the calibration of the phase shift quantity is finished, the measurement can be started, firstly, a cavity length value is roughly input, and according to a curve of the calibrated stepping voltage and the interference cavity length, a stepping voltage value can be obtained when the phase shift quantity is pi/2 under the cavity length. And the stepping voltage is used for phase shifting to obtain 9 frames of phase-shifting interferograms, the prior 5 frames of images are subjected to optimal sequence operation, and high-quality interferogram groups are screened and subjected to phase extraction.

The invention greatly improves the self-adaptive phase shifting capability of the phase shifting interference system from the algorithm level and has good reflection in the customer group; in addition, the method does not need to increase any hardware cost, and meets the actual development requirements of enterprises. The wavelength tuning phase-shifting interference method based on the wavelength tuning phase-shifting interference technical principle can realize self-adaptive phase-shifting operation and improve the detection precision and stability.

In summary, the adaptive wavelength tuning phase shift method of the invention is composed of a phase shift calibration algorithm and an adaptive phase shift algorithm, which complement each other. The phase shift amount of the wavelength tuning phase shift technology is affected by the length of the interference cavity, so that the phase shift amount needs to be calibrated for precise phase extraction under the condition that the cavity length is unknown. The relation between the step voltage and the cavity length is found through calibration, in the detection process, a coarse calibration value of the cavity length is input, the proper step voltage can be obtained, a group of interferograms with proper phase intervals are further obtained, and the better voltage selection effect can be achieved.

While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.