阅读说明：本技术 一种改进的相移相位测量方法及系统 (Improved phase shift phase measurement method and system ) 是由 李娇声 章勤男 于 2021-09-30 设计创作，主要内容包括：本发明公开一种改进的相移相位测量方法及系统,包括以下步骤：数据获取,获取两幅差分干涉图,其中,差分干涉图为获取的干涉图两两相减去除背景项后的图；数据处理,将差分干涉图的表达式用矩阵的形式来表示,然后利用因式分解的方法对矩阵不断迭代,直至收敛,计算得到与待测相位和相移量相关的向量；计算,基于相关的向量,计算待测相位。本技术方案不需要进行长时间的迭代,且不需要任何近似条件的假设,对干涉图的条纹数量、形状以及相移量分布没有要求,即可快速得到高精度的相移相位测量结果。(The invention discloses an improved phase shift phase measurement method and system, comprising the following steps: acquiring data, and acquiring two differential interferograms, wherein the differential interferograms are images obtained by subtracting every two acquired interferograms from each other and removing background items; data processing, namely representing an expression of the differential interference pattern in a matrix form, continuously iterating the matrix by using a factorization method until convergence, and calculating to obtain a vector related to a phase to be measured and a phase shift quantity; and calculating, namely calculating the phase to be measured based on the relevant vector. According to the technical scheme, long-time iteration is not needed, any assumption of approximate conditions is not needed, the number, the shape and the phase shift distribution of the fringes of the interference pattern are not required, and a high-precision phase shift phase measurement result can be obtained quickly.)

1. An improved phase shift phase measurement method, comprising the steps of:

acquiring data, and acquiring two differential interferograms, wherein the differential interferograms are images obtained by subtracting every two interferograms from each other and removing background items;

data processing, namely representing the expression of the differential interference pattern in a matrix form, continuously iterating the matrix by using a factorization method until convergence, and calculating to obtain a vector related to a phase to be measured and a phase shift quantity;

and calculating, based on the correlated vector, the phase to be measured.

2. The improved phase shift phase measurement method as set forth in claim 1, wherein said differential interferogram is expressed by the expression:

wherein, Ib_m,k(x, y) denotes a differential interferogram, the subscript M denotes a pixel subscript index, the number of pixels in each image is M, i.e., M e (1,2,3.. M) is satisfied, k denotes a few differential interferograms, and k is 1, 2.

3. The improved phase shift phase measurement method of claim 2,

expressing the expression of the differential interference pattern in a matrix form:

Ib＝(c-s)(uv)^T

＝VU^T

where c and s represent column vectors, respectively, denoted asAndu and v represent other column vectors, respectively, and are expressed as u ═ cos θ_k-1} and v ═ sin θ_kThe matrices V and U are denoted V ═ c-s and U ═ uv; wherein]^TRepresenting a transpose operation.

4. An improved phase shift phase measurement method as set forth in claim 3 wherein said data processing comprises:

presetting an initial phase shift quantity, randomly presetting an initial phase shift quantity theta, and calculating to obtain an initial phase u₀And initial v₀；

Calculate U₀、V₀Based on the initial u₀And initial v₀Calculate the initial matrix U₀＝(u₀v₀) Initial matrix V₀；

Iteration based on the initial matrix V₀Calculating an initial vectorDistributed and updated to V₁Based on said V₁Calculating to obtain U₁Completing one iteration; repeating the iterative process until the convergence precision is reached, and outputting final V and U values;

and calculating to obtain the phase to be measured based on the final V and U values.

5. The improved phase shift phase measurement method of claim 4,

obtaining the V₀The process comprises the following steps: using V ═ Ib [ U (U) ]^TU)^-1]And known differential interferograms to obtain V₀；

With the resultant V₀According toCalculating initial vector distribution and updating the initial vector distribution to V₁Then V is added₁Substituted U ═ V^TV)^-1V^TIb]^-1To obtain a new U₁。

6. An improved phase shift phase measurement system, comprising:

the data acquisition module is used for acquiring two differential interferograms, wherein the differential interferograms are images obtained by subtracting every two interferograms from each other and removing background items;

the data processing module is used for expressing the expression of the differential interference pattern in a matrix form, continuously iterating the matrix by using a factorization method until convergence, and calculating to obtain a vector related to the phase to be measured and the phase shift quantity;

and the calculation module is used for calculating the phase to be measured based on the related vector.

7. The improved phase shift phase measurement system of claim 6, wherein said data processing module comprises:

a first processing module for expressing the differential interferogram as:

wherein, Ib_m,k(x, y) denotes a differential interferogram, the subscript M denotes a pixel subscript index, the number of pixels in each image is M, i.e., M e (1,2,3.. M) is satisfied, k denotes a few differential interferograms, and k is 1, 2.

8. The improved phase shift phase measurement system of claim 7, wherein said data processing module further comprises:

a second processing module, configured to represent a processing result of the first processing module in a matrix form:

Ib＝(c-s)(uv)^T

＝VU^T

where c and s represent column vectors, respectively, denoted asAndu and v represent other column vectors, respectively, and are expressed as u ═ cos θ_k-1} and v ═ sin θ_kThe matrices V and U are denoted V ═ c-s and U ═ uv; wherein]^TRepresenting a transpose operation.

9. The improved phase shift phase measurement system of claim 8, wherein said data processing module further comprises:

the third processing module comprises:

the fourth processing submodule is used for presetting the initial phase shift quantity, randomly presetting the initial phase shift quantity theta, and calculating to obtain an initial u and an initial v;

a fifth processing submodule for calculating U₀、V₀Based on the initial u₀And initial v₀Calculate the initial matrix U₀＝(u₀v₀) Initial matrix V₀(ii) a Also for performing iterative processing, based on the initial matrix V₀Calculating initial vector distribution and updating to V₁Based on said V₁Calculating to obtain U₁Completing one iteration; repeating the iterative process until the convergence precision is reached, and outputting final V and U values;

and the sixth processing submodule is used for calculating to obtain the phase to be measured based on the final V and U values.

10. The improved phase shifting phase measurement system of claim 9,

the fifth processing submodule uses V ═ Ib [ U (U)^TU)^-1]And known differential interferograms to obtain V₀；

With the resultant V₀According toCalculating initial vector distribution and updating the initial vector distribution to V₁Then V is added₁Substituted U ═ V^TV)^-1V^TIb]^-1To obtain a new U₁。

Technical Field

The invention relates to the field of optical interferometry or digital holography, in particular to the field of optical interferometry or digital holography by using a phase shift technology.

Background

The phase shift interferometry is widely applied to the fields of precision mechanical element detection, quantitative phase imaging, flow field measurement, materials, life science and the like because of the advantages of non-contact, full field, high precision, rapidness and the like. In the process of realizing quantitative phase imaging and other phase demodulation, the high-precision demodulation of the interference fringe pattern is a key step for ensuring accurate phase acquisition. The earliest proposed multi-step phase shift algorithms, including least square algorithm, fixed-step multi-step phase shift algorithm, etc., are widely used due to their advantages of high precision and rapidity. However, such algorithms need to know the phase shift amount in advance or require step size distribution such as the phase shift amount, the accuracy of phase solution depends on the accuracy of the phase shift amount, and factors such as air disturbance, nonlinear characteristics of a phase shift device and instability of laser frequency can cause deviation of the phase shift amount.

The method for extracting the phase from the phase shift interference fringe pattern with unknown phase shift amount can directly extract the phase to be measured from the acquired phase shift interference pattern without calculating the phase shift amount in advance, and is an effective method capable of reducing the influence of vibration, air flow and the like on the phase shift measurement precision. To date, researchers have proposed a number of high-precision phase shift algorithms under unknown phase shift quantities, among which the accepted higher precision are the improved least squares algorithm (AIA) and principal component analysis algorithm (PCA), and the improved principal component analysis method (APCA) for solving the phase shift quantity distribution problem. Besides, there are also some independent component analysis methods and orthogonal normalization algorithms proposed based on the stripe orthogonality property, and self-calibration algorithms based on linear correlation. However, in the above algorithms, the AIA algorithm has a problem of time consumption because of the need for continuous iteration to satisfy the convergence condition, and other algorithms have a problem that the calculation accuracy is affected by the number of stripes, although the time is fast, like the PCA and APCA algorithms. In order to solve the influence of the stripe sparsity on the calculation accuracy, a plurality of phase shift algorithms which are not influenced by the number of stripes are proposed. The medium frequency space spectrum matching algorithm (MSSM) and the phase shift amount searching algorithm (PSS) can reduce the influence of the number of interference fringes on the calculation precision to a certain extent, but the MSSM algorithm needs to carry out filtering and has requirements on the distribution of the phase shift amount; the PSS algorithm has few limitations, but requires a certain search, which is relatively time-consuming.

The above algorithm is always affected by the phase shift amount distribution, the fringe distribution and the number to a certain extent, the calculation accuracy is unstable, the application range is limited, and the algorithm is not suitable for actual phase detection to a certain extent. Therefore, a phase shift measurement method is needed to solve the above problems.

Disclosure of Invention

The invention aims to provide a phase shift phase measurement method and a phase shift phase measurement device which are not influenced by the shape and the number of stripes and are not limited by application.

In one aspect, to achieve the above object, the present invention provides an improved phase shift phase measurement method, comprising the steps of:

acquiring data, and acquiring two differential interferograms, wherein the differential interferograms are images obtained by subtracting every two interferograms from each other and removing background items;

data processing, namely representing the expression of the differential interference pattern in a matrix form, continuously iterating the matrix by using a factorization method until convergence, and calculating to obtain a vector related to a phase to be measured and a phase shift quantity;

and calculating, based on the correlated vector, the phase to be measured.

Optionally, the expression of the differential interferogram is:

wherein, Ib_m,k(x, y) denotes a differential interferogram, the subscript M denotes a pixel subscript index, the number of pixels in each image is M, i.e., M e (1,2,3.. M) is satisfied, k denotes a few differential interferograms, and k is 1, 2.

Optionally, the expression of the differential interferogram is expressed in a matrix form:

Ib＝(c-s)(uv)^T

＝VU^T

where c and s represent column vectors, respectively, denoted asAndu and v represent other column vectors, respectively, and are expressed as u ═ cos θ_k-1} and v ═ sin θ_kThe matrices V and U are denoted V ═ c-s and U ═ uv; wherein]^TRepresenting a transpose operation.

Optionally, the data processing includes:

presetting an initial phase shift quantity, randomly presetting an initial phase shift quantity theta, and calculating to obtain an initial phase u₀And initial v₀；

Calculate U₀、V₀Based on the initial u₀And initial v₀Calculate the initial matrix U₀＝(u₀v₀) Initial matrix V₀；

Iteration based on the initial matrix V₀Calculating initial vector distribution and updating to V₁Based on said V₁Calculating to obtain U₁Completing one iteration; repeating the iterative process until the convergence precision is reached, and outputting final V and U values;

and calculating to obtain the phase to be measured based on the final V and U values.

Optionally, obtaining said V₀The process comprises the following steps: using V ═ Ib [ U (U) ]^TU)^-1]And known differential interferograms to obtain V₀；

With the resultant V₀According toCalculating initial vector distribution and updating the initial vector distribution to V₁Then V is added₁Substituted U ═ V^TV)^-1V^TIb]^-1To obtain a new U₁。

In another aspect, to achieve the above object, the present invention further discloses an improved phase shift phase measurement system, including:

the data acquisition module is used for acquiring two differential interferograms, wherein the differential interferograms are images obtained by subtracting every two interferograms from each other and removing background items;

the data processing module is used for expressing the expression of the differential interference pattern in a matrix form, continuously iterating the matrix by using a factorization method until convergence, and calculating to obtain a vector related to the phase to be measured and the phase shift quantity;

and the calculation module is used for calculating the phase to be measured based on the related vector.

Optionally, the data processing module includes:

a first processing module for expressing the differential interferogram as:

wherein, Ib_m,k(x, y) denotes a differential interferogram, the subscript M denotes a pixel subscript index, the number of pixels in each image is M, i.e., M e (1,2,3.. M) is satisfied, k denotes a few differential interferograms, and k is 1, 2.

Optionally, the data processing module further includes:

a second processing module, configured to represent a processing result of the first processing module in a matrix form:

Ib＝(c-s)(uv)^T

＝VU^T

where c and s represent column vectors, respectively, denoted asAndu and v represent other column vectors, respectively, and are expressed as u ═ cos θ_k-1} and v ═ sin θ_kThe matrices V and U are denoted V ═ c-s and U ═ uv; wherein]^TRepresenting a transpose operation.

Optionally, the data processing module further includes:

the third processing module comprises:

the fourth processing submodule is used for presetting the initial phase shift quantity, randomly presetting the initial phase shift quantity theta, and calculating to obtain an initial u and an initial v;

a fifth processing submodule for calculating U₀、V₀Based on the initial u₀And initial v₀Calculate the initial matrix U₀＝(u₀v₀) Initial matrix V₀(ii) a Also for performing iterative processing, based on the initial matrix V₀Calculating initial vector distribution and updating to V₁Based on said V₁Calculating to obtain U₁Completing one iteration; repeating the iterative process until the convergence precision is reached, and outputting final V and U values;

and the sixth processing submodule is used for calculating to obtain the phase to be measured based on the final V and U values.

Optionally, the fifth processing submodule utilizes V ═ Ib [ U (U)^TU)^-1]And known differential interferograms to obtain V₀；

With the resultant V₀According toCalculating initial vector distribution and updating the initial vector distribution to V₁Then V is added₁Substituted U ═ V^TV)^-1V^TIb]^-1To obtain a new U₁。

The invention has the technical effects that: the invention provides a rapid, high-precision, stable and general random phase shift phase measurement scheme, which does not need long-time iteration, does not need any assumption of approximate conditions, has no requirements on the number, shape and phase shift distribution of interference patterns, and can rapidly obtain a high-precision phase shift phase measurement result.

Drawings

FIG. 1 is a flow chart of an improved phase shift phase measurement method according to a first embodiment of the present invention;

FIG. 2 is a schematic diagram of an improved phase shift measurement according to a second embodiment of the present invention;

FIG. 3 is a diagram showing simulation results of the first embodiment of the present invention, wherein (a) and (b) simulate two phase-shifted interferograms obtained by using the method; (c) presetting a reference phase; (d) the proposed DM-UV algorithm (e) APCA (f) AIA calculated phase distribution; (g) proposed DM-UV algorithm (h) APCA (i) phase deviation result of AIA calculation;

FIG. 4 is a graph showing experimental results using an improved phase shift phase measurement method according to one embodiment of the present invention, (a) one of the experimental interferograms; (b) a reference phase; (c) the proposed DM-UV algorithm (d) APCA and (e) AIA algorithm calculate the obtained phase distribution; (f) proposed DM-UV algorithm (g) APCA and (h) AIA algorithm calculated phase deviation results. .

Detailed Description

Reference will now be made in detail to various exemplary embodiments of the invention, the detailed description should not be construed as limiting the invention but as a more detailed description of certain aspects, features and embodiments of the invention.

It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. Further, for numerical ranges in this disclosure, it is understood that each intervening value, between the upper and lower limit of that range, is also specifically disclosed. Every smaller range between any stated value or intervening value in a stated range and any other stated or intervening value in a stated range is encompassed within the invention. The upper and lower limits of these smaller ranges may independently be included or excluded in the range.

It will be apparent to those skilled in the art that various modifications and variations can be made in the specific embodiments of the present disclosure without departing from the scope or spirit of the disclosure. Other embodiments will be apparent to those skilled in the art from consideration of the specification. The specification and examples are exemplary only.

As used herein, the terms "comprising," "including," "having," "containing," and the like are open-ended terms that mean including, but not limited to.

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and 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.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

Example one

The embodiment of the invention discloses an improved phase shift phase measurement method, as shown in fig. 1, comprising:

acquiring data, and acquiring two differential interferograms, wherein the differential interferograms are images obtained by subtracting every two interferograms from each other and removing background items;

data processing, namely representing the expression of the differential interference pattern in a matrix form, continuously iterating the matrix by using a factorization method until convergence, and calculating to obtain a vector related to a phase to be measured and a phase shift quantity;

and calculating, based on the correlated vector, the phase to be measured.

In this embodiment, a mach-zehnder interference system is built, a phase shifter is used in a reference light path to introduce phase shift, and 200 phase shift interferograms with samples being polystyrene beads are collected. From these, 3 phase-shifted interferograms having an arbitrary phase shift amount difference are selected, and one of the phase-shifted interferograms is shown in fig. 4 (a). The area of the interference pattern with the object is subjected to truncation calculation, and the size of the truncated area is 168 x 468 pixels. The interference system is not limited to a single-channel interference system and a multi-channel system of a double-channel interference system, a three-channel interference system and a four-channel interference system.

As a preferred implementation manner, in this embodiment, taking a single-channel interference system as an example, the expression of the differential interferogram is:

wherein, Ib_m,k(x, y) denotes a differential interferogram, the subscript M denotes a pixel subscript index, the number of pixels in each image is M, i.e., M e (1,2,3.. M) is satisfied, k denotes a few differential interferograms, and k is 1, 2.

Specifically, the intensity of the interference pattern in which three selected phase differences are different by any phase shift amount can be expressed as:

where a (x, y) and b (x, y) represent the background and intensity terms of the interferogram, θ₁And theta₂Respectively representing the phase shift amount difference from the first interferogram.

As a preferred embodiment, the expression of the differential interferogram is represented in the form of a matrix:

wherein c and s represent column vectors, respectively, represented asAndu and v represent other column vectors, respectively, and are expressed as u ═ cos θ_k-1} and v ═ sin θ_kThe matrices V and U are denoted V ═ c-s and U ═ uv; wherein]^TRepresenting a transpose operation. Specifically, the matrix form models the differential interferogram as the product of two matrices: the left matrix V, with size M × 2, contains components describing the modulation phase, and the right matrix U, with size 2 × k, contains components describing the phase shift. Thus, once the matrix V is obtained, the phase information to be measured can be expressed as:

as a preferred embodiment, the data processing includes:

presetting an initial phase shift quantity, randomly presetting an initial phase shift quantity theta, and calculating to obtain an initial phase u₀And initial v₀；

Calculate U₀、V₀Based on the initial u₀And initial v₀Calculate the initial matrix U₀＝(u₀ v₀) Initial matrix V₀；

Iteration based on the initial matrix V₀Calculating initial vector distribution and updating to V₁Based on said V₁Calculating to obtain U₁Completing one iteration; repeating the iterative process until the convergence precision is reached, and outputting final V and U values;

and calculating to obtain the phase to be measured based on the final V and U values.

In this embodiment, the calculation error of convergence may be defined as:

where n denotes n iterations, n 1,2,3.Andrespectively representing the phase distribution obtained by the current iteration and the last iteration.

As a preferred embodiment, said V is obtained₀The process comprises the following steps: using V ═ Ib [ U (U) ]^TU)^-1]And known differential interferograms to obtain V₀Where Ib is the two differential interferograms obtained above, in known quantities;

with the resultant V₀According toCalculating initial vector distribution and updating the initial vector distribution to V₁Then V is added₁Substituted U ═ V^TV)^-1V^TIb]^-1To obtain a new U₁。

As shown in fig. 3, to verify the feasibility of the present solution, the feasibility of the method is first verified using a set of simulated interferograms with a height of 36.6rad, where the interferograms are 300 × 300 pixels in size; wherein the background term and the modulation term are respectively set as:

a(x,y)＝80exp(-0.05((x-0.01)²+y²))+40

b(x,y)＝100exp(-0.05(x²+y²))

the predetermined phase distribution isThe predetermined phase shift values are 1.5rad and 5rad, respectively. In order to make the simulated interferogram close to reality, the present embodiment adds white gaussian noise with a signal-to-noise ratio of 35dB to the three interferograms. Wherein the two phase-shifted interferograms and the predetermined phase are shown in fig. 3 (a-c). In order to compare the calculation accuracy, the phase to be measured is solved by using an AIA algorithm and an APCA algorithm respectively. As shown in fig. 3(d-f), the phase distributions calculated by the proposed method (DM-VU) and APCA and AIA algorithms, and the phases calculated by the above three algorithms are subtracted from the preset phase to quantitatively analyze the accuracy of the algorithm, to obtain a phase deviation profile, as shown in fig. 3(g-i), and the root mean square error RMSE value thereof is calculated and the calculation times are compared, as shown in fig. 1. As can be seen from the table, the method has a significant advantage in accuracy, and the computation time is an order of magnitude faster than the iterative AIA algorithm.

TABLE 1

As shown in fig. 4, in order to demonstrate the advantages of the phase shift phase measurement method according to the present invention over the conventional method, a representative least squares iterative method (AIA) and an improved principal component analysis method (APCA) of the conventional method are used for comparison, wherein a reference phase for comparison is calculated by AIA using 200 phase shift interferograms, as shown in fig. 4 (b). After the three selected phase-shift interferograms are calculated by using the method and APCA and AIA algorithms, the obtained phase distribution and the deviation distribution of the phase distribution and the reference phase are shown in (c-e) and (f-h) of fig. 4. It is obvious from the result of the phase deviation distribution that the phase deviation of the method is minimum, and secondly, the AIA algorithm, which is the maximum of the calculation deviation because the number of the interference pattern fringes calculated by the APCA algorithm is small. In order to quantitatively analyze the above results, the calculation accuracy and the calculation time of each method are shown in table 2. It is also clear from table 2 that the method has significant advantages in computational accuracy, as well as being an order of magnitude faster than the AIA algorithm.

TABLE 2

Example two

The second embodiment of the present invention discloses an improved phase shift phase measurement system, as shown in fig. 2, comprising

The data acquisition module is used for acquiring two differential interferograms, wherein the differential interferograms are images of the interferograms after background items are removed;

the data processing module is used for expressing the expression of the differential interference pattern in a matrix form, continuously iterating the matrix by using a factorization method until convergence, and calculating to obtain a vector related to the phase to be measured and the phase shift quantity;

and the calculation module is used for calculating the phase to be measured based on the related vector.

As a preferred embodiment, the data processing module comprises:

a first processing module for expressing the differential interferogram as:

wherein, Ib_m,k(x, y) denotes a differential interferogram, the subscript M denotes a pixel subscript index, the number of pixels in each image is M, i.e., M e (1,2,3.. M) is satisfied, k denotes a few differential interferograms, and k is 1, 2.

As a preferred embodiment, the data processing module further comprises:

a second processing module, configured to represent a processing result of the first processing module in a matrix form:

Ib＝(c-s)(uv)^T

＝VU^T

where c and s represent column vectors, respectively, denoted asAndu and v represent other column vectors, respectively, and are expressed as u ═ cos θ_k-1} and v ═ sin θ_kThe matrices V and U are denoted V ═ c-s and U ═ uv; wherein]^TRepresenting a transpose operation.

As a preferred embodiment, the data processing module further comprises:

the third processing module comprises:

the fourth processing submodule is used for presetting the initial phase shift quantity, randomly presetting the initial phase shift quantity theta, and calculating to obtain an initial u and an initial v;

a fifth processing submodule for calculating U₀、V₀Based on the initial u₀And initial v₀Calculate the initial matrix U₀＝(u₀v₀) Initial matrix V₀(ii) a Also for performing iterative processing, based on the initial matrix V₀Calculating initial vector distribution and updating to V₁Based on said V₁Calculating to obtain U₁Completing one iteration; repeating the iterative process until the convergence precision is reached, and outputting final V and U values;

and the sixth processing submodule is used for calculating to obtain the phase to be measured based on the final V and U values.

As a preferred embodiment, the fifth processing submodule uses V ═ Ib [ U (U)^TU)^-1]And known differential interferograms to obtain V₀；

With the resultant V₀According toCalculating initial vector distribution and updating the initial vector distribution to V₁Then V is added₁Substituted U ═ V^TV)^-1V^TIb]^-1To obtain a new U₁。

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.