CN108195408B - Two-step phase extraction method, system and medium based on tilt phase shift error correction - Google Patents
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Abstract
The invention provides a two-step phase extraction method, a system and a storage medium based on inclined phase shift error correction, wherein the method comprises the following steps: collecting two random interferograms; removing the background light intensity of the two random interference patterns through high-pass filtering; normalizing the two filtered random interferograms to remove modulation amplitude disturbance of the two random interferograms; solving the two random interference images after normalization processing to obtain random tilt phase shift error parameters between the two random interference images through nonlinear error minimization; and extracting the phase based on the random tilt phase shift error parameter between the two random interferograms. The invention overcomes the influences of random tilt phase shift error caused by external environment vibration, background light intensity and modulation amplitude disturbance caused by air disturbance and light source instability and the like in the phase-shift interferometry phase extraction process. In addition, the method provided by the invention only needs to collect two interferograms, and has high phase extraction speed and high precision.
Description
Technical Field
The invention relates to the technical field of phase-shifting interferometry, in particular to a two-step phase extraction method, a two-step phase extraction system and a two-step phase extraction medium based on inclined phase-shifting error correction.
Background
With the continuous improvement of the requirements of people on the precision of optical measurement, the phase-shifting interferometry is rapidly developed, and the phase extraction is used as a primary link in the phase-shifting interferometry and plays a crucial role in the measurement precision of a system.
In order to improve the precision of the phase-shifting interferometry system, a large amount of research work is done by domestic and foreign scholars, and the overall research work is divided into two research parts: the first is the research on the principle of different phase-shifting interferometry systems, and the measurement precision and the stability thereof are improved by optimizing the original measurement experimental device, or a novel phase-shifting interferometry optical system is designed, so that the influence caused by the defects of components, environmental interference and the like is reduced; another is the study of the phase extraction method. The traditional phase extraction method can effectively solve the phase under the condition that the phase shift value in the phase shift interference is known. The traditional phase extraction algorithm includes a three-step method, a four-step method, a five-step method, a modified five-step method, an N-frame algorithm, a phase averaging method and the like. In the phase-shifting interferometry process, the problems of air disturbance, external environment mechanical vibration, phase shifter nonlinearity, light source instability and the like are caused, so that inevitable background light intensity disturbance and phase-shifting errors are caused, the phase extraction precision is reduced, and the phase-shifting interferometry precision is reduced.
For phase extraction of interferograms with random phase shift errors, a plurality of methods are proposed by scholars at home and abroad, and mainly comprise an advanced iterative method (AIA), a Principal Component Analysis (PCA), a Schmidt orthogonal transformation (GS), a Fourier Transform (FT), an extreme value method (EVI) and the like. These methods, while applicable to interferograms with random phase shift errors, are not applicable to interferograms with random tilt phase shift errors.
In order to solve the problem of random tilt phase shift error caused by vibration, some researchers have proposed some phase extraction methods, which mainly include: the method comprises a phase extraction method based on optical flow random tilt factor correction, a phase extraction method based on nonlinear least square iteration calculation random tilt factor, a three-step iteration method, a phase extraction method based on nonlinear error minimization and other expansion methods. Based on the nonlinear least square iteration method and the three-step iteration method, a large amount of iterations are needed in the calculation process, and the time consumption is long. The optical flow method and the nonlinear error minimization method can quickly extract the phase from the interference image with random inclined phase shift error. But the optical flow method and the non-linear error minimization method cannot be applied to interferograms with modulation amplitude disturbances and random tilt phase shift errors.
Disclosure of Invention
The invention mainly aims to provide a two-step phase extraction method, a system and a medium based on tilt phase shift error correction, which overcome random tilt phase shift errors caused by external environment vibration and background light intensity and modulation amplitude disturbance influences caused by air disturbance and light source instability.
In order to achieve the above object, the present invention provides a two-step phase extraction method based on skew phase shift error correction, comprising:
collecting two random interferograms;
removing the background light intensity of the two random interference patterns through high-pass filtering;
normalizing the two filtered random interferograms to remove modulation amplitude disturbance of the two random interferograms;
solving the two random interference images after normalization processing to obtain random tilt phase shift error parameters between the two random interference images through nonlinear error minimization;
and extracting the phase based on the random tilt phase shift error parameter between the two random interferograms.
Wherein, the step of removing the background light intensity of the two random interferograms by high-pass filtering comprises:
in the presence of background light intensity and modulation amplitude perturbations, and random tilt phase shift errors, the two interferograms are represented as:
I1(x,y)＝a1(x,y)+b1(x,y)cos(φ(x,y))
I2(x,y)＝a2(x,y)+b2(x,y)cos(φ(x,y)+δ(x,y))；
wherein, a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents modulation amplitude; when a phase-shifting interferometry system is subject to mechanical vibration disturbances, δ (x, y) is a linear function expressed as:
δ(x,y)＝α0+α1x+α2y；
wherein alpha is0Is the average value of the phase shift values, [ alpha ]1,α2]Is the phase shift value tilt factor; the two random interferograms after removal of background light intensity are expressed as:
the step of normalizing the two filtered random interferograms and removing the modulation amplitude disturbance of the two random interferograms comprises:
and solving the modulation amplitude, wherein the modulation amplitude solving formula is as follows:
wherein m is an interferogram coefficient, and H {. cndot } represents a Hilbert-Huang transform;
removing the interference pattern after background light intensity
Andnormalization processing is carried out to remove modulation amplitude, and the two random interference graphs after modulation amplitude disturbance is removed are represented as follows:
wherein, the step of solving the random tilt phase shift error parameter between the two normalized random interferograms through the nonlinear error minimization comprises:
performing inner product operation on the two random interferograms after the normalization processing, performing convolution operation on the two random interferograms and a Gaussian function, and deriving an expression of the inclined phase shift amount;
preliminarily estimating a gradient factor and an average value of the gradient phasor based on the gradient phasor expression;
and optimizing the inclination factor and the average value of the preliminary estimation inclination phase shift quantity through nonlinear error minimization to solve the phase.
Wherein the method further comprises: and verifying the effectiveness of the phase extraction method.
Furthermore, the present invention proposes a two-step phase extraction system based on a tilted phase shift error correction, comprising a memory, a processor and a computer program stored on said memory, said computer program being adapted to perform the following operations when executed by said processor:
collecting two random interferograms;
removing the background light intensity of the two random interference patterns through high-pass filtering;
normalizing the two filtered random interferograms to remove modulation amplitude disturbance of the two random interferograms;
solving the two random interference images after normalization processing to obtain random tilt phase shift error parameters between the two random interference images through nonlinear error minimization;
and extracting the phase based on the random tilt phase shift error parameter between the two random interferograms.
Wherein the computer program when executed by the processor further performs the following:
in the presence of background light intensity and modulation amplitude perturbations, and random tilt phase shift errors, the two interferograms are represented as:
I1(x,y)＝a1(x,y)+b1(x,y)cos(φ(x,y))
I2(x,y)＝a2(x,y)+b2(x,y)cos(φ(x,y)+δ(x,y))；
wherein, a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents modulation amplitude; when a phase-shifting interferometry system is subject to mechanical vibration disturbances, δ (x, y) is a linear function expressed as:
δ(x,y)＝α0+α1x+α2y；
wherein alpha is0Is the average value of the phase shift values, [ alpha ]1,α2]Is the phase shift value tilt factor; the two random interferograms after removal of background light intensity are expressed as:
wherein the computer program when executed by the processor further performs the following:
and solving the modulation amplitude, wherein the modulation amplitude solving formula is as follows:
wherein m is an interferogram coefficient, and H {. cndot } represents a Hilbert-Huang transform;
removing the interference pattern after background light intensity
And
normalization processing is carried out to remove modulation amplitude, and the two random interference graphs after modulation amplitude disturbance is removed are represented as follows:
wherein the computer program when executed by the processor further performs the following:
performing inner product operation on the two random interferograms after the normalization processing, performing convolution operation on the two random interferograms and a Gaussian function, and deriving an expression of the inclined phase shift amount;
preliminarily estimating a gradient factor and an average value of the gradient phasor based on the gradient phasor expression;
and optimizing the inclination factor and the average value of the preliminary estimation inclination phase shift quantity through nonlinear error minimization to solve the phase.
Furthermore, the present invention also proposes a computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements the steps of the method as described above.
According to the method, the background light intensity of two interference patterns is removed through high-pass filtering, modulation amplitude disturbance is removed through a normalization method, random tilt phase shift error parameters between the two interference patterns are solved through nonlinear error minimization, and finally the phase can be extracted quickly. The invention overcomes the influences of random tilt phase shift error caused by external environment vibration, background light intensity and modulation amplitude disturbance caused by air disturbance and light source instability and the like in the phase-shift interferometry phase extraction process. In addition, the method provided by the invention only needs to collect two interferograms, and has high phase extraction speed and high precision.
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FIG. 1 is a schematic flow diagram of a two-step phase extraction method based on skew-phase error correction according to the present invention;
FIG. 2 is a schematic flow diagram of a two-step phase extraction method based on skew phase error correction;
FIG. 3 is a computer simulated initial phase, tilt phase shift error, and interferograms thereof for an embodiment of the present invention;
FIG. 4 is a diagram illustrating the phase extraction result in the presence of tilt phase shift error in the computer simulation in the embodiment of the present invention.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Specifically, as shown in fig. 1, the two-step phase extraction method based on the skew phase shift error correction provided by the present invention includes:
step S1, collecting two random interferograms;
step S2, removing the background light intensity of the two random interferograms through high-pass filtering;
step S3, normalization processing is carried out on the two filtered random interferograms, and modulation amplitude disturbance of the two random interferograms is removed;
step S4, solving the two random interferograms after normalization processing to obtain random tilt phase shift error parameters between the two random interferograms through nonlinear error minimization;
and step S5, extracting a phase based on the random tilt phase shift error parameter between the two random interferograms.
Wherein the step of solving the random tilt phase shift error parameter between the two random interferograms through the nonlinear error minimization may include:
performing inner product operation on the two random interferograms after the normalization processing, performing convolution operation on the two random interferograms and a Gaussian function, and deriving an expression of the inclined phase shift amount;
preliminarily estimating a gradient factor and an average value of the gradient phasor based on the gradient phasor expression;
and optimizing the inclination factor and the average value of the preliminary estimation inclination phase shift quantity through nonlinear error minimization to solve the phase.
Compared with the prior art, the two-step phase extraction method based on the inclined phase shift error correction solves the random phase shift error between the two interferograms through normalization and nonlinear error minimization, and overcomes the influences of the random inclined phase shift error caused by external environment vibration, background light intensity and modulation amplitude disturbance caused by air disturbance and light source instability and the like.
The embodiment of the present invention is described in detail below with reference to fig. 2:
the invention provides a two-step phase extraction method based on tilt phase shift error correction, which comprises the steps of removing background light intensity of two interference patterns through high-pass filtering, removing modulation amplitude disturbance through a normalization method, solving random tilt phase shift error parameters between the two interference patterns through nonlinear error minimization, and finally quickly extracting a phase.
The specific processing flow is shown in fig. 2, and includes:
step 1: the background light intensity is removed. In the presence of background light intensity and modulation amplitude perturbations, and in the presence of random tilt phase shift errors, the two interferograms can be represented as:
a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents the modulation amplitude. When the phase-shifting interferometry system is not disturbed by mechanical vibration, δ (x, y) is a constant; when a phase-shifting interferometry system is disturbed by mechanical vibrations, δ (x, y) is no longer a fixed constant but a linear function:
δ(x,y)＝α0+α1x+α2y (2)
wherein alpha is0Is the average value of the phase shift values, [ alpha ]1,α2]Is the phase shift value tilt factor. After background noise is removed by the two random phase-shifting interferograms, the two random phase-shifting interferograms can be expressed as:
step 2: and removing modulation amplitude disturbance. Solving for the modulation amplitude in equation (3) can remove the effect of modulation amplitude disturbance. The modulation amplitude solving formula is as follows:
and m is an interference pattern coefficient. H {. cndot } represents a Hilbert-yellow transform. In order to eliminate the influence of modulation amplitude, we will remove the interference pattern after background light intensity
And
and carrying out normalization processing to remove modulation amplitude.
And step 3: simplifying to obtain the expression of the phase shift quantity. Performing inner product operation on the two interferograms, and performing convolution operation on the two interferograms and a Gaussian function to obtain:
then, the expression of the phase shift quantity δ (x, y) can be obtained by dividing the formula (6):
and 4, step 4: and preliminarily solving the inclination factor and the average value of the phase shift vector. C (0,0) ═ α can be obtained by the above formula0Thus, α can be obtained0The estimated values of (c) are:
the derivatives of equation (7) are derived in the x-direction and the y-direction, respectively, and then divided to obtain the estimated value of β:
then passes through a least squares error function
Can solve out
Since the tilt factor is generally small, α will be1' the initial value is set to 0, and then alpha can be obtained by solving the minimum value of the above formula1Is estimated.
And 5: the tilt factor and the mean value of the phase shift quantities are further optimized. After the initial estimation value of each parameter of the tilt phase shift quantity is obtained, the initial estimation value is further optimized by utilizing nonlinear error minimization, and the three-dimensional error function is as follows:
the initial value of the tilt phase shift is
When the error function takes the minimum value, the optimal estimated value of the random phase shift quantity can be solved.
The tilt phase shift quantity is obtained as:
step 6: the phase information is solved.
To verify the validity of the method, simulation simulations were performed in each case with a computer.
Case (2): in phase-shifting interferometry, the disturbance of background light intensity and modulation amplitude is often caused by the instability of the external environment, and the phase-shifting amount also has an oblique phase-shifting error. The parameters of the two random phase-shifting interferometers are thus set to:
background light intensity a0(x,y)＝0.2exp(-1.8(x2+y2)),a1(x,y)＝0.4exp(-1.8(x2+y2))；
Modulation amplitude b0(x,y)＝0.2exp(-0.2(x2+y2)),b1(x,y)＝0.4exp(-0.2(x2+y2))；
Phase of an object
(ii) a The amount of tilt phase shift between the first and second interferograms is: δ (x, y) ═ 0.75+0.05x +0.15 y. Furthermore, 0.05 times of rand white Gaussian noise is added.
Numerical simulation generates an initial phase of 512 × 512 pixels, as shown in fig. 3(d), and its corresponding wrapped phase is as shown in fig. 3 (e). Fig. 3(a) and (b) are two interferograms, respectively, and fig. 3(c) is a phase shift amount in which a tilt error exists between the two interferograms. Fig. 4(a) shows the estimated and solved tilt phase shift amount by the method, and fig. 4(b) and 4(c) show the phase extracted by the method and the continuous phase after unwrapping, respectively.
Compared with the prior art, the method, the system and the medium for extracting the two-step phase based on the slope phase shift error correction are provided by the embodiment of the invention, firstly, the background light intensity of two interferograms is removed through high-pass filtering, then, the modulation amplitude disturbance is removed through a normalization method, then, the random slope phase shift error parameter between the two interferograms is solved through nonlinear error minimization, and finally, the phase can be quickly extracted. The invention overcomes the influences of random tilt phase shift error caused by external environment vibration, background light intensity and modulation amplitude disturbance caused by air disturbance and light source instability and the like in the phase-shift interferometry phase extraction process. In addition, the method provided by the invention only needs to collect two interferograms, and has high phase extraction speed and high precision.
In addition, the present invention further provides a two-step phase extraction system based on tilt phase shift error correction, which includes a memory, a processor, and a computer program stored in the memory, wherein the computer program implements the steps of the method described above when being executed by the processor, and details are not repeated herein.
In addition, the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the method are implemented, which are not described herein again.
The above description is only for the preferred embodiment of the present invention and is not intended to limit the scope of the present invention, and all equivalent structures or flow transformations made by the present specification and drawings, or applied directly or indirectly to other related arts, are included in the scope of the present invention.
Claims (8)
1. A two-step phase extraction method based on inclined phase shift error correction is characterized by comprising the following steps:
collecting two random interferograms;
removing the background light intensity of the two random interference patterns through high-pass filtering;
normalizing the two filtered random interferograms to remove modulation amplitude disturbance of the two random interferograms;
solving the two random interference images after normalization processing to obtain random tilt phase shift error parameters between the two random interference images through nonlinear error minimization;
extracting a phase based on a random tilt phase shift error parameter between the two random interferograms;
the step of solving the random tilt phase shift error parameter between two random interferograms through nonlinear error minimization comprises the following steps:
performing inner product operation on the two random interferograms after the normalization processing, performing convolution operation on the two random interferograms and a Gaussian function, and deriving an expression of the inclined phase shift amount;
preliminarily estimating a gradient factor and an average value of the gradient phasor based on the gradient phasor expression;
and optimizing the inclination factor and the average value of the preliminary estimation inclination phase shift quantity through nonlinear error minimization to solve the phase.
2. The two-step phase extraction method based on tilted phase shift error correction according to claim 1, wherein the step of removing the background light intensity of the two random interferograms by high-pass filtering comprises:
in the presence of background light intensity and modulation amplitude perturbations, and random tilt phase shift errors, the two interferograms are represented as:
wherein, a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents modulation amplitude; when a phase-shifting interferometry system is subject to mechanical vibration disturbances, δ (x, y) is a linear function expressed as:
δ(x,y)＝α0+α1x+α2y；
wherein alpha is0Is the average value of the phase shift values, [ alpha ]1,α2]Is the phase shift value tilt factor; the two random interferograms after removal of background light intensity are expressed as:
3. the two-step phase extraction method based on tilted phase shift error correction according to claim 1, wherein the step of normalizing the filtered two random interferograms and removing the modulation amplitude perturbation of the two random interferograms comprises:
and solving the modulation amplitude, wherein the modulation amplitude solving formula is as follows:
wherein m is an interferogram coefficient, and H {. cndot } represents a Hilbert-Huang transform;
removing the interference pattern after background light intensity
And
normalization processing is carried out to remove modulation amplitude, and the two random interference graphs after modulation amplitude disturbance is removed are represented as follows:
4. the two-step phase extraction method based on tilted phase shift error correction according to claim 1, further comprising: and verifying the effectiveness of the phase extraction method.
5. A two-step phase extraction system based on tilt-shift-error correction, comprising a memory, a processor and a computer program stored on the memory, the computer program when executed by the processor performing the operations of:
collecting two random interferograms;
removing the background light intensity of the two random interference patterns through high-pass filtering;
normalizing the two filtered random interferograms to remove modulation amplitude disturbance of the two random interferograms;
solving the two random interference images after normalization processing to obtain random tilt phase shift error parameters between the two random interference images through nonlinear error minimization;
extracting a phase based on a random tilt phase shift error parameter between the two random interferograms;
the computer program when executed by the processor further performs the following:
performing inner product operation on the two random interferograms after the normalization processing, performing convolution operation on the two random interferograms and a Gaussian function, and deriving an expression of the inclined phase shift amount;
preliminarily estimating a gradient factor and an average value of the gradient phasor based on the gradient phasor expression;
and optimizing the inclination factor and the average value of the preliminary estimation inclination phase shift quantity through nonlinear error minimization to solve the phase.
6. The two-step phase extraction system based on tilted dephasing error correction according to claim 5, wherein the computer program when executed by the processor further performs the following:
in the presence of background light intensity and modulation amplitude perturbations, and random tilt phase shift errors, the two interferograms are represented as:
wherein, a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents modulation amplitude; when a phase-shifting interferometry system is subject to mechanical vibration disturbances, δ (x, y) is a linear function expressed as:
δ(x,y)＝α0+α1x+α2y；
wherein alpha is0Is the average value of the phase shift values, [ alpha ]1,α2]Is the phase shift value tilt factor; the two random interferograms after removal of background light intensity are expressed as:
7. the two-step phase extraction system based on tilted-phase-shift-error correction according to claim 6, wherein the computer program when executed by the processor further performs the following operations:
and solving the modulation amplitude, wherein the modulation amplitude solving formula is as follows:
wherein m is an interferogram coefficient, and H {. cndot } represents a Hilbert-Huang transform;
removing the interference pattern after background light intensity
And
normalization processing is carried out to remove modulation amplitude, and the two random interference graphs after modulation amplitude disturbance is removed are represented as follows:
8. a computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, which computer program, when being executed by a processor, carries out the steps of the method according to any one of claims 1-4.
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