CN108195408A - Based on two step phase extraction methods, system and the medium for tilting Phase-shifting Errors correction - Google Patents
Based on two step phase extraction methods, system and the medium for tilting Phase-shifting Errors correction Download PDFInfo
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Abstract
Included the present invention provides a kind of based on the two step phase extraction methods, system and storage medium, the method that tilt Phase-shifting Errors correction：Acquire two width Random figures；The background light intensity of two width Random figures is removed by high-pass filtering；Filtered two width Random figure is normalized, the modulation amplitude disturbance of two width Random figures of removal；To two width Random figures after normalized, the random inclination Phase-shifting Errors parameter between two width Random figures is solved by nonlinearity erron minimum；Phase is gone out based on the random Phase-shifting Errors parameter extraction that tilts between two width Random figures.During phase-shifting interference measuring phase extraction, Phase-shifting Errors are tilted at random as caused by being vibrated external environment and by influences such as the fixed caused background light intensity of air agitation and flashing and modulation amplitude disturbances.In addition, method provided by the invention need to only acquire two width interference patterns, phase extraction speed is fast, and precision is high.
Description
Technical field
The present invention relates to phase-shifting interference measuring technical field more particularly to a kind of two steps based on inclination Phase-shifting Errors correction
Phase extraction method, system and medium.
Background technology
With the continuous improvement that people require Optical Measurement Precision, phase-shifting interference measuring is developed rapidly, phase
Extraction plays the measuring precision most important effect as the primary link in phase-shifting interference measuring.
In order to improve the precision of phase-shifting interference measuring system, domestic and foreign scholars have done numerous studies work, have totally been divided into two
A study portion：One is research to different phase-shifting interference measuring system principles, by optimizing original measurement experiment device
Measurement accuracy and its stability or design Novel Phase-shifted interferometric optical system are improved, so as to reduce component defect, ring
The influence that border interference etc. is brought；The other is the research to phase extraction method.Traditional phase extraction method is done in phase shift
Phase could be effectively solved in the case of relating to known to phase shift value.Traditional phase extraction algorithms have three-step approach, four step rule, five steps
Method, modified five-step approach, N frames algorithm and phase average method etc..During phase-shifting interference measuring, due to air agitation,
External environment mechanical oscillation, non-linear and flashing the problems such as determining of phase shifter, often bring inevitable background
Light intensity disturbance, Phase-shifting Errors, result in phase extraction accuracy decline, so as to reduce phase-shifting interference measuring precision.
It is main to wrap for there are the phase extraction of random Phase-shifting Errors interference pattern, domestic and foreign scholars propose many methods
Include advanced iterative method (AIA), Principal Component Analysis (PCA), Schmidt's orthogonalization (GS), fourier transform method (FT), extreme value
Method (EVI) etc..Although these methods can be adapted for there are the interference pattern of random Phase-shifting Errors, but be not suitable for existing and incline at random
The interference pattern of oblique Phase-shifting Errors.
In order to solve the problems, such as to tilt Phase-shifting Errors at random as caused by vibration, there is scholar to propose some phase extraction sides
Method mainly includes：Based on optical flow method random obliquity factor correction phase extraction method, based on non-linear least square iteration
The phase extraction method of random obliquity factor, three step iterative methods, the phase extraction method minimized based on nonlinearity erron are calculated,
And other expanding methods.It is needed in calculating process largely repeatedly based on non-linear least square iterative method and three step iterative methods
In generation, takes longer.Optical flow method and nonlinearity erron minimization method can be comparatively fast from the interference patterns that there are random inclination Phase-shifting Errors
Middle extraction phase.But optical flow method and nonlinearity erron minimization method are not applied for there are modulation amplitude disturbance and tilt shifting at random
The interference pattern of phase error.
Invention content
It is a primary object of the present invention to provide a kind of two step phase extraction methods based on inclination Phase-shifting Errors correction, be
System and medium, overcome and tilt Phase-shifting Errors at random as caused by being vibrated external environment and determined by air agitation and flashing
Caused background light intensity and modulation amplitude disturbing influence.
In order to achieve the above object, the present invention proposes a kind of based on the two step phase extraction sides for tilting Phase-shifting Errors correction
Method, including：
Acquire two width Random figures；
The background light intensity of two width Random figures is removed by high-pass filtering；
Filtered two width Random figure is normalized, the modulation amplitude of two width Random figures of removal is disturbed
It is dynamic；
To two width Random figures after normalized, two width Randoms are solved by nonlinearity erron minimum
Random inclination Phase-shifting Errors parameter between figure；
Phase is gone out based on the random Phase-shifting Errors parameter extraction that tilts between the two width Random figure.
Wherein, which is characterized in that it is described by high-pass filtering remove two width Random figures background light intensity the step of wrap
It includes：
It to be disturbed when there are background light intensity and modulation amplitude, and in the case of the random inclination Phase-shifting Errors of presence, two width are done
Chart is related to be shown 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 phase shift is done
When relating to measuring system and being interfered by mechanical oscillation, δ (x, y) is a linear function, is expressed as：
δ (x, y)=α0+α1x+α2y；
Wherein α0It is the average value of phase shift value, [α1,α2] it is phase shift value obliquity factor；Two width Random figures remove background
It is expressed as after light intensity：
Wherein, it is described that filtered two width Random figure is normalized, two width Random figures of removal
The step of modulation amplitude disturbs includes：
Modulation amplitude is solved, wherein, modulation amplitude solution formula is：
Wherein, m is interference pattern coefficient, and H { } represents Hilbert-Huang transform；
By the interference pattern after removal background light intensityWithRemoval modulation amplitude is normalized,
Two width Random charts after removal modulation amplitude disturbance are shown as：
Wherein, it is described by nonlinearity erron minimum solve normalization after two width Random figures between it is random
The step of tilting Phase-shifting Errors parameter includes：
Two width Random figures after normalized are carried out with inner product operation, then convolution algorithm is carried out with Gaussian function,
It derives and tilts amount of phase shift expression formula；
Based on the inclination amount of phase shift expression formula, the obliquity factor and average value of amount of phase shift are tilted according to a preliminary estimate；
It is minimized by nonlinearity erron excellent to the obliquity factor for tilting amount of phase shift according to a preliminary estimate and average value progress
Change, solve phase.
Wherein, the method further includes：The validity of phase extraction method is verified.
In addition, the present invention also proposes a kind of two step phase extraction systems based on inclination Phase-shifting Errors correction, including storage
Device, processor and the computer program being stored on the memory, when the computer program is run by the processor
Realize following operation：
Acquire two width Random figures；
The background light intensity of two width Random figures is removed by high-pass filtering；
Filtered two width Random figure is normalized, the modulation amplitude of two width Random figures of removal is disturbed
It is dynamic；
To two width Random figures after normalized, two width Randoms are solved by nonlinearity erron minimum
Random inclination Phase-shifting Errors parameter between figure；
Phase is gone out based on the random Phase-shifting Errors parameter extraction that tilts between the two width Random figure.
Wherein, following operation is also realized when the computer program is run by the processor：
It to be disturbed when there are background light intensity and modulation amplitude, and in the case of the random inclination Phase-shifting Errors of presence, two width are done
Chart is related to be shown 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 phase shift is done
When relating to measuring system and being interfered by mechanical oscillation, δ (x, y) is a linear function, is expressed as：
δ (x, y)=α0+α1x+α2y；
Wherein α0It is the average value of phase shift value, [α1,α2] it is phase shift value obliquity factor；Two width Random figures remove background
It is expressed as after light intensity：
Wherein, following operation is also realized when the computer program is run by the processor：
Modulation amplitude is solved, wherein, modulation amplitude solution formula is：
Wherein, m is interference pattern coefficient, and H { } represents Hilbert-Huang transform；
By the interference pattern after removal background light intensityWithRemoval modulation amplitude is normalized,
Two width Random charts after removal modulation amplitude disturbance are shown as：
Wherein, following operation is also realized when the computer program is run by the processor：
Two width Random figures after normalized are carried out with inner product operation, then convolution algorithm is carried out with Gaussian function,
It derives and tilts amount of phase shift expression formula；
Based on the inclination amount of phase shift expression formula, the obliquity factor and average value of amount of phase shift are tilted according to a preliminary estimate；
It is minimized by nonlinearity erron excellent to the obliquity factor for tilting amount of phase shift according to a preliminary estimate and average value progress
Change, solve phase.
In addition, the present invention also proposes a kind of computer readable storage medium, stored on the computer readable storage medium
There is the step of computer program, the computer program realizes method as described above when being run by processor.
The embodiment of the present invention proposes a kind of based on the two step phase extraction methods, system and the Jie that tilt Phase-shifting Errors correction
Matter, this method are removed the background light intensity of two width interference patterns by high-pass filtering, then remove modulated amplitude by normalization method first
Degree disturbance, then the random inclination Phase-shifting Errors parameter solved between two width interference patterns is minimized by nonlinearity erron, finally
Can phase be gone out with rapid extraction.During phase-shifting interference measuring phase extraction, caused by external environment vibration
It is random tilt Phase-shifting Errors and by air agitation and flashing it is fixed caused by the shadows such as background light intensity and modulation amplitude disturbance
It rings.In addition, method provided by the invention need to only acquire two width interference patterns, phase extraction speed is fast, and precision is high.
Description of the drawings
Fig. 1 is that the present invention is based on the flow diagrams for the two step phase extraction methods for tilting Phase-shifting Errors correction；
Fig. 2 is the refinement flow diagram based on the two step phase extraction methods for tilting Phase-shifting Errors correction；
Fig. 3 is Computer Simulation of embodiment of the present invention initial phase, tilts Phase-shifting Errors and its interference pattern；
Fig. 4 is that Computer Simulation of the embodiment of the present invention has the phase extraction result figure tilted in the case of Phase-shifting Errors.
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, it is right
The present invention is further elaborated.
Specific embodiment
It should be appreciated that specific embodiment described herein is not intended to limit the present invention only to explain the present invention.
Specifically, it is as shown in Figure 1, provided by the invention a kind of based on the two step phase extraction sides for tilting Phase-shifting Errors correction
Method, including：
Step S1 acquires two width Random figures；
Step S2 removes the background light intensity of two width Random figures by high-pass filtering；
Filtered two width Random figure is normalized in step S3, removes the tune of two width Random figures
Amplitude disturbance processed；
To two width Random figures after normalized, two width are solved by nonlinearity erron minimum by step S4
Random inclination Phase-shifting Errors parameter between Random figure；
Step S5 goes out phase based on the random Phase-shifting Errors parameter extraction that tilts between the two width Random figure.
Wherein, the random inclination phase shift solved by nonlinearity erron minimum between two width Random figures misses
The step of poor parameter, can include：
Two width Random figures after normalized are carried out with inner product operation, then convolution algorithm is carried out with Gaussian function,
It derives and tilts amount of phase shift expression formula；
Based on the inclination amount of phase shift expression formula, the obliquity factor and average value of amount of phase shift are tilted according to a preliminary estimate；
It is minimized by nonlinearity erron excellent to the obliquity factor for tilting amount of phase shift according to a preliminary estimate and average value progress
Change, solve phase.
Compared with prior art, a kind of two step phase extraction methods based on inclination Phase-shifting Errors correction proposed by the present invention,
Minimized by normalization and nonlinearity erron and solve the random Phase-shifting Errors between two width interference patterns, the method overcome by
External environment tilted at random caused by vibrating Phase-shifting Errors and by air agitation and flashing it is fixed caused by background light intensity and
The influences such as modulation amplitude disturbance.
The embodiment of the present invention is described in detail below in conjunction with Fig. 2：
The present invention proposes a kind of two step phase extraction methods based on inclination Phase-shifting Errors correction, and this method passes through first
High-pass filtering removes the background light intensity of two width interference patterns, and then removing modulation amplitude by normalization method disturbs, then by non-thread
Property minimize the error solve between two width interference patterns random and tilt Phase-shifting Errors parameter, finally can phase be gone out with rapid extraction
Position.
Specific process flow as shown in Fig. 2, including：
Step 1：Remove background light intensity.It to be disturbed when there are background light intensity and modulation amplitude, and there is random inclination phase shift
In the case of error, two width interference patterns can be expressed as：
a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents modulation amplitude.Work as phase-shifting interference measuring
When system is not interfered by mechanical oscillation, δ (x, y) is a constant；When phase-shifting interference measuring system is done by mechanical oscillation
When disturbing, δ (x, y) is no longer a fixed constant, but a linear function：
δ (x, y)=α0+α1x+α2y (2)
Wherein α0It is the average value of phase shift value, [α1,α2] it is phase shift value obliquity factor.The random phase-shift interference removal of two width
It can be expressed as after ambient noise：
Step 2：Remove modulation amplitude disturbance.Modulation amplitude disturbance can be removed by solving modulation amplitude in formula (3)
Influence.Modulation amplitude solution formula is：
M is interference pattern coefficient.H { } represents Hilbert-Huang transform.In order to eliminate the influence of modulation amplitude, we will go
Except the interference pattern after background light intensityWithRemoval modulation amplitude is normalized.
Step 3：Abbreviation obtains the expression formula of amount of phase shift.To two width interference patterns carry out inner product operation, then with Gaussian function into
Row convolution algorithm obtains：
Then the expression formula of amount of phase shift δ (x, y) can be obtained by formula (6) being divided by：
Step 4：The preliminary obliquity factor and average value for solving amount of phase shift.C (0,0)=α can be obtained by above formula0, because
This can obtain α0Estimated value be：
Derivation is carried out respectively in x directions and y directions to formula (7), then is divided by and can obtain the estimated value of β：
Then pass through minimum mean-square error functionIt can solve
Since obliquity factor is typically small, by α1' initial value be set as 0, then again by solving the minimum value of above formula
It can obtain α1Estimation.
Step 5：Advanced optimize the obliquity factor and average value of amount of phase shift.It obtains tilting the initial of each parameter of amount of phase shift
Nonlinearity erron minimum is recycled to advanced optimize after estimated value to it, three-dimensional error function is：
Tilt phase shift initial value beIt can just be solved when error function obtains minimum value
The optimal estimation value of random amount of phase shift.
Obtaining inclination amount of phase shift is：
Step 6：Solve phase information.
In order to verify the validity of this method, with computer to carrying out analog simulation in the case of various.
Case：In phase-shifting interference measuring, unstable background light intensity and the modulation amplitude of often causing of external environment
Disturbance, amount of phase shift, which can also exist, tilts Phase-shifting Errors.Therefore the parameter by the random phase shift interference of two width is set as：
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))；
Object phase；Inclination phase shift between first width interference pattern and the second width interference pattern
It measures and is：δ (x, y)=0.75+0.05x+0.15y.In addition 0.05 times of rand white Gaussian noises are added.
Numerical simulation generates the initial phase of 512 × 512 pixels, as shown in Fig. 3 (d), corresponding wrapped phase such as Fig. 3
(e).Fig. 3 (a) and (b) are two width interference patterns respectively, and Fig. 3 (c) is that there are the amount of phase shift of heeling error between two width interference patterns.Figure
4 (a) is the inclination amount of phase shift that solves of this method estimation, Fig. 4 (b) and Fig. 4 (c) represents respectively phase that this method extracts with
Continuous phase after unpacking.
Compared with prior art, what the embodiment of the present invention proposed is a kind of based on the two step phase extractions for tilting Phase-shifting Errors correction
Method, system and medium, this method are removed the background light intensity of two width interference patterns by high-pass filtering, then pass through normalization first
Method removal modulation amplitude disturbance, then the random inclination phase shift solved between two width interference patterns is minimized by nonlinearity erron and is missed
Poor parameter finally can go out phase with rapid extraction.During phase-shifting interference measuring phase extraction, by extraneous ring
Border tilts Phase-shifting Errors and at random by the fixed caused background light intensity of air agitation and flashing and modulated amplitude caused by vibrating
The influences such as degree disturbance.In addition, method provided by the invention need to only acquire two width interference patterns, phase extraction speed is fast, and precision is high.
In addition, the present invention also proposes a kind of two step phase extraction systems based on inclination Phase-shifting Errors correction, including storage
Device, processor and the computer program being stored on the memory, when the computer program is run by the processor
The step of realizing method as described above, details are not described herein.
In addition, the present invention also proposes a kind of computer readable storage medium, stored on the computer readable storage medium
There is the step of computer program, the computer program realizes method as described above when being run by processor, herein no longer
It repeats.
The foregoing is merely the preferred embodiment of the present invention, are not intended to limit the scope of the invention, every utilization
Equivalent structure or the flow transformation that description of the invention and accompanying drawing content are made, are directly or indirectly used in other relevant skills
Art field, is included within the scope of the present invention.
Claims (10)
- It is 1. a kind of based on the two step phase extraction methods for tilting Phase-shifting Errors correction, which is characterized in that including：Acquire two width Random figures；The background light intensity of two width Random figures is removed by high-pass filtering；Filtered two width Random figure is normalized, the modulation amplitude disturbance of two width Random figures of removal；To two width Random figures after normalized, by nonlinearity erron minimum solve two width Random figures it Between random tilt Phase-shifting Errors parameter；Phase is gone out based on the random Phase-shifting Errors parameter extraction that tilts between the two width Random figure.
- It is 2. according to claim 1 based on the two step phase extraction methods for tilting Phase-shifting Errors correction, which is characterized in that institute The step of removing the background light intensity of two width Random figures by high-pass filtering is stated to include：It to be disturbed when there are background light intensity and modulation amplitude, and in the case of the random inclination Phase-shifting Errors of presence, two width interference patterns It is expressed as：Wherein, a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents modulation amplitude；Work as phase-shifting interference measuring When system is interfered by mechanical oscillation, δ (x, y) is a linear function, is expressed as：δ (x, y)=α0+α1x+α2y；Wherein α0It is the average value of phase shift value, [α1,α2] it is phase shift value obliquity factor；Two width Random figures remove background light intensity After be expressed as：
- It is 3. according to claim 1 based on the two step phase extraction methods for tilting Phase-shifting Errors correction, which is characterized in that institute It states and filtered two width Random figure is normalized, the step of the modulation amplitude disturbance of two width Random figures of removal Suddenly include：Modulation amplitude is solved, wherein, modulation amplitude solution formula is：Wherein, m is interference pattern coefficient, and H { } represents Hilbert-Huang transform；By the interference pattern after removal background light intensityWithRemoval modulation amplitude is normalized, removes Two width Random charts after modulation amplitude disturbance are shown as：
- 4. the two step phase extraction methods based on inclination Phase-shifting Errors correction according to claim 1,2 or 3, feature exist In the random step for tilting Phase-shifting Errors parameter solved by nonlinearity erron minimum between two width Random figures Suddenly include：Two width Random figures after normalized are carried out with inner product operation, then convolution algorithm is carried out with Gaussian function, is derived Go out to tilt amount of phase shift expression formula；Based on the inclination amount of phase shift expression formula, the obliquity factor and average value of amount of phase shift are tilted according to a preliminary estimate；It is minimized by nonlinearity erron and the obliquity factor and average value of the amount of phase shift of inclination according to a preliminary estimate is optimized, asked Solve phase.
- It is 5. according to claim 4 based on the two step phase extraction methods for tilting Phase-shifting Errors correction, which is characterized in that institute The method of stating further includes：The validity of phase extraction method is verified.
- It is 6. a kind of based on the two step phase extraction systems for tilting Phase-shifting Errors correction, which is characterized in that including memory, processor And the computer program on the memory is stored in, following behaviour is realized when the computer program is run by the processor Make：Acquire two width Random figures；The background light intensity of two width Random figures is removed by high-pass filtering；Filtered two width Random figure is normalized, the modulation amplitude disturbance of two width Random figures of removal；To two width Random figures after normalized, by nonlinearity erron minimum solve two width Random figures it Between random tilt Phase-shifting Errors parameter；Phase is gone out based on the random Phase-shifting Errors parameter extraction that tilts between the two width Random figure.
- It is 7. according to claim 6 based on the two step phase extraction systems for tilting Phase-shifting Errors correction, which is characterized in that institute It states when computer program is run by the processor and also realizes following operation：It to be disturbed when there are background light intensity and modulation amplitude, and in the case of the random inclination Phase-shifting Errors of presence, two width interference patterns It is expressed as：Wherein, a1(x,y),a2(x, y) represents background light intensity, b1(x,y),b2(x, y) represents modulation amplitude；Work as phase-shifting interference measuring When system is interfered by mechanical oscillation, δ (x, y) is a linear function, is expressed as：δ (x, y)=α0+α1x+α2y；Wherein α0It is the average value of phase shift value, [α1,α2] it is phase shift value obliquity factor；Two width Random figures remove background light intensity After be expressed as：
- It is 8. according to claim 7 based on the two step phase extraction systems for tilting Phase-shifting Errors correction, which is characterized in that institute It states when computer program is run by the processor and also realizes following operation：Modulation amplitude is solved, wherein, modulation amplitude solution formula is：Wherein, m is interference pattern coefficient, and H { } represents Hilbert-Huang transform；By the interference pattern after removal background light intensityWithRemoval modulation amplitude is normalized, removes Two width Random charts after modulation amplitude disturbance are shown as：
- It is 9. according to claim 8 based on the two step phase extraction systems for tilting Phase-shifting Errors correction, which is characterized in that institute It states when computer program is run by the processor and also realizes following operation：Two width Random figures after normalized are carried out with inner product operation, then convolution algorithm is carried out with Gaussian function, is derived Go out to tilt amount of phase shift expression formula；Based on the inclination amount of phase shift expression formula, the obliquity factor and average value of amount of phase shift are tilted according to a preliminary estimate；It is minimized by nonlinearity erron and the obliquity factor and average value of the amount of phase shift of inclination according to a preliminary estimate is optimized, asked Solve phase.
- 10. a kind of computer readable storage medium, which is characterized in that be stored with computer on the computer readable storage medium Program, the step of method as described in any one of claim 1-5 is realized when the computer program is run by processor.
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| CN110926375A (en) * | 2019-12-25 | 2020-03-27 | 哈尔滨工业大学（深圳） | Quick phase extraction method based on diamond vector normalization |
| CN111006611A (en) * | 2019-12-20 | 2020-04-14 | 哈尔滨工业大学（深圳） | Rapid high-precision phase extraction method based on two-step nonlinear phase shifting |
| CN112066909A (en) * | 2020-08-24 | 2020-12-11 | 南京理工大学 | Anti-vibration interference measurement method based on inclined plane high-precision extraction |
| CN112097677A (en) * | 2020-08-26 | 2020-12-18 | 南京理工大学 | Rapid high-precision phase restoration method for anti-vibration interferometry |
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| CN111006611B (en) * | 2019-12-20 | 2021-10-22 | 哈尔滨工业大学（深圳） | Rapid high-precision phase extraction method based on two-step nonlinear phase shifting |
| CN110926375A (en) * | 2019-12-25 | 2020-03-27 | 哈尔滨工业大学（深圳） | Quick phase extraction method based on diamond vector normalization |
| CN110926375B (en) * | 2019-12-25 | 2021-11-23 | 哈尔滨工业大学（深圳） | Quick phase extraction method based on diamond vector normalization |
| CN112066909A (en) * | 2020-08-24 | 2020-12-11 | 南京理工大学 | Anti-vibration interference measurement method based on inclined plane high-precision extraction |
| CN112066909B (en) * | 2020-08-24 | 2022-04-08 | 南京理工大学 | Anti-vibration interference measurement method based on inclined plane high-precision extraction |
| CN112097677A (en) * | 2020-08-26 | 2020-12-18 | 南京理工大学 | Rapid high-precision phase restoration method for anti-vibration interferometry |
| CN112097677B (en) * | 2020-08-26 | 2022-03-18 | 南京理工大学 | Rapid high-precision phase restoration method for anti-vibration interferometry |
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