CN107796301A - The phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse - Google Patents

The phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse Download PDF

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CN107796301A
CN107796301A CN201710851113.6A CN201710851113A CN107796301A CN 107796301 A CN107796301 A CN 107796301A CN 201710851113 A CN201710851113 A CN 201710851113A CN 107796301 A CN107796301 A CN 107796301A
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msub
mrow
msup
mfrac
sin
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姚勇
雷何兵
刘昊鹏
吴昊堃
杨彦甫
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Shenzhen Graduate School Harbin Institute of Technology
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Shenzhen Graduate School Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02083—Interferometers characterised by particular signal processing and presentation
    • G01B9/02085—Combining two or more images of different regions
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration
    • G01B9/02075—Reduction or prevention of errors; Testing; Calibration of particular errors

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Abstract

The invention provides a kind of phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse, comprise the following steps：Three width Random figures are carried out subtraction, eliminate the main flow component of background light intensity by S1, three width Random figures of collection；S2, Schimidt orthogonalization is carried out to differential interferometry figure（GS）Processing, eliminate phase shift deviation；Error existing for S3, analysis differential interferometry figure, and derive General Elliptic formula；S4, by least square ellipse be fitted rapid solving go out elliptic parameter；S5, phase information solved according to elliptic parameter.The beneficial effects of the invention are as follows：The influence that bias light strong disturbance is brought caused by external environmental interference is take into account, precision is improved by least square ellipse fitting, it is applied widely.

Description

The phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse
Technical field
The present invention relates to phase extraction method, more particularly to one kind to be fitted based on Schimidt orthogonalization and least square ellipse Phase extraction method.
Background technology
With the fast development of science and technology, the raising of component integrated level, industry is also got over to piece test required precision Come higher.In order to improve measurement accuracy, people are mainly studied in terms of two：First, improve measuring method；Second, research New shape recovery key algorithm.Micro- measuring surface form technology can be divided into by the difference of the mode of action between tested surface to be contacted Formula e measurement technology and non-contact measuring technology.Although contact type measurement is with higher measurement accuracy, because it can be to inspection Surveying sample surfaces causes damage gradually to be eliminated by industrial quarters.Non-planar contact surfaces topography measurement method based on various principles is not It is disconnected to occur, it is enhanced in measurement accuracy and measuring speed.Optical measuring method in noncontact measuring method is most A kind of one of measuring method favored.Phase-shifting interference measuring technology is one of most popular noncontact measuring method.
Phase-shifting interference measuring technology is due to having the advantages that high accuracy, non-cpntact measurement are widely used in high-accuracy optics The detection of surface measurement field, such as heavy caliber spherical mirror, optical element surface measurement.Object phase information extraction is phase shift interference A most vital step in measurement.The amount of phase shift that each width interference pattern is required in traditional phase extraction algorithms is one Constant.But during phase shift, due to mechanical oscillation and phase shifter it is non-linear the problems such as, often bring inevitably Phase-shifting Errors and bias light strong disturbance, this will cause phase extraction precision drastically to decline.
In recent decades, in order to solve the problems, such as random phase shift, researchers propose a large amount of phase extraction algorithms.Substantially Two classes can be classified as：Iterative algorithm and noniterative algorithm.The Typical Representative of iterative algorithm is advanced iterative algorithm (AIA). AIA needs successive ignition to realize high accuracy.Therefore it is seldom in the real-time optical measuring system of high-resolution interference pattern. In order to shorten the calculating time of phase extraction algorithms, scholars propose many noniterative algorithms, including：Maximum minimum is calculated Method (EVI), Schimidt orthogonalization algorithm (GS), Principal Component Analysis Algorithm (PCA), Fourier Transform Algorithm (Keris), European square Battle array norm algorithm (EMN), Lee's Sa such as ellipse fitting algorithm (LSEF) and other improved algorithms.PCA algorithms require each width The phase shift value of interference pattern is evenly distributed between (0,2 π).Keris algorithms are more sensitive to noise.The requirement of LSEF algorithms is first built Two quadrature components.EMN algorithms first solve random amount of phase shift, then solve phase information.Figuring mostly in these algorithms Method can only effectively extract phase in the case where interference fringe quantity is more than 1.
GS algorithms are a kind of quickly non-iterative phase extraction algorithms, but in traditional GS algorithms, done a large amount of approximations, So as to reduce phase extraction precision.
The content of the invention
It is ellipse based on Schimidt orthogonalization and least square the invention provides one kind in order to solve the problems of the prior art The phase extraction method of circle fitting.
The invention provides a kind of phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse, including Following steps：
Three width Random figures are carried out subtraction, eliminate the main flow of background light intensity by S1, three width Random figures of collection Component；
S2, Schimidt orthogonalization processing is carried out to differential interferometry figure, eliminate phase shift deviation；
Error existing for S3, analysis differential interferometry figure, and derive General Elliptic formula；
S4, by least square ellipse be fitted rapid solving go out elliptic parameter；
S5, phase information solved according to elliptic parameter.
As a further improvement on the present invention, step S1 includes：
In phase-shifting interference measuring, the intensity distribution of phase-shift interference can be expressed as：
Wherein, a (x, y), b (x, y), φ (x, y) represent background light intensity, modulation amplitude and object phase, δ respectivelymRepresent The phase shift value of m width interference patterns；
Second width interference pattern, the 3rd width interference pattern are subtracted the first width interference pattern and obtained：
I10=b10sin(φ(x,y))
I20=b20sin(φ(x,y)+δ)
Wherein,
As a further improvement on the present invention, step S2 includes：
To differential interferometry figure I10With differential interferometry figure I20Schimidt orthogonalization processing is carried out,
Wherein, C1For I10Carry out the coefficient after GS orthogonalizations, C2For I20Carry out the coefficient after GS orthogonalizations, k2For traditional GS The item that algorithm neglects, to differential interferometry figure I10With differential interferometry figure I20After carrying out Schimidt orthogonalization, Phase-shifting Errors are eliminated Influence.
As a further improvement on the present invention, step S3 includes：
General Elliptic formula is derived,
The differential interferometry figure after GS orthogonalizations is carried out to be modified to：
Wherein n1For the background perturbation between the second width interference pattern and the first width interference pattern, n2For k2Coefficient is done with the 3rd width The background perturbation sum between figure and the first width interference pattern is related to, is oval general type by elliptic parameter form abbreviation
It is equivalent to：
Wherein, elliptic parameter is：
Least square ellipse fitting is carried out to above formula and solves elliptic parameter.
As a further improvement on the present invention, step S4 includes：
Least square ellipse fitting solves elliptic parameter,
α=[a1,α2,α3,α4,α5]
The cost function of least square fitting is：
Least square ellipse fitting is exactly to solve α values when J obtains minimum value, that is, solves the intrinsic of M smallest eigens Vector：
M α=λ α
Wherein,
As a further improvement on the present invention, step S5 includes：
After solving elliptic parameter, object phase information is solved by elliptic parameter, solution formula is as follows：
The beneficial effects of the invention are as follows：Pass through such scheme, it is contemplated that caused by external environmental interference bias light The influence that strong disturbance is brought, precision is improved by least square ellipse fitting, it is applied widely.
Brief description of the drawings
Fig. 1 is a kind of flow for the phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse of the present invention Figure.
Fig. 2 is a kind of calculating for the phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse of the present invention Machine simulation interference pattern receives the phase extraction result figure in the case of background perturbation influences.
Fig. 3 is a kind of calculating for the phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse of the present invention Phase extraction result figure in the case of machine simulation fringe number is less.
Embodiment
The invention will be further described for explanation and embodiment below in conjunction with the accompanying drawings.
As shown in figure 1, a kind of phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse, this method Phase information can be extracted by gathering the random phase-shift interference of three width.This method includes following steps：To three width with Machine interference pattern carries out subtraction, so as to eliminate the main flow component of background light intensity；Schmidt is being carried out just to differential interferometry figure Friendshipization processing, eliminates phase shift deviation；General Elliptic formula is derived and there is error in analysis；It is quick by least square ellipse fitting Solve elliptic parameter；Phase information is solved according to elliptic parameter.
This method specifically includes：
Step 1：In phase-shifting interference measuring, the intensity distribution of phase-shift interference can be expressed as：
A (x, y), b (x, y), φ (x, y) represent background light intensity, modulation amplitude and object phase respectively.δmRepresent m width The phase shift value of interference pattern.
Second, third width interference pattern is subtracted into the first width interference pattern to obtain：
I10=b10sin(φ(x,y))
I20=b20sin(φ(x,y)+δ)
Wherein
Step 2：To differential interferometry figure I10And I20Carry out Schimidt orthogonalization processing.
Wherein C1For I10Carry out the coefficient after GS orthogonalizations, C2For I20Carry out the coefficient after GS orthogonalizations, k2For traditional GS The item that algorithm neglects.To differential interferometry figure I10And I20After carrying out Schimidt orthogonalization, we can eliminate the shadow of Phase-shifting Errors Ring.
Step 3：Derive General Elliptic formula.
It may be influenceed in view of background light intensity by external environment and produce disturbance, and fringe-pattern analysis process produces Error, the differential interferometry figure entered after GS orthogonalizations can be modified to：
Wherein n1For the background perturbation between the second width interference pattern and the first width interference pattern, n2For k2Coefficient is done with the 3rd width Relate to the background perturbation sum between figure and the first width interference pattern.It is oval general type by elliptic parameter form abbreviation
It can be equivalent to：
Wherein, elliptic parameter is：
Least square ellipse fitting is carried out to above formula can solve elliptic parameter.
Step 4：Least square ellipse fitting solves elliptic parameter.
α=[α1,a2,a3,a4,a5]
The cost function of least square fitting is：
Least square ellipse fitting is exactly to solve a values when J obtains minimum value, that is, solves the intrinsic of M smallest eigens Vector：
Ma=λ a
Wherein,
After solving elliptic parameter, object phase information can be solved by elliptic parameter, solution formula is as follows：
In order to verify the validity of this method and accuracy, we carry out simulating, verifying to this method in varied situations. The numbered analog simulation is carried out in the MATLAB in Intel I3 3.4GHz processors.
Case 1：Assuming that the unstability of external environment, background light intensity and modulation light intensity can have disturbance, amount of phase shift also can Error be present.The parameter of the random phase shift interference of three width is arranged to by we：
Background light intensity：a0(x, y)=0.2exp (- 1.8 (x2+y2)),a1(x, y)=0.25exp (- 1.8 (x2+y2)),
a2(x, y)=0.3exp (- 1.8 (x2+y2)).
Modulate light intensity:b0(x, y)=0.2exp (- 0.2 (x2+y2)),b1(x, y)=0.25exp (- 0.2 (x2+y2)),
b2(x, y)=0.3exp (- 0.2 (x2+y2)).
Object phase:Phase shift value:δ0=0.3491rad, δ1=1.0472rad, δ2= 2.8560rad.
In addition, 5% white Gaussian noise (0.05 times of rand function in corresponding Matlab) is added also in interference pattern.Pass through Parameter above generates the Random figure that three width sizes are 512x512 pixels.Referring to Fig. 2, (a) is the phase diagram of simulation, (b)-(d) is three width Random figures, and (e) is least square ellipse matched curve figure, and (f) is the method provided by the invention Extract phase, the vicinal information that (g) calculates by Phase- un- wrapping computing again, (h) continuous phase go out in x=256 two Dimension figure.
Case 2：In high-accuracy phase-shifting interference measuring, interference fringe is often less than 1.But in existing many phases Require that number of interference fringes is more than 1 and could effectively extract phase in extraction algorithm.In order to verify set forth herein algorithm in the feelings The accuracy of condition, we carry out analog simulation to situation of the number of interference fringes less than 1.Background light intensity is am(x, y)=0.2exp (-1.8(x2+y2)), modulation light intensity is bm(x, y)=0.2exp (- 0.2 (x2+y2)), object phase is：Amount of phase shift is：δ0=0.3491rad, δ1=0.7854rad, δ2=1.5708rad.
In addition, 0.5% white Gaussian noise (0.005 times of rand in corresponding Matlab) is added also in interference pattern.Pass through Parameter above generates the Random figure that three width sizes are 512x512 pixels.Referring to Fig. 3, (a) is the phase diagram of simulation, (b)-(d) is three width Random figures, and (e) is least square ellipse matched curve figure, and (f) is the method provided by the invention Phase, the continuous phase information that (g) calculates by Phase- un- wrapping computing again are extracted, (h) continuous phase goes out in x=256 X-Y scheme.
Case 1 and case 2 illustrate that this method can effectively extract the phase information of interference pattern at different conditions, With stronger robustness.
A kind of phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse provided by the invention is had Advantages below：
1) the shortcomings that being limited instant invention overcomes the number of interference fringes in traditional Schimidt orthogonalization phase extraction algorithms, In the case that fringe number is less still can extracted with high accuracy go out phase information.
2) present invention take into account the influence that bias light strong disturbance is brought caused by external environmental interference, pass through minimum Two, which multiply ellipse fitting, improves precision, applied widely.
3) present invention has stronger robustness at different conditions.
A kind of phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse provided by the invention, is overcome Traditional Schimidt orthogonalization phase extraction algorithms require the shortcomings that fringe number is limited in interference pattern, and overcome background light intensity Disturbance, non-linear Phase-shifting Errors etc. influence.This method need not calculate the realization of phase shift value can and accurately extract phase.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to is assert The specific implementation of the present invention is confined to these explanations.For general technical staff of the technical field of the invention, On the premise of not departing from present inventive concept, some simple deduction or replace can also be made, should all be considered as belonging to the present invention's Protection domain.

Claims (6)

  1. A kind of 1. phase extraction method being fitted based on Schimidt orthogonalization and least square ellipse, it is characterised in that including with Lower step：
    Three width Random figures are carried out subtraction by S1, three width Random figures of collection, eliminate the main flow point of background light intensity Amount；
    S2, Schimidt orthogonalization processing is carried out to differential interferometry figure, eliminate phase shift deviation；
    Error existing for S3, analysis differential interferometry figure, and derive General Elliptic formula；
    S4, by least square ellipse be fitted rapid solving go out elliptic parameter；
    S5, phase information solved according to elliptic parameter.
  2. 2. the phase extraction method according to claim 1 being fitted based on Schimidt orthogonalization and least square ellipse, its It is characterised by, step S1 includes：
    In phase-shifting interference measuring, the intensity distribution of phase-shift interference can be expressed as：
    Wherein, a (x, y), b (x, y), φ (x, y) represent background light intensity, modulation amplitude and object phase, δ respectivelymRepresent m width The phase shift value of interference pattern；
    Second width interference pattern, the 3rd width interference pattern are subtracted the first width interference pattern and obtained：
    I10=b10sin(φ(x,y))
    I20=b20sin(φ(x,y)+δ)
    Wherein,
  3. 3. the phase extraction method according to claim 1 being fitted based on Schimidt orthogonalization and least square ellipse, its It is characterised by, step S2 includes：
    To differential interferometry figure I10With differential interferometry figure I20Schimidt orthogonalization processing is carried out,
    <mrow> <msubsup> <mi>I</mi> <mn>10</mn> <mi>%</mi> </msubsup> <mo>=</mo> <msub> <mi>b</mi> <mn>10</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>b</mi> <mn>10</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <msub> <mi>C</mi> <mn>1</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>I</mi> <mo>^</mo> </mover> <mn>20</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>20</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <msub> <mi>b</mi> <mn>20</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>b</mi> <mn>20</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>b</mi> <mn>20</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>I</mi> <mn>20</mn> <mi>%</mi> </msubsup> <mo>=</mo> <msub> <mover> <mi>I</mi> <mo>^</mo> </mover> <mn>20</mn> </msub> <mo>/</mo> <mo>|</mo> <mo>|</mo> <msub> <mover> <mi>I</mi> <mo>^</mo> </mover> <mn>20</mn> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Wherein, C1For I10Carry out the coefficient after GS orthogonalizations, C2For I20Carry out the coefficient after GS orthogonalizations, k2For traditional GS algorithms The item neglected, to differential interferometry figure I10With differential interferometry figure I20After carrying out Schimidt orthogonalization, the shadow of Phase-shifting Errors is eliminated Ring.
  4. 4. the phase extraction method according to claim 1 being fitted based on Schimidt orthogonalization and least square ellipse, its It is characterised by, step S3 includes：
    General Elliptic formula is derived,
    The differential interferometry figure after GS orthogonalizations is carried out to be modified to：
    Wherein n1For the background perturbation between the second width interference pattern and the first width interference pattern, n2For k2Coefficient and the 3rd width interference pattern And the first background perturbation sum between width interference pattern, it is oval general type by elliptic parameter form abbreviation
    <mrow> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>)</mo> </mover> <mn>10</mn> </msub> <mo>-</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <msup> <msub> <mi>C</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>)</mo> </mover> <mn>20</mn> </msub> <mo>-</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <msup> <msub> <mi>C</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> </mrow>
    It is equivalent to：
    Wherein, elliptic parameter is：
    <mrow> <msub> <mi>C</mi> <mn>1</mn> </msub> <mo>=</mo> <msqrt> <mfrac> <mn>1</mn> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> </mfrac> </msqrt> <mo>,</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> <mo>=</mo> <msqrt> <mfrac> <mn>1</mn> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> </mfrac> </msqrt> <mo>,</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>&amp;alpha;</mi> <mn>3</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> </mfrac> <mo>,</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>&amp;alpha;</mi> <mn>4</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> </mfrac> </mrow>
    Least square ellipse fitting is carried out to above formula and solves elliptic parameter.
  5. 5. the phase extraction method according to claim 1 being fitted based on Schimidt orthogonalization and least square ellipse, its It is characterised by, step S4 includes：
    Least square ellipse fitting solves elliptic parameter,
    α=[α1,α2,α3,α4,a5]
    The cost function of least square fitting is：
    <mrow> <mi>J</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mi>&amp;alpha;</mi> <mi>T</mi> </msup> <msub> <mi>&amp;xi;</mi> <mi>n</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow>
    Least square ellipse fitting is exactly to solve a values when J obtains minimum value, that is, solves the eigenvector of M smallest eigens：
    Ma=λ a
    Wherein,
    <mrow> <mi>M</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <msub> <mi>&amp;xi;</mi> <mi>n</mi> </msub> <mi>T</mi> </msup> <msub> <mi>&amp;xi;</mi> <mi>n</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>.</mo> </mrow>
  6. 6. the phase extraction method according to claim 1 being fitted based on Schimidt orthogonalization and least square ellipse, its It is characterised by, step S5 includes：
    After solving elliptic parameter, object phase information is solved by elliptic parameter, solution formula is as follows：
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