CN104614083B - A kind of method of recovering phase shifting interference PHASE DISTRIBUTION and obtaining phase-shift phase between two width figure - Google Patents

Abstract

The invention discloses a kind of method of recovering phase shifting interference PHASE DISTRIBUTION and obtaining phase-shift phase between two width figure, first each width interference pattern is write as to the form of a matrix, each interference pattern is a column vector matrix; Obtain acquisition background component by a low pass filter again; Then by the column vector of two phase shifting interferences composition subtracting background component respectively, obtain a pair of vector that has angle, form a sub spaces and complete the vectorization of interference pattern by these two vectors; Then utilize Schimidt orthogonalization method to draw an orthogonal basis of subspace by a base on subspace, and further obtain corresponding orthonormal basis, utilize the orthonormal basis obtaining to obtain the angle between two original signals. Adopt the present invention not only can, in the hope of the PHASE DISTRIBUTION between two width phase shifting interferences, can also further try to achieve the variation of phase-shift phase by a series of phase shifting interferences.

Description

A kind of method of recovering phase shifting interference PHASE DISTRIBUTION and obtaining phase-shift phase between two width figure

Technical field

The present invention relates to optical imaging field, a kind of in particular method of obtaining the phase-shift phase between two width figure based on Schmidt's orthogonalization, and the method for recovery phase shifting interference PHASE DISTRIBUTION.

Background technology

In recent years, recovering the distribution of phase place to be measured from the interference pattern of unknown phase-shift phase, is the focus of phase place restoration methods research, mainly comprises Fourier transformation method and the alternative manner based on the principle of least square, anticosine method, principal component analysis method etc.

Wherein, recovering phase place to be measured based on Fourier transformation method, is by single width interference pattern is carried out to spatial domain Fourier transformation, isolates real part and the imaginary part of-1 grade of frequency spectrum of interference pattern in frequency domain, utilizes arctan function to calculate PHASE DISTRIBUTION to be measured. This method can recover phase information to be measured from single width interference pattern, but requires interference pattern to have certain additional spatial domain carrier frequency to meet 0 grade and-1 grade of requirement that frequency spectrum is separated. Utilize Fourier transformation method to determine the phase-shift phase between interference pattern, by interference pattern is carried out to spatial domain Fourier transformation, calculate the overall phase-shift phase of interference pattern at carrier frequency frequency place, then try to achieve phase place to be measured by conventional phase shifting method, but phase method for position based on Fourier transformation all requires to introduce in interference pattern certain space carrier frequency.

In the phase-shift phase or phase extraction method based on the principle of least square, what first propose is the least square solution of the K width interference pattern in known phase shift amount situation; Least square alternative manner in unknown phase-shift phase situation and the improvement alternative manner based on the principle of least square were developed again afterwards, set first arbitrarily the initial value of one group of phase-shift phase as interative computation phase-shift phase, by phase-shift phase and phase place to be measured are replaced to interative computation, can calculate phase place to be measured and phase-shift phase simultaneously. In addition, develop the least square alternative manner based on diffraction principle, meet in phase place to be measured under the prerequisite of diffraction law distribution, minimum use three width interference patterns just can be determined the phase-shift phase of interference pattern, but in actual measurement, the PHASE DISTRIBUTION of some object does not meet diffraction law, has limited in a way the application of the method. For improving the computational speed of interative computation, develop the alternative manner of another kind of definite phase-shift phase, utilize the statistical property of object light ripple to calculate the iteration initial value close to interference pattern actual phase shift amount, and then carry out interative computation to improve computational accuracy, thereby accelerate the speed that phase-shift phase extracts.

The light intensity sequence changing by time domain is determined background light intensity and the modulate intensity of interference pattern, obtain the phase place of every width interference pattern with inverse cosine function, then utilize the phase place of multi-frame interferometry figure to average, can not need the in the situation that of accurately controlling phase-shift phase, to measure phase place to be measured, this method phase extraction result is accurate, but operand is large, computing time is long.

Phase place restoration methods based on principal component analysis can be recovered rapidly phase place from the interference pattern of a series of unknown phase-shift phases. In general, principal component analysis method mainly comprises three steps: 1. utilize the data of interference pattern, obtain a covariance matrix; 2. utilize singular value decomposition method by covariance matrix diagonalization; 3. obtain first principal component and the Second principal component, of interference pattern by Hotelling transform, i.e. two of interference pattern quadrature components. Principal Component Analysis Method is recovered phase place, owing to need to removing by the method for time domain average the background of interference pattern, therefore, requires the phase-shift phase of interference pattern to be evenly distributed within the scope of 0 to 2 π, and service condition is harsher.

From less interference pattern, quick high accuracy recovers the focus that phase place is research, as recovered phase place etc. from single width figure, two width figure, three width figure. From single width interference pattern, extract exactly phase information, have a wide range of applications at aspects such as surface profile, thermograde and distortion measurements. In static phase is measured, phase-shifting technique is to recover accurately phase place the best way, but for dynamic process and fast transient process, phase-shifting technique is just inapplicable, and for these situations, the research that recovers phase unwrapping from single width figure is more and more. The method of Fourier transformation can be recovered phase place from single width carrier coded fringes, but this method is to noise-sensitive, and in the time that the phase place in interference pattern changes greatly, the phase error recovering is very large. Be from single width striped, to recover the important method of phase place based on regularization Phase Tracking, this method utilizes system linearity equation to analyze the striped of open loop or sealing, owing to adopting sef-adapting filter, can solve the problem existing in fourier transform technique. But this method need to utilize interative computation to solve system of linear equations, thereby can bring convergence and problem consuming time.

In addition, some are only constantly seen in report from the method for two width phase shifting interferences recovery phase places, these methods are conducive to reduce the such environmental effects such as vibration, variations in flow, the in the situation that of phase-shift phase the unknown, rebuild phase place and do not occur symbol fuzzy problem from minimum interference pattern. From two width figure, recover phase place and mainly contain three kinds of methods, first method is to utilize Fourier transformation to recover phase place; Second method is the product that first obtains modulation amplitude and phase place sine by certain conversion, then utilizes arctan function to recover phase place; The third method first obtain the phase-shift phase between two width figure, then recover PHASE DISTRIBUTION. The two step phase place restoration methods based on Fourier transformation are a kind of basic skills that solve phase place from two width phase shifting interferences, and its major defect is to noise-sensitive. It is relatively good that optical flow approach based on regularization suppresses noise effects, and the phase-shift phase between two width interference patterns is not had to particular/special requirement, but will utilize the method for iteration to solve the parameter of calculating bar graph direction, and therefore, the major defect of this method is that amount of calculation is large. Utilize two step phase place restoration methods of Schimidt orthogonalization can calculate rapidly and accurately PHASE DISTRIBUTION, but require at least to exist more than one striped to change in interference pattern.

Therefore, prior art has yet to be improved and developed.

Summary of the invention

The object of the present invention is to provide a kind of method of recovering phase shifting interference PHASE DISTRIBUTION and obtaining phase-shift phase between two width figure, be intended to solve the existing method of recovering PHASE DISTRIBUTION to be measured from the interference pattern of unknown phase-shift phase large or require at least to exist in interference pattern the problems such as more than one striped variation to noise-sensitive, amount of calculation.

Technical scheme of the present invention is as follows:

A method of obtaining phase-shift phase between two width figure, it comprises the following steps:

S1: by two width phase shifting interference vectorizations, be specially: each width interference pattern is write as to the form of a matrix, each interference pattern is a column vector matrix; Obtain acquisition background component by a low pass filter again; Then by the column vector of two phase shifting interferences composition subtracting background component respectively, obtain a pair of vector that has angle, form a sub spaces and complete the vectorization of interference pattern by these two vectors;

S2: utilize Schimidt orthogonalization by two vectorial orthogonalizations, obtain two angles between original signal, be the phase-shift phase between two width phase shifting interferences, be specially: utilize Schimidt orthogonalization method to draw an orthogonal basis of subspace by a base on subspace, and further obtain corresponding orthonormal basis, utilize the orthonormal basis obtaining to obtain the angle between two original signals.

The described method of obtaining phase-shift phase between two width figure, its by two width phase shifting interference vectorizations further concrete grammar be: the light intensity of first measuring k pixel in n width phase shifting interference; By high-pass filter elimination DC component wherein, retain modulation amplitude again, draw i.e. two orthogonal vectors of two orthogonal signalling of interference pattern.

The described method of obtaining phase-shift phase between two width figure, in its n width phase shifting interference, the light intensity of k pixel is:

In formula, a_kAnd b_kRepresent respectively flip-flop and modulation amplitude in interference pattern,Tested phase place, θ_nBe the phase-shift phase of n width phase shifting interference, K is the pixel quantity in interference pattern, to the interference pattern of a width size Nx × Ny, K=Nx × Ny; N is phase shift step number, for two step phase place restoration methods, N=2.

The described method of obtaining phase-shift phase between two width figure, its elimination DC component wherein, draws two orthogonal signalling I of interference pattern_c,k,I_s,kMethod be:

It is equivalent to: ${\tilde{I}}_{n,k}={\mathrm{\α}}_n{I}_{c,k}+{\mathrm{\β}}_n{I}_{s,k}$

In formula,

The described method of obtaining phase-shift phase between two width figure, it utilizes Schimidt orthogonalization by two vectorial orthogonalizations, and the method that obtains two angles between original signal is:

$\mathrm{\θ}=\arctan \left(\frac{\mathrm{norm}1}{\mathrm{norm}2}\right),$

Wherein, θ is two angles between vector, and norm1 and norm2 are respectively two vectorial moulds,

Recover a method for phase shifting interference PHASE DISTRIBUTION, it utilizes phase-shift phase acquisition methods as above to obtain two angles between signal, then utilizes the angle between two signals that obtain to obtain PHASE DISTRIBUTION by trigonometric function formula.

The method of described recovery phase shifting interference PHASE DISTRIBUTION, the method that the angle between two signals that its utilization is obtained obtains PHASE DISTRIBUTION is:

Wherein,For PHASE DISTRIBUTION value,WithIt is the vector of two width phase shifting interferences.

Beneficial effect of the present invention: the present invention is first by two width phase shifting interference vectorizations, after through Schmidt's orthogonal transformation, calculate the phase-shift phase between two width phase shifting interferences, then calculate PHASE DISTRIBUTION by simple formula. The present invention calculates faster than existing Schmidt's transform method speed, and precision is higher.

Brief description of the drawings

Fig. 1 is method flow diagram provided by the invention.

Fig. 2 is the phase shifting interference for simulation.

Fig. 3 is that the algorithm proposing according to the present invention calculates phase-shift phase datagram.

Fig. 4 is the PHASE DISTRIBUTION figure of the method for the present invention recovery of obtaining.

Fig. 5 is the error amount of the PHASE DISTRIBUTION figure that obtains of method of the present invention and standard value contrast.

Detailed description of the invention

For making object of the present invention, technical scheme and advantage clearer, clear and definite, developing simultaneously referring to accompanying drawing, the present invention is described in more detail for embodiment.

The basic idea of Schimidt orthogonalization (GS) is to utilize projection theory to construct a new orthogonal basis on the basis of existing orthogonal basis. In linear algebra, if one group of vector in the inner product space can Zhang Chengyi sub spaces, this group vector is just called a base of this sub spaces so. Schimidt orthogonalization provides a kind of method, can draw by a base on this subspace an orthogonal basis of subspace, and can further obtain corresponding orthonormal basis. Wherein, two vectorial u of Schimidt orthogonalization₁，u₂, mainly contain three steps:

${\tilde{u}}_1=u_1/\sqrt{<u_1,u_1>}=u_1/\left|\right|u_1\left|\right|$ Formula 1

${\hat{u}}_2=u_2-<u_2,{\tilde{u}}_1>\&CenterDot;{\tilde{u}}_1$ Formula 2

${\tilde{u}}_2={\hat{u}}_2/\sqrt{<{\hat{u}}_2,{\hat{u}}_2>}={\hat{u}}_2/\left|\right|{\hat{u}}_2\left|\right|$ Formula 3

Wherein,The vector after orthonomalization,<>be inner product operator.

Technical problem to be solved by this invention is, overcomes the shortcoming of prior art, and a kind of processing method of combination time domain spatial information (si) is provided, and obtains the method for phase information from two width phase shifting interferences. Basic skills is: first by two width phase shifting interference vectorizations; After through Schmidt's orthogonal transformation, calculate the phase-shift phase between two width phase shifting interferences; Calculate PHASE DISTRIBUTION by formula again.

Specifically comprise the following steps:

Step S1: by two width phase shifting interference vectorizations, be specially: each width interference pattern is write as to the form of a matrix, each interference pattern is a column vector matrix; Obtain acquisition background component by a low pass filter again; Then by the column vector of two phase shifting interferences composition subtracting background component respectively, obtain a pair of vector that has angle, form a sub spaces and complete the vectorization of interference pattern by these two vectors;

Step S2: utilize Schimidt orthogonalization by two vectorial orthogonalizations, obtain two angles between original signal, be the phase-shift phase between two width phase shifting interferences, be specially: utilize Schimidt orthogonalization method to draw an orthogonal basis of subspace by a base on subspace, and further obtain corresponding orthonormal basis, utilize the orthonormal basis obtaining to obtain the angle between two original signals.

Step S3: utilize the phase-shift phase that simple trigonometric function formula can obtain by previous step to obtain PHASE DISTRIBUTION.

In phase shift interference is measured, in n width phase shifting interference, the light intensity of k pixel can be expressed as:

Formula 4

In formula, a_kAnd b_kRepresent respectively flip-flop and modulation amplitude in interference pattern,Tested phase place, θ_nBe the phase-shift phase of n width phase shifting interference, K is the pixel quantity in interference pattern, to the interference pattern of a width size Nx × Ny, K=Nx × Ny; N is phase shift step number, for two step phase place restoration methods, N=2.

Described flip-flop a_kCan be filtered out by a high-pass filter. The interference pattern vector of filtering flip-flopCan be expressed as:

Formula 5

The interference pattern vector of filtering DC componentCan further be expressed as:

${\tilde{I}}_{n,k}={\mathrm{\&alpha;}}_n{I}_{c,k}+{\mathrm{\&beta;}}_n{I}_{s,k}$ Formula 6

In formula,The interference pattern of wiping out background is by two orthogonal signalling I_c,k,I_s,kComposition, therefore, utilizes Schimidt orthogonalization by two vectorial orthogonalizations, obtains two angles between original signal, is exactly the phase-shift phase between two width phase shifting interferences.

For the two width interference patterns that have phase shift, its inner product algorithm is defined as:

$<{\tilde{I}}_{1,k},{\tilde{I}}_{2,k}>=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\tilde{I}}_{1,k}\&CenterDot;{\tilde{I}}_{2,k}$ Formula 7

By formula (1) and (7), can obtain:

Formula 8

Wherein,

Express for formula of reduction, think θ₁＝0,θ₂=θ, described θ is: the phase-shift phase between two width phase shifting interferences.

Can obtain according to formula (2):

Formula 9

Wherein,For in subspace, perpendicular to vectorVector.

If have at least a striped to be approximated as follows in interference pattern:

Formula 10

Therefore, formula (9) can be written as:

Formula 11

Different with GS algorithm, the bright method providing of this law will notNormalization, and ask two angles between vector, two vectorial moulds can be expressed as:

Formula 12

So the angle between two vectors is:

$\mathrm{\&theta;}=\arctan \left(\frac{\mathrm{norm}1}{\mathrm{norm}2}\right)$ Formula 13

Wherein, norm1 and norm2 are two vectorial moulds.

Finally, according to following formula 14, obtain PHASE DISTRIBUTION:

Formula 14

The algorithm that the present invention proposes is known through putting into practice, can be faster than current GS algorithm computational speed, and precision is higher.

The present invention verifies proposed method by simulation phase shift bar graph. Simulation bar graph intensity distribution determined by formula 4, interference pattern size is 500 × 500 pixels. Its background distributions is a (x, y)=120exp[-0.0 (x²+y²)], modulated amplitude is distributed as b (x, y)=100exp[-0.2 (x²+y²)], PHASE DISTRIBUTION to be measured isWherein x, y ∈ [2.5,2.5]. Phase-shift phase is made as θ=0.1:0.1:6.5, that is, phase-shift phase initial value is 0.1 radian, does not have 0.1 radian to increase progressively, till being increased to 6.5rad. The random Gaussian additive noise that to have added signal to noise ratio in interference pattern be 5%.

The phase shifting interference simulating as shown in Figure 2. The phase-shift phase being obtained by institute of the present invention extracting method as shown in Figure 3. Be that error ratio is larger by the known phase-shift phase of obtaining of formula in pi/2 left and right, this is because theory of algorithm itself causes, other algorithms also have this problem at special angle, but except this special angle, this algorithm is very accurately.

Meanwhile, shown in accompanying drawing 4 is the PHASE DISTRIBUTION recovering according to phase-shift phase, and Fig. 5 is the compare error of Practical Calculation value with theoretical value, can see, and worst error is only 0.08rad. . Can see from result, the bright method providing of this law is very accurate.

Advantage of the present invention is that orthogonal of Schmidt asks the phase-shift phase between two width figure, then obtains PHASE DISTRIBUTION by phase-shift phase. The method that the present invention proposes, not only can, in the hope of the PHASE DISTRIBUTION between two width phase shifting interferences, can also further try to achieve the variation of phase-shift phase by a series of phase shifting interferences. Try to achieve phase-shift phase and can proofread and correct phase-shifter.

Should be understood that, application of the present invention is not limited to above-mentioned giving an example, and for those of ordinary skills, can be improved according to the above description or convert, and all these improvement and conversion all should belong to the protection domain of claims of the present invention.

Claims (5)

1. a method of obtaining phase-shift phase between two width figure, is characterized in that, comprises followingStep:

S1: by two width phase shifting interference vectorizations, be specially: write each width interference pattern as oneThe form of individual matrix, each interference pattern is a column vector matrix; Again by a LPFDevice obtains acquisition background component; Then the column vector of two phase shifting interference compositions is deducted respectivelyBackground component, obtains a pair of vector that has angle, forms a sub spaces complete by these two vectorsBecome the vectorization of interference pattern;

S2: utilize Schimidt orthogonalization by two vectorial orthogonalizations, obtain between two original signalsAngle, be the phase-shift phase between two width phase shifting interferences, be specially: utilize Schmidt justFriendshipization method draws an orthogonal basis of subspace by a base on subspace, and furtherObtain corresponding orthonormal basis, utilize the orthonormal basis obtaining to obtain between two original signalsAngle;

Utilize Schimidt orthogonalization by two vectorial orthogonalizations, obtain between two original signalsThe method of angle is:

$\mathrm{\&theta;}=arctan\left(\frac{norm1}{norm2}\right),$

Wherein, θ is two angles between vector, norm1 and norm2 be respectively two toThe mould of amount,

2. the method for obtaining phase-shift phase between two width figure according to claim 1, its spyLevy and be, by two width phase shifting interference vectorizations further concrete grammar be: first measureThe light intensity of k pixel in n width phase shifting interference; Again by high-pass filter elimination whereinDC component, retain modulation amplitude, two orthogonal signalling that draw interference pattern two orthogonalVector.

3. the method for obtaining phase-shift phase between two width figure according to claim 1, its spyLevy and be, in n width phase shifting interference, the light intensity of k pixel is:

Wherein, a_kAnd b_kRepresent respectively flip-flop and modulation amplitude in interference pattern,BeTested phase place,Be the phase-shift phase of n width phase shifting interference, K is the pixel count in interference patternAmount, to the interference pattern of a width size Nx × Ny, K=Nx × Ny; N is phase shift step number, forTwo step phase place restoration methods, N=2.

4. the method for obtaining phase-shift phase between two width figure according to claim 1, its spyLevy and be, elimination DC component wherein, draws two orthogonal signalling I of interference pattern_c,k,I_s,k'sMethod is:

It is equivalent to: ${\tilde{I}}_{n,k}={\mathrm{\&alpha;}}_n{I}_{c,k}+{\mathrm{\&beta;}}_n{I}_{s,k}$

In formula, α_n＝cos[θ_n],β_n＝sin[θ_n],

5. a method of recovering phase shifting interference PHASE DISTRIBUTION, is characterized in that, utilizesPhase-shift phase acquisition methods described in claim 1-4 any one obtains two folders between signalAngle, then utilizes the angle between two signals that obtain to obtain phase place by trigonometric function formulaDistribute; The method that angle between two signals that utilization is obtained obtains PHASE DISTRIBUTION is:

Wherein,For PHASE DISTRIBUTION value,WithIt is the vector of two width phase shifting interferences.