CN104330027A - Phase extraction method in phase-shifting interferometry based on error complementary correction - Google Patents

Abstract

The invention relates to a phase extraction method in phase-shifting interferometry based on error complementary correction. The phase extraction method aims at overcoming the problems that: 1, current linear phase shifting errors commonly exist in various interference systems, thus influencing phase information extraction precision; 2, when the current linear errors exceed 5%, the phase extraction error is rapidly increased; 3, current formulas are tedious and large in operand, and includes involution and evolution, thus being easy to cause imaginary phase solution and strange phase solution with oversized error points. The phase extraction method is specifically performed according to the following steps of: 1, adopting a traditional five-frame algorithm which has the expressing form defined as a formula described in the description; 2, adopting light intensity which has the same frame sequence with the traditional five-frame algorithm, putting in the constructed new five-frame algorithm to obtain the phase information of the new five-frame algorithm, wherein the constructed five-frame algorithm form is defined as a formula described in the description; 3, establishing an error complementation five-frame algorithm. The phase extraction method in phase-shifting interferometry based on error complementary correction is applied to the technical field of three-dimensional shape optical detection of space objects.

Description

A kind of phase-shifting interference measuring phase extraction method revised based on error complementation

Technical field

The present invention relates to the phase information extracting method in phase-shifting interference measuring.

Background technology

Along with the development of micro-nano process technology, the accuracy requirement of component surface pattern is more and more higher, it is also proposed higher requirement to corresponding detection means.Phase shifting interferometry, with advantages such as its high precision, high-level efficiency, noncontacts, becomes the measuring method that Shape measure field is ideal.(1) in phase-shifting interference measuring, phase information is obtained by each frame interferogram of Phase-shifting algorithm process, and Linear phase-shift error is prevalent in all kinds of interference system, affects the precision that phase information extracts.(2) in phase-shifting interference measuring, although traditional fixed step size Phase-shifting algorithm computing is simple, but it is all comparatively responsive to Linear phase-shift error except five frame algorithms, and five frame algorithms only have good rejection ability to the linear error within 5%, when linear error is more than 5%, phase extraction error sharply increases.(3) in phase-shifting interference measuring, although any fixed step size Phase-shifting algorithm can realize linear error immunity, formula is loaded down with trivial details, and operand is large, comprises power extracting operation, easily occurs that imaginary bit is separated mutually and separate situation mutually with the Singularity of super large error point.

Summary of the invention

The object of the invention is to be prevalent in all kinds of interference system to solve (1) existing Linear phase-shift error, affecting phase information extraction accuracy; (2), when existing linear error is more than 5%, phase extraction error sharply increases; (3) and existing formula loaded down with trivial details, operand is large, comprises power extracting operation, easily occurs that imaginary bit separates the problem of separating situation with the Singularity of super large error point mutually mutually.And propose a kind of phase-shifting interference measuring phase extraction method revised based on error complementation.

Above-mentioned goal of the invention is achieved through the following technical solutions:

A kind of phase-shifting interference measuring phase extraction method revised based on error complementation, it is characterized in that: complementary by the error between traditional five frame algorithms and five frame algorithms of structure, significantly reduce the impact that Linear phase-shift error is extracted phase information, specifically carry out according to following steps:

Step one, traditional five frame algorithm expression-forms are:

Wherein, for position phase to be separated, I ₁, I ₂, I ₃, I ₄, I ₅respectively corresponding phase shift measure-π ,-pi/2,0, pi/2, π time each frame sequence light intensity, obtain the phase information that traditional five frames extract;

Step 2, adopt and the light intensity of traditional five frame algorithm same number of frames sequences, substitute into the new five frame algorithms constructed, obtain the phase information that new five frame algorithms extract, five frame algorithm patterns of structure are:

Step 3, mean operation is directly done mutually in the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms solve, carry out error complementation, obtain the position phase after error correction.

Invention effect

Adopt a kind of phase-shifting interference measuring phase extraction method revised based on error complementation of the present invention, (1) the complementary correction algorithm of error that the present invention uses reduces Linear phase-shift error to the impact of phase information extraction accuracy, and extraction accuracy improves two orders of magnitude; (2) the complementary correction algorithm of the error of the present invention's use, mean operation is directly done mutually in the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms solve, error just can complementaryly be revised, when can avoid linear error more than 5%, the problem that phase extraction error sharply increases, makes phase extraction error-reduction 15%; (3) the complementary correction algorithm of error that the present invention uses revises principle based on error complementation, utilize fixed step size Phase-shifting algorithm to the features of response of Linear phase-shift error, by structure five new frame algorithms and traditional five frame algorithms carry out error complementation, computing simple and fast, without power extracting operation, avoid occurring that imaginary bit separates the problem of separating situation with the Singularity of super large error point mutually mutually.

As shown in table 1, can find out that the error complementation five frame algorithms of proposition and the measurement result PV value of Stoilov algorithm and RMS value are all comparatively close, and other two kinds of algorithms are relatively large.But when adopting Stoilov algorithm to extract phase place, in full interference field 342065 data points, there are 6437 imaginary number phase place solutions, caused shortage of data, account for 1.9% of sum.And the complementary correction algorithm of the error proposed does not exist this problem, and do not comprise extracting operation, more succinct quick, there is the advantage of oneself uniqueness in phase information extraction.

Accompanying drawing explanation

Fig. 1 is the linear error response distribution situation of traditional five frame algorithms;

Fig. 2 is the linear error response distribution situation of the five new frame algorithms of structure;

Fig. 3 is the linear error response distribution situation of the complementary correction algorithm of error proposed;

Fig. 4 (a) is the traditional five frame algorithms calculating gained phase errors of embodiment one;

Fig. 4 (b) is embodiment one error complementary correction algorithm calculating gained phase error;

Fig. 4 (c) is embodiment one stoilov five frame algorithm calculating gained phase error;

Fig. 5 is embodiment two microsphere surface morphology phase shift diffraction interference survey sheet;

Interferogram when phase shift step-length gets-π in the five frame interferograms that Fig. 6 (a) collects for embodiment two;

In the five frame interferograms that Fig. 6 (b) collects for embodiment two phase shift step-length get-pi/2 time interferogram;

Interferogram when phase shift step-length gets 0 in the five frame interferograms that Fig. 6 (c) collects for embodiment two;

Interferogram when phase shift step-length gets pi/2 in the five frame interferograms that Fig. 6 (d) collects for embodiment two;

Interferogram when phase shift step-length gets π in the five frame interferograms that Fig. 6 (e) collects for embodiment two;

Fig. 7 (a) is three frame algorithm solution phase result figure traditional in embodiment two, and rad is Rad, and pixel is pixel unit;

Fig. 7 (b) is five frame algorithm solution phase result figure traditional in embodiment two;

Fig. 7 (c) is Stoilov algorithm solution phase result figure in embodiment two;

Fig. 7 (d) is embodiment two medial error complementary correction algorithm solution phase result figure;

Fig. 8 (a) adopts the complementary correction algorithm of error to extract and absolutely dry after unpacking relates to field phase data for embodiment two;

Fig. 8 (b) adopts the complementary correction algorithm of error to extract and topographic data after Wavefront Fitting for embodiment two.

Embodiment

Embodiment one: a kind of phase-shifting interference measuring phase extraction method revised based on error complementation, is characterized in that: a kind of phase-shifting interference measuring phase extraction method revised based on error complementation is specifically carried out according to following steps:

Step one, traditional five frame algorithm expression-forms are:

Wherein, for position phase to be separated, I ₁, I ₂, I ₃, I ₄, I ₅respectively corresponding phase shift measure-π ,-pi/2,0, pi/2, π time each frame sequence light intensity, obtain the phase information that traditional five frames extract;

Step 2, adopt and the light intensity of traditional five frame algorithm same number of frames sequences, substitute into the new five frame algorithms constructed, obtain the phase information that new five frame algorithms extract, five frame algorithm patterns of structure are;

Step 3, mean operation is directly done mutually in the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms solve, carry out error complementation, obtain the position phase after error correction.

The linear error response distribution situation of formula (1) (2) respectively as shown in Figure 1, 2.

Embodiment two: present embodiment and embodiment one unlike: adopt the light intensity with traditional five frame algorithm same number of frames sequences in described step 2, namely phase shift measure-π ,-pi/2,0, pi/2, π (phase shift step-length gets pi/2) time, the five frame algorithm patterns constructed under any step-length become formula (2) described form, and the five frame algorithm patterns constructed under any step-length are:

$\mathrm{\φ}=\arctan [\frac{1}{\sin \left(\mathrm{\β}\right)}\·\frac{2(I_2-I_4)-(I_1-I_5)}{4I_3-2(I_2+I_4)}]---\left(3\right)$

In formula: for position phase to be separated, I ₁, I ₂, I ₃, I ₄, I ₅the light intensity of each frame sequence when corresponding phase shift step-length gets β respectively.Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment one or two unlike: formula treats Xie Weixiang described in (3) concrete computation process be:

Five frame light intensity system of equations in interference field under any unique step are as shown in formula (4):

$\left\{\begin{array}{c}{I}_1=A+B\·\cos (\mathrm{\φ}-2\·\mathrm{\β})\\ I_2=A+B\·\cos (\mathrm{\φ}-\mathrm{\β})\\ I_3=A+B\·\cos \left(\mathrm{\φ}\right)\\ I_4=A+B\·\cos (\mathrm{\φ}+\mathrm{\β})\\ I_5=A+B\·\cos (\mathrm{\φ}+2\·\mathrm{\β})\end{array}\right.---\left(4\right)$

In formula: for position phase to be separated, I is the light intensity of each frame sequence in interference field, I ₁, I ₂, I ₃, I ₄, I ₅respectively corresponding phase shift step measure-2 β ,-β, 0, β, 2 β time each frame sequence light intensity; A is light intensity DC component, and B is light intensity AC compounent, and β is phase shift step-length;

By I ₂with I ₄, I ₁with I ₅do difference, through trigonometric function and the computing of difference eliminate indigestion, after arrangement, obtain formula (5), (6) respectively:

I ₂-I ₄＝2B·sin(φ)·sin(β) (5)

I ₁-I ₅＝2B·sin(φ)·sin(2β) (6)

Formula (6) is launched by double angle formula, obtains formula (7):

I ₁-I ₅＝4B·sin(φ)·sin(β)·cos(β) (7)

Formula (5) is multiplied by two times, does difference with formula (7), and arrangement obtains formula (6):

2·(I ₂-I ₄)-(I ₁-I ₅)＝4B·sin(φ)·sin(β)·［1-cos(β)］ (8)

By I ₂with I ₄do and, and carry out trigonometric function and difference eliminate indigestion obtain formula (9):

I ₂+I ₄＝2A+2B·cos(φ)·cos(β) (9)

By I ₃be multiplied by 4 times, do difference with the formula (9) of two times, DC component A is eliminated, and abbreviation arranges and obtains formula (10):

4I ₃-2·(I ₂+I ₄)＝4B·cos(φ)·［1-cos(β)］ (10)

Formula (8) and formula (10) be divided by, 1-cos (β) item and 4B are divided out, and are moved on the left of equal sign by sin (β) and obtain formula (11):

$\frac{1}{\sin \left(\mathrm{\β}\right)}\·\frac{2(I_2-I_4)-(I_1-I_5)}{4I_3-2(I_2+I_4)}=\tan \left(\mathrm{\φ}\right)---\left(11\right)$

By the equal sign both sides negate arctangent operation of formula (11), the five frame algorithms constructed under obtaining any unique step, the form as described in formula (3).

Other step and parameter identical with embodiment one or two.

Embodiment four: present embodiment and embodiment one, two or three unlike: the described revised position of step 3 medial error is specially mutually:

The linear error response distribution situation of formula (12) respectively as shown in Figure 3.Carry out contrast from Fig. 1 and Fig. 2, when equivalent linear error, for same initial phase, the position phase resolution error of two kinds of algorithms is in the same order of magnitude and amplitude is very close, but symbol is contrary; Therefore, mean operation is directly done mutually in the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms solve, error just can complementaryly be revised.

As seen from Figure 3, although fail to realize linear error immunity completely, position phase resolution error reduces two orders of magnitude, is enough to the demand meeting high precision interferometry; Owing to there is not extracting operation, there will not be imaginary bit to separate the abnormal conditions with super large error point mutually in solution procedure, computing is more succinct fast.

Other step and parameter and embodiment one, two or three identical.

Embodiment 1: treat the numerical simulation in Xie Weixiang (-pi/2, pi/2) scope.

In interval (-pi/2, pi/2), get 200 sampled points, uniform sampling, as treating Xie Weixiang, application of formula (13) calculates five frame light intensity values corresponding to each sampled point.

Wherein, A is interference field DC component, value 100; B is interference field AC compounent, value 80; φ separates position phase sampler value for waiting; K is linear error coefficient, value 15%; β is theoretical step size, value pi/2; α is the random Phase-shifting Errors introduced, and value is the random value in interval (-0.0038 π, 0.0038 π).

Five corresponding for each sampled point calculated frame light intensity values are substituted into traditional five frame methods respectively the complementary correction algorithm of the error that the present invention proposes and solve a phase in any unique step algorithm.For the ease of calculating, any unique step algorithms selection five frame stoilov algorithm.Calculate gained phase error as shown in Figure 4.Wherein, Fig. 4 (a) is traditional five frame algorithm result of calculations; The complementary five frame algorithm result of calculations of error that Fig. 4 (b) proposes for the present invention; Fig. 4 (c) is stoilov five frame algorithm result of calculation.

Tradition five frame algorithm phase extraction error PV values are 9 × 10 ^-3π, the error that the present invention proposes complementary correction algorithm phase extraction error PV value is 1.1 × 10 ^-4π, stoilov five the phase extraction error PV value of frame algorithm be 1.16 × 10 ^-4π.

Visible, the error that the present invention proposes complementary five frame algorithms are compared with traditional five frame algorithms, and nearly two orders of magnitude of error-reduction, phase extraction error PV value is suitable with stoilov five frame algorithm.As can be seen from Fig. 4 (b), under the impact of small stochastic error, namely algorithm shows linear error response characteristic, also shows the feature of random fluctuation simultaneously.

Embodiment 2: microsphere surface morphology phase shift diffraction interference experiments of measuring

Microsphere surface morphology phase shift diffraction interference is measured as shown in Figure 5.The linearly polarized light of laser emitting is assembled through lens after spatial filter filtering, collimator and extender, at the aperture place of pin hole catoptron, diffraction occurs, and produces ideal ball ground roll.

Part spherical wave is as measurement light, and assembled to microsphere surface by object lens, beam center is concentric with microballoon.Another part is as reference light, and go directly CCD.Measure light to reflect through measured surface, carry topographical information and be similar to former road and return, reflected by the metallic diaphragm on pin hole mirror surface and turn to, formed with reference light and interfere.Phase shifter micro-displacement platform drives microballoon to move along measuring light optical axis direction, produces phase shift, and is recorded the interferogram of several stripe order recognition by CCD.Obtain initial phase distribution finally by Phase-shifting algorithm process interferogram, and phase information is scaled difference in height information, complete measurement.

In order to verify feasibility and the validity of the error complementary correction algorithm phase extraction method of proposition, the 3mm diameter aviation ball selecting surface topography good carries out actual measurement, theoretical phase shift step-length pi/2, and adds the Linear phase-shift error of about 25%.Meanwhile, for the ease of Wavefront Fitting, interference fringe is adjusted to close to vertical bar line, reduces the out of focus item of alignment error introducing and the impact of cue ball difference item.The five frame interferograms collected are as shown in Fig. 6 (a), Fig. 6 (b), Fig. 6 (c), Fig. 6 (d), Fig. 6 (e).

Complementary correction algorithm Fig. 7 (d) of the error adopting traditional three frame algorithm patterns 7 (a), traditional five frame algorithm patterns 7 (b), Stoilov five frame algorithm pattern 7 (c) and the present invention to propose respectively carries out phase extraction, and separates parcel.Choose middle row analysis, separate phase result as shown in Figure 7.In theory, do not comprise the straight interference fringe of defocusing amount alignment error, the PHASE DISTRIBUTION of separating after parcel is an approximate clinoplane, chooses wherein data line and must obtain an approximate straight line.But three frame algorithms are comparatively responsive to linear error, Non-uniform responsivity in phase region, makes the phase place after separating parcel form the curve of a fluctuation.The linear error rejection ability of tradition five frame algorithms significantly better than traditional three frame algorithms, but still can find out regular fluctuation, and the fluctuating range of marginal position is larger than centre position, this also illustrates the unevenness that out of focus introduces Phase-shifting Errors.Because Stoilov five frame algorithm has the immunity of Linear phase-shift error, so the phase data extracted in Fig. 7 (c) is very close to ideal line.The phase data that Fig. 7 (d) solves for adopting the complementary correction algorithm of the error of the present invention's proposition, equally very close to ideal line, and appearance without exception, illustrate that this algorithm is practical, there is excellent linear error rejection ability.

Fig. 8 (a) adopts the complementary correction algorithm of error to extract and absolutely dry after unpacking relates to field phase data for embodiment two; Fig. 8 (b) adopts the complementary correction algorithm of error to extract and topographic data after Wavefront Fitting for embodiment two.Its pattern error PV value is 0.131 λ, RMS value is 0.017 λ.The sphere pattern error result adopting the complementary correction algorithm of above-mentioned traditional three frame algorithms, traditional five frame algorithms, stoilov five frame algorithm, error four kinds of algorithms to record is as shown in table 1.Can find out, measurement result PV value and the RMS value of the complementary correction algorithm of the error of proposition and Stoilov algorithm are all comparatively close, and other two kinds of algorithms are relatively large.But when adopting Stoilov algorithm to extract phase place, in full interference field 342065 data points, there are 6437 imaginary number phase place solutions, caused shortage of data, account for 1.9% of sum.And the complementary correction algorithm of the error proposed does not exist this problem, and do not comprise extracting operation, more succinct quick, there is the advantage of oneself uniqueness in phase information extraction.

Table 1

Claims (4)

1. based on the phase-shifting interference measuring phase extraction method that error complementation is revised, it is characterized in that: a kind of phase-shifting interference measuring phase extraction method revised based on error complementation is specifically carried out according to following steps:

Step one, traditional five frame algorithm expression-forms are:

Wherein, for position phase to be separated, I ₁, I ₂, I ₃, I ₄, I ₅respectively corresponding phase shift measure-π ,-pi/2,0, pi/2, π time each frame sequence light intensity, obtain the phase information that traditional five frames extract;

Step 2, adopt and the light intensity of traditional five frame algorithm same number of frames sequences, substitute into the new five frame algorithms constructed, obtain the phase information that new five frame algorithms extract, five frame algorithm patterns of structure are;

Step 3, mean operation is directly done mutually in the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms solve, carry out error complementation, obtain the position phase after error correction.

2. a kind of based on the complementary phase-shifting interference measuring phase extraction method revised of error according to claim 1, it is characterized in that: in described step 2, adopt the light intensity with traditional five frame algorithm same number of frames sequences, namely phase shift measure-π ,-pi/2,0, pi/2, π time, the five frame algorithm patterns constructed under any step-length become formula (2) described form, and the five frame algorithm patterns constructed under any step-length are:

$\mathrm{\φ}=\arctan [\frac{1}{\sin \left(\mathrm{\β}\right)}\·\frac{2(I_2-I_4)-(I_1-I_5)}{4I_3-2(I_2+I_4)}]---\left(3\right)$

In formula: for position phase to be separated, I ₁, I ₂, I ₃, I ₄, I ₅the light intensity of each frame sequence when corresponding phase shift step-length gets β respectively.

3. a kind of based on the complementary phase-shifting interference measuring phase extraction method revised of error according to claim 2, it is characterized in that: formula treats Xie Weixiang described in (3) concrete computation process be:

Five frame light intensity system of equations in interference field under any unique step are as shown in formula (4):

$\left\{\begin{array}{c}{I}_1=A+B\·\cos (\mathrm{\φ}-2\·\mathrm{\β})\\ I_2=A+B\·\cos (\mathrm{\φ}-\mathrm{\β})\\ I_3=A+B\·\cos \left(\mathrm{\φ}\right)\\ I_4=A+B\·\cos (\mathrm{\φ}+\mathrm{\β})\\ I_5=A+B\·\cos (\mathrm{\φ}+2\·\mathrm{\β})\end{array}\right.---\left(4\right)$

In formula: for position phase to be separated, I is the light intensity of each frame sequence in interference field, I ₁, I ₂, I ₃, I ₄, I ₅respectively corresponding phase shift step measure-2 β ,-β, 0, β, 2 β time each frame sequence light intensity; A is light intensity DC component, and B is light intensity AC compounent, and β is phase shift step-length.

By I ₂with I ₄, I ₁with I ₅do difference, through trigonometric function and the computing of difference eliminate indigestion, after arrangement, obtain formula (5), (6) respectively:

I ₂-I ₄＝2B·sin(φ)·sin(β) (5)

I ₁-I ₅＝2B·sin(φ)·sin(2β) (6)

Formula (6) is launched by double angle formula, obtains formula (7):

I ₁-I ₅＝4B·sin(φ)·sin(β)·cos(β) (7)

Formula (5) is multiplied by two times, does difference with formula (7), and arrangement obtains formula (6):

2·(I ₂-I ₄)-(I ₁-I ₅)＝4B·sin(φ)·sin(β)·[1-cos(β)] (8)

By I ₂with I ₄do and, and carry out trigonometric function and difference eliminate indigestion obtain formula (9):

I ₂+I ₄＝2A+2B·cos(φ)·cos(β) (9)

By I ₃be multiplied by 4 times, do difference with the formula (9) of two times, DC component A is eliminated, and abbreviation arranges and obtains formula (10):

4I ₃-2·(I ₂+I ₄)＝4B·cos(φ)·[1-cos(β)] (10)

Formula (8) and formula (10) be divided by, 1-cos (β) item and 4B are divided out, and are moved on the left of equal sign by sin (β) and obtain formula (11):

$\frac{1}{\sin \left(\mathrm{\β}\right)}\·\frac{2(I_2-I_4)-(I_1-I_5)}{4I_3-2(I_2+I_4)}=\tan \left(\mathrm{\φ}\right)---\left(11\right)$

By the equal sign both sides negate arctangent operation of formula (11), the five frame algorithms constructed under obtaining any unique step, the form as described in formula (3).

4. a kind of based on the complementary phase-shifting interference measuring phase extraction method revised of error according to claim 3, it is characterized in that: the described revised position of step 3 medial error is mutually: