CN104330027B - 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 based on the complementary amendment of error

Technical field

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

Background technology

With the continuous development of micro-nano process technology, component surface pattern required precision more and more higher, to corresponding Detection meanss it is also proposed higher requirement.Phase shifting interferometry is, the advantages of its high accuracy, high efficiency, noncontact, becoming The ideal measuring method in Shape measure field.(1) in phase-shifting interference measuring, phase information is each by Phase-shifting algorithm process Frame interferogram is obtained, and Linear phase-shift error is prevalent in all kinds of interference systems, the precision for affecting phase information to extract. (2) in phase-shifting interference measuring, although traditional fixed step size Phase-shifting algorithm computing is simple, to linear shifting in addition to five frame algorithms Phase error is more sensitive, and five frame algorithms only have good rejection ability to the linearity error within 5%, when linearity error surpasses When 5%, phase extraction error is increased dramatically.(3) in phase-shifting interference measuring, although any fixed step size Phase-shifting algorithm can be real Existing linearity error immunity, but formula is loaded down with trivial details, and operand is big, comprising power extracting operation, imaginary bit easily occurs and mutually solves and super large mistake Not good enough Singularity mutually solves situation.

The content of the invention

The invention aims to solve (1) existing Linear phase-shift error be prevalent in all kinds of interference systems, shadow Ring phase information extraction accuracy；(2), when existing linearity error is more than 5%, phase extraction error is increased dramatically；(3) it is and existing Formula is loaded down with trivial details, and operand is big, comprising power extracting operation, imaginary bit easily occurs and mutually solve mutually solving feelings with the Singularity of super large error dot The problem of condition.And propose a kind of phase-shifting interference measuring phase extraction method based on the complementary amendment of error.

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

A kind of phase-shifting interference measuring phase extraction method based on the complementary amendment of error, it is characterised in that：By tradition five Error between frame algorithm and five frame algorithms of construction is complementary, and the shadow that Linear phase-shift error is extracted to phase information is greatly reduced Ring, specifically follow the steps below：

Step one, traditional five frames algorithm expression-form are：

Wherein,For position phase to be solved, I₁、I₂、I₃、I₄、I₅Respectively correspond to phase shift measure-π ,-pi/2,0, pi/2, π when it is each The light intensity of frame sequence, obtains the phase information that traditional five frame is extracted；

Step 2, the new five frames algorithm constructed using the light intensity with traditional five frames algorithm same number of frames sequence, substitution, obtain new five The phase information that frame algorithm is extracted, five frame algorithm patterns of construction are：

Step 3, the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms are solved mutually directly is done average fortune Calculate, carry out error complementation, obtain the position phase after error correction.

Invention effect

Using a kind of phase-shifting interference measuring phase extraction method based on the complementary amendment of error of the present invention, (1) present invention The error complementation correction algorithm for using reduces impact of the Linear phase-shift error to phase information extraction accuracy, and extraction accuracy improves Two orders of magnitude；(2) the error complementation correction algorithm that the present invention is used, by five traditional frame algorithms and two kinds new of five frame algorithm Mean operation is mutually directly done in the position that algorithm is solved, and error just complementary can be corrected, and when can avoid linearity error more than 5%, position mutually carries The problem that error is increased dramatically is taken, makes phase extraction error reduce by 15%；(3) the error complementation correction algorithm base that the present invention is used In the complementary amendment principle of error, using features of response of the fixed step size Phase-shifting algorithm to Linear phase-shift error, by the new of construction Five frame algorithms carry out error complementation, computing simple and fast, without power extracting operation, it is to avoid imaginary bit occur with traditional five frames algorithm The problem that situation is mutually solved with the Singularity of super large error dot is solved mutually.

As shown in table 1, it can be seen that the error five frame algorithms of complementation of proposition and measurement result PV of both Stoilov algorithms Value and RMS value are all closer to, and other two kinds of algorithms are relatively large.But when extracting phase place using Stoilov algorithms, complete 6437 imaginary number phase place solutions are occurred in that in 342065 data points of interference field, shortage of data is caused, the 1.9% of sum is accounted for.And But there is no this in the error complementation correction algorithm of proposition, and do not include extracting operation, more succinct quick, believe in place There is in terms of breath extraction the advantage of oneself uniqueness.

Description of the drawings

Fig. 1 is the linearity error response distribution situation of traditional five frames algorithm；

Fig. 2 is the linearity error response distribution situation of the five new frame algorithms of construction；

Fig. 3 is the linearity error response distribution situation of the error complementation correction algorithm for proposing；

Fig. 4 (a) calculates gained phase error for one traditional five frames algorithm of embodiment；

Fig. 4 (b) calculates gained phase error for one error of embodiment complementation correction algorithm；

Fig. 4 (c) calculates gained phase error for one stoilov of embodiment, five frame algorithms；

Fig. 5 is two microsphere surface morphology phase shift diffraction interference of embodiment measurement figure；

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

In the five frame interferograms that Fig. 6 (b) is collected for embodiment two phase shift step-length take-pi/2 when interferogram；

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

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

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

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

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

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

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

Fig. 8 (a) is extracted using error complementation correction algorithm for embodiment two and absolutely dry after unpacking relates to field phase data；

Fig. 8 (b) is embodiment two using the topographic data after error complementation correction algorithm extraction and Wavefront Fitting.

Specific embodiment

Specific embodiment one：A kind of phase-shifting interference measuring phase extraction method based on the complementary amendment of error, its feature It is：What a kind of phase-shifting interference measuring phase extraction method based on the complementary amendment of error was specifically followed the steps below：

Step one, traditional five frames algorithm expression-form are：

Wherein,For position phase to be solved, I₁、I₂、I₃、I₄、I₅Respectively correspond to phase shift measure-π ,-pi/2,0, pi/2, π when it is each The light intensity of frame sequence, obtains the phase information that traditional five frame is extracted；

Step 2, the new five frames algorithm constructed using the light intensity with traditional five frames algorithm same number of frames sequence, substitution, obtain new five The phase information that frame algorithm is extracted, five frame algorithm patterns of construction are；

Step 3, the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms are solved mutually directly is done average fortune Calculate, carry out error complementation, obtain the position phase after error correction.

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

Specific embodiment two：Present embodiment from unlike specific embodiment one：In the step 2 using with The light intensity of traditional five frame algorithm same number of frames sequences, i.e. phase shift measure-π ,-pi/2,0, pi/2, π (phase shift step-length takes pi/2) when, arbitrarily walk Five frame algorithm patterns of long lower construction are changed into formula (2) form, and the five frame algorithm patterns constructed under any step-length are：

In formula：For position phase to be solved, I₁、I₂、I₃、I₄、I₅The light of each frame sequence when phase shift step-length takes β is corresponded to respectively By force.Other steps and parameter are identical with specific embodiment one.

Specific embodiment three：Present embodiment from unlike specific embodiment one or two：Formula is treated described in (3) Xie WeixiangConcrete calculating process be：

Shown in five frame light intensity equation group such as formula (4) in interference field under any unique step：

In formula：For position phase to be solved, light intensity of the I for each frame sequence in interference field, I₁、I₂、I₃、I₄、I₅Correspond to respectively and move Mutually step measure -2 β,-β, 0, β, 2 β when each frame sequence light intensity；A is light strong DC component, and B is light intensity AC compounent, and β is phase shift Step-length；

By I₂With I₄、I₁With I₅Make the difference, Jing trigonometric functions and differenceization accumulate computing, and formula (5), (6) are respectively obtained after arrangement：

I₂-I₄=2Bsin (φ) sin (β) (5)

I₁-I₅=2Bsin (φ) sin (2 β) (6)

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

I₁-I₅=4Bsin (φ) sin (β) cos (β) (7)

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

2·(I₂-I₄)-(I₁-I₅)=4Bsin (φ) sin (β) ［ 1-cos (β) ］ (8)

By I₂With I₄Do and, and carry out trigonometric function and differenceization and accumulate obtaining formula (9)：

I₂+I₄=2A+2Bcos (φ) cos (β) (9)

By I₃4 times are multiplied by, are made the difference with two times of formula (9), DC component A is eliminated, abbreviation is arranged and obtains formula (10)：

4I₃-2·(I₂+I₄)=4Bcos (φ) ［ 1-cos (β) ］ (10)

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

The equal sign both sides of formula (11) are negated into arctangent operation, the five frame algorithms constructed under any unique step are obtained, it is such as public Form described in formula (3).

Other steps and parameter are identical with specific embodiment one or two.

Specific embodiment four：Present embodiment from unlike specific embodiment one, two or three：In the step 3 Position after error correction is mutually specially：

The linearity error response distribution situation of formula (12) is as shown in Figure 3 respectively.Contrasted with Fig. 2 from Fig. 1, In the case of equivalent linearity error, for same initial phase, the position phase resolution error of two kinds of algorithms is in the same order of magnitude and width Value is sufficiently close to, but symbol is contrary；Therefore, the position for five traditional frame algorithms being solved with new five frame algorithms, two kinds of algorithms is mutually straight Connect and do mean operation, error just complementary can be corrected.

As seen from Figure 3, although fail to realize completely linearity error immunity, but position phase resolution error reduces two quantity Level, it is sufficient to meet the demand of high accuracy interferometry；Due to there is no extracting operation, be not in imaginary bit phase in solution procedure The abnormal conditions of solution and super large error dot, computing are more succinct quick.

Other steps and parameter and specific embodiment one, two or three are identical.

Embodiment 1：Treat the numerical simulation in the range of Xie Weixiang (- pi/2, pi/2).

200 sampled points are taken in interval (- pi/2, pi/2), uniform sampling, as Xie Weixiang is treated, is counted using formula (13) Calculate the corresponding five frames light intensity value of each sampled point.

Wherein, A be interference field DC component, value 100；B be interference field AC compounent, value 80；φ is to treat Xie Weixiang Sampled value；K be linearity error coefficient, value 15%；β is theoretical step size, value pi/2；α is the random Phase-shifting Errors for introducing, and is taken It is worth for the random value in interval (- 0.0038 π, 0.0038 π).

Each sampled point for calculating corresponding five frames light intensity value is substituted into into traditional five frames method respectively Error complementation correction algorithm proposed by the present inventionWith And position phase is solved in any unique step algorithm.For the ease of calculating, five frame stoilov algorithms of any unique step algorithms selection.Meter Calculate gained phase error as shown in Figure 4.Wherein, Fig. 4 (a) is traditional five frames algorithm result of calculation；Fig. 4 (b) is present invention proposition Error complementation five frame algorithm result of calculations；Fig. 4 (c) is five frame algorithm result of calculations of stoilov.

Traditional five frame algorithm phase extraction error PV values are 9 × 10^-3π, error complementation correction algorithm position proposed by the present invention It is 1.1 × 10 mutually to extract error PV value^-4The phase extraction error PV value of five frame algorithm of π, stoilov is 1.16 × 10^-4π。

It can be seen that, compared with traditional five frames algorithm, error reduces nearly two to five frame algorithms of error complementation proposed by the present invention The order of magnitude, phase extraction error PV value are suitable with five frame algorithms of stoilov.As can be seen that small with chance error from Fig. 4 (b) Under the influence of difference, algorithm shows linearity error response characteristic, while also showing the feature of random fluctuation.

Embodiment 2：The measurement experiment of microsphere surface morphology phase shift diffraction interference

The measurement of microsphere surface morphology phase shift diffraction interference is as shown in Figure 5.The line polarized light Jing space filterings of laser emitting Assemble through lens after device filtering, collimator and extender, diffraction occurs at the aperture of pin hole reflecting mirror, ideal spherical face ripple is produced.

A part of spherical wave converges to microsphere surface by object lens as measurement light, and beam center is concentric with microsphere.Another portion It is allocated as reference light, through CCD.Measurement light Jing measured surface reflections, carry the approximate backtracking of topographical information, by pin hole mirror table The metallic diaphragm reflection in face is turned to, and is formed with reference light and is interfered.Phase shifter micro-displacement platform drives microsphere along measurement light optical axis side To movement, phase shift is produced, and the interferogram of several stripe order recognitions is recorded by CCD.Interferogram is processed finally by Phase-shifting algorithm to obtain First phase bit distribution is obtained, and phase information is scaled into difference in height information, complete measurement.

In order to verify the feasibility and effectiveness of the error complementation correction algorithm phase extraction method of proposition, from surface shape The good 3mm diameter aviation balls of looks carry out actual measurement, theoretical phase shift step-length pi/2, and add about 25% Linear phase-shift to miss Difference.Meanwhile, for the ease of Wavefront Fitting, interference fringe is adjusted to vertical bar stricture of vagina is close to, the out of focus item that alignment error is introduced is reduced And the impact of cue ball difference item.Shown in five frame interferogram such as Fig. 6 (a) for collecting, Fig. 6 (b), Fig. 6 (c), Fig. 6 (d), Fig. 6 (e).

Traditional three frame algorithm Fig. 7 (a), traditional five frame algorithm Fig. 7 (b), five frames algorithm Fig. 7 (c) of Stoilov is respectively adopted with And error complementation correction algorithm Fig. 7 (d) proposed by the present invention carries out phase extraction, and unpacking.Choosing middle row is carried out point Analysis, solution phase result are as shown in Figure 7.In theory, the straight interference fringe not comprising defocusing amount alignment error, the phase place after unpacking An approximate clinoplain is distributed as, wherein data line is chosen and is necessarily obtained an approximate straight line.However, three frame algorithms It is more sensitive to linearity error, the interval interior Non-uniform responsivity of phase place so that the phase place after unpacking forms the curve of a fluctuation. The linearity error rejection ability of traditional five frame algorithms is significantly better than traditional three frames algorithm, but it can be seen that the fluctuation of regularity, And the fluctuating margin of marginal position is larger than centre position, this also illustrates that out of focus introduces the inhomogeneities of Phase-shifting Errors. The characteristics of there is the immunity of Linear phase-shift error due to five frame algorithms of Stoilov, so the phase data ten extracted in Fig. 7 (c) Tap nearly ideal line.Fig. 7 (d) is using the error proposed by the present invention complementation phase data that solves of correction algorithm same ten Nearly ideal line is tapped, and point without exception occurs, and illustrates that the algorithm is practical, with excellent linearity error rejection ability.

Fig. 8 (a) is extracted using error complementation correction algorithm for embodiment two and absolutely dry after unpacking relates to field phase data；Figure 8 (b) is embodiment two using the topographic data after error complementation correction algorithm extraction and Wavefront Fitting.Its pattern error PV value For 0.131 λ, RMS value is 0.017 λ.Using above-mentioned traditional three frames algorithm, traditional five frames algorithm, five frame algorithms of stoilov, error The sphere pattern error result that four kinds of algorithms of complementary correction algorithm are measured is as shown in table 1.As can be seen that the error for proposing mutually is studied for a second time courses one has flunked The measurement result PV value of both normal operation method and Stoilov algorithms and RMS value are all closer to, and other two kinds of algorithms are relatively Greatly.But when phase place is extracted using Stoilov algorithms, occur in that 6437 imaginary number phase places in 342065 data points of full interference field Solution, causes shortage of data, accounts for the 1.9% of sum.And there is no this in the error complementation correction algorithm for proposing, and not It is comprising extracting operation, more succinct quick, the advantage with oneself uniqueness in terms of phase information extraction.

Table 1

Claims (4)

1. a kind of based on the complementary phase-shifting interference measuring phase extraction method corrected of error, it is characterised in that：It is a kind of to be based on error What the phase-shifting interference measuring phase extraction method of complementary amendment was specifically followed the steps below：

Step one, traditional five frames algorithm expression-form are：

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

Wherein, φ is position phase to be solved, I₁、I₂、I₃、I₄、I₅Respectively correspond to phase shift measure-π ,-pi/2,0, pi/2, π when each frame sequence Light intensity, obtain the phase information that traditional five frames algorithm is extracted；

Step 2, the new five frames algorithm constructed using the light intensity with traditional five frames algorithm same number of frames sequence, substitution, are obtained new five frame and are calculated The phase information that method is extracted, the new five frames algorithm pattern of construction is；

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

Step 3, mean operation is mutually directly done in the position that five traditional frame algorithms and new five frame algorithms, two kinds of algorithms are solved, enter Row error is complementary, obtains the position phase after error correction.

2. a kind of based on the complementary phase-shifting interference measuring phase extraction method corrected of error, its feature according to claim 1 It is：In the step 2 using the light intensity with traditional five frames algorithm same number of frames sequence, i.e. phase shift measure-π ,-pi/2,0, pi/2, π When, the new five frames algorithm pattern constructed under any step-length is changed into formula (2) form, and five frames constructed under any unique step are calculated Method form is：

$\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：φ is position phase to be solved, I₁、I₂、I₃、I₄、I₅The light intensity of each frame sequence when phase shift step-length takes β is corresponded to respectively, and β is Phase shift step-length.

3. a kind of based on the complementary phase-shifting interference measuring phase extraction method corrected of error, its feature according to claim 2 It is：Formula treats Xie Weixiang described in (3)Concrete calculating process be：

Shown in five frame light intensity equation group such as formula (4) in interference field under any unique step：

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

In formula：φ is position phase to be solved, and I is the light intensity of each frame sequence in interference field, I₁、I₂、I₃、I₄、I₅Phase shift step is corresponded to respectively Measure -2 β,-β, 0, β, 2 β when each frame sequence light intensity；A is light strong DC component, and B is light intensity AC compounent, and β is that phase shift is walked It is long；

By I₂With I₄、I₁With I₅Make the difference, Jing trigonometric functions and differenceization accumulate computing, and formula (5), (6) are respectively obtained after arrangement：

I₂-I₄=2Bsin (φ) sin (β) (5)

I₁-I₅=2Bsin (φ) sin (2 β) (6)

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

I₁-I₅=4Bsin (φ) sin (β) cos (β) (7)

Formula (5) is multiplied by into two times, is made the difference with formula (7), and arrangement obtains formula (8)：

2·(I₂-I₄)-(I₁-I₅)=4Bsin (φ) sin (β) [1-cos (β)] (8)

By I₂With I₄Do and, and carry out trigonometric function and differenceization and accumulate obtaining formula (9)：

I₂+I₄=2A+2Bcos (φ) cos (β) (9)

By I₃Quadruplication times, is made the difference with two times of formula (9), and light strong DC component A is eliminated, and abbreviation is arranged and obtains formula (10)：

4I₃-2·(I₂+I₄)=4Bcos (φ) [1-cos (β)] (10)

Formula (8) is divided by with formula (10), 1-cos (β) items and 4B are divided out, and sin (β) is moved to obtain on the left of equal sign public affairs Formula (11)：

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

The equal sign both sides of formula (11) are negated into arctangent operation, the five frame algorithms constructed under any unique step, such as formula (3) are obtained Described form.

4. a kind of based on the complementary phase-shifting interference measuring phase extraction method corrected of error, its feature according to claim 3 It is：Position in the step 3 after error correction is mutually：

$\mathrm{\φ}=\frac{1}{2}\·\{arctan\[\frac{2(I_2-I_4)}{2I_3-(I_1+I_5)}\]+arctan\[\frac{2(I_2-I_4)-(I_1-I_5)}{4I_3-2(I_2+I_4)}\]\}---\left(12\right).$