CN105758295B - A kind of matched dual wavelength simultaneous phase shifting interferometric method of space-time mixing - Google Patents
A kind of matched dual wavelength simultaneous phase shifting interferometric method of space-time mixing Download PDFInfo
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- CN105758295B CN105758295B CN201610168731.6A CN201610168731A CN105758295B CN 105758295 B CN105758295 B CN 105758295B CN 201610168731 A CN201610168731 A CN 201610168731A CN 105758295 B CN105758295 B CN 105758295B
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- 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
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Abstract
The invention discloses a kind of space-times to mix matched dual wavelength simultaneous phase shifting interferometric method, it include: to construct road dual wavelength simultaneous phase shifting dual wavelength interference system altogether, the laser of two different wave lengths is set to form dual wavelength mixed interference bar graph along identical path, phase-shift phase is generated by the way that piezoceramic transducer is mobile, while acquiring N width dual wavelength simultaneous phase shifting dual wavelength interference pattern using single black-white CCD；Principal component analysis is carried out to the N width interference pattern, the phase-shift phase under two wavelength is obtained, then the phase-shift phase under the two wavelength is corrected, the phase-shift phase after correction is substituted into least-squares iteration algorithm, calculates the wrapped phase under two wavelength；The wrapped phase of described two wavelength is subtracted each other and unpacked, phase distribution to be measured under synthetic wavelength is obtained.The square law device proposed is simple, and measurement range is big, and precision is high, reliable and stable, low to phase-shifter required precision.
Description
Technical field
The present invention relates to digital hologram measurement or optical interferometry fields, and in particular to a kind of space-time mixing is matched double
Wavelength simultaneous phase shifting interferometric method.
Background technique
Optical interferometry technology is widely used in the measuring three-dimensional morphology of object, has high-precision, and the whole audience is untouchable
The characteristics of.For Single wavelength interferometry, available high-precision object surface appearance, if but unconnected pixels point in interference pattern
Between corresponding object height difference be greater than half illumination optical maser wavelength if, will have phase fuzzy problem.In order to solve this
A problem proposes dual wavelength interferometry or multi-wavelength interference art.For dual wavelength interferometry, synthetic wavelength Λ is by two
Wavelength X1And λ2It obtains, i.e. Λ=λ1λ2/|λ1-λ2|.It is poor to make to two obtained Single wavelength wrapped phases, obtains dual wavelength package
Phase, and this phase might have the jump problem of 2 π, and a unpacking is carried out to it and operates available object under test
Synthetic wavelength phase.Solves the phase fuzzy problem of Single wavelength to a certain extent in this way.
Before obtaining synthetic wavelength phase, need first from the wrapped phase extracted in interference pattern under two wavelength, these extractions
Method usually has three classes: the first kind is airspace fourier transform method, and the second class is airspace phase shift method, and third class is time domain phase shift
Method.Airspace fourier transform method and airspace phase shift method may be used to dynamic phasing measurement, but precision does not have time domain phase shift method height,
And the measurement accuracy of airspace fourier transform method is larger by filter window and influence of noise, can also lose the space of some objects
Frequency information；Airspace phase shift method can be realized with multiple CCD, but device is complicated, can also be realized with a black-white CCD,
But some detailed information of object may be lost, and precision is also high without time domain phase shift method；The time domain phase shift being suggested at present
There are two types of forms for method, and one is need to acquire one group of phase shifting interference respectively under two Single wavelengths to extract two Single wavelengths
Wrapped phase, but measurement process is cumbersome, is easy to be influenced by extraneous vibration and air agitation, another kind is that acquisition is a series of
Simultaneous phase shifting dual wavelength interference pattern extracts the wrapped phase under two Single wavelengths, but existing wrapped phase extracting method exists
Following problems: high to phase-shift phase required precision, unstable, precision is low, and the interference pattern needed is more.
Summary of the invention
Be directed to it is existing in the prior art to larger mutation-ure bulk measurement when occur phase ambiguity, calculate it is unstable, smart
It spends not high and high and measurement process complexity technical problem is required to ambient stable and phase-shifter Phase shift precision, the present invention provides
A kind of space-time mixes matched simultaneous phase shifting dual wavelength interferometric method.
Method provided by the invention the following steps are included:
Road simultaneous phase shifting dual wavelength interference system altogether is constructed, the laser of two different wave lengths is made to form double wave along identical path
Long mixed interference bar graph generates phase-shift phase by the way that piezoceramic transducer is mobile, while acquiring N width using single black-white CCD
Simultaneous phase shifting dual wavelength interference pattern；
Principal component analysis is carried out to the N width interference pattern, the phase-shift phase under two wavelength is obtained, then to the two wavelength
Under phase-shift phase corrected, after correction phase-shift phase substitute into least-squares iteration algorithm, calculate the packet under two wavelength
Wrap up in phase；
The wrapped phase of described two wavelength is subtracted each other and unpacked, phase distribution to be measured under synthetic wavelength is obtained.
Specifically, the N width simultaneous phase shifting dual wavelength interference pattern, in the time domain, it is desirable that two wavelength phase shift amounts are substantially
It is evenly distributed in the integer period, and there are two positive integer ns1And n2, make n2/n1≈λ1/λ2, wherein λ1With λ2It is described total
The wavelength and λ of two light sources of road simultaneous phase shifting dual wavelength interference system1> λ2, n2/n1For fraction in lowest term, the CCD acquires N
After width figure, the mobile distance of piezoceramic transducer is pn1λ1, wherein p is any positive integer, and piezoelectric ceramics moving step length is big
Cause is equal, other N > 2n2p。
Specifically, the N width simultaneous phase shifting dual wavelength interference pattern meets in every width interference pattern on airspace in two waves
There is integer interference fringe under length, that is, corresponds to wavelength X1, there is n1Q interference fringe, q are any positive integers.
Specifically, the number of interference fringes that can be differentiated in phase shift dual wavelength interference pattern at the same time with correspond to wavelength X1It is dry
It is consistent to relate to fringe number, and airspace fringe number requires to relax are as follows: number of interference fringes in phase shift dual wavelength interference pattern at the same time
No less than n1。
Specifically, the synthetic wavelength phase carries out a phase solution after directly being subtracted each other by wrapped phase under two wavelength
Package operation obtains.
Specifically, when object is not added the simultaneous phase shifting dual wavelength interference pattern interference fringe be vertical bar line, and with it is black
White CCD target surface horizontal pixel direction is vertical (or parallel).
Compared with prior art, the present invention has the following advantages:
(1) compared to Single wavelength interferometric method, method provided by the invention can measure change of gradient larger object,
The measurement range for jumping height at object transition is increased, the application field of interferometry has been expanded.
(2) compared to other dual wavelength interferometric methods, the method for the present invention is reliable and stable, and precision is high, measurement process letter
It is single, do not need calibration phase-shift phase.
(3) device that the method for the present invention uses is simple, not high to phase shifting devices required precision, and collection process is simple, only needs
Interference pattern is acquired with a black-white CCD.
(4) the advantages of present invention incorporates principal component analysis and least-squares iterations, by limit interference pattern time domain with
The condition for needing to meet under airspace has good inhibiting effect to ambient noise, compared to least-squares iteration algorithm extract to
Object phase is surveyed, required the number of iterations is less, realizes correct, stable, high-precision phase measurement.
Detailed description of the invention
Fig. 1 is phase shift dual wavelength interferometer measuration system schematic diagram while the method for the present invention uses.
Fig. 2 is to be extracted simultaneously from N width simultaneous phase shifting dual wavelength interference pattern in one embodiment using the method for the present invention
Two wavelength under wrapped phase distribution map.
Fig. 3 is one piece of regular handset light guide plate under the synthetic wavelength recovered in one embodiment using the method for the present invention
In a light guiding points phase distribution figure.
Wherein, it is marked in attached drawing 1 specifically:
1 is diode pumped solid state laser；2 be He-Ne laser；
3-4 is variable center density decay piece；5-7 is plane mirror；
8-9 is broadband beam splitter prism；10 be piezoceramic transducer；
11 be the first microcobjective；12 be the second microcobjective；
13 be black-white CCD；14 be object under test；
15 be computer.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
First embodiment
The present embodiment will in conjunction with the accompanying drawings and embodiments to it is described while phase shift dual wavelength interferometer measuration system make it is further
Explanation.
As shown in Figure 1, the system includes: the diode pumped solid state laser 1 and a wavelength that a wavelength is 532nm
For the He-Ne laser 2 of 632.8nm；Two beam laser are divided into two-beam line, a branch of object light, Yi Shucan after beam splitter 8 converges
Examine light；By the adjusting of plane mirror 5 and beam splitter 8, propagate object light and the road reference light Dou Shigong under two kinds of wavelength；Object
The reflecting mirror 7 that light is pasted on piezoceramic transducer 10 after object under test 14 and by the first microcobjective 11 with process
It reflects and the reference light for passing through the second microcobjective 12 converges and interferes at beam splitter 9, herein with reference to light by reflecting
When mirror 7 reflects, angle of reflection is 45 degree, adjusts beam splitter 9, so that the interference fringe of two wavelength and 13 target surface of black-white CCD are lateral
Pixel orientation is vertical, and the direction of vertical bar line can be adjusted by beam splitter 9；After light beam under two wavelength interferes respectively
It is superimposed by light intensity, merges in 13 target surface of black-white CCD and form simultaneous phase shifting dual wavelength interference pattern；Here the resolution of black-white CCD 13
Rate is 1280 × 1024, and Pixel Dimensions are 5.2 μm of 5.2 μ m.
Controlling piezoceramic transducer 10 by computer 15 drives reflecting mirror 7 mobile, phase-shift phase is generated, then by black and white
The interference pattern of CCD13 record at this time, as soon as every movement time piezoceramic transducer 10, black-white CCD 13 records an interference pattern, most
After obtain N width simultaneous phase shifting dual wavelength interference pattern, the mobile interval of piezoceramic transducer 10 is generally equal here, finally
The mobile distance of piezoceramic transducer 10 is approximately 5 times of 632.8nm wavelength, is approximately 6 times of 532nm wavelength.Wherein, it is
The parameter of beam splitter 8-9 is the same in system；The parameter of microcobjective 11-12 is the same, enlargement ratio 25, numerical aperture
It is 0.4.Object under test 14 is 5.5 cun of common mobile phone light guide panels in the present embodiment.
Second embodiment
The present embodiment will mix matched dual wavelength simultaneously to a kind of space-time of the present invention in conjunction with the accompanying drawings and embodiments
Phase shift interference measurement method is described further.
Step 1: acquisition N width simultaneous phase shifting dual wavelength interference pattern:
After light path system is put up, piezoceramic transducer and black-white CCD are driven with computer, it is double to obtain N width simultaneous phase shifting
Wavelength-interferometric figure, n-th width interference pattern its light distribution can indicate are as follows:
Here x, y indicate the space coordinate in black-white CCD image planes, n=1, and 2 ..., N, N indicate a total of N width simultaneously
Phase shift dual wavelength interference pattern, two laser wavelength lambdas1=632.8nm and λ2=532nm, and, A (x, y) is background light intensity,
WithIt is illustrated respectively in λ1And λ2Under modulate intensity, here With
It is illustrated respectively in λ1And λ2Under phase modulation,WithThe n-th width figure is respectively indicated in λ1And λ2Under corresponding phase-shift phase.
Step 2: carrying out principal component analysis to N width simultaneous phase shifting dual wavelength interference pattern, the package phase under two wavelength is obtained
Shifting amount:
It enables K indicate the pixel sum of interference pattern, every width interference pattern is write as the matrix that size is 1 × K, then the n-th width
The interference light intensity expression formula of k-th of pixel of figure is
It is required according to PCA method, needs to eliminate the background of all simultaneous phase shifting dual wavelength interference patterns, the light after eliminating background
It is distributed as by force
Here
IfWithIt is distributed approximately evenly in [0,2 π T respectively1] and [0,2 π T2] in range, wherein T1And T2It is all constant.
Two positive integer ns can be found1And n2, there is n2/n1≈λ1/λ2, n here2/n1It is fraction in lowest term.SoWork as T1=n1When p (p is any positive integer), there is T2=n2P, at this moment at k-th of pixel
Background item be approximately
Going the interference pattern after background to be expressed as a matrix form, i.e.,
HereIt is the row vector that size is 1 × K, []TRepresent transposition operator, matrixSize be N × K.
Covariance matrix can indicate are as follows:
According to the property of matrix it is found that covariance matrix C can be turned to diagonally
D=UCUT (7)
Here, D is diagonal matrix, and U is orthogonally transformed matrix, and Matrix C, D and U are N × N square matrix.We can use surprise
Different value decomposes (SVD) method to obtain U and D.
Next, we are back to discuss influence problem of the striped quantity in interference pattern to precision, and meet two waves
Long phase-shift phase while the another use on complete cycle.In formula (6), the element that the i-th row jth arranges in covariance matrix C can
To be expressed as
Wherein
Because according to orthogonality of trigonometric function, it is understood that when for λ1Number of interference fringes be n1Positive integer times
When, have
Under normal circumstances, the fringe number that can be differentiated in phase shift dual wavelength interference pattern at the same time with correspond to λ1Interference item
Line number is consistent, and in the case where not considering that precision decreases, as long as there is no less than n in dual wavelength interference pattern1It is a dry
Striped is related to, formula (10) is also able to satisfy.At this moment
Then, according to orthogonality of trigonometric function, meeting phase-shift phaseWithAll it is evenly distributed on complete cycle [0,2
πT1] and [0,2 π T2] on when, so that it may obtain the feature vector of four pairwise orthogonals of covariance matrix C, they are respectively corresponded
Four rows before orthogonal transform matrix U.It is write as row vector form, is had
At this moment, the package phase-shift phase under our available two wavelength, i.e.,
But for the orthogonal matrix U, U that we obtain1、U2、U3、U4Sequence is uncertain in four rows before U.This meeting
The phase-shift phase or phase-shift phase for obtaining mistake will appear symbol problem.For this purpose, we enable wavelength X1Corresponding laser intensity is obviously big
In wavelength X2Corresponding laser intensity, then we are rightWithUnpacking operation is carried out respectively, is obtainedWithIf soHaveOtherwiseIfHaveOtherwiseThis
Sample we just obtained the corresponding correct phase-shift phase of two wavelength.
Step 3: obtaining the wrapped phase under two wavelength according to the phase-shift phase after correction
Phase-shift phase under two wavelength after correction is substituted into least-squares iteration algorithm (referring to document " Single-
wavelengthphase retrieval method from simultaneous multi-wavelength in-
Linephase-shifting interferograms " OpticsExpress.22,30910-30923 (2014)) in, so that it may
To obtain the wrapped phase under different wave length.
BecauseWithIndicate n-th k-th of pixel of width figure
Actual light intensity value at point, then N width figure is in the quadratic sum that light intensity and actual light intensity difference are discussed in k-th of pixel processing
Make EkMinimum has
Convolution (15) and two wavelength phase shift amounts after being obtained and corrected by PCA algorithmWithIt is availableValue, it is hereby achieved that the corresponding wrapped phase of different wave length at k-th of pixel
It can be obtained by the wrapped phase of all pixels point to (16) by formula (14).Then, it enables At this momentSo theoretical light intensity of the n-th width figure all pixels point
Quadratic sum with actual light intensity difference is
Make EnMinimum has
According to what is acquiredWithIt can be obtained by by formula (18)Value, thus
Obtain the phase-shift phase that the n-th width figure corresponds to different wave length
It can be obtained by the corresponding phase-shift phase of N width figure by formula (17) to (19).Here wushu (14) to (19) is as most
Small two multiply an iteration process of iterative method, and under normal circumstances, the number of iterations is more, and obtained phase accuracy is higher, directly
Phase-shift phase to two wavelength meets the condition of convergence, i.e.,
Here, ε indicates that preset convergence threshold, m indicate the number of iterations.
Reach least-squares iteration algorithmic statement condition after, so that it may obtain under two wavelength containing space carrier frequency to
Survey the wrapped phase of objectWithAs shown in Figure 2.
Step 4: the wrapped phase under two wavelength of acquisition object under test
Same above step obtains under different wave length from N width simultaneous phase shifting dual wavelength dual wavelength interference pattern when object is not added
Wrapped phaseWithTo obtain the wrapped phase under two wavelength of object under testWithWe carry out following grasp
Make:
Step 5: obtaining synthetic wavelength phase distribution.
Due to λ1> λ2, therefore will obtainWithPhase reducing is carried out, there may be packages for the phase obtained after subtracting each other
It with the hopping phenomenon of 2 π, can be solved these problems by a unpacking process, then obtain the phase point under synthetic wavelength
Cloth:
Here ψΛIndicate the phase under synthetic wavelength, h indicates the optical path difference that light generates after object under test, Λ=λ1λ2/
|λ-λ2| it is synthetic wavelength.
Because of λ here1=632.8nm, λ2=532nm, there is λ1/λ2≈ 6/5, i.e. n1=5, n2=6.When taken interference pattern is full
Sufficient at least five striped, and for λ1Phase-shift phase when being evenly distributed in 5 positive integer times period, there is principal component analysis to obtain
Phase-shift phase it is more accurate, then obtained phase-shift phase is brought into least-squares iteration algorithm and is iterated operation, then
It is fewer to meet the number of iterations required when the condition of convergence, the calculating time is shorter, if these conditions are not met, reaches convergence
When condition, required the number of iterations is more, it is also possible to the phenomenon that iteration does not restrain occurs.It is at least to better meet fringe number
5 condition, the interference fringe of phase shift dual wavelength interference pattern is vertical bar line while when being not added object here, and with black-white CCD target
Face horizontal pixel direction is vertical.Here N=30 meets sinusoidal signal sampling theorem, because of interference pattern number N > 2T2=12.
So far, the method proposed through the invention, can be from the N width simultaneous phase shifting dual wavelength interference pattern of acquisition, simultaneously
The wrapped phase distribution under two wavelength is extracted, and then the phase distribution obtained under the synthetic wavelength of object under test is as shown in Figure 3.
The present invention is not limited to above-mentioned specific embodiment, according to above content, according to the ordinary technical knowledge of this field
And customary means, under the premise of not departing from above-mentioned basic fundamental thought of the invention, the present invention can also make other diversified forms
Equivalence replacement, modification or change, such as using different optical interference circuits and different wave length light source, these all fall within guarantor of the invention
It protects among range.
Claims (6)
1. a kind of space-time mixes matched simultaneous phase shifting dual wavelength interferometric method, which is characterized in that comprise the steps of:
Road simultaneous phase shifting dual wavelength interference system altogether is constructed, so that the laser of two different wave lengths is formed dual wavelength along identical path and mixes
Interference fringe picture is closed, generates phase-shift phase by the way that piezoceramic transducer is mobile, while simultaneously using single black-white CCD acquisition N width
Phase shift dual wavelength interference pattern；
Principal component analysis is carried out to the N width interference pattern, obtains the phase-shift phase under two wavelength:
Wherein,λ1With λ2For the road simultaneous phase shifting altogether
The wavelength and λ of two light sources of dual wavelength interference system1> λ2, a total of N width simultaneous phase shifting dual wavelength interference pattern of N expression,
WithThe n-th width figure is respectively indicated in λ1And λ2Under corresponding phase-shift phase；
Then the phase-shift phase under the two wavelength is corrected, comprising:
It is rightWithUnpacking operation is carried out respectively, is obtainedWith
IfHaveOtherwiseIfHaveOtherwise
Phase-shift phase after correction is substituted into least-squares iteration algorithm, calculates the wrapped phase under two wavelength；
The wrapped phase of described two wavelength is subtracted each other and unpacked, phase distribution to be measured under synthetic wavelength is obtained.
2. space-time according to claim 1 mixes matched simultaneous phase shifting dual wavelength interferometric method, it is characterised in that:
The N width simultaneous phase shifting dual wavelength interference pattern, in the time domain, it is desirable that two wavelength phase shift amounts are distributed approximately evenly in integer
In period, and there are two positive integer ns1And n2, make n2/n1≈λ1/λ2, n2/n1For fraction in lowest term, after the CCD acquisition N width figure,
The mobile distance of piezoceramic transducer is pn1λ1, wherein p is any positive integer, and piezoelectric ceramics moving step length is generally equal
, other N > 2n2p。
3. simultaneous phase shifting dual wavelength interferometric method according to claim 1, it is characterised in that: the same phase of N width
Dual wavelength interference pattern is moved, on airspace, meet has integer interference fringe under two wavelength in every width interference pattern, i.e., corresponding
In wavelength X1, there is n1Q interference fringe, q are any positive integers.
4. simultaneous phase shifting dual wavelength interferometric method according to claim 3, which is characterized in that phase shift double wave at the same time
The number of interference fringes that can be differentiated in long interference pattern with correspond to wavelength X1Number of interference fringes be consistent, and airspace fringe number
It is required that can relax are as follows: number of interference fringes is no less than n in phase shift dual wavelength interference pattern at the same time1。
5. simultaneous phase shifting dual wavelength interferometric method according to claim 1, which is characterized in that the composite wave appearance
Position, after directly being subtracted each other by wrapped phase under two wavelength, carries out a Phase- un- wrapping and operates to obtain.
6. space-time according to claim 1 mixes matched simultaneous phase shifting dual wavelength interferometric method, it is characterised in that:
When object is not added the interference fringe of the simultaneous phase shifting dual wavelength interference pattern be vertical bar line, and with black-white CCD target surface transverse direction picture
Plain direction is perpendicular or parallel.
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| CN106643474B (en) * | 2016-09-23 | 2019-03-08 | 华南师范大学 | A kind of orthonormalization multistep phase-shifting phase measurement method |
| CN107764203B (en) * | 2017-10-27 | 2019-08-23 | 北京理工大学 | Dual wavelength phase shift interference non-spherical measuring method and device based on part penalty method |
| CN108775861B (en) * | 2018-07-09 | 2019-09-27 | 南京理工大学 | One kind being based on effective wavelength π/(2k) phase shift dual wavelength time domain phase demodulating method |
| CN111947592B (en) * | 2020-06-29 | 2021-10-08 | 中国科学院上海光学精密机械研究所 | Dynamic dual-wavelength phase-shifting interference measuring device and measuring method |
| CN113155058A (en) * | 2021-04-29 | 2021-07-23 | 范金坪 | Multi-wavelength dynamic phase measurement device and method based on spatial domain carrier frequency phase shift |
| CN116486120B (en) * | 2023-03-17 | 2024-01-19 | 广东工业大学 | Phase-shift interference pattern space pixel matching method |
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