CN102175332B - Method for recovering phases from interferograms containing phase-shift error - Google Patents
Method for recovering phases from interferograms containing phase-shift error Download PDFInfo
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Abstract
The invention provides a method for recovering phases from interferograms containing a phase-shift error. The method comprises the following steps of: testing a tested member by using a universal phase-shift interferometer; introducing a linear carrier frequency into the interferograms, and operating the interferometer for acquiring a group of phase-shift interferograms; rearranging data on the phase-shift interferograms to acquire a new image, and performing fast Fourier transform on the new image to acquire frequency spectrum of the new image; and filtering the frequency spectrum to obtain a phase spectrum and remove errors. After inverse Fourier transform is performed on the phase spectrum, an expanded recovery phase is obtained via arc tangent calculation and unwrapping operation; after the expanded phase is recovered to the original size, the tested phase can be obtained. The invention can remove the influences caused by the phase-shift error by using a few (for example four) phase-shift interferograms, and recover the exact tested phase so as to achieve the aim of improving the measurement precision of the phase-shift interferometer under non-ideal measurement environments and instrument conditions.
Description
Technical field
The invention belongs to interference of light metrology and measurement field, particularly a kind of method of from the interferogram that contains the phase shift error, recovering phase place.
Background technology
The movable phase interfere art is widely used now optical surface shape measuring technology, and this technology uses interferometer to gather one group of phase-shift interference, has specific phase differential between every width of cloth figure, can recover tested phase place according to interferogram.These phase differential are called amount of phase shift or phase shift step-length, through the phase shifter generation of interferometer, if amount of phase shift is inaccurate, bring error will for the phase place of recovering.And in practical application, the non-linear hardware factor that waits of the phase shifter of interferometer, or environmental factor such as vibration all can produce the amount of phase shift error, and this becomes the major reason of restriction movable phase interfere art measuring accuracy.
In order from the interferogram that contains the phase shift error, to recover phase place accurately; A lot of phase recuperation techniques have been developed; These technology mainly contain three types: one type is the algorithm of specific interferogram quantity of requirement and phase shift step-length; These algorithms have resistant function to the phase shift error of particular types, breathe out blue five-step approach like Harry, can alleviate the influence that the linear distortion of amount of phase shift causes.Second type is the vibration compensation algorithm, through the correction to the error phase recovered, can suppress to vibrate the influence that the amount of phase shift error that causes causes.The shortcoming of these two types of technology is, and is only effective to the phase shift error of particular form.Three types of technology as unknown quantity, is found the solution amount of phase shift with tested phase place simultaneously, therefore no longer requires amount of phase shift to be necessary for exact value.These class methods are all effective to multi-form phase shift error; But be usually directed to complex calculation; The interative computation in the process of iteration for example, the windowing Fourier transformation operation of windowing Fourier transform least square method, these computings length consuming time; And need select controlled variable modestly, otherwise possibly cause calculating failure.
Summary of the invention
The technical matters that the present invention solved is to provide a kind of method of from the interferogram that contains the phase shift error, recovering phase place.
The technical solution that realizes the object of the invention is: a kind of method of from the interferogram that contains the phase shift error, recovering phase place may further comprise the steps:
1, a kind of method of from the interferogram that contains the phase shift error, recovering phase place is characterized in that, may further comprise the steps:
Step 2, the data on the above-mentioned phase-shift interference that collects are arranged again obtain a width of cloth new images; Wherein a kind of arrangement mode again is: establish new images and be initially sky; First row of each width of cloth phase-shift interference are inserted the new images right side in order, and promptly first row with first width of cloth interferogram are listed as as first of new images, and first row of second width of cloth interferogram are as the secondary series of new images; By that analogy; After first row of whole phase-shift interferences were arranged completion, the secondary series with each width of cloth interferogram inserted the new images right side in order again, and all row on each width of cloth phase-shift interference are inserted into new images; Used formula is:
s′(Mx+m，y)＝s
m(x，y)
X, y are the horizontal ordinate in the image in the formula, and M is a phase-shift interference quantity, m=0, and 1,2 ..., M-1, s
mRepresent m width of cloth phase-shift interference, s ' expression new images;
Another kind arrangement mode again is: establish new images and be initially sky; First row of each width of cloth phase-shift interference is inserted the new images below in order; Promptly go as first of new images with first row of first width of cloth interferogram, first row of second width of cloth interferogram is as second row of new images, by that analogy; After first row of whole phase-shift interferences is arranged completion; Second row with each width of cloth interferogram inserts the new images below in order again, and all row on each width of cloth phase-shift interference are inserted into new images, and used formula is:
s′(x，My+m)＝s
m(x，y)；
Step 3, above-mentioned new images is carried out Fast Fourier Transform (FFT) obtain its frequency spectrum, afterwards frequency spectrum is carried out filtering and obtain phase spectrum side by side except error, the formula that frequency spectrum is carried out filtering is:
S
+1(f
x，f
y)＝S(f
x，f
y)·g(f
x，f
y)
Wherein S is a frequency spectrum, S
+ 1Be phase spectrum, f
x, f
yBe the frequency domain coordinate, the spectral window function does
f
0=1/M, f
cBe carrier frequency, σ is the parameter of control filter window size;
Step 4, from phase spectrum, recover the phase place of expansion, promptly phase spectrum is carried out inversefouriertransform after, conciliate the recovery phase place that the parcel computing is expanded through arctangent computation, the used formula of phase place that from phase spectrum, recovers expansion is:
In the formula
Be the recovery phase place of expansion, x ' is the horizontal ordinate after expanding, FT
-1Expression inversefouriertransform, Re{} and Im{} are respectively to be got real part and gets the imaginary-part operation symbol, and unwrap{} representes to separate the parcel computing;
Step 5, the recovery phase place
that will expand return to original size; Thereby obtain tested phase place; In the time of will expanding phase place and return to original size; Need confirm mode of operation according to the situation of step 2; When the mode of arranging view data in the step 2 again is when being undertaken by row, handle according to first kind of situation, when the mode of arranging view data in the step 2 again is when being undertaken by row; Handle according to second kind of situation, two kinds of situation are respectively:
First kind of situation: in the recovery phase place
of expansion; Since first row; Every interval M row; Promptly extract row; The row of all extractions are made up in order, promptly obtain with identical recovery phase place
formula of original phase size be:
Second kind of situation: in the recovery phase place
of expansion; Since first row; Every interval M is capable; Promptly extract delegation; The row of all extractions is made up in order, promptly obtain with identical recovery phase place
formula of original phase size be:
Int [] expression rounds operational character in the formula, and y ' is the ordinate after expanding.
The present invention compared with prior art, its remarkable advantage is: need not suppose that 1) the phase shift error satisfies particular form, therefore all effective to various types of phase shift errors; 2) phase-shift interference of use lesser amt, for example four width of cloth can be realized, can reduce the interferogram acquisition time; 3) since only use fixed number of times Fast Fourier Transform (FFT), matrix add multiplying and a small amount of sort operation, so computing velocity is fast; 4) most parameters can confirm automatically that remaining can be provided by experience in this method, need not to adjust repeatedly according to different objects, has very high automaticity.
Below in conjunction with accompanying drawing the present invention is described in further detail.
Description of drawings
The synoptic diagram of Fig. 1 for one group of movable phase interfere diagram data is arranged again, wherein figure (a) is for arranging operation chart, and figure (b) is the operating result to one group of emulating image.
Fig. 2 uses filtering to extract the synoptic diagram of phase spectrum at frequency domain.
The four step phase-shift interferences that Fig. 3 uses for embodiment.
Fig. 4 arranges the new images that obtains among the embodiment to phase-shift interference again.
Fig. 5 will be for expanding the face shape figure after phase place returns to original size among the embodiment.
Embodiment
In conjunction with Fig. 1, Fig. 2, a kind of method of from the interferogram that contains the phase shift error, recovering phase place of the present invention may further comprise the steps:
Step 2, the data on the above-mentioned phase-shift interference that collects are arranged again obtain a width of cloth new images; The mode that data on the phase-shift interference are arranged again is: establish new images and be initially sky; First row of each width of cloth phase-shift interference are inserted the new images right side in order; Promptly first row with first width of cloth interferogram are listed as as first of new images; The secondary series that first of second width of cloth interferogram is listed as as new images, by that analogy, after first row of whole phase-shift interferences are arranged completion; Secondary series with each width of cloth interferogram inserts the new images right side in order again, and all row on each width of cloth phase-shift interference are inserted into new images; Fig. 1 has shown the data of four width of cloth phase-shift interferences has been arranged the operation that obtains new images again that used formula is:
s′(Mx+m，y)＝s
m(x，y)(1)
X, y are the horizontal ordinate in the image in the formula, and M is a phase-shift interference quantity, m=0, and 1,2 ..., M-1, s
mRepresent m width of cloth phase-shift interference, s ' expression new images.
Data on the phase-shift interference are arranged again also have other a kind of mode:
If new images is initially sky,, promptly go as first of new images with first row of first width of cloth interferogram with the first capable new images below of inserting in order of each width of cloth phase-shift interference; First row of second width of cloth interferogram is as second row of new images; By that analogy, after first row of whole phase-shift interferences was arranged completion, second row with each width of cloth interferogram inserted the new images below in order again; All row on each width of cloth phase-shift interference are inserted into new images, and used formula is:
s′(x，My+m)＝s
m(x，y)(2)
Step 3, above-mentioned new images is carried out Fast Fourier Transform (FFT) obtain its frequency spectrum, afterwards frequency spectrum is carried out filtering and obtain phase spectrum side by side except error; Phase spectrum and error spectrum is separated from each other because of the linear carrier frequency of step 1 introducing in frequency spectrum, and is as shown in Figure 2, therefore can use spectral window to extract phase spectrum S
+ 1, get rid of the error spectrum, the formula that frequency spectrum is carried out filtering is:
S
+1(f
x，f
y)＝S(f
x，f
y)·g(f
x，f
y)(3)
Wherein S is a frequency spectrum, S
+ 1Be phase spectrum, f
x, f
yBe the frequency domain coordinate, the spectral window function does
f
0=1/M, f
cBe carrier frequency, σ is for the parameter of control filter window size, at frequency spectrum coordinate (f
0, 0) and the peaked position of search in the neighborhood located, this position is (f
0+ f
c, 0), thus can confirm f
cThe parameter σ of control filter window size can rule of thumb confirm, for example for the phase-shift interference of original size 256 * 256, and desirable 16/256～32/256 (unit is a normalized frequency) of σ.
Step 4, from phase spectrum, recover the phase place of expansion, promptly phase spectrum is carried out inversefouriertransform after, conciliate the recovery phase place that the parcel computing is expanded through arctangent computation; The used formula of phase place that from phase spectrum, recovers expansion is:
In the formula
Be the recovery phase place of expansion, x ' is the horizontal ordinate after expanding, FT
1Expression inversefouriertransform, Re{} and Im{} are respectively to be got real part and gets the imaginary-part operation symbol, and unwrap{} representes to separate the parcel computing.Can select as required
disappeared or the out of focus computing that disappears.
Step 5, will expand phase place and return to original size, thereby obtain tested phase place.
In the time of will expanding phase place and return to original size; Need confirm mode of operation according to the situation of step 2; When the mode of arranging view data in the step 2 again is when being undertaken by row, handle according to first kind of situation, when the mode of arranging view data in the step 2 again is when being undertaken by row; Handle according to second kind of situation, two kinds of situation are respectively:
First kind of situation: in expansion phase place
; Since first row; Every interval M row; Promptly extract row; The row of all extractions are made up in order, promptly obtain with identical recovery phase place
formula of original phase size be:
Second kind of situation: in expansion phase place
; Since first row; Every interval M is capable; Promptly extract delegation; The row of all extractions is made up in order, promptly obtain with identical recovery phase place
formula of original phase size be:
Int [] expression rounds operational character in the formula, and y ' is the ordinate after expanding.
Below in conjunction with embodiment the present invention is described in further detail:
Utilize the level crossing of a bore 100mm of Zygo GPI digital phase shift interferometer measurement, use algorithm of the present invention to recover tested phase place.
Step 1: level crossing is placed the interferometer optical system for testing, and the adjustment reference mirror tilts to introduce linear carrier frequency, and the operative interventions appearance is gathered four step phase-shift interferences again, and is as shown in Figure 3;
Step 2: according to Fig. 1 is that mode shown in the formula (1) is arranged again the data of 4 width of cloth phase-shift interferences and obtained 1 width of cloth new images, as shown in Figure 4;
Step 3: new images is carried out Fourier transform obtain its frequency spectrum, the method according to preamble can be confirmed the filter parameter f in the formula (4)
0=0.25, f
c=0.0107, σ=0.0195 (unit all is normalized spatial frequency), thus can carry out frequency domain filtering calculating according to formula (3) and formula (4);
Step 4: the result to a last step carries out inversefouriertransform, the computing of arctangent cp cp operation reconciliation parcel according to formula (5), to unpacking the phase place cancellation, obtains result shown in the left figure of Fig. 5;
Step 5: will expand phase place and return to original size, shown in the right figure of Fig. 5.
Claims (1)
1. a method of from the interferogram that contains the phase shift error, recovering phase place is characterized in that, may further comprise the steps:
Step 1, the general phase-shifting interferometer test measured piece of use; In interferogram, introduce linear carrier frequency through the reference mirror of adjustment interferometer or the tilt quantity of test block; When 10 or more quasi-parallel vertical bar line to interferogram, occurring; The operative interventions appearance collects one group of phase-shift interference, and this group phase-shift interference comprises 2 π/δ width of cloth, and wherein δ is an interferometer phase shift step-length;
Step 2, the data on the above-mentioned phase-shift interference that collects are arranged again obtain a width of cloth new images; Wherein a kind of arrangement mode again is: establish new images and be initially sky; First row of each width of cloth phase-shift interference are inserted the new images right side in order, and promptly first row with first width of cloth interferogram are listed as as first of new images, and first row of second width of cloth interferogram are as the secondary series of new images; By that analogy; After first row of whole phase-shift interferences were arranged completion, the secondary series with each width of cloth interferogram inserted the new images right side in order again, and all row on each width of cloth phase-shift interference are inserted into new images; Used formula is:
s′(Mx+m，y)＝s
m(x，y)
X, y are the horizontal ordinate in the image in the formula, and M is a phase-shift interference quantity, m=0, and 1,2 ..., M-1, s
mRepresent m width of cloth phase-shift interference, s ' expression new images;
Another kind arrangement mode again is: establish new images and be initially sky; First row of each width of cloth phase-shift interference is inserted the new images below in order; Promptly go as first of new images with first row of first width of cloth interferogram, first row of second width of cloth interferogram is as second row of new images, by that analogy; After first row of whole phase-shift interferences is arranged completion; Second row with each width of cloth interferogram inserts the new images below in order again, and all row on each width of cloth phase-shift interference are inserted into new images, and used formula is:
s′(x，My+m)＝s
m(x，y)；
Step 3, above-mentioned new images is carried out Fast Fourier Transform (FFT) obtain its frequency spectrum, afterwards frequency spectrum is carried out filtering and obtain phase spectrum side by side except error, the formula that frequency spectrum is carried out filtering is:
S
+1(f
x，f
y)＝S(f
x，f
y).g(f
x，f
y)
Wherein S is a frequency spectrum, S
+ 1Be phase spectrum, f
x, f
yBe the frequency domain coordinate, the spectral window function does
f
0=1/M, f
cBe carrier frequency, σ is the parameter of control filter window size;
Step 4, from phase spectrum, recover the phase place of expansion, promptly phase spectrum is carried out inversefouriertransform after, conciliate the recovery phase place that the parcel computing is expanded through arctangent computation, the used formula of phase place that from phase spectrum, recovers expansion is:
In the formula
Be the recovery phase place of expansion, x ' is the horizontal ordinate after expanding, FT
-1Expression inversefouriertransform, Re{} and Im{} are respectively to be got real part and gets the imaginary-part operation symbol, and unwrap{} representes to separate the parcel computing;
Step 5, the recovery phase place
that will expand return to original size; Thereby obtain tested phase place; When the recovery phase place of expanding is returned to original size; Need confirm mode of operation according to the situation of step 2; When the mode of arranging view data in the step 2 again is when being undertaken by row, handle according to first kind of situation, when the mode of arranging view data in the step 2 again is when being undertaken by row; Handle according to second kind of situation, two kinds of situation are respectively:
First kind of situation: in the recovery phase place
of expansion; Since first row; Every interval M row; Promptly extract row; The row of all extractions are made up in order, promptly obtain with identical recovery phase place
formula of original phase size be:
Second kind of situation: in the recovery phase place
of expansion; Since first row; Every interval M is capable; Promptly extract delegation; The row of all extractions is made up in order, promptly obtain with identical recovery phase place
formula of original phase size be:
Int [] expression rounds operational character in the formula, and y ' is the ordinate after expanding.
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| CN102507020B (en) * | 2011-11-01 | 2013-05-08 | 南京理工大学 | Microlens array-based synchronized phase-shifting interference test method and test device |
| CN103604508B (en) * | 2013-12-02 | 2016-03-02 | 青岛大学 | A kind of self-adaptation eliminates the wavefront reconstruction method of droop error |
| CN103630336B (en) * | 2013-12-02 | 2016-04-20 | 南京理工大学 | The dynamic interferometry method of array is postponed based on random phase retardation |
| CN104330027B (en) * | 2014-11-18 | 2017-04-12 | 哈尔滨工业大学 | Phase extraction method in phase-shifting interferometry based on error complementary correction |
| CN106482633B (en) * | 2015-08-24 | 2019-01-18 | 南京理工大学 | It is a kind of based on π/the multiple-beam interference phase extraction methods of 4 phase shifts |
| CN106643474B (en) * | 2016-09-23 | 2019-03-08 | 华南师范大学 | A kind of orthonormalization multistep phase-shifting phase measurement method |
| CN106441082B (en) * | 2016-10-08 | 2019-03-08 | 深圳扑浪创新科技有限公司 | A kind of phase recovery method and device |
| CN106840418B (en) * | 2017-01-22 | 2019-04-16 | 中国工程物理研究院机械制造工艺研究所 | A kind of anti-vibration method of phase-shifting interferometer |
| CN109632112B (en) * | 2018-12-25 | 2020-11-27 | 南京理工大学 | Spatial position registration method of synchronous phase-shifting interferogram of dynamic interferometer |
| CN111121661B (en) * | 2019-12-17 | 2021-09-17 | 南京理工大学 | Narrow-band non-monochromatic light n +1 amplitude phase shift test algorithm for smooth surface topography measurement |
| CN112066909B (en) * | 2020-08-24 | 2022-04-08 | 南京理工大学 | Anti-vibration interference measurement method based on inclined plane high-precision extraction |
| CN112097677B (en) * | 2020-08-26 | 2022-03-18 | 南京理工大学 | Rapid high-precision phase restoration method for anti-vibration interferometry |
| CN112378348B (en) * | 2020-10-28 | 2021-10-08 | 华中科技大学 | Iterative phase correction method for low-quality fringe image |
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| CN1975321A (en) * | 2006-12-19 | 2007-06-06 | 中国科学院上海光学精密机械研究所 | Phase-shift interference image information processing system and processing method thereof |
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| CN101862180A (en) * | 2009-04-16 | 2010-10-20 | 南京理工大学 | Near infrared spectrum (NIR) dual field interference imaging device |
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