CN102175332A - 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, by the phase shifter generation of interferometer, if amount of phase shift is inaccurate, bring error will for the phase place of recovering.And in actual applications, 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 classes: a class 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 as Harry, can alleviate the influence that the linear distortion of amount of phase shift causes.Second class is the vibration compensation algorithm, by 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 this two classes 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 may cause calculating failure.
Summary of the invention
Technical matters solved by the invention is to provide a kind of method of recovering phase place from the interferogram that contains the phase shift error.
The technical solution that realizes the object of the invention is: a kind of method of recovering phase place from the interferogram that contains the phase shift error may further comprise the steps:
Step 2, the data on the above-mentioned phase-shift interference that collects are rearranged obtain a width of cloth new images;
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;
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 by arctangent computation;
Step 5, will expand phase place and return to original size, thereby obtain tested phase place.
The present invention compared with prior art, its remarkable advantage is: do not need 1) to suppose that 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 of parameter can determine 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 rearranged, 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 rearranges the new images that obtains among the embodiment to phase-shift interference.
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 recovering phase place from the interferogram that contains the phase shift error of the present invention may further comprise the steps:
Step 2, the data on the above-mentioned phase-shift interference that collects are rearranged obtain a width of cloth new images; The mode that data on the phase-shift interference are rearranged is: establish new images and be initially sky, first row of each amplitude shift interference figure are inserted the new images right side in turn, promptly first row with first width of cloth interferogram are listed as first of new images, first row of second width of cloth interferogram are as the secondary series of new images, by that analogy, after the first row arrangement of whole phase-shift interferences is finished, secondary series with each width of cloth interferogram inserts the new images right side in turn again, and all row on each amplitude shift interference figure are inserted into new images; Fig. 1 has shown that the data to four amplitude shift interference figure rearrange the operation that obtains new images, and used formula is:
In the formula
x,
yBe the horizontal ordinate in the image,
MBe phase-shift interference quantity,
m=0,1,2 ...,
M-1,
s m Expression the
mAmplitude shift interference figure,
s' expression new images.
Data on the phase-shift interference are rearranged another mode in addition:
If new images is initially sky, first row of each amplitude shift interference figure is inserted the new images below in turn, 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 the first row arrangement of whole phase-shift interferences was finished, second row with each width of cloth interferogram inserted the new images below in turn again, all row on each amplitude shift interference figure are inserted into new images, and used formula is:
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, 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:
Wherein
SBe frequency spectrum,
S + 1Be phase spectrum,
f x ,
f y Be the frequency domain coordinate, the spectral window function is
f 0=1/
M,
f c Be carrier frequency,
σBe the parameter of control filter window size, the frequency spectrum coordinate (
f 0, 0) the peaked position of search in the neighborhood located, this position be (
f 0+
f c , 0), thus can determine
f c The parameter of control filter window size
σCan rule of thumb determine, for example for the phase-shift interference of original size 256 * 256,
σDesirable 16/256 ~ 32/256(unit is a normalized frequency).
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 by arctangent computation; The used formula of phase place that recovers expansion from phase spectrum is:
(5)
In the formula
φ e Be the recovery phase place of expansion,
x' be the horizontal ordinate after the expansion,
FT -1Expression inversefouriertransform, Re{} and Im{} are respectively to be got real part and gets the imaginary-part operation symbol,
UnwrapThe parcel computing is separated in { } expression.It is right to select as required
φ e Disappear 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 determine mode of operation according to the situation of step 2, when the mode that rearranges view data in the step 2 is when being undertaken by row, handle according to first kind of situation, when the mode that rearranges view data in the step 2 is by row when being undertaken, handle according to second kind of situation, two kinds of situations are respectively:
First kind of situation: in the expansion phase place
φ e In, since first row, every interval
MRow promptly extract row, and the row of all extractions are made up in turn, promptly obtain the recovery phase place identical with the original phase size
φ, formula is:
(6)
Second kind of situation: in the expansion phase place
φ e In, since first row, every interval
MOK, promptly extract delegation, the row of all extractions is made up in turn, promptly obtain the recovery phase place identical with the original phase size
φ, formula is:
Int[in the formula] represent to round operational character, y ' is the ordinate after expanding.
The present invention is described in further detail below in conjunction with embodiment:
Utilize bore 100 of Zygo GPI digital phase shift interferometer measurement
MmLevel crossing, use algorithm of the present invention to recover tested phase place.
Step 1: level crossing is placed the interferometer optical system for testing, adjust reference mirror and tilt to introduce linear carrier frequency, the operative interventions instrument is gathered four step phase-shift interferences again, as shown in Figure 3;
Step 2: to be mode shown in the formula (1) to the data of 4 amplitude shift interference figure rearrange obtains 1 width of cloth new images according to Fig. 1, 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 determined the filter parameter in the formula (4)
f 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 previous 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 (6)
1. a method of recovering phase place from the interferogram that contains the phase shift error 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 by 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 instrument collects one group of phase-shift interference, this group phase-shift interference comprise the collection 2 π/
δThe width of cloth, wherein
δBe interferometer phase shift step-length;
Step 2, the data on the above-mentioned phase-shift interference that collects are rearranged obtain a width of cloth new images;
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;
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 by arctangent computation;
Step 5, will expand phase place and return to original size, thereby obtain tested phase place.
2. the method for from the interferogram that contains the phase shift error, recovering phase place according to claim 1, it is characterized in that, the mode that data on the step 2 pair phase-shift interference rearrange is: establish new images and be initially sky, first row of each amplitude shift interference figure are inserted the new images right side in turn, promptly first row with first width of cloth interferogram are listed as first of new images, first row of second width of cloth interferogram are as the secondary series of new images, by that analogy, after the first row arrangement of whole phase-shift interferences is finished, secondary series with each width of cloth interferogram inserts the new images right side in turn again, and all row on each amplitude shift interference figure are inserted into new images; Used formula is:
In the formula
x,
yBe the horizontal ordinate in the image,
MBe phase-shift interference quantity,
m=0,1,2 ...,
M-1,
s m Expression the
mAmplitude shift interference figure,
s' expression new images.
3. the method for from the interferogram that contains the phase shift error, recovering phase place according to claim 1, it is characterized in that, the another kind of mode that data on the step 2 pair phase-shift interference rearrange is: establish new images and be initially sky, first row of each amplitude shift interference figure is inserted the new images below in turn, 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 the first row arrangement of whole phase-shift interferences is finished, second row with each width of cloth interferogram inserts the new images below in turn again, all row on each amplitude shift interference figure are inserted into new images, and used formula is:
。
4. the method for recovering phase place from the interferogram that contains the phase shift error according to claim 1 is characterized in that the formula that step 3 pair frequency spectrum carries out filtering is:
Wherein
SBe frequency spectrum,
S + 1Be phase spectrum,
f x ,
f y Be the frequency domain coordinate, the spectral window function is
f 0=1/
M,
f c Be carrier frequency,
σParameter for control filter window size.
5. the method for recovering phase place from the interferogram that contains the phase shift error according to claim 1 is characterized in that, step 4 is recovered expansion from phase spectrum the used formula of phase place is:
In the formula
φ e Be the recovery phase place of expansion,
x' be the horizontal ordinate after the expansion,
FT -1Expression inversefouriertransform, Re{} and Im{} are respectively to be got real part and gets the imaginary-part operation symbol,
UnwrapThe parcel computing is separated in { } expression.
6. the method for from the interferogram that contains the phase shift error, recovering phase place according to claim 1, it is characterized in that, when step 5 will be expanded phase place and return to original size, need determine mode of operation according to the situation of step 2, when the mode that rearranges view data in the step 2 is when being undertaken by row, handle according to first kind of situation, when the mode that rearranges view data in the step 2 is when being undertaken by row, handle according to second kind of situation, two kinds of situations are respectively:
First kind of situation: in the expansion phase place
φ e In, since first row, every interval
MRow promptly extract row, and the row of all extractions are made up in turn, promptly obtain the recovery phase place identical with the original phase size
φ, formula is:
Second kind of situation: in the expansion phase place
φ e In, since first row, every interval
MOK, promptly extract delegation, the row of all extractions is made up in turn, promptly obtain the recovery phase place identical with the original phase size
φ, formula is:
Int[in the formula] represent to round operational character, y ' is the ordinate after expanding.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102507020A (en) * | 2011-11-01 | 2012-06-20 | 南京理工大学 | Microlens array-based synchronized phase-shifting interference test method and test device |
| CN103604508A (en) * | 2013-12-02 | 2014-02-26 | 青岛大学 | Wavefront reconstruction method capable of eliminating tilt errors self-adaptively |
| CN103630336A (en) * | 2013-12-02 | 2014-03-12 | 南京理工大学 | Dynamic interference measuring method based on random fast axis azimuth delay array |
| CN104330027A (en) * | 2014-11-18 | 2015-02-04 | 哈尔滨工业大学 | Phase extraction method in phase-shifting interferometry based on error complementary correction |
| CN106441082A (en) * | 2016-10-08 | 2017-02-22 | 南方科技大学 | Phase recovery method and device |
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| CN106643474A (en) * | 2016-09-23 | 2017-05-10 | 华南师范大学 | Normalizaion and orthogonalization method for multistep phase shift and phase position measurement |
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20060120621A1 (en) * | 2000-01-06 | 2006-06-08 | Canon Kabushiki Kaisha | Demodulation and phase estimation of two-dimensional patterns |
| CN1975321A (en) * | 2006-12-19 | 2007-06-06 | 中国科学院上海光学精密机械研究所 | Information processing system and processing method of phase-shifting interference image |
| CN101862180A (en) * | 2009-04-16 | 2010-10-20 | 南京理工大学 | Near infrared spectrum (NIR) dual field interference imaging device |
-
2011
- 2011-01-21 CN CN2011100237403A patent/CN102175332B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20060120621A1 (en) * | 2000-01-06 | 2006-06-08 | Canon Kabushiki Kaisha | Demodulation and phase estimation of two-dimensional patterns |
| CN1975321A (en) * | 2006-12-19 | 2007-06-06 | 中国科学院上海光学精密机械研究所 | Information processing system and processing method of phase-shifting interference image |
| CN101862180A (en) * | 2009-04-16 | 2010-10-20 | 南京理工大学 | Near infrared spectrum (NIR) dual field interference imaging device |
Non-Patent Citations (2)
| Title |
|---|
| 《光子学报》 19991031 朱煜 干涉仪移相器相位移pi/2标定方法的研究 952-954 全文 第28卷, 第10期 2 * |
| 《光电工程》 20040930 吴栋 移相干涉仪环境微扰的外差检测及信号处理 53-56 1-6 第31卷, 第9期 2 * |
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| 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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