CN110081988A - A method of space carrier frequency phase shift algorithm is used for the demodulation of four wave lateral shear interferometer wavefront slopes - Google Patents
A method of space carrier frequency phase shift algorithm is used for the demodulation of four wave lateral shear interferometer wavefront slopes Download PDFInfo
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- 230000010363 phase shift Effects 0.000 title claims abstract description 19
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- 238000006073 displacement reaction Methods 0.000 claims description 3
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
- G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
- G01J9/0215—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods by shearing interferometric methods
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Abstract
The present invention relates to a kind of methods that space carrier frequency phase shift algorithm is used for the demodulation of four wave lateral shear interferometer wavefront slopes, belong to field of optical detection.Space carrier frequency phase shift algorithm is used for the demodulation of four wave lateral shear interferometer wavefront slopes by this method, finally to realize unified, high-precision dynamic wavefront measurement.Especially by the relationship between control screen periods and image sensor pixel size, to control the phase-shift phase between carrier fringe adjacent pixel, and the suitable phase shift algorithm of final choice realizes the demodulation of wavefront slope.Fast Fourier Transform (FFT) method (Fast Fourier Transform is utilized compared to traditional four wave lateral shear interferometers, FFT wavefront slope) is demodulated, this method calculating process is simple, high-precision unified dynamic wavefront measurement may be implemented in the interrupted spectra being related to there is no FFT method and edge effect.
Description
Technical field
The invention belongs to the manufacture of advanced optics and detection fields, and in particular to a kind of that space carrier frequency phase shift algorithm is used for four
The method of wave lateral shear interferometer wavefront slope demodulation.
Background technique
Interferometer be using the wavelength of light as a kind of high-precision of measurement unit, highly sensitive metrology and measurement instrument, it
It is widely used in optical measurement.Interference fringe is the track of the identical point of optical path difference in interferometer interference field, according to interference
Shape, movement, density degree of striped etc. can demodulate to obtain the optical path difference information of tested light.
Four wave lateral shear interferometers are a kind of grating types by propositions such as French scientist Jerome Primo in 2000
Lateral shear interferometer.Light is tested through optical grating diffraction, 90% or more diffraction light energy concentrates on four beam first-order diffraction light.This four
Beam first-order diffraction light is along respective diffraction angular direction onwards transmission, and finally mutual dislocation and coherent superposition on the viewing screen, form
Interference fringe.By handling interference fringe, demodulation obtains fringe phase, can acquire the wavefront slope of tested light, most
Optical path difference information is obtained using restoration algorithm afterwards.
Currently from there are mainly three types of the methods of interference fringe demodulation phase, respectively the Schlieren method, FFT (Fast Fourier
Transform) method and phase-shifting method, the wherein precision highest of phase-shifting method, but its interference for needing to acquire several different phase-shift phases
Figure, it is more sensitive to extraneous ambient vibration；The Schlieren method and FFT method only need a width interference pattern, influenced by ambient vibration it is smaller,
It can be used for dynamically measuring, but processing accuracy is lower.In consideration of it, nineteen ninety Shough et al. proposes space carrier frequency phase shift
(Spatial-carrier phase shifting SCPS) method, specific method are the angles by controlling two interfering beams
The carrier phase amount for obtaining neighbor pixel is equal to the interference pattern of pi/2, and assumes phase phase of several consecutive points on tested surface
Together, then adjacent several pixels can substitute the pixel obtained in time domain by phase shifter phase shift in space, so
Phase can be calculated by phase shift formula afterwards.Although space carrier frequency phase shift method only handles single width interference pattern, its processing result
The processing accuracy that phase-shifting method can be reached approximately, in combination with FFT method dynamic measurement and the high-precision advantage of phase-shifting method.
The method of four traditional wave lateral shear interferometer demodulated interferential fringe phases is FFT method, but due to side in FFT method
The influence of the factors such as edge effect, interrupted spectra and spectral resolution limitation, causes its algorithm operation quantity larger and processing result precision
It is affected.
Space carrier frequency phase shifting method is used for four wave lateral shear interferometers by the present invention, passes through control screen periods and image
Relationship between sensor pixel size controls the phase-shift phase between carrier fringe neighbor pixel, is realized using phase shift algorithm
Interference fringe phase, that is, wavefront slope high-precision is restored, final to realize the measurement of optical path difference Dynamic High-accuracy.
Summary of the invention
The purpose of the present invention is space carrier frequency phase shift method is used for four wave lateral shear interferometer interference fringe phases, i.e. quilt
The Dynamic High-accuracy measurement of optical path difference is realized in the demodulation for surveying light wave front slope.This method passes through control screen periods and figure first
As the relationship between sensor pixel size, so that the carrier phase amount between adjacent pixel is pi/2, phase shift algorithm is then utilized
Solution obtains the wavefront slope of four direction.
The technical solution adopted by the present invention is that: it is a kind of that space carrier frequency phase shift algorithm is used for four wave lateral shear interferometer waves
The method of front slope demodulation, comprising:
Step 1: four wave lateral shear interferometer systems of building, comprising:
Two-dimentional complex amplitude grating, for generating four beam first-order diffraction light, the two dimension complex amplitude grating is by amplitude grating and phase
Position grating be formed by stacking, the amplitude grating period be p × p, light hole having a size ofPhase grating is by 0 phase and π phase
It is alternately arranged, the period is 2p × 2p；
Imaging sensor, for acquiring interference fringe, Pixel Dimensions
Tested light is incident on two-dimentional complex amplitude grating, and through optical grating diffraction, most diffraction light energies concentrate on four beams one
Grade diffraction light, this four beams diffraction light form interference fringe, utilize image in position of image sensor mutual dislocation and coherent superposition
The interference fringe of sensor acquisition, i.e., the resilient optical path difference information for obtaining tested light；Change screen periods or selection is suitable
Imaging sensor so that the carrier phase amount of interference fringe neighbor pixel be pi/2；
Step 2: the light intensity expression of four wave lateral shear interferometers are as follows:
Wherein I (x, y) is interference fringe light intensity, and a (x, y) is interference fringe background light intensity, and b (x, y) is modulation degree, s x
The shearing displacement in direction or the direction y, k are wave number, and p is the amplitude grating period；
When assuming that when the corresponding background light intensity of 10 adjacent position points, modulation degree and identical tested light phase, solution point
The formula of wavefront slope is as follows at (m, n):
Wherein, I0=I (m, n), I1=I (m-1, n), I2=I (m+1, n), I3=I (m, n-1), I4=I (m, n+1), I5
=I (m-1, n+1), I6=I (m+1, n-1), I7=I (m-1, n-1), I8=I (m+1, n+1), I9=I (m-2, n-2)；
Wherein, W is tan before tested light wave-1For arctan function；
The wavefront slope of four direction is found out using formula (2)-(5), final restore obtains tested light optical path difference information.
The advantages of the present invention over the prior art are that:
(1) operation of the present invention is simple, and operand is low, can accelerate to restore speed, realize optical path difference transient measurement.
(2) marginal error of the present invention is small, and recovery accuracy is high, can almost realize unified measurement.
Detailed description of the invention
Fig. 1 is four wave lateral shear interferometer system schematics；
Fig. 2 is four wave lateral shear interferometer two dimension complex amplitude grating schematic diagrams；
Fig. 3 is the light intensity position that wavefront slope needs to use at solution point (m, n)；
Fig. 4 is tested wavefront distribution schematic diagram；
Fig. 5 is the wavefront slope in the direction x extracted using the present invention；
Fig. 6 is the wavefront slope in the direction y extracted using the present invention；
Fig. 7 is the wavefront slope in the direction x+y extracted using the present invention；
Fig. 8 is the wavefront slope in the direction x-y extracted using the present invention；
Fig. 9 is that the wavefront restored using the wavefront slope that the present invention extracts is distributed.
Specific embodiment
With reference to the accompanying drawing and specific embodiment further illustrates the present invention.
A kind of method that space carrier frequency phase shift algorithm is used for the demodulation of four wave lateral shear interferometer wavefront slopes of the present invention,
If Fig. 1 show four wave lateral shear interferometer system schematics, tested light is incident on two-dimentional complex amplitude grating, spreads out through grating
It penetrates, most diffraction light energies concentrate on four beam first-order diffraction light, this four beams diffraction light is mutually wrong in position of image sensor
Position and coherent superposition form interference fringe.The interference fringe acquired using imaging sensor, i.e., the resilient light for obtaining tested light
Path difference information.
Two-dimentional complex amplitude grating (as shown in Figure 2), for generating four beam first-order diffraction light.The grating is by amplitude grating and phase
Position grating be formed by stacking, the amplitude grating period be p × p, light hole having a size ofPhase grating is by 0 phase and π phase
It is alternately arranged, the period is 2p × 2p；
Imaging sensor, for acquiring interference fringe, Pixel Dimensions
The light intensity expression of four wave lateral shear interferometers are as follows:
Wherein I (x, y) is interference fringe light intensity, and a (x, y) is interference fringe background light intensity, and b (x, y) is modulation degree, s x
The shearing displacement in direction or the direction y, k are wave number, and p is the amplitude grating period.
When assuming that the corresponding background light intensity of 10 adjacent position points shown in Fig. 3, modulation degree and tested light phase are identical
When, the formula of wavefront slope is as follows at solution point (m, n):
As shown in figure 3, I0=I (m, n), I1=I (m-1, n), I2=I (m+1, n), I3=I (m, n-1), I4=I (m, n+
1), I5=I (m-1, n+1), I6=I (m+1, n-1), I7=I (m-1, n-1), I8=I (m+1, n+1), I9=I (m-2, n-2).
Wherein W is tan before tested light wave-1For arctan function.
Shown in the light intensity expression of four wave lateral shear interferometer interference fringes such as claim 2 Chinese style (1), wherein striped is carried on the back
Scape light intensity a (x, y), the wavefront slope of modulation degree b (x, y) and four direction It is unknown.Therefore, in order to solve wavefront slope, six equations are at least needed.
For simplicity, it enables,
Then light intensity expression becomes:
After imaging sensor acquires, the light intensity expression of discretization are as follows:
Wherein m, n are the pixel coordinate in transverse and longitudinal direction, due toThereforeLight
Strongly expressed formula is rewritten are as follows:
In order to acquire the wavefront slope at point (m, n), the light intensity using as shown in Figure 3 ten consecutive points is needed, and assume
Their corresponding background light intensity, modulation degree and phase are identical, that is, assume:
Similarly, it is assumed that a (x, y), b (x, y),Respectively in this ten consecutive points
It is worth identical.
As shown in figure 3, this corresponding light intensity expression of ten points is respectively as follows:
Therefore,
According to formula (6), then shown in the solution formula of wavefront slope such as formula (2)~(5).
When wavefront to be measured is defocus aberration shown in (such as Fig. 4), with the direction x acquired of the present invention, the direction y, the direction x+y and
Respectively as shown in figures 5-8, the wavefront restored is as shown in Figure 9 for the wavefront slope in the direction x-y.As can be seen that the present invention proposes
Method can accurately extract the wavefront slopes of four wave lateral shear interferometers, and finally realize that the high-precision of wavefront is restored.
Claims (1)
1. a kind of method that space carrier frequency phase shift algorithm is used for the demodulation of four wave lateral shear interferometer wavefront slopes, feature exist
In, comprising:
Step 1: four wave lateral shear interferometer systems of building, comprising:
Two-dimentional complex amplitude grating, for generating four beam first-order diffraction light, the two dimension complex amplitude grating is by amplitude grating and phase light
Grid are formed by stacking, the amplitude grating period be p × p, light hole having a size ofPhase grating is by 0 phase and π phase alternation
It arranges, the period is 2p × 2p；
Imaging sensor, for acquiring interference fringe, Pixel Dimensions
Tested light is incident on two-dimentional complex amplitude grating, and through optical grating diffraction, most diffraction light energies concentrate on four beam level-ones and spread out
Light is penetrated, this four beams diffraction light forms interference fringe, utilize image sensing in position of image sensor mutual dislocation and coherent superposition
The interference fringe of device acquisition, i.e., the resilient optical path difference information for obtaining tested light；Change screen periods or the suitable figure of selection
As sensor, so that the carrier phase amount of interference fringe neighbor pixel is pi/2；
Step 2: the light intensity expression of four wave lateral shear interferometers are as follows:
Wherein I (x, y) is interference fringe light intensity, and a (x, y) is interference fringe background light intensity, and b (x, y) is modulation degree, and s is the direction x
Or the shearing displacement in the direction y, k are wave number, p is the amplitude grating period；
When assuming that when the corresponding background light intensity of 10 adjacent position points, modulation degree and identical tested light phase, solution point (m, n)
The formula for locating wavefront slope is as follows:
Wherein, I0=I (m, n), I1=I (m-1, n), I2=I (m+1, n), I3=I (m, n-1), I4=I (m, n+1), I5=I
(m-1, n+1), I6=I (m+1, n-1), I7=I (m-1, n-1), I8=I (m+1, n+1), I9=I (m-2, n-2)；
Wherein, W is tan before tested light wave-1For arctan function；
The wavefront slope of four direction is found out using formula (2)-(5), final restore obtains tested light optical path difference information.
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Cited By (2)
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| CN111772574A (en) * | 2020-06-06 | 2020-10-16 | 宁波明星科技发展有限公司 | Method and device for eliminating defocusing during wavefront aberration measurement |
| CN114137713A (en) * | 2021-11-17 | 2022-03-04 | 华中科技大学 | Real-time quantitative phase imaging method and system for unmarked thick sample |
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