CN116295874A - Checkerboard grating diffraction calculation error elimination method in transverse shearing interferometer - Google Patents
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Abstract
The invention discloses a method for eliminating diffraction calculation errors of checkerboard gratings in a transverse shearing interferometer, wherein an optical system of the transverse shearing interferometer comprises the following steps: the optical system to be measured is fixedly arranged on an optical platform to be measured of a transverse shearing interferometer, the optical illumination system emits incoherent light, and the light sequentially passes through the object plane grating, the optical system to be measured and the image plane grating and is received by the optical detection element; uniformly shifting the phase-shifting object plane grating or the image plane grating to obtain two shearing interference patterns in the vertical direction; and (3) separating and solving the shearing phases of the diffracted light of the 0 th order and the +1 th order or the 0 th order and the-1 th order in the two vertical directions by using a least square method, and reconstructing the wavefront. According to the method, the shearing phase is accurately solved by considering that each diffraction order has different light intensity coefficients, so that errors brought by the checkerboard grating in the full-optical-path diffraction calculation process are eliminated, and the wavefront reconstruction precision is improved.
Description
Technical Field
The invention relates to the technical field of optical measurement, in particular to a method for eliminating diffraction calculation errors of a checkerboard grating in a transverse shearing interferometer.
Background
The transverse shearing interferometer is a typical interferometer structure, uses the grating as a light-splitting element, and has the advantages of simple structure, quasi-common light path, no need of additional construction of ideal reference wave and the like. When the transverse shearing interferometer is used for optical measurement, only the object plane grating or the image plane grating is uniformly phase-shifted to obtain a series of shearing interference patterns in the x and y directions, and the differential phase is obtained by means of a least square method and the like, so that the wave surface can be reconstructed.
In the existing algorithm, the problem of low wave surface reconstruction precision caused by inaccurate differential phase calculation still exists. There are many higher order diffracted lights in the shearing interference field due to the diffraction effect of the image plane grating.
Patent CN104111120B proposes a brand new ten-step phase shift method, which effectively suppresses diffraction of + -3 and + -5 orders, extracts + -1-order shearing phase, but cannot accurately solve the difference result between +1 or-1 and 0-order diffracted light. For other prior art, the phases of the corresponding diffraction orders can be separated by fourier transform methods, but a filter needs to be added in the system.
The patent CN112229604A carries out integral solution on the shearing phases of the 0 level and the-1 level and the 0 level and the +1 level, and obtains the shearing phases of the-1 level and the +1 level diffraction light under the double shearing rate. However, the method does not consider that each diffraction order has different light intensity coefficients, and cannot simply consider two kinds of interference light as a whole, especially under the condition of large numerical aperture, the influence of the light intensity coefficients on the intensity of the interference field is not negligible.
In fact, the intensity coefficients of different pixels are different for the detection region, and if the influence on the solution of the shearing phase is ignored, an error is introduced in the final wavefront solution. This effect is particularly pronounced when the numerical aperture of the optical system is large.
Based on the above discussion, for the checkerboard grating transverse shearing interferometer, no algorithm which has simple algorithm logic, does not need to add an optical filter element and can accurately solve the differential phase exists at present.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a checkerboard grating diffraction calculation error elimination method in a transverse shearing interferometer, which is used for measuring wave aberration of an optical system.
The specific technical scheme of the invention is as follows:
a checkerboard grating diffraction calculation error elimination method in a transverse shearing interferometer comprises the following steps:
step one: the optical system to be measured is fixedly arranged on an optical platform to be measured of a transverse shearing interferometer, the optical illumination system emits incoherent light, and the light sequentially passes through the object plane grating, the optical system to be measured and the image plane grating and is received by the optical detection element; the object plane grating is formed by two groups of one-dimensional grating lines with mutually perpendicular directions; the optical axis direction is a z axis, and according to the right rule, two directions perpendicular to the z axis are an x axis and a y axis respectively; the image plane grating is a checkerboard grating, and two diagonal lines of the checkerboard grating are respectively perpendicular to the directions of the x axis and the y axis; the ratio of the periods of the image plane grating to the object plane grating is the same as the imaging magnification of the optical system to be tested, and the duty ratio of the image plane grating to the object plane grating is 50%;
step two: moving the object plane grating to enable light to pass through a one-dimensional grating line perpendicular to the x-axis direction, and uniformly shifting the object plane grating or the image plane grating to obtain a shearing interference pattern in the x-axis direction; the shearing phase expression in the x direction obtained by the least square method is as follows:
in delta 1 、δ 2 Parameters obtained for least square method, C -1，0 Is the light intensity coefficient when the x-direction-1 st order interferes with the 0 th order diffraction light, C 1，0 The light intensity coefficient is the light intensity coefficient when the x-direction +1 level interferes with the 0 level diffraction light; phi (phi) -1,0 Is x squareShear phase of diffracted light to-1 and 0 orders, phi 1,0 Shear phase of the diffracted light of x-direction +1 and 0 orders;
for the calculated phi -1,0 Or phi 1,0 Phase unwrapping is carried out to obtain a shearing phase in the x direction;
step three: moving the object plane grating to enable light to pass through a one-dimensional grating line perpendicular to the y-axis direction, and uniformly shifting the object plane grating or the image plane grating to obtain a shearing interference pattern in the y-axis direction; the shearing phase expression in the y direction obtained by the least square method is as follows:
wherein C is -1，0 ' is the light intensity coefficient when the y-direction-1 st order interferes with the 0 th order diffraction light, C 1，0 ' is the light intensity coefficient when the y direction +1 level interferes with the 0 level diffraction light; phi (phi) -1,0 ' shear phase of diffracted light of y-direction-1 st order and 0 th order, phi 1,0 ' is the shear phase of the y-direction +1st and 0 th diffraction light;
for the calculated phi -1,0 ' or phi 1,0 ' phase unwrapping to obtain a shearing phase in the y direction;
step four: and reconstructing the wave fronts represented by the shearing phases in the x direction and the y direction to obtain reconstructed wave fronts with errors eliminated.
Further, the phase unwrapping method adopted in the second step and the third step adopts a branch cutting method.
In the fourth step, a differential Zernike method is used to reconstruct the wavefront represented by the shear phases in the x-direction and the y-direction.
Further, in the second and third steps, the object plane grating or the image plane grating is uniformly phase-shifted, and each phase shift amount is 2pi (i-1)/Q, where Q is the phase shift frequency, i=1, 2.
Further, the object plane grating is two groups of one-dimensional Ronchi grating lines with mutually perpendicular directions.
The beneficial effects of the invention are as follows:
according to the invention, under the condition that the existing structure of the transverse shearing interferometer is not changed, the influence caused by the high-order diffracted light is eliminated, meanwhile, the shearing phase is accurately solved by considering that each diffraction order has different light intensity coefficients, the error caused by the checkerboard grating in the full-optical-path diffraction calculation process is eliminated, and the wavefront reconstruction precision is improved.
Drawings
FIG. 1 is a schematic diagram of the optical system of a transverse shearing interferometer of the present invention.
Fig. 2 is a schematic view of an object plane grating of the present invention.
Fig. 3 is a schematic view of an image plane grating of the present invention.
Fig. 4 is a schematic view of the numerical aperture of the present invention.
FIG. 5 is a schematic view of the exit pupil plane of the optical system under test of the present invention.
FIG. 6 is a flow chart of a method of eliminating checkerboard grating diffraction calculation errors in accordance with the present invention.
Fig. 7 is a diagram of a comparison of an original wavefront and a reconstructed wavefront in an embodiment of the present invention, where (a) is an original wavefront schematic and (b) is a reconstructed wavefront schematic.
In the figure, an optical illumination system 1, an object plane grating 2, an optical system to be measured 3, an image plane grating 4, an optical detection element 5, a computer processing system 6 and an exit pupil 7 of the optical system to be measured.
Detailed Description
The objects and effects of the present invention will become more apparent from the following detailed description of the preferred embodiments and the accompanying drawings, in which the present invention is further described in detail. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The optical system of the transverse shearing interferometer used in the invention is shown in fig. 1, and the optical system is sequentially provided with an optical illumination system 1, an object plane grating 2, an optical system to be measured 3, an image plane grating 4 and an optical detection element 5 from left to right along an optical axis. The optical illumination system 1 and the object plane grating 2 are positioned at the object space of the optical system 3 to be measured, and the object plane grating 2 is positioned at the object plane of the optical system 3 to be measured; the image plane grating 4 and the optical detection element 5 are located at the image side of the optical system 3 to be detected, and the image plane grating 4 is located at the image plane of the optical system 3 to be detected. The optical axis direction is set as the z axis, and two directions perpendicular to the z axis are respectively set as the x axis and the y axis according to the right rule.
The optical illumination system 1 is arranged to emit incoherent light having a wavelength lambda.
As shown in fig. 2, the object plane grating 2 is two groups of one-dimensional Ronchi grating lines perpendicular to the direction of the x axis, the left side is one-dimensional Ronchi grating lines perpendicular to the direction of the y axis, and the right side is one-dimensional Ronchi grating lines perpendicular to the direction of the y axis; the periods of the two groups of one-dimensional Ronchi grating lines are P1, the duty ratio is 50%, and the two groups of one-dimensional Ronchi grating lines are used for carrying out spatial coherence modulation on incoherent light emitted by the optical illumination system 1.
As shown in fig. 3, the image plane grating 4 is a checkerboard grating, two diagonal lines of which are perpendicular to the x-axis and y-axis directions respectively, the period is P2, the duty ratio is 50%, and the two diagonal lines are used for generating diffraction wave fronts of different orders.
The imaging magnification of the optical system under test 3 is M, and m=p2/P1. The ratio of the period of the image plane grating 4 to the period of the object plane grating 2 is the same as the imaging magnification of the optical system 3 to be tested, namely P2: p1=m.
The optical detection element 5 is a CCD or CMOS camera, etc. for receiving optical imaging. The optical detection element 5 is connected with the computer processing system 6, a circular interference field area with the normalized radius of l is detected by taking the intersection point of the optical axis and the plane of the optical detection element 5 as the center of a circle, the light intensity data of the circular interference field area is transmitted to the computer processing system 6, and the shearing phase is calculated and the wavefront is reconstructed in the computer processing system 6.
As shown in fig. 4 and 5, the image space aperture angle of the optical system 3 to be measured is U, and when the transverse shearing interferometer system is in air, the image space numerical aperture s=sinu, and the shearing rate is normalized
As shown in fig. 6, based on the above optical system of the transverse shearing interferometer, the present invention is implemented by the following specific steps:
step one: and shifting the phase of the grating along the x-axis direction to obtain the shearing phase of the x-direction.
The method is realized by the following substeps:
(1.1) moving the object plane grating 2 along the y axis, and enabling the light path to pass through a one-dimensional Ronchi grating line perpendicular to the x axis direction; the object plane grating 2 or the image plane grating 4 is evenly phase-shifted along the x-axis direction, the phase shift times Q are determined according to the accuracy of the phase shifter, Q can be 4, 8, 16, 32, 64 and the like, and each phase shift amount is 2pi (i-1)/Q, i=1, 2, and Q; a series of x-direction shearing interferograms are obtained, and the light intensity data of the shearing interferograms in the circular interference field area are transmitted to a computer processing system 6 for calculation by an optical detection element 5.
(1.2) determining that the maximum diffraction order in the x direction is mmax=ceil (2*l/S) according to the normalized radius l and the normalized shear rate S, and the ceil function is an upward rounding function.
In the computer processing system 6, the interference field expression in the x-direction is:
wherein I represents the intensity of the interference field, a coordinate system XOY is newly built on the exit pupil spherical surface of the optical system 3 to be measured, wherein the X-axis direction is the same as the X-axis direction, the Y-axis direction is the same as the Y-axis direction, (X, Y) is the exit pupil spherical surface coordinate of the optical system 3 to be measured, as shown in figure 5, the values are [ -l, l]. The checkerboard grating frequency spectrum value corresponding to the X-direction m diffraction order and the Y-direction n diffraction order is as follows
For the wavefront to be measured, alpha i Is the amount of phase shift.
The following matrix is obtained using the least squares method:
calculating according to formula (2) to obtain a parameter delta 1 、δ 2 Is the value of (1):
A*(δ 0 δ 1 δ 2 … … δ p δ q ) T ＝B (2)
if the maximum diffraction order mMax in the X direction is an odd number, p=3×mmax, q=3×mmax+1; if mMax is even, p=3×mmax-1, q=3×mmax.
Obtaining the shear phase phi in the x direction according to (3) -1,0 Or phi 1,0 Is the value of (1):
wherein C is -1，0 Is the light intensity coefficient when the x-direction-1 st order interferes with the 0 th order diffraction light, C 1，0 The light intensity coefficient is the light intensity coefficient when the x-direction +1 level interferes with the 0 level diffraction light; phi (phi) -1,0 Shear phase of diffracted light of x-direction-1 st order and 0 th order, phi 1,0 The shear phase of the diffracted light is in the x-direction +1 order and 0 order.
(1.3) phi for the step (1.2) -1,0 Or phi 1,0 Phase unwrapping is performed to obtain a shearing phase delta W in the x direction x . In this embodiment, a branch cutting method is used for phase unwrapping.
Step two: and shifting the phase of the grating along the y-axis direction to obtain the shearing phase of the y-axis direction.
The method is realized by the following substeps:
(2.1) moving the object plane grating 2 along the y axis, so that the light path passes through a one-dimensional Ronchi grating line perpendicular to the y axis direction; the object plane grating 2 or the image plane grating 4 is evenly phase-shifted along the y-axis direction, the phase shift frequency is Q, the phase shift quantity is 2 pi (i-1)/Q each time, i=1, 2,. Q, a series of shearing interference patterns in the y-axis direction are obtained, and the light intensity data of the shearing interference patterns in the circular interference field area are transmitted to the computer processing system 6 by the optical detection element 5 for calculation.
(2.2) determining that the maximum diffraction order in the y direction is nmax=ceil (2*l/S) according to the normalized radius l and the normalized shear rate S. In the computer processing system 6, the interference field expression in the y-direction is:
the following matrix is obtained using the least squares method:
calculating according to formula (5) to obtain a parameter delta 1 ′、δ 2 ' value:
A′*(δ 0 ′ δ 1 ′ δ 2 ′ … … δ p ′ δ q ′) T ＝B' (5)
if the maximum diffraction order nMax in the Y direction is an odd number, p=3×nmax, q=3×nmax+1; if nMax is even, p=3×nmax-1, q=3×nmax.
Obtaining the shear phase phi in the y direction according to (6) -1,0 ' or phi 1,0 ' value:
wherein C is -1，0 ' is the light intensity coefficient when the y-direction-1 st order interferes with the 0 th order diffraction light, C 1，0 ' is the light intensity coefficient when the y direction +1 level interferes with the 0 level diffraction light; phi (phi) -1,0 ' shear phase of diffracted light of y-direction-1 st order and 0 th order，φ 1,0 ' is the shear phase of the diffracted light of the y-direction +1 order and 0 order.
(2.3) phi for the step (2.2) -1,0 ' or phi 1,0 ' phase unwrapping to obtain a shearing phase DeltaW in the y direction y . In this embodiment, a branch cutting method is used for phase unwrapping.
Step three: differential Zernike method is used for delta W x 、ΔW y Reconstructing the represented wavefront to obtain a reconstructed wavefront, and comparing the original wavefront with the reconstructed wavefront to obtain a reconstruction error.
In this embodiment, an original wavefront is taken as a preset aberration plane of the optical system, a series of interferograms including original wavefront information in the x direction and the y direction are generated through simulation, and a differential phase is solved from the interferograms to obtain a reconstructed wavefront. As shown in fig. 7, in this embodiment, the reconstruction accuracy is 99.9956% by calculation, that is, the reconstruction error is 0.0044%, which proves that the error cancellation effect of the present invention is good.
According to the invention, under the condition of not changing the existing structure of the transverse shearing interferometer, the influence caused by the high-order diffracted light is eliminated, meanwhile, the diffraction calculation error of the checkerboard grating caused by different light intensity coefficients of each diffraction order is eliminated, and the wavefront reconstruction precision is improved.
It will be appreciated by persons skilled in the art that the foregoing description is a preferred embodiment of the invention, and is not intended to limit the invention, but rather to limit the invention to the specific embodiments described, and that modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for elements thereof, for the purposes of those skilled in the art. Modifications, equivalents, and alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (5)
1. The checkerboard grating diffraction calculation error elimination method in the transverse shearing interferometer is characterized by comprising the following steps:
step one: the optical system to be measured is fixedly arranged on an optical platform to be measured of a transverse shearing interferometer, the optical illumination system emits incoherent light, and the light sequentially passes through the object plane grating, the optical system to be measured and the image plane grating and is received by the optical detection element; the object plane grating is formed by two groups of one-dimensional grating lines with mutually perpendicular directions; the optical axis direction is a z axis, and according to the right rule, two directions perpendicular to the z axis are an x axis and a y axis respectively; the image plane grating is a checkerboard grating, and two diagonal lines of the checkerboard grating are respectively perpendicular to the directions of the x axis and the y axis; the ratio of the periods of the image plane grating to the object plane grating is the same as the imaging magnification of the optical system to be tested, and the duty ratio of the image plane grating to the object plane grating is 50%;
step two: moving the object plane grating to enable light to pass through a one-dimensional grating line perpendicular to the x-axis direction, and uniformly shifting the object plane grating or the image plane grating to obtain a shearing interference pattern in the x-axis direction; the shearing phase expression in the x direction obtained by the least square method is as follows:
in delta 1 、δ 2 Parameters obtained for least square method, C -1，0 Is the light intensity coefficient when the x-direction-1 st order interferes with the 0 th order diffraction light, C 1，0 The light intensity coefficient is the light intensity coefficient when the x-direction +1 level interferes with the 0 level diffraction light; phi (phi) -1,0 Shear phase of diffracted light of x-direction-1 st order and 0 th order, phi 1,0 Shear phase of the diffracted light of x-direction +1 and 0 orders;
for the calculated phi -1,0 Or phi 1,0 Phase unwrapping is carried out to obtain a shearing phase in the x direction;
step three: moving the object plane grating to enable light to pass through a one-dimensional grating line perpendicular to the y-axis direction, and uniformly shifting the object plane grating or the image plane grating to obtain a shearing interference pattern in the y-axis direction; the shearing phase expression in the y direction obtained by the least square method is as follows:
wherein C is -1，0 ' is the light intensity coefficient when the y-direction-1 st order interferes with the 0 th order diffraction light, C 1，0 ' is the light intensity coefficient when the y direction +1 level interferes with the 0 level diffraction light; phi (phi) -1,0 ' shear phase of diffracted light of y-direction-1 st order and 0 th order, phi 1,0 ' is the shear phase of the y-direction +1st and 0 th diffraction light;
for the calculated phi -1,0 ' or phi 1,0 ' phase unwrapping to obtain a shearing phase in the y direction;
step four: and reconstructing the wave fronts represented by the shearing phases in the x direction and the y direction to obtain reconstructed wave fronts with errors eliminated.
2. The method for eliminating diffraction calculation errors of checkerboard grating in a transverse shearing interferometer according to claim 1, wherein the phase unwrapping method adopted in the second and third steps adopts a branch-cut method.
3. The method for eliminating diffraction calculation errors of checkerboard grating in a transverse shearing interferometer according to claim 1, wherein in the fourth step, a differential Zernike method is adopted to reconstruct wave fronts represented by shearing phases in an x direction and a y direction.
4. The method for eliminating diffraction calculation errors of checkerboard grating in a transverse shearing interferometer according to claim 1, wherein in the second and third steps, the object plane grating or the image plane grating is uniformly phase-shifted by 2 pi (i-1)/Q, wherein Q is the number of phase shifts, i=1, 2.
5. The method for removing diffraction calculation errors of checkerboard grating in a transverse shearing interferometer according to claim 1, wherein the object plane grating is two sets of one-dimensional Ronchi grating lines with mutually perpendicular directions.
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