CN117629583A - Double-grating Langerhans shearing interference high-precision phase extraction method - Google Patents
Double-grating Langerhans shearing interference high-precision phase extraction method Download PDFInfo
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Abstract
A double-grating Langerhans shearing interference high-precision phase extraction method is based on a double-grating Langerhans shearing interferometer. The interferometer structure comprises: the system comprises a light source, an illumination system, an object plane diffraction grating plate, an image plane diffraction grating plate, a two-dimensional photoelectric sensor and a calculation processing unit. And respectively placing an object plane diffraction grating plate and an image plane diffraction grating plate on the object plane and the image plane of the optical imaging system to be measured, calculating shearing phases in the x-axis direction and the y-axis direction by collecting R shearing interference fringe patterns, and then carrying out wavefront reconstruction to obtain the wavefront to be measured. The method has simple solving process, eliminates the influence of higher-order diffraction light in the Langmuir shearing interference on the phase extraction precision, and improves the wave aberration detection precision of the optical imaging system to be detected. The method has the advantages of reducing errors of a phase extraction system, adjusting the shearing rate s of the grating shearing interferometer and the like, and can improve the wave aberration detection precision of an optical imaging system.
Description
Technical Field
The invention relates to the technical field of optical detection and interferometry, in particular to a high-precision phase extraction method of double-grating Langerhans shearing interference, which is suitable for a wave aberration detection device of a projection objective of a photoetching machine or other optical imaging systems based on a double-grating Langerhans shearing interferometer.
Background
The double-grating Langerhans shearing interferometry technique is a transverse shearing interferometry technique which utilizes an incoherent light source and adopts an object plane grating to modulate the spatial coherence of an interference field, and is one of the main stream techniques of online wave aberration detection of a projection objective of a high-end photoetching machine at present. The technology does not need a reference mirror or a diffraction aperture to provide standard wave front, has the advantages of a common light path structure, strong anti-interference capability, no space optical path difference, high detection precision, high sensitivity and the like, and simultaneously improves the light source utilization rate due to the adoption of a grating structure on an object plane. In addition, the object and image plane grating can be integrated on a mask stage and a silicon wafer stage of the photoetching machine, so as to meet the detection requirements of DUV and EUV photoetching machine projection objective wave aberration. The Langerhans shearing interference introduces a phase shift interference technology, the phase shift amount is changed by transversely moving the grating, a series of shearing interference patterns with different phase shift amounts are acquired, the shearing phase is calculated, and then wave front reconstruction is carried out to obtain wave aberration of the optical imaging system to be measured.
In order to obtain the wavefront to be measured, the phase extraction is required for the acquired shearing interference pattern. Phase extraction is an important step in interferometry, and its accuracy directly affects the accuracy of detection of the wave aberration of the final optical imaging system. For a double-grating Langerhans shearing interferometer, the high-precision extraction of the shearing phase by utilizing the shearing interference pattern is a precondition for obtaining the high-precision detection of the wave aberration of the final optical imaging system to be detected.
When the shearing rate s is smaller, in the interference field of the Langgch shearing interferometer, besides the interference between +1-1-order diffraction light and 0-order diffraction light, the higher-order diffraction light can also interfere with the 0-order diffraction light, and the interference of the multi-order diffraction light exists, so that the extraction precision of the shearing phase is seriously reduced. Under the condition of ensuring a better experimental environment, the existence of multi-level high-order diffracted light is a main error source of the Langerhans shearing interferometer, so that the elimination of the interference of high-order diffracted light is a precondition that the Langerhans shearing interferometer is applied to the wave aberration detection of a high-precision optical imaging system.
Prior art 1 (matthiu Visser, martijn k. Dekker, petra Hegeman, et al extended source interferometry for at-wavelength test of EUV-optics, emerging Lithographic TechnoIogies Iii, pts land 2,1999.3676: p.253-263.) proposes an extended light source interferometer for wave aberration detection of EUV lithographic projection objective lens, where both the object plane grating and the image plane grating are one-dimensional langqi gratings, and a five-step phase shift method is adopted to reduce the influence introduced by interference of ±3-order diffracted light and 0-order diffracted light, so as to improve the accuracy of phase extraction, but it is difficult to eliminate interference of other higher-order diffracted light and 0-order diffracted light.
In prior art 2 (Wu Fei, tang Feng, wang Xiangchao, etc., phase extraction method based on the langevice, chinese patent No. 201410360070.8) adopts interference of the diffraction light of ±1 st order and the diffraction light of 0 th order to perform phase extraction, and the influence of the diffraction light of ±3 rd order and the diffraction light of ±5 th order on the phase extraction is eliminated by a nine-step phase shift method, so that the accuracy of phase extraction is improved to a certain extent, but the method still cannot eliminate the interference of the diffraction light of higher order when the diffraction light of ±7 th order and higher exists.
Prior art 3 (Lu Yunjun, tang Feng, wang Xiangchao, etc., a method for detecting wave aberration of an optical imaging system based on grating shearing interference, chinese patent No. 201910183242.1, etc.) and prior art 4 (Lu Yunjun, tang Feng, wang Xiangchao, etc., a method for detecting wave aberration of an optical imaging system based on grating shearing interference, chinese patent No. CN 201910183243.6) both use differential phases of 1 st order diffracted light and 0 th order diffracted light as shearing phases, and consider that shearing phases of +1 st order diffracted light and 0 th order diffracted light and shearing phases of-1 st order diffracted light and 0 th order diffracted light are equal, and such approximation processing causes an error in the shearing phase extraction of 1 st order diffracted light and 0 th order diffracted light, although the influence of all higher order diffracted light other than ±1 st order diffracted light in the grating shearing interferometer system can be eliminated.
In prior art 5 (Lu Yunjun, tang Feng, wang Xiangchao, etc., the method for detecting high-precision wave aberration by grating shearing interference, chinese patent application No. CN 202010934328.6) proposes a phase extraction method capable of eliminating the influence of all higher-order diffracted lights except ±1-order diffracted lights in a grating shearing interferometer system, but the method obtains shearing phases of +1-order diffracted lights and-1-order diffracted lights by solving a linear equation set, and the solving process is complex.
For a double-grating Langerhans shearing interferometer measuring system with a large numerical aperture, no detection method which has a simple solving process, is suitable for any system shearing rate s, can directly extract phases through a Langerhans shearing interference pattern and can eliminate the influence of all high-order diffracted lights except the interference of + -1-order diffracted lights and 0-order diffracted lights in the double-grating Langerhans shearing interferometer measuring system exists at present.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a high-precision phase extraction method based on a double-grating Langerhans shearing interferometer. The method can directly eliminate the influence of all high-order diffracted lights of the image plane grating except the interference of + -1-order diffracted lights and 0-order diffracted lights in the detection process of the Langmuir shearing interferometer by shearing interference fringe patterns, has simple solving process, eliminates errors caused by phase extraction in the wave front reconstruction process by adopting the shearing phases of the + 1-order diffracted lights and the-1-order diffracted lights, and improves the wave aberration detection accuracy of the optical imaging system to be detected.
In order to achieve the above object, the technical solution of the present invention is as follows:
the method adopts a detection device which is a double-grating Langerhans shearing interferometer and comprises the following steps: the system comprises a light source, an illumination system, an object plane diffraction grating plate, a first three-dimensional displacement table, an image plane diffraction grating plate, a second three-dimensional displacement table, a two-dimensional photoelectric sensor and a calculation processing unit; the light source and the illumination system output space incoherent light, the object plane diffraction grating plate is arranged on a first three-dimensional displacement table, the image plane diffraction grating plate is arranged on a second three-dimensional displacement table, the object plane diffraction grating plate comprises two groups of one-dimensional gratings with mutually perpendicular grating line directions, the image plane diffraction grating plate comprises a group of chessboard gratings or two groups of one-dimensional gratings with mutually perpendicular grating line directions, the two-dimensional photoelectric sensor is connected with the calculation processing unit, an xyz coordinate system is established, the x-axis direction is along the grating line direction of a second grating on the object plane diffraction grating plate, the y-axis direction is along the grating line direction of the first grating on the object plane diffraction grating plate, and the z-axis direction is along the optical axis direction of the Langmuir shearing interferometer; the displacement axes of the first three-dimensional displacement table and the second three-dimensional displacement table are respectively in the directions of an x axis, a y axis and a z axis; the method is characterized by comprising the following steps:
(1) Placing the optical imaging system to be tested in the Langmuir shearing interferometer system, and adjusting the Langmuir shearing interferometer to enable the light source and the illumination system to be positioned at the object side of the optical imaging system to be tested, and the image plane diffraction grating plate to be positioned at the image side of the optical imaging system to be tested; the object plane diffraction grating plate is arranged on a first three-dimensional displacement table, the first three-dimensional displacement table is adjusted, the object plane diffraction grating plate is positioned on an object plane of the optical imaging system to be tested, and a first grating of a grating line on the object plane diffraction grating plate along the y-axis direction moves into a position of an object space view field point to be tested of the optical imaging system to be tested; the image plane diffraction grating plate is arranged on a second three-dimensional displacement table, the second three-dimensional displacement table is adjusted, the image plane diffraction grating plate is positioned on the image plane of the optical imaging system to be measured, and a chessboard grating or a one-dimensional grating in the corresponding direction on the image plane diffraction grating plate moves into the position of a field point to be measured of the image side of the optical imaging system to be measured, and the included angle between the diagonal direction of the chessboard grating and the x axis (or the y axis) is 45 degrees;
(2) The first three-dimensional displacement table and the second three-dimensional displacement table are adjusted to align a first grating of a grating line on the object plane diffraction grating plate along the y-axis direction and a chessboard grating on the image plane diffraction grating plate, and the positions of the two-dimensional photoelectric sensors are adjusted to enable a series of shearing interference patterns with clear and visible stripes to be obtained on the detection surface;
(3) The second three-dimensional displacement table moves the checkerboard grating along the x-axis direction for R times, wherein R=3n+1 is the phase shift step number, and n=1, 2,3 …; the two-dimensional photoelectric sensor acquires a shearing interference pattern after each movementAnd to a computing processing unit, wherein +.>For the phase shift amount, r=1, 2,3 … is the ordinal number of the phase shift steps; a series of clear shearing interference patterns of stripes in the x-axis direction are obtained through the phase shift of the chessboard grating, and according to R interference fringe patterns, the following formula is adoptedSolving to obtain the shearing phase phi of the x-axis direction x ：
Wherein phi is x Representing gradient information of the measured wavefront in the x-axis direction for the shear phase of the measured wavefront in the x-axis direction;the phase shift amount along the x-axis direction obtained by the acquisition is +.>A shearing interference pattern at the time; />The phase shift amounts along the x-axis direction obtained by the acquisition are respectivelyA shearing interference pattern at the time;
(4) Moving the first three-dimensional displacement table, moving a second grating of the grating line on the object plane diffraction grating plate along the x-axis direction into the position of a field point to be detected of an object space of the optical imaging system to be detected, readjusting the first three-dimensional displacement table and the second three-dimensional displacement table, and aligning the second grating of the grating line on the object plane diffraction grating plate along the x-axis direction and the chessboard grating on the image plane diffraction grating plate;
(5) The second three-dimensional displacement table moves the checkerboard grating along the y-axis direction for R times, wherein R=3n+1 is the phase shift step number, and n=1, 2,3 …; the two-dimensional photoelectric sensor acquires a shearing interference pattern after each movementAnd to a computing processing unit, wherein +.>R=1, 2,3 … is the phase shiftOrdinal number of steps; a series of clear shearing interference patterns of stripes in the y-axis direction are obtained through the phase shift of the chessboard grating, and the shearing phase phi in the y-axis direction is obtained according to R interference fringe patterns and the following formula y ：
Wherein phi is y Representing gradient information of the measured wavefront in the y-axis direction for the shear phase of the measured wavefront in the y-axis direction;the phase shift amount along the y-axis direction obtained by the acquisition is +.>π、/>A shearing interference pattern at the time; />The phase shift amounts along the y-axis direction obtained by the acquisition are respectivelyA shearing interference pattern at the time;
(6) The phase extraction result is subjected to phase unwrapping, and the shearing rate between the +1 order diffraction light and the 0 order diffraction light is defined as s, and the shearing phases phi in the x-axis direction and the y-axis direction are respectively determined x 、Φ y Multiplying by 2 to obtain a differential wavefront DeltaW with a shear rate of 2s in the x-axis direction and the y-axis direction x And DeltaW y :
ΔW x ＝2Φ x ＝φ(x+Δ,y)-φ(x-Δ,y)
ΔW y ＝2Φ y ＝φ(x,y+Δ)-φ(x,y-Δ)
Wherein phi (x, y) is the wavefront to be measured, delta is the offset of the light spot of the +1 order diffraction light received on the two-dimensional photoelectric sensor relative to the light spot of the 0 order diffraction light;
(7) For DeltaW according to the system shear rate of 2s x And DeltaW y And obtaining wave aberration W of the measured optical imaging system through a Langerhans shearing interference wavefront reconstruction algorithm.
The double-grating Langerhans shearing interference high-precision phase extraction method has the period P of the one-dimensional grating on the object plane diffraction grating plate o Period P with checkerboard grating or one-dimensional grating on image plane diffraction grating plate i The ratio is equal to the magnification M of the optical imaging system under test, defined as follows:
the period P of the chessboard grating on the image plane diffraction grating plate i The product of the numerical aperture NA of the optical imaging system to be tested divided by twice the wavelength lambda of the spatial incoherent light output by the light source and the illumination system and the system shear rate s is defined as follows:
according to the double-grating Langerhans shearing interference high-precision phase extraction method, an object plane diffraction grating plate consists of two object plane one-dimensional gratings with the duty ratio of 50%, and the two object plane one-dimensional gratings are a first grating with a grating line along the y-axis direction and a second grating with a grating line along the x-axis direction respectively.
The checkerboard grating on the image plane diffraction grating plate is placed in a state that the diagonal directions of the light transmission unit and the light shielding unit are parallel to the directions of the x axis and the y axis, and the checkerboard grating is a Langerhans grating when seen along the directions of the x axis and the y axis, and the duty ratio is 50%.
According to the double-grating Langerhans shearing interference high-precision phase extraction method, the grating duty ratio of the object plane diffraction grating plate and the image plane diffraction grating plate is 1:1.
The invention has the technical effects that: aiming at the defects of the prior art, the invention provides a high-precision phase extraction method based on a double-grating Langgy shearing interferometer, which can eliminate the influence of all high-order diffraction light of an image plane grating except the interference of + -1-order diffraction light and 0-order diffraction light on the phase extraction precision in the detection process of the Langgy shearing interferometer directly through a grating shearing interference pattern, and performs wavefront reconstruction according to the shearing phases of +1-order diffraction light and-1-order diffraction light, thereby improving the wave aberration detection precision of a detected optical imaging system. The wave aberration detection method of the grating Langerhans shearing interference is optimized from the algorithm angle, the interference of higher-order diffracted light is eliminated, the wave aberration detection precision is improved, and an additional mechanical mechanism is not needed.
Drawings
FIG. 1 is a schematic diagram of a dual grating Langerhans shearing interferometer apparatus employed in the present invention;
FIG. 2 is a flow chart of a phase extraction method according to the present invention;
FIG. 3 is a schematic view of an object plane diffraction grating plate;
FIG. 4 is a schematic diagram of an image plane diffraction grating plate checkerboard grating;
FIG. 5 is a schematic diagram of the overlap region of +1 and-1 diffraction orders in a shearing interference field;
FIG. 6 is a schematic diagram of the relationship between the shear rate s of a grating Langerhans shearing interferometer system and the numerical aperture NA of the optical imaging system under test;
wherein, 1, the object plane diffracts the grating plate; 2. a first three-dimensional displacement table; 3. an optical imaging system to be tested; 4. an image plane diffraction grating plate; 5. a second three-dimensional displacement table; 6. a two-dimensional photoelectric sensor; 7. a calculation processing unit; 8. a light source and an illumination system.
Detailed Description
For a better understanding of the present invention, its objects, technical solutions and advantages, reference should be made to the following description of the present invention with reference to the accompanying drawings and examples, which should not be taken to limit the scope of the invention.
The invention discloses a double-grating Langerhans shearing interference high-precision phase extraction method, which adopts a Langerhans shearing interferometer device as shown in figure 1, and comprises the following steps: the system comprises a light source, an illumination system 8, an object plane diffraction grating plate 1, a first three-dimensional displacement table 2, an image plane diffraction grating plate 4, a second three-dimensional displacement table 5, a two-dimensional photoelectric sensor 6 and a calculation processing unit 7; the light source and the illumination system 8 output space incoherent light, the object plane diffraction grating plate 1 is arranged on the first three-dimensional displacement table 2, the image plane diffraction grating plate 4 is arranged on the second three-dimensional displacement table 5, and the two-dimensional photoelectric sensor 6 is connected with the calculation processing unit 7;
establishing an xyz coordinate system, wherein the x-axis direction is along the grating line direction of the second grating 102 on the object plane diffraction grating plate 1, the y-axis direction is along the grating line direction of the first grating 101 on the object plane diffraction grating plate 1, and the z-axis direction is along the optical axis direction of the Langerhans shearing interferometer; the displacement axes of the first three-dimensional displacement table 2 and the second three-dimensional displacement table 5 are respectively in the directions of an x axis, a y axis and a z axis;
the first three-dimensional displacement table 2 is used for moving a first grating 101 of a grating line on the object plane diffraction grating plate 1 along the y-axis direction and a second grating 102 of the grating line along the x-axis direction into the position of an object space to-be-detected view field point of the optical imaging system 3 to be detected;
the second three-dimensional displacement table 5 is used for moving the chessboard grating on the image plane diffraction grating plate 4 into the position of the field point to be detected on the image side of the optical imaging system 3 to be detected, and periodically moving the chessboard grating on the image plane diffraction grating plate 4 in the x-axis direction and the y-axis direction;
the two-dimensional photoelectric sensor 6 can be a camera, a charge coupled device CCD, a CMOS image sensor or a two-dimensional photoelectric detector array, and the detection surface of the two-dimensional photoelectric sensor is used for receiving shearing interference fringes generated by diffraction of a chessboard grating on the image plane diffraction grating plate 4;
the calculation processing unit 7 is used for collecting and storing the shearing interference patterns and processing and analyzing the shearing interference patterns;
the object plane diffraction grating plate 1 comprises a period P as shown in figure 3 o Two groups of one-dimensional gratings with the duty ratio of 50% and mutually perpendicular grating line directions are respectively a first grating 101 with the grating line along the y-axis direction and a second grating 102 with the grating line along the x-axis direction;
the first grating 101 and the second grating 102 are phase gratings or amplitude gratings;
the checkerboard grating on the image plane diffraction grating plate 4 is shown in figure 4, the checkerboard grating is placed in a state that the diagonal directions of the light transmission unit and the light shielding unit are parallel to the directions of the x axis and the y axis, the checkerboard grating is a Langmuir grating when seen along the directions of the x axis and the y axis, and the period of the checkerboard grating is P i And the duty cycle is 50%;
the chessboard grating can be a phase grating or an amplitude grating;
the period P of the one-dimensional grating on the object plane diffraction grating plate 1 o Period P with checkerboard grating on image plane diffraction grating plate 4 i The following relationship is satisfied:
P o ＝M·P i (1)
where M is the magnification of the optical imaging system 3 under test.
Fig. 5 is a schematic diagram showing an overlapping region of +1 order and-1 order diffracted lights in a shearing interference field, and a maximum diffraction order M of diffracted lights included in the overlapping region is:
wherein the ceil function is an upward rounding function, and s is the shear rate of the system. Because the checkerboard grating on the image plane diffraction grating plate 4 in the Langerhans shearing interferometer system adopted by the invention is a binary amplitude grating with the duty ratio of 50%, and the even-order diffraction light is absent, the maximum diffraction order M can be further expressed as:
wherein the mod function is a modulo operation function.
The amount of higher-order diffracted light contained in the overlap region of +1 and-1 orders of diffracted light in the shearing interference field is related to the shearing rate s of the system, and the larger the shearing rate s is, the smaller the amount of higher-order diffracted light contained in the overlap region is, whereas the larger the amount of higher-order diffracted light is contained. The more higher order diffracted light contained in the shearing interference field, the greater the resulting shearing phase extraction error.
FIG. 6 shows the shear rate s of a grating Langerhans shearing interferometer system and the numerical aperture NA of the optical imaging system 3 under test, the period P of the checkerboard grating on the image plane diffraction grating plate 4 i Schematic of the relationship between the two. The shear rate s of the system is defined as the ratio of the diffraction angle to the full aperture angle (the shear rate between normalized 1 st order diffracted light and 0 th order diffracted light):
wherein, beta is the diffraction angle of the 1 st-order diffraction light, alpha is the full aperture angle of the light spot, and lambda is the wavelength.
Based on the double grating lange shearing interferometer system, in an ideal case, the checkerboard grating on the image plane diffraction grating plate 4 only diffracts light of 0 th order and odd diffraction order, and the light energy is mainly concentrated on the 0 th order and + -1 st order diffraction light, and the diffraction light of each odd diffraction order interferes with the 0 th diffraction light in a far field. Taking the example of a shear direction along the x-direction, the interference field received on the two-dimensional photosensor 6 can be written as:
wherein A is 0 An amplitude of 0 th diffraction order, m diffraction order, k=1, 2,3, …, a m For the amplitude of the m-order diffracted light, η m For complex coherence between m-order diffraction light and 0-order diffraction light, phi m Shear phase of m-order diffracted light and 0-order diffracted light, Φ -m Is the shear phase of the-m-order diffracted light and the 0-order diffracted light. Let the amplitude A of 0 th order diffracted light 0 1, then A m And eta m The following relationship is satisfied:
shear phase Φ of m-order diffracted light and 0-order diffracted light m And-shear phase Φ of m-order diffracted light and 0-order diffracted light -m Can be expressed as follows:
Φ m ＝φ(x+mΔ,y)-φ(x,y)+α -m (7)
Φ -m ＝-φ(x-mΔ,y)+φ(x,y)-α m (8)
wherein phi (x, y) is the wavefront to be measured, delta is the offset of the 1 st-order diffraction light spot relative to the 0 th-order light spot received by the two-dimensional photoelectric sensor 6, alpha m For the phase difference of m-order diffraction light and 0-order diffraction light, alpha -m Is the phase difference of-m-order diffraction light and 0-order diffraction light, and alpha m And alpha -m The following relationship is satisfied:
when a phase shift is introduced, the light intensity expression may be rewritten as:
wherein,c is the background light intensity m ＝2A 0 A m η m ，/>For the amount of phase shift caused by shifting the checkerboard grating in the shearing direction by each step in phase-shifting interferometry +.>The phase shift amount of the m-th diffraction light when the grating moves along the shearing direction is expressed as follows:
where r=3n+1 is the number of phase shift steps, n=1, 2,3 …, and r=1, 2,3 … is the number of phase shift steps.
Based on the specific theory of multi-beam interference of the double-grating Langerhans shearing interferometer system, the high-precision phase extraction method of double-grating Langerhans shearing interference is provided, and comprises the following steps:
(1) Placing the optical imaging system 3 to be tested in the Langmuir shearing interferometer system, and adjusting the Langmuir shearing interferometer to enable the light source and the illumination system 8 to be positioned at the object side of the optical imaging system 3 to be tested, and the image plane diffraction grating plate 4 to be positioned at the image side of the optical imaging system 3 to be tested; the object plane diffraction grating plate 1 is arranged on the first three-dimensional displacement table 2, the first three-dimensional displacement table 2 is adjusted, the object plane diffraction grating plate 1 is positioned on the object plane of the optical imaging system 3 to be tested, and a first grating 101 of a grating line on the object plane diffraction grating plate 1 along the y-axis direction moves into the position of a field point to be tested of an object space of the optical imaging system 3 to be tested; the image plane diffraction grating plate 4 is arranged on a second three-dimensional displacement table 5, the second three-dimensional displacement table 5 is adjusted, the image plane diffraction grating plate 4 is positioned on the image plane of the optical imaging system 3 to be measured, a chessboard grating or a one-dimensional grating in the corresponding direction on the image plane diffraction grating plate 4 is moved into the position of a point of a field of view to be measured in the image space of the optical imaging system 3 to be measured, and an included angle between the diagonal direction of the chessboard grating and an x axis (or a y axis) is 45 degrees;
(2) The first three-dimensional displacement table 2 and the second three-dimensional displacement table 5 are adjusted to align a first grating 101 of a grating line on the object plane diffraction grating plate 1 along the y-axis direction and a chessboard grating on the image plane diffraction grating plate 4, and the positions of the two-dimensional photoelectric sensors 6 are adjusted to enable a series of shearing interference patterns with clear and visible stripes to be obtained on a detection surface;
(3) Fig. 2 shows a flow chart of a phase extraction method of the present invention, which comprises the following specific steps:
firstly, determining diffraction order m, phase shift moving step number R and phase shift interval according to system shear rate s of the Langerhans shearing interferometer:
the maximum diffraction order m is determined as follows:
wherein the ceil function is an upward rounding function, and the mod function is a modulo arithmetic function;
the diffraction orders of the langevice system are determined by the method as follows: 1, ±3, ±5, …, ± (2 n-1), wherein n=1, 2,3 …;
then determining a phase shift movement step number R=3n+1 according to n;
secondly, determining the phase shift quantity caused by each step of the checkerboard grating moving along the shearing direction according to the phase shift moving step number RThe following are provided:
(4) The second three-dimensional displacement table 5 moves the checkerboard grating along the x-axis direction for R times, wherein r=3n+1 is the number of phase shift steps, n=1, 2,3 …; the two-dimensional photoelectric sensor 6 acquires a shearing interference pattern after each movementAnd transmitted to the calculation processing unit 7, wherein +.>For the phase shift amount, r=1, 2,3 … is the ordinal number of the phase shift steps; the shearing interference fringe diagram with clear R fringes in the x-axis direction is obtained through the phase shift of the chessboard grating, and the shearing phase in the x-axis direction is calculated according to the R shearing interference fringe diagram by the following method:
in order to restrain the influence of the grating Langerhans shearing interference high-order diffracted light on the phase extraction precision, the acquisition phase shift interval is thatR interferograms of (2), i.e. the phase shift amounts per step are +.>R of the phase shift sequence, where r=1, 2,3 … is the ordinal number of the phase shift steps. Phase shift boundary (0,)>Considered separately from the remaining phase shift amounts and will +.>Is arranged at->The light intensity expression of each step can be obtained in the range:
wherein the method comprises the steps ofAnalysis can result in a total required R-step phase shift;
from (14) to (16), the shear phase phi of the optical imaging system 3 under test in the x-axis direction can be obtained x ：
Wherein phi is x Representing gradient information of the measured wavefront in the x-axis direction for the shear phase of the measured wavefront in the x-axis direction;the phase shift amount along the x-axis direction obtained by the acquisition is +.>A shearing interference pattern at the time; />The phase shift amounts along the x-axis direction obtained by the acquisition are respectivelyA shearing interference pattern at the time;
(5) Moving the first three-dimensional displacement table 2, moving the second grating 102 of the grating line on the object plane diffraction grating plate 1 along the x-axis direction into the position of the field point to be detected of the object space of the optical imaging system 3 to be detected, readjusting the first three-dimensional displacement table 2 and the second three-dimensional displacement table 5, and aligning the second grating 102 of the grating line on the object plane diffraction grating plate 1 along the x-axis direction and the chessboard grating on the image plane diffraction grating plate 4;
(6) The second three-dimensional displacement table 5 moves the checkerboard grating along the y-axis direction for R times, wherein r=3n+1 is the number of phase shift steps, n=1, 2,3 …; the two-dimensional photoelectric sensor 6 acquires a shearing interference pattern after each movementAnd transmitted to the calculation processing unit 7, wherein +.>For the phase shift amount, r=1, 2,3 … is the ordinal number of the phase shift steps; the shearing interference fringe pattern with clear R fringes in the y-axis direction is obtained through the phase shift of the chessboard grating, and the shearing phase phi of the optical imaging system 3 to be tested along the y-axis direction is obtained according to the R shearing interference fringe patterns and similar light intensity expressions of formulas (14) to (16) y ：
Wherein phi is y Representing gradient information of the measured wavefront in the y-axis direction for the shear phase of the measured wavefront in the y-axis direction;the phase shift amount along the y-axis direction obtained by the acquisition is +.>π、/>A shearing interference pattern at the time; />The phase shift amounts along the y-axis direction obtained by the acquisition are respectivelyA shearing interference pattern at the time;
(7) Phase unwrapping the above-mentioned shear phase extraction result, and defining the shear rate between +1st-order diffracted light and 0-order diffracted light as s, and respectively subjecting the shear phases phi in x-axis direction and y-axis direction to x 、Φ y Multiplying by 2 to obtain a differential wavefront DeltaW with a shear rate of 2s in the x-axis direction and the y-axis direction x And DeltaW y :
ΔW x ＝2Φ x ＝φ(x+Δ,y)-φ(x-Δ,y) (19)
ΔW y ＝2Φ y ＝φ(x,y+Δ)-φ(x,y-Δ) (20)
Wherein phi (x, y) is the wavefront to be measured, delta is the offset of the light spot of the +1 order diffraction light received on the two-dimensional photoelectric sensor 6 relative to the light spot of the 0 order diffraction light;
(8) For DeltaW according to the system shear rate of 2s x And DeltaW y The wave aberration W of the optical imaging system 3 to be tested is obtained through the Langerhans shearing interference wave front reconstruction algorithm.
Compared with the prior art 2, the method can directly extract the shearing phases in the x-axis direction and the y-axis direction through the collected shearing interference fringe patterns, has a simple solving process, can theoretically eliminate the influence of all the high-order diffraction light of the image plane grating except the interference of the + -1-order diffraction light and the 0-order diffraction light on the phase extraction precision in the detection process of the Langmuir shearing interferometer for any system shearing rate s, and carries out wave front reconstruction according to the shearing phases of the +1-order diffraction light and the-1-order diffraction light, thereby improving the wave aberration detection precision of the optical imaging system to be detected. The phase extraction method of the grating Langerhans shearing interference is optimized from the algorithm angle, the interference of higher-order diffracted light is eliminated, the wave aberration detection precision is improved, and an additional mechanical mechanism is not needed.
Claims (3)
1. The method adopts a detection device which is a double-grating Langerhans shearing interferometer and comprises the following steps: the system comprises a light source, an illumination system (8), an object plane diffraction grating plate (1), a first three-dimensional displacement table (2), an image plane diffraction grating plate (4), a second three-dimensional displacement table (5), a two-dimensional photoelectric sensor (6) and a calculation processing unit (7); the light source and the illumination system (8) output space incoherent light, the object plane diffraction grating plate (1) is arranged on the first three-dimensional displacement table (2), the image plane diffraction grating plate (4) is arranged on the second three-dimensional displacement table (5), the object plane diffraction grating plate (1) comprises two groups of one-dimensional gratings with mutually perpendicular grating line directions, the image plane diffraction grating plate (4) comprises a group of chessboard gratings or two groups of one-dimensional gratings with mutually perpendicular grating line directions, the two-dimensional photoelectric sensor (6) is connected with the calculation processing unit (7) and establishes an xyz coordinate system, the x-axis direction is along the grating line direction of the second grating (102) on the object plane diffraction grating plate (1), the y-axis direction is along the grating line direction of the first grating (101) on the object plane diffraction grating plate (1), and the z-axis direction is along the optical axis direction of the Langmuir shearing interferometer; the displacement axes of the first three-dimensional displacement table (2) and the second three-dimensional displacement table (5) are respectively in the directions of an x axis, a y axis and a z axis; the method is characterized by comprising the following steps:
(1) placing the optical imaging system (3) to be tested in the Langerhans shearing interferometer system, and adjusting the Langerhans shearing interferometer to enable the light source and the illumination system (8) to be positioned at the object side of the optical imaging system (3) to be tested, and the image plane diffraction grating plate (4) to be positioned at the image side of the optical imaging system (3) to be tested; adjusting the first three-dimensional displacement table (2) to enable the object plane diffraction grating plate (1) to be positioned on the object plane of the optical imaging system (3) to be measured, and enabling a first grating (101) of a grating line on the object plane diffraction grating plate (1) to move into a position of an object space view field point to be measured of the optical imaging system (3) to be measured along the y-axis direction; adjusting the second three-dimensional displacement table (5) to enable the image plane diffraction grating plate (4) to be positioned on the image plane of the optical imaging system (3) to be measured, and enabling the chessboard grating on the image plane diffraction grating plate (4) or the one-dimensional grating in the corresponding direction to move into the position of the field point to be measured of the image side of the optical imaging system (3) to be measured, wherein the included angle between the diagonal direction of the chessboard grating and the x-axis (or the y-axis) is 45 degrees;
(2) the first three-dimensional displacement table (2) and the second three-dimensional displacement table (5) are adjusted to align a first grating (101) of a grating line on the object plane diffraction grating plate (1) along the y-axis direction and a chessboard grating on the image plane diffraction grating plate (4), and the positions of the two-dimensional photoelectric sensors (6) are adjusted to enable a series of shearing interference patterns with clear and visible stripes to be obtained on a detection surface;
(3) moving the second three-dimensional displacement table (5) along the x-axis direction by R times, wherein R=3n+1 is the phase shift step number, and n=1, 2,3 …; the two-dimensional photoelectric sensor (6) acquires a shearing interference pattern after each movementAnd to a calculation processing unit (7), wherein +.>For the phase shift amount, r=1, 2,3 … is the ordinal number of the phase shift steps; a series of clear shearing interference patterns of stripes in the x-axis direction are obtained through the phase shift of the chessboard grating, and the shearing phase phi in the x-axis direction is obtained according to R interference fringe patterns and the following formula x ：
Wherein phi is x Representing gradient information of the measured wavefront in the x-axis direction for the shear phase of the measured wavefront in the x-axis direction;the phase shift amount along the x-axis direction obtained by the acquisition is +.>A shearing interference pattern at the time; />The phase shift amounts along the x-axis direction obtained by the acquisition are respectivelyA shearing interference pattern at the time;
(4) moving the first three-dimensional displacement table (2), moving a second grating (102) of a grating line on the object plane diffraction grating plate (1) along the x-axis direction into the position of a field point to be detected of an object space of the optical imaging system (3) to be detected, readjusting the first three-dimensional displacement table (2) and the second three-dimensional displacement table (5), and aligning the second grating (102) of the grating line on the object plane diffraction grating plate (1) along the x-axis direction and the chessboard grating on the image plane diffraction grating plate (4);
(5) the second three-dimensional displacement table (5) moves the chessboard grating along the y-axis direction for R times, wherein R=3n+1 is the phase shift step number, and n=1, 2,3 …; the two-dimensional photoelectric sensor (6) acquires a shearing interference pattern after each movementAnd to a calculation processing unit (7), wherein +.>For the phase shift amount, r=1, 2,3 … is the ordinal number of the phase shift steps; obtaining a series of clear stripe scissors in the y-axis direction through the phase shift of the chessboard gratingThe shearing phase phi of the y-axis direction is obtained by solving the cutting interference pattern according to the R interference fringe patterns according to the following formula y ：
Wherein phi is y Representing gradient information of the measured wavefront in the y-axis direction for the shear phase of the measured wavefront in the y-axis direction;the phase shift amount along the y-axis direction obtained by the acquisition is +.>A shearing interference pattern at the time; />The phase shift amounts along the y-axis direction obtained by the acquisition are respectivelyA shearing interference pattern at the time;
(6) the phase extraction result is subjected to phase unwrapping, and the shearing rate between the +1 order diffraction light and the 0 order diffraction light is defined as s, and the shearing phases phi in the x-axis direction and the y-axis direction are respectively determined x 、Φ y Multiplying by 2 to obtain a differential wavefront DeltaW with a shear rate of 2s in the x-axis direction and the y-axis direction x And DeltaW y :
ΔW x ＝2Φ x ＝φ(x+Δ,y)-φ(x-Δ,y)
ΔW y ＝2Φ y ＝φ(x,y+Δ)-φ(x,y-Δ)
Wherein phi (x, y) is the wavefront to be measured, delta is the offset of the light spot of +1 order diffraction light received on the two-dimensional photoelectric sensor (6) relative to the light spot of 0 order diffraction light;
(7) for DeltaW according to the system shear rate of 2s x And DeltaW y By Langerhans shearing to drynessThe wave aberration W of the tested optical imaging system (3) is obtained through a wave front reconstruction algorithm.
2. The double-grating lange shearing interference high-precision phase extraction method according to claim 1, wherein the ratio of the period of the one-dimensional grating on the object plane diffraction grating plate (1) to the period of the checkerboard grating or the one-dimensional grating on the image plane diffraction grating plate (4) is equal to the magnification of the optical imaging system (3) to be measured; the period of the checkerboard grating on the image plane diffraction grating plate (4) is equal to the wavelength of the space incoherent light output by the light source and the illumination system (8) divided by twice the product of the numerical aperture of the optical imaging system (3) to be tested and the system shearing rate s.
3. The double-grating lange shearing interference high-precision phase extraction method according to claim 1, characterized in that the object plane diffraction grating plate (1) consists of two object plane one-dimensional gratings with a duty ratio of 50%, namely a first grating (101) with a grating line along the y-axis direction and a second grating (102) with a grating line along the x-axis direction; the chessboard grating on the image plane diffraction grating plate (4) is placed in a state that the diagonal directions of the light transmission unit and the light shielding unit are parallel to the directions of the x axis and the y axis, and the grating is a Langerhans grating when seen along the directions of the x axis and the y axis, and the duty ratio is 50%; the duty ratio of the object plane diffraction grating to the image plane diffraction grating is 1:1.
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