CN107462179B - The nanometer accuracy measurement method of two point light source spacing - Google Patents
The nanometer accuracy measurement method of two point light source spacing Download PDFInfo
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- CN107462179B CN107462179B CN201710547369.8A CN201710547369A CN107462179B CN 107462179 B CN107462179 B CN 107462179B CN 201710547369 A CN201710547369 A CN 201710547369A CN 107462179 B CN107462179 B CN 107462179B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/14—Measuring arrangements characterised by the use of optical techniques for measuring distance or clearance between spaced objects or spaced apertures
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
Abstract
A kind of nanometer accuracy measurement method of two point light source spacing, planar array detector is placed below two point light sources, establish the mathematical model of two point light source interference field, by controlling the opening and closing of point light source and combining image processing techniques, obtain the bigness scale value of point light source spacing, then two point light sources are kept to open, acquire the interference pattern of two point light sources, solve interferometric phase, according to planar array detector coordinate system, 9 fittings obtain zernike polynomial coefficient value before carrying out zernike polynomial to obtained interferometric phase.By the partial derivative for calculating aberration term coefficient, and the coefficient value of the collected interferometric phase fitting zernike polynomial of planar array detector is combined, the amendment of the vertical range Z, planar array detector rotation angle, θ and planar array detector inclination angle γ to the line center and planar array detector photosurface of point light source spacing d, point light source are realized using the definition of partial derivative.By iterative calculation, the exact value of point light source spacing d is obtained, realizes the nanometer accuracy measurement of two point light source spacing.
Description
Technical field
The invention belongs to optical measurement more particularly to the nanometer accuracy measurement methods of two point light source spacing.
Background technique
Two point light source has a variety of applications in interferometer measuration system, and its spacing is the important parameter of interferometer measuration system.
For example, using in the Dual-slit Interference Experiment system in double small hole, the density journey of the effect of distance interference fringe of two point light source apertures
Degree；First technology 1 (referring to: Tang Feng, Wang Xiangchao etc., point-diffraction interference wave aberration measuring instrument and detection method, patent of invention
201310126148.5) a kind of point-diffraction interference wave aberration measuring instrument and detection method, in the method, double fiber optic points are proposed
The high-acruracy survey of light source spacing is to carry out a necessary condition for diffraction rapid alignment.In addition, the spacing of two point light sources can also
With the lateral resolution for evaluating optical system.Currently, for the measurement of two point light source spacing, common method mainly makes
With measuring tools such as vernier caliper, measuring microscopes, dimensional measurement is carried out by contact or cordless.However, actually making
In, that there are measurement accuracy is low for these measurement methods, can only reach the deficiency of micron dimension precision.In answering for high-acruracy survey
It with field, needs to reach higher measurement accuracy, lacks corresponding measuring instrument or method at present.
Summary of the invention
In order to solve the above-mentioned technical problem the present invention, provides a kind of high-precision measuring method of two point light source spacing, benefit
With the quantitative relationship of point light source spacing and inclination of wave front aberration, the point light source spacing nano-precision based on wave aberration theory is proposed
Measurement method realizes the high-acruracy survey of point light source spacing.
The main purpose of the present invention is to provide a kind of nanometer accuracy measurement methods of two point light source spacing.It is above-mentioned to reach
Purpose, the invention is realized by the following technical scheme:
Planar array detector is placed in below two point light sources by the first step, and planar array detector photosurface and two point light
The line in source is substantially parallel, center and the planar array detector photosurface distance Z of the line of two point light sources0Meet formula
Z0≥d/2tan(sin-1(NA)), (1.1)
The length of long sides L of planar array detector photosurface meets formula
L≥d+2Z0tan(sin-1(NA)), (1.2)
And the length of short sides l of planar array detector photosurface meets formula
l≥2Z0tan(sin-1(NA)), (1.3)
Wherein, d is the spacing of two point light sources, and NA is the numerical aperture of point light source outgoing beam；
Second step, successively by point light source S1And S2It opens, and another point light source is kept to be in close state, battle array is visited in face
It surveys on device and acquires point light source S respectively1The light spot image A1 and point light source S of outgoing2The light spot image A2 of outgoing.Pass through digital picture
Processing, it is former by planar array detector coordinate system of the midpoint of the line between the center of light spot image A1 and the center of light spot image A2
The position point o, establishes planar array detector coordinate system o-xy, and solution obtains point light source S1And S2Between distance bigness scale value d0, with center of circle position
In planar array detector coordinate origin o, range is without departing from light spot image A1 and the circle of the overlapping region light spot image A2 as analysis
The effective coverage of calculating；
Third step establishes the mathematical model of two point sotuce fields: using the line direction of two point light sources as X-axis side
To, cross line midpoint and perpendicular to light source line direction be used as Y-axis, along the light direction of propagation be Z-direction, establish system coordinates
It is O-XYZ, wherein Z axis passes through the origin o of planar array detector coordinate system, planar array detector coordinate system o-xy is established, if two points
The three-dimensional coordinate of light source is (- d/2,0,0) and (d/2,0,0), seat of each pixel in built coordinate system on planar array detector
It is designated as (x ", y ", z "), the coordinate of each pixel is (x, y) in planar array detector coordinate system.
When planar array detector coordinate system o-xy plane is θ relative to the rotation angle of system coordinate system O-XY plane, need
Following formula are used to be coordinately transformed
Wherein, (x', y') is transformed coordinate, and (x, y) is the coordinate before transformation.
When the tilt angle of planar array detector and X-axis and Y-axis is respectively γxAnd γyWhen, it needs using following formula again
It is coordinately transformed
Wherein, (x ", y ", z ") is transformed coordinate, and (x', y') is after correcting rotation amount existing for planar array detector
Coordinate, Z0For two point light source lines center at a distance from planar array detector (1) photosurface.According to the calculating of optical path difference OPD
Formula
Generate phase distribution in planar array detector plane；
4th step, by point light source S1And S2It is kept open, collects point light source S using planar array detector1With light
Source S2The interference image of emergent light solves interferometric phase using phase shift method or spatial carrier method, according to the face battle array detection established
Device coordinate system obtains zernike polynomial coefficient value, remembers to 9 fittings before obtained interferometric phase progress zernike polynomial
For Z01~Z09；
5th step sets the inclination angle current value of planar array detector for the first time in calculatingWithIt is 0, face battle array is visited
Survey device rotation angle current value be
θcur=tan-1(-Z03/Z02), (1.7)
Wherein, Z02、Z03Respectively indicate the 2nd that the interferometric phase fitting zernike polynomial of acquired image obtains
The coefficient value of (X inclination) and the 3rd (Y inclination)；By the vertical range at the line center of point light source and planar array detector photosurface
Bigness scale value be set as current value Zcur, by the bigness scale value d of point light source spacing0For current value dcur；
6th step, first by the inclination angle of planar array detector, the rotation angle of planar array detector, point light source line center with
The vertical range of planar array detector photosurface and the current value of point light source spacing substitute into formula (1.4), (1.5) and (1.6) and calculate
Perfect Interferometry phase carries out zernike polynomial the 2nd (X inclination) coefficient Z to obtained interferometric phase2curIt is fitted, and
Solve the coefficient Z of zernike polynomial the 2nd (X inclination)2The partial derivative of spacing d about point light sourceAccording to formula
Solve the correction value d of point light source spacingcal, wherein Z02Indicate that the interferometric phase of acquired image is fitted Ze Nike
The coefficient value of the 2nd (X inclination) that multinomial obtains；
Then, by the correction value d of point light source spacingcalIt is set as the current value d of point light source spacingcur, substitute into formula
(1.4), (1.5) and (1.6) recalculate Perfect Interferometry phase, carry out zernike polynomial the 7th to obtained interferometric phase
Coefficient Z7curIt is fitted, and solves the coefficient Z of zernike polynomial the 7th (3 grades of X comas)7Local derviation about vertical range Z
NumberAccording to formula
Solve the correction value Z of vertical rangecal, wherein Z07Indicate that the interferometric phase of acquired image is fitted Ze Nikeduo
The coefficient value of the 7th (3 grades of X comas) that item formula obtains；
Then, by the correction value Z of vertical rangecalIt is set as the current value Z of vertical rangecur, substitution formula (1.4),
(1.5) and (1.6) recalculate Perfect Interferometry phase, carry out zernike polynomial the 3rd (Y inclination) to obtained interferometric phase
Coefficient Z3curIt is fitted, and solves the coefficient Z of zernike polynomial the 3rd (Y inclination)3Angle, θ is rotated about planar array detector
Partial derivativeAccording to formula
Solve the correction value θ of planar array detector rotation anglecal, wherein Z03Indicate that the interferometric phase of acquired image is quasi-
Close the coefficient value of the 3rd (Y inclination) that zernike polynomial obtains；
Then, by the correction value θ of planar array detector rotation anglecalIt is set as the rotation angle current value of planar array detector
θcur, substitute into formula (1.4), (1.5) and (1.6) and recalculate Perfect Interferometry phase, Ze Nike is carried out to obtained interferometric phase
The 4th (defocus) coefficient Z of multinomial4curWith the 6th (3 grades of ± 45 ° of astigmatisms) coefficient Z6curIt is fitted, solves Ze Nike respectively
The coefficient Z of multinomial the 4th (defocus) and the 6th (3 grades of ± 45 ° of astigmatisms)4And Z6About planar array detector inclination angle γxIt is inclined
DerivativeWithAnd solve the coefficient Z of zernike polynomial the 6th (3 grades of ± 45 ° of astigmatisms)6It is tilted about planar array detector
Angle γyPartial derivativeAccording to formula
Solve planar array detector inclination angleWithCorrection value, wherein Z04、Z06Respectively indicate acquired image
The coefficient value of the 4th (defocus) and the 6th (3 grades of ± 45 ° of astigmatisms) that interferometric phase fitting zernike polynomial obtains；
Finally, by planar array detector inclination angle correction valueWithIt is set as planar array detector inclination angle current value
With
7th step repeats step 6, until calculated result difference value is less than 5nm, gained twice for the front and back of point light source spacing d
The two point light source spacing d arrived, as the nanometer accuracy measurement value of spacing.
As seen from the above technical solution provided by the invention, the present invention provides a kind of achievable two point light source spacing
The measurement method of nanometer accuracy measurement, compared to use the measuring tools such as measuring microscope or vernier caliper measurement method have more
High measurement accuracy.
Detailed description of the invention
Fig. 1 is two point light source gap measuring device schematic diagram of the invention；
Fig. 2 is the geometrical model schematic diagram of two point light source distance measurement.
Specific embodiment
With reference to the attached drawing in the embodiment of the present invention, technical solution in the embodiment of the present invention carries out clear, complete
Ground description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this
The embodiment of invention, every other implementation obtained by those of ordinary skill in the art without making creative efforts
Example, belongs to protection scope of the present invention.
Embodiment 1:
A kind of nanometer accuracy measurement method of two point light source spacing, using planar array detector 1 to point light source S1With point light source S2
Spacing measure, the planar array detector 1 uses CCD element, the point light source S1With point light source S2For single mode optical fiber
Output end face；The nanometer accuracy measurement method of the point light source spacing includes the following steps:
The first step, as shown in Figure 1, two-way coherent light is directed respectively into point light source S1With point light source S2Corresponding two single modes
Optical fiber, planar array detector 1 are placed in point light source S1With point light source S2Lower section, and the photosurface of planar array detector 1 and point light source S1With
Point light source S2Line it is substantially parallel, point light source S1With point light source S2Line center and planar array detector 1 photosurface away from
From Z0Meet formula
Z0≥d/2tan(sin-1(NA)), (1.1)
The length of long sides L of 1 photosurface of planar array detector meets formula
L≥d+2Z0tan(sin-1(NA)), (1.2)
And the length of short sides l of 1 photosurface of planar array detector meets formula
l≥2Z0tan(sin-1(NA)), (1.3)
Wherein, d is point light source S1With point light source S2Spacing, NA be point light source S1Numerical aperture (the point light source of outgoing beam
S1With point light source S2The numerical aperture of outgoing beam is identical)；
Second step, successively by point light source S1And S2It opens, and another point light source is kept to be in close state, battle array is visited in face
It surveys on device 1 and acquires point light source S respectively1The light spot image A1 and point light source S of outgoing2The light spot image A2 of outgoing.Pass through digital picture
Processing, it is former by planar array detector coordinate system of the midpoint of the line between the center of light spot image A1 and the center of light spot image A2
The position point o, establishes planar array detector coordinate system o-xy, and solution obtains point light source S1And S2Between distance bigness scale value d0, with center of circle position
In planar array detector coordinate origin o, range is without departing from light spot image A1 and the circle of the overlapping region light spot image A2 as analysis
The effective coverage of calculating；
Third step, as shown in Fig. 2, establishing two point light source S1、S2The mathematical model of interference field: with point light source S1With light
Source S2Line direction as X-direction, line midpoint is crossed and perpendicular to light source line direction as Y-axis, along light propagation side
To for Z-direction, system coordinate system O-XYZ is established, wherein Z axis passes through the origin o of planar array detector coordinate system, and set up an office light source
S1With point light source S2Three-dimensional coordinate be (- d/2,0,0) and (d/2,0,0), each pixel is building seat on planar array detector 1
The coordinate of mark system is (x ", y ", z "), and the coordinate of each pixel is (x, y) in planar array detector coordinate system.
When 1 coordinate system o-xy plane of planar array detector is θ relative to the rotation angle of system coordinate system O-XY plane, need
Following formula are used to be coordinately transformed
Wherein, (x', y') is transformed coordinate, and (x, y) is the coordinate before transformation.
When the tilt angle of planar array detector 1 and X-axis and Y-axis is respectively γxAnd γyWhen, it needs using following formula again
It is coordinately transformed
Wherein, (x ", y ", z ") is transformed coordinate, and (x', y') is after correcting rotation amount existing for planar array detector 1
Coordinate, Z0For point light source S1With point light source S2Line center at a distance from planar array detector (1) photosurface.According to light path
The calculation formula of poor OPD
Generate phase distribution in planar array detector plane；
4th step, by point light source S1And S2It is kept open, collects point light source S using planar array detector 11And point
Light source S2The interference image of emergent light solves interferometric phase using phase shift method or spatial carrier method, visits according to the face battle array established
Device coordinate system is surveyed, to 9 fittings before obtained interferometric phase progress zernike polynomial, obtains zernike polynomial coefficient value,
It is denoted as Z01~Z09；
5th step sets the inclination angle current value of planar array detector 1 for the first time in calculatingWithIt is 0, face battle array is visited
Survey device 1 rotation angle current value be
θcur=tan-1(-Z03/Z02), (1.7)
Wherein, Z02、Z03Respectively indicate the 2nd that the interferometric phase fitting zernike polynomial of acquired image obtains
The coefficient value of (X inclination) and the 3rd (Y inclination)；By the vertical range at the line center of point light source and 1 photosurface of planar array detector
Bigness scale value be set as current value Zcur, by the bigness scale value d of point light source spacing0It is set as current value dcur；
6th step, first by the inclination angle of planar array detector 1, the rotation angle of planar array detector 1, point light source line center
Formula (1.4), (1.5) and (1.6) meter is substituted into the vertical range of 1 photosurface of planar array detector and the current value of point light source spacing
Perfect Interferometry phase is calculated, zernike polynomial the 2nd (X inclination) coefficient Z is carried out to obtained interferometric phase2curIt is fitted,
And solve the coefficient Z of zernike polynomial the 2nd (X inclination)2The partial derivative of spacing d about point light sourceAccording to formula
Solve the correction value d of point light source spacingcal, wherein Z02Indicate that the interferometric phase of acquired image is fitted Ze Nike
The coefficient value of the 2nd (X inclination) that multinomial obtains；
Then, by the correction value d of point light source spacingcalIt is set as the current value d of point light source spacingcur, substitute into formula
(1.4), (1.5) and (1.6) recalculate Perfect Interferometry phase, carry out zernike polynomial the 7th to obtained interferometric phase
Coefficient Z7curIt is fitted, and solves the coefficient Z of zernike polynomial the 7th (3 grades of X comas)7Local derviation about vertical range Z
NumberAccording to formula
Solve the correction value Z of vertical rangecal, wherein Z07Indicate that the interferometric phase of acquired image is fitted Ze Nikeduo
The coefficient value of the 7th (3 grades of X comas) that item formula obtains；
Then, by the correction value Z of vertical rangecalIt is set as the current value Z of vertical rangecur, substitution formula (1.4),
(1.5) and (1.6) recalculate Perfect Interferometry phase, carry out zernike polynomial the 3rd (Y inclination) to obtained interferometric phase
Coefficient Z3curIt is fitted, and solves the coefficient Z of zernike polynomial the 3rd (Y inclination)3Angle is rotated about planar array detector 1
The partial derivative of θAccording to formula
Solve the correction value θ that planar array detector 1 rotates anglecal, wherein Z03Indicate that the interferometric phase of acquired image is quasi-
Close the coefficient value of the 3rd (Y inclination) that zernike polynomial obtains；
Then, planar array detector 1 is rotated to the correction value θ of anglecalIt is set as the rotation angle current value of planar array detector 1
θcur, substitute into formula (1.4), (1.5) and (1.6) and recalculate Perfect Interferometry phase, Ze Nike is carried out to obtained interferometric phase
The 4th (defocus) coefficient Z of multinomial4curWith the 6th (3 grades of ± 45 ° of astigmatisms) coefficient Z6curIt is fitted, solves Ze Nike respectively
The coefficient Z of multinomial the 4th (defocus) and the 6th (3 grades of ± 45 ° of astigmatisms)4And Z6About 1 inclination angle γ of planar array detectorxIt is inclined
DerivativeWithAnd solve the coefficient Z of zernike polynomial the 6th (3 grades of ± 45 ° of astigmatisms)6Incline about planar array detector 1
Oblique angle γyPartial derivativeAccording to formula
Solve 1 inclination angle of planar array detectorWithCorrection value, wherein Z04、Z06Respectively indicate acquired image
The obtained coefficient value of the 4th (defocus) and the 6th (3 grades of ± 45 ° of astigmatisms) of interferometric phase fitting zernike polynomial；
Finally by 1 inclination angle correction value of planar array detectorWithIt is set as 1 inclination angle current value of planar array detector
With
7th step repeats step 6, until calculated result difference value is less than 5nm, gained twice for the front and back of point light source spacing d
The two point light source spacing d arrived, as the nanometer accuracy measurement value of spacing.
Claims (1)
1. a kind of nanometer accuracy measurement method of two point light source spacing, using planar array detector (1), it is characterised in that including as follows
Step:
Planar array detector (1) is placed in point light source S by the first step1With point light source S2Lower section, and planar array detector (1) is photosensitive
Face and point light source S1With point light source S2Line it is substantially parallel, point light source S1With point light source S2Line center and face battle array detect
The distance Z of device (1) photosurface0Meet formula (1.1):
Z0≥d/2tan(sin-1(NA)), (1.1)
The length of long sides L of planar array detector (1) photosurface meets formula (1.2):
L≥d+2Z0tan(sin-1(NA)), (1.2)
The length of short sides l of planar array detector (1) photosurface meets formula (1.3):
l≥2Z0tan(sin-1(NA)), (1.3)
Wherein, d is point light source S1With point light source S2Spacing, NA be point light source S1With point light source S2The numerical aperture of outgoing beam；
Second step, successively by point light source S1With point light source S2It opens, and another point light source is kept to be in close state, in face battle array
Detector acquires point light source S on (1) respectively1The light spot image A1 and point light source S of outgoing2The light spot image A2 of outgoing, passes through number
Image procossing, using the midpoint of the line between the center of light spot image A1 and the center of light spot image A2 as planar array detector coordinate
It is the position origin o, establishes planar array detector coordinate system o-xy, solution obtains point light source S1With point light source S2Between distance bigness scale value
d0, planar array detector coordinate origin o is located at the center of circle, range is without departing from light spot image A1 and the overlapping region light spot image A2
Effective coverage of the circle as analytical calculation；
Third step establishes the mathematical model of two point light source interference field: using the line direction of two point light sources as X-direction, mistake
Line midpoint and perpendicular to the direction of light source line as Y-axis, the light direction of propagation is Z-direction, establishes system coordinate system O-
XYZ, wherein Z axis by the origin o of planar array detector coordinate system, if the three-dimensional coordinate of two point light sources be respectively (- d/2,0,
0) and (d/2,0,0), each pixel in the coordinate of the O-XYZ coordinate system is (x ", y ", z ") on planar array detector (1),
The coordinate of each pixel is (x, y) in planar array detector coordinate system:
When planar array detector coordinate system o-xy plane is θ relative to the rotation angle of system coordinate system O-XY plane, need to make
It is coordinately transformed with formula (1.4):
Wherein, (x', y') is transformed coordinate, and (x, y) is the coordinate before transformation；
When the tilt angle of planar array detector (1) and X-axis and Y-axis is respectively γxAnd γyWhen, need with formula (1.5) again into
Row coordinate transform:
Wherein, (x ", y ", z ") is transformed coordinate, and (x', y') is after correcting rotation amount existing for planar array detector (1)
Coordinate, Z0For point light source S1With point light source S2Line center at a distance from planar array detector (1) photosurface, according to optical path difference
The calculation formula (1.6) of OPD
Generate phase distribution in planar array detector (1) plane；
4th step, by point light source S1With point light source S2It is kept open, acquires point light source S using planar array detector (1)1With
Point light source S2The interference image of emergent light solves interferometric phase using phase shift method or spatial carrier method, visits according to the face battle array
Device coordinate system is surveyed, to 9 fittings before obtained interferometric phase progress zernike polynomial, obtains zernike polynomial coefficient value,
It is denoted as Z01~Z09；
5th step sets the inclination angle current value of planar array detector (1) for the first time in calculatingWithIt is 0, face battle array detection
The current value of device (1) rotation angle are as follows:
θcur=tan-1(-Z03/Z02), (1.7)
Wherein, Z02、Z03Respectively indicate the 2nd and the 3rd that the interferometric phase fitting zernike polynomial of acquired image obtains
The coefficient value of item；The line center of point light source and the bigness scale value of the vertical range of planar array detector (1) photosurface are set as working as
Preceding value Zcur, by the bigness scale value d of point light source spacing0It is set as current value dcur；
6th step, including substep:
1) first by the inclination angle of planar array detector (1), the rotation angle of planar array detector (1), point light source line center and face
The vertical range of array detector (1) photosurface and the current value of point light source spacing substitute into formula (1.4), (1.5) and (1.6) and calculate
Perfect Interferometry phase carries out the 2nd term coefficient Z of zernike polynomial to obtained interferometric phase2curIt is fitted, and solves damp Buddhist nun
Gram of multinomial the 2nd coefficient Z2The partial derivative of spacing d about point light sourceAccording to formula
Solve the correction value d of two point light source spacingcal, wherein Z02Indicate that the interferometric phase of acquired image is fitted Ze Nikeduo
The 2nd coefficient value that item formula obtains；
2) by the correction value d of point light source spacingcalIt is set as the current value d of two point light source spacingcur, substitution formula (1.4),
(1.5) and (1.6) recalculate Perfect Interferometry phase, carry out the 7th term coefficient of zernike polynomial to obtained interferometric phase
Z7curIt is fitted, and solves zernike polynomial the 7th coefficient Z7Partial derivative about vertical range ZAccording to formula
Solve the correction value Z of vertical rangecal, wherein Z07Indicate that the interferometric phase of acquired image is fitted zernike polynomial
The 7th obtained coefficient value；
3) by the correction value Z of vertical rangecalIt is set as the current value Z of vertical rangecur, substitute into formula (1.4), (1.5) and
(1.6) Perfect Interferometry phase is recalculated, the 3rd term coefficient Z of zernike polynomial is carried out to obtained interferometric phase3curIntended
It closes, and solves zernike polynomial the 3rd coefficient Z3Partial derivative about planar array detector (1) rotation angle, θAccording to
Formula
Solve the correction value θ of planar array detector (1) rotation anglecal, wherein Z03Indicate the interferometric phase fitting of acquired image
The 3rd coefficient value that zernike polynomial obtains；
4) by the correction value θ of planar array detector (1) rotation anglecalIt is set as the rotation angle current value θ of planar array detector (1)cur,
It substitutes into formula (1.4), (1.5) and (1.6) and recalculates Perfect Interferometry phase, it is multinomial to carry out Ze Nike to obtained interferometric phase
The 4th term coefficient Z of formula4curWith the 6th term coefficient Z6curIt is fitted, solves zernike polynomial the 4th and the 6th coefficient respectively
Z4And Z6About planar array detector (1) inclination angle γxPartial derivativeWithAnd it solves zernike polynomial the 6th and is
Number Z6About planar array detector (1) inclination angle γyPartial derivativeAccording to formula
Solve planar array detector (1) inclination angleWithCorrection value, wherein Z04、Z06Respectively indicate the dry of acquired image
Relate to the 4th and the 6th coefficient value that phase-fitting zernike polynomial obtains；
5) by planar array detector (1) inclination angle correction valueWithIt is set as the current value at planar array detector (1) inclination angle
With
7th step repeats step 6, until calculated result difference value is less than 5nm twice for the front and back of point light source spacing d, it is obtained
Two point light source spacing d is the nanometer accuracy measurement value of two point light source spacing.
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| CN104570621A (en) * | 2015-01-14 | 2015-04-29 | 清华大学 | Feedback regulation method for optical grating diffraction wave surface error in double-beam exposure system |
| CN105528489A (en) * | 2015-12-19 | 2016-04-27 | 北京海颐威工程技术有限公司 | Method for two-dimensional and three-dimensional mixing in modeling software |
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