CN106595529B - Larger radius of curvature nonzero digit interferometric method and device based on virtual Newton's ring - Google Patents
Larger radius of curvature nonzero digit interferometric method and device based on virtual Newton's ring Download PDFInfo
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- 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
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Abstract
The present invention proposes a kind of spherical surface larger radius of curvature nonzero digit measurement method and device based on virtual Newton's ring.Circle carrier frequency Newton ring interference figure is converted to line carrier frequency interference pattern using second order polar coordinate transform by this method, using under second order polar coordinates line carrier frequency Newton ring interference figure to be measured and line carrier frequency standard Newton ring interference figure be superimposed the Moire fringe to be formed, pass through the low frequency moiré topography after demodulation low-pass filtering, the wavefront differential data for extracting spherical surface to be measured Yu standard spherical surface, is deduced the calculation formula of radius of curvature.The model of Feisuo type spherical surface larger radius of curvature non-zero position detecting system based on ZEMAX software, existing hysterisis error when correcting that Newton ring interference figure acquires in nonzero digit detection using the method for finite iteration.Feisuo type spherical surface larger radius of curvature non-zero position detecting system is constructed, the verifying of the spherical surface larger radius of curvature nonzero digit measuring technique based on virtual Newton's ring is completed.
Description
Technical field
The invention belongs to optical measuring technique, especially a kind of larger radius of curvature nonzero digit interferometry based on Newton's ring
Method and device.
Background technique
Spherical mirror is a kind of optical element common in optical system, there is important application in all kinds of optical systems.Example
Such as, in Next Generation Lithographies projection objective system (Extreme Ultra-violet, abbreviation EUV), it is totally reflected using 13.5nm
Formula lithographic objective.It include 6 off-axis spherical surfaces or aspherical mirror in the system, the processing quality of spherical reflector is to whole system
Imaging effect has crucial influence.Radius of curvature (radius of curvature, ROC) is characterization optical spherical surface mirror optics
The Important Parameters of characteristic.Curvature radius of spherical reflector has very big influence to the image quality of optical system.Spheric reflection
In the process of mirror, the radius of curvature for accurately measuring measurement spherical mirror is the important process of optical workshop inspection.
Requirement with the development of Large optical system, for the radius of curvature measurement precision of larger radius of curvature aspherical elements
Also higher and higher.Yang Yongying of Zhejiang University in 2001 et al. is mentioned on the basis of analyzing various larger radius of curvature measurement methods
Laser Newton Rings method is gone out.The measurable radius of curvature measurement range of this method is 1~25m, and relative error is better than 0.3%.
Foucault Knife-edge Shadow method is that the relatively common method of larger radius of curvature aspherical elements is measured in optical workshop.This method
Precision depends on the precision of range-measurement system, can achieve 0.05%, but this method is harsher to environmental requirement.Auto-collimation is micro-
Mirror method can measure convex surface and concave surface spherical optics element, be suitble to the detection of optical elements of large caliber, but the method measurement accuracy
It is limited to the error of focusing of human eye and the position error of length measurement system, and measurement range is by length measurement system and working distance of microscope
Limitation.Differential confocal method based on laser spherical interferometer is common one of the method for spherical optics element curvature radius.It is to be measured
Aspherical elements are moved along guide rail direction, and part to be measured generates zero order interference fringe in opal and confocal position.Opal and confocal position
The distance between set be spherical surface to be measured radius of curvature, measurement accuracy depends on the distance between opal position and confocal position
Measurement accuracy, is limited to the limitation of test environment and rail length, and the measurement range of this method is limited.Mianyang engineering object in 2011
Graduate Hengyu Yi et al. is managed to propose through design compensation device to reduce interference cavity length.Compensator and mirror to be measured constitute one
A zooming system, by adjusting test of the compensating glass realization to different curvature radius, relative error is better than 4.2 × 10-4.For biography
The altogether limitation of burnt mensuration, 2014 American National Standard technical research institute (NIST) Quandou Wang et al. propose
Replace the test method of standard spherical mirror using bifocal zone plate.This method is limited to the design of bifocal zone plate and processing essence
Degree, and measurement cost is higher.
Summary of the invention
The purpose of the present invention is to provide a kind of larger radius of curvature nonzero digit interferometric method and dress based on Newton's ring
It sets, in the case where guaranteeing experimental precision, while correcting spherical surface larger radius of curvature nonzero digit using the method for finite iteration and examining
Hysterisis error in examining system largely reduced the influence that hysterisis error measures larger radius of curvature.
The technical solution for realizing the aim of the invention is as follows: a kind of spherical surface larger radius of curvature non-zero based on virtual Newton's ring
Position measurement method, spherical mirror radius of curvature measurement detecting step are as follows:
The Newton ring interference figure T (x, y) of step 1, acquisition spherical surface to be measured.
Step 2 detects ZEMAX model emulation standard sphere curvature radius by sphere curvature radius nonzero digit as R0Return
Journey error W_retrace is simultaneously substituted into the emulation corrugated data of standard Newton ring interference figure, and emulation obtains standard Newton ring interference
Scheme T0(x, y):
T0(x, y)=A0(x,y)+B0(x,y)cos[2πf0(x2+y2)]
A0(x, y) is the background light intensity of standard Newton ring interference figure under cartesian coordinate, B0(x, y) is under cartesian coordinate
The intetference-fit strengthening of standard Newton ring interference figure, f0For the line carrier frequency system of standard Newton ring interference figure under cartesian coordinate
Number, (x, y) are the coordinate at any point on the Newton ring interference figure of spherical surface to be measured under cartesian coordinate.
Step 3, Newton ring interference figure T (x, y) and standard Newton ring interference by the spherical surface to be measured under cartesian coordinate system
Scheme T0(x, y) is converted to the interference pattern under second order polar coordinate system:
Newton ring interference figure to be measured: T (ρ, θ)=A (ρ, θ)+B (ρ, θ) cos (2 π fc ρ)
Standard Newton ring interference figure: T0(ρ, θ)=A0(ρ,θ)+B0(ρ,θ)cos(2πf0ρ)
A (ρ, θ) is the background light intensity of Newton ring interference figure to be measured under second order polar coordinates, B (ρ, θ) be under second order polar coordinates to
Survey the intetference-fit strengthening of Newton ring interference figure, fcFor the line carrier frequency coefficient of Newton ring interference figure to be measured under second order polar coordinates；
(ρ, θ) is the polar coordinates at any point on the Newton ring interference figure of spherical surface to be measured under second order polar coordinate system.
A0(ρ, θ) is the background light intensity of standard Newton ring interference figure under second order polar coordinates, B0(ρ, θ) is under second order polar coordinates
The intetference-fit strengthening of standard Newton ring interference figure, f0For the line carrier frequency system of standard Newton ring interference figure under second order polar coordinates
Number.
Low frequency moiré topography is obtained by low-pass filtering after step 4, superposition Moire fringe, light intensity S (ρ, θ) expression formula is such as
Under:
S (ρ, θ)=A'(ρ, θ)+B'(ρ, θ) cos [2 π ρ (fc-f0)]
Wherein, A'(ρ, θ) be second order polar coordinates under background light intensity, B'(ρ, θ) be second order polar coordinates under contrast,
fc-f0For the line carrier frequency coefficient of low frequency moiré topography under second order polar coordinates.
Low frequency moiré topography under second order polar coordinates is recovered wave by Fourier transformation phase demodulating method by step 5
Face data, and the wavefront differential data being converted under cartesian coordinate system, seek the radius of curvature R of spherical surface to be measuredi:
w0The thickness of the airspace of (x, y) between cartesian coordinate system subscript director sphere and reference planes, w (x, y)
The thickness of airspace between spherical surface to be measured under cartesian coordinate system and reference planes；R0For the curvature half of standard spherical surface
Diameter, (x, y) are the coordinate at any point on the Newton ring interference figure of spherical surface to be measured under cartesian coordinate system.
Step 6, by the radius of curvature R of spherical surface to be measurediIt substitutes into sphere curvature radius nonzero digit detection ZEMAX model, asks
Take hysterisis error W_retracei, when the spherical surface to be measured that the sphere curvature radius to be measured that this circulation obtains was recycled with last time
When being more than or equal to 50mm of radius of curvature, return step 2；Otherwise circulation is terminated, the radius of curvature R of spherical surface to be measured is obtainedout。
A kind of device of the spherical surface larger radius of curvature nonzero digit measurement method based on virtual Newton's ring, in step 1, acquisition to
The device for surveying the Newton ring interference figure T (x, y) of spherical surface is as follows: including polarizing frequency stabilized He-Ne laser, convex lens, space filtering
Device, spectroscope, colimated light system, standard mirror, imaging system and ccd detector, wherein common optical axis sets gradually polarization frequency stabilization He-Ne
Laser, convex lens, spatial filter, spectroscope, colimated light system, standard mirror and spherical surface to be measured, imaging system and ccd detector
Common optical axis is arranged on spectroscopical reflected light path；All optical elements are coaxially contour relative to substrate；By polarization frequency stabilization He-Ne
Laser issues a monochromic beam, and planoconvex lens are assembled, filtered by spatial filter, be incident to spectroscope, through spectroscope point
For transmitted light and reflected light, transmitted light is incident to colimated light system, forms collimated light beam, after collimated light beam enters standard mirror, part
Collimated light beam by standard mirror rear surface reflect, formed standard light, another part collimated light beam by standard mirror be incident to
Spherical surface is surveyed, the front surface reflection through spherical surface to be measured forms test light, and standard light and test light return along input path, pass through
Spectroscope is reflected into imaging system, is imaged on ccd detector target surface, the image grayscale letter recorded on ccd detector target surface
Breath, the Newton ring interference figure T (x, y) of spherical surface as to be measured.
Compared with prior art, the present invention its remarkable advantage is: (1) experimentation is simple, and ensure that experimental precision.
(2) influence that hysterisis error measures spherical surface larger radius of curvature is greatly weakened.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the spherical surface larger radius of curvature nonzero digit measurement method of virtual Newton's ring.
Fig. 2 is that the present invention is based on the realization device figures of the spherical surface larger radius of curvature nonzero digit measurement method of virtual Newton's ring.
Fig. 3 is Newton ring interference figure and standard Newton ring interference figure to be measured in the embodiment of the present invention: wherein (a) is Descartes
Newton ring interference figure to be measured under coordinate is (b) the Newton ring interference figure to be measured under second order polar coordinates, (c) is cartesian coordinate
It down include the standard Newton ring interference figure of hysterisis error, it is (d) dry for the standard Newton's ring under second order polar coordinates comprising hysterisis error
Relate to figure
Fig. 4 is the Moire fringe in the embodiment of the present invention under second order polar coordinates: (a) being the Moire fringe before filtering, (b) is
Filtered Moire fringe.
Fig. 5 is the wavefront differential data of spherical surface and standard spherical surface to be measured in the embodiment of the present invention: being (a) under second order polar coordinates
Corrugated differential data, be (b) the corrugated differential data under cartesian coordinate.
Fig. 6 is the radius of curvature measurement simulation result of spherical surface to be measured in the embodiment of the present invention.
Specific embodiment
Present invention is further described in detail with reference to the accompanying drawing.
Integral Thought of the invention are as follows: circle carrier frequency Newton ring interference figure is converted into line carrier frequency using second order polar coordinate transform
Interference pattern utilizes the line carrier frequency Newton ring interference figure to be measured and line carrier frequency standard Newton ring interference figure superposition shape under second order polar coordinates
At Moire fringe, by demodulation low-pass filtering after low frequency moiré topography, extract the wave of spherical surface to be measured Yu standard spherical surface
Preceding differential data is deduced the calculation formula of radius of curvature.
In conjunction with Fig. 1, a kind of spherical surface larger radius of curvature nonzero digit measurement method based on virtual Newton's ring, spherical surface mirror curvature half
Diameter measures detecting step are as follows:
The Newton ring interference figure T (x, y) of step 1, acquisition spherical surface 7 to be measured.
Step 2 detects ZEMAX model emulation standard sphere curvature radius by sphere curvature radius nonzero digit as R0Return
Journey error W_retrace is simultaneously substituted into the emulation corrugated data of standard Newton ring interference figure, and emulation obtains standard Newton ring interference
Scheme T0(x, y):
T0(x, y)=A0(x,y)+B0(x,y)cos[2πf0(x2+y2)]
A0(x, y) is the background light intensity of standard Newton ring interference figure under cartesian coordinate, B0(x, y) is under cartesian coordinate
The intetference-fit strengthening of standard Newton ring interference figure, f0For the line carrier frequency system of standard Newton ring interference figure under cartesian coordinate
Number, (x, y) are the coordinate at any point on the Newton ring interference figure of spherical surface 7 to be measured under cartesian coordinate.
Step 3, Newton ring interference figure T (x, y) and standard Newton ring interference by the spherical surface to be measured 7 under cartesian coordinate system
Scheme T0(x, y) is converted to the interference pattern under second order polar coordinate system:
Newton ring interference figure to be measured: T (ρ, θ)=A (ρ, θ)+B (ρ, θ) cos (2 π fc ρ)
Standard Newton ring interference figure: T0(ρ, θ)=A0(ρ,θ)+B0(ρ,θ)cos(2πf0ρ)
A (ρ, θ) is the background light intensity of Newton ring interference figure to be measured under second order polar coordinates, B (ρ, θ) be under second order polar coordinates to
Survey the intetference-fit strengthening of Newton ring interference figure, fcFor the line carrier frequency coefficient of Newton ring interference figure to be measured under second order polar coordinates.
(ρ, θ) is the polar coordinates at any point on the Newton ring interference figure of spherical surface 7 to be measured under second order polar coordinate system.
A0(ρ, θ) is the background light intensity of standard Newton ring interference figure under second order polar coordinates, B0(ρ, θ) is under second order polar coordinates
The intetference-fit strengthening of standard Newton ring interference figure, f0For the line carrier frequency system of standard Newton ring interference figure under second order polar coordinates
Number.
Low frequency moiré topography is obtained by low-pass filtering after step 4, superposition Moire fringe, light intensity S (ρ, θ) expression formula is such as
Under:
S (ρ, θ)=A'(ρ, θ)+B'(ρ, θ) cos [2 π ρ (fc-f0)]
Wherein, A'(ρ, θ) be second order polar coordinates under background light intensity, B'(ρ, θ) be second order polar coordinates under contrast,
fc-f0For the line carrier frequency coefficient of low frequency moiré topography under second order polar coordinates.
Low frequency moiré topography under second order polar coordinates is recovered wave by Fourier transformation phase demodulating method by step 5
Face data, and the wavefront differential data being converted under cartesian coordinate system, seek the radius of curvature R of spherical surface 7 to be measuredi:
w0The thickness of the airspace of (x, y) between cartesian coordinate subscript director sphere and reference planes, w (x, y) are
The thickness of airspace under cartesian coordinate between spherical surface to be measured and reference planes.R0For the radius of curvature of standard spherical surface, (x,
It y) is the coordinate at any point on the Newton ring interference figure of spherical surface 7 to be measured under cartesian coordinate system.
Step 6, by the radius of curvature R of spherical surface 7 to be measurediIt substitutes into sphere curvature radius nonzero digit detection ZEMAX model, asks
Take hysterisis error W_retracei, when the ball to be measured that 7 radius of curvature of spherical surface to be measured that this circulation obtains was recycled with last time
When being more than or equal to 50mm of 7 radius of curvature of face, return step 2, to W_retraceiIt updates；Otherwise circulation is terminated, is obtained to be measured
The radius of curvature R of spherical surface 7out。
In conjunction with Fig. 2, a kind of device of the spherical surface larger radius of curvature nonzero digit measurement method based on virtual Newton's ring, step 1
In, the device for acquiring the Newton ring interference figure T (x, y) of spherical surface 7 to be measured is as follows: including polarizing frequency stabilized He-Ne laser 1, convex lens
2, spatial filter 3, spectroscope 4, colimated light system 5, standard mirror 6, imaging system 8 and ccd detector 9, wherein common optical axis is successively
Setting polarization frequency stabilized He-Ne laser 1, convex lens 2, spatial filter 3, spectroscope 4, colimated light system 5, standard mirror 6 and ball to be measured
Face 7, imaging system 8 and 9 common optical axis of ccd detector are arranged on the reflected light path of spectroscope 4；All optical elements are relative to base
Bottom is coaxially contour；One monochromic beam is issued by polarization frequency stabilized He-Ne laser 1, planoconvex lens 2 are assembled, and spatial filter 3 is passed through
Filtering, is incident to spectroscope 4, divides through spectroscope 4 for transmitted light and reflected light, and transmitted light is incident to colimated light system 5, forms collimation
Light beam, after collimated light beam enters standard mirror 6, part collimated light beam is reflected by the rear surface of standard mirror 6, forms standard light, separately
A part of collimated light beam is incident to spherical surface 7 to be measured by standard mirror 6, the front surface reflection through spherical surface 7 to be measured, forms test light,
Standard light and test light are returned along input path, imaging system 8 are reflected by spectroscope 4, in 9 target surface of ccd detector
Upper imaging, the image grayscale information recorded on 9 target surface of ccd detector, the Newton ring interference figure T (x, y) of spherical surface 7 as to be measured.
Colimated light system 5 achievees the effect that incident beam collimating outgoing using the simple combination mode of concave-convex lens.
Interference light light beam is imaged on CCD target surface by imaging system 8 by the way of lens group combination.
Compared with prior art, the present invention its remarkable advantage is: (1) experimentation is simple, and ensure that experimental precision.
(2) influence that hysterisis error measures spherical surface larger radius of curvature is greatly weakened.
Embodiment:
Feisuo type sphere curvature radius non-zero position detecting system is constructed, measured piece is that radius of curvature standard value is
The concave mirror of 41400mm, effective aperture 50mm；Canonical reference sphere curvature radius is 51000mm, and effective aperture is
50mm。
The Newton ring interference figure T (x, y) of step 1, acquisition spherical surface 7 to be measured.
Step 2 detects ZEMAX model emulation standard sphere curvature radius by sphere curvature radius nonzero digit as R0Return
Journey error W_retrace is simultaneously substituted into the emulation corrugated data of standard Newton ring interference figure, and emulation obtains standard Newton ring interference
Scheme T0(x, y):
T0(x, y)=A0(x,y)+B0(x,y)cos[2πf0(x2+y2)]
A0(x, y) is the background light intensity of standard Newton ring interference figure under cartesian coordinate, B0(x, y) is under cartesian coordinate
The intetference-fit strengthening of standard Newton ring interference figure, f0For the line carrier frequency system of standard Newton ring interference figure under cartesian coordinate
Number, (x, y) are the coordinate at any point on the Newton ring interference figure of cartesian coordinate subscript director sphere 7.
Step 3, Newton ring interference figure T (x, y) and standard Newton ring interference by the spherical surface to be measured 7 under cartesian coordinate system
Scheme T0(x, y) is converted to the interference pattern under second order polar coordinate system, such as Fig. 3:
Newton ring interference figure to be measured: T (ρ, θ)=A (ρ, θ)+B (ρ, θ) cos (2 π fc ρ)
Standard Newton ring interference figure: T0(ρ, θ)=A0(ρ,θ)+B0(ρ,θ)cos(2πf0ρ)
A (ρ, θ) is the background light intensity of Newton ring interference figure to be measured under second order polar coordinates, B (ρ, θ) be under second order polar coordinates to
Survey the intetference-fit strengthening of Newton ring interference figure, fcFor the line carrier frequency coefficient of Newton ring interference figure to be measured under second order polar coordinates.
(ρ, θ) is the polar coordinates at any point on the Newton ring interference figure of spherical surface 7 to be measured under second order polar coordinate system.
A0(ρ, θ) is the background light intensity of standard Newton ring interference figure under second order polar coordinates, B0(ρ, θ) is under second order polar coordinates
The intetference-fit strengthening of standard Newton ring interference figure, f0For the line carrier frequency system of standard Newton ring interference figure under second order polar coordinates
Number.
Low frequency moiré topography, such as Fig. 4, light intensity S (ρ, θ) table are obtained by low-pass filtering after step 4, superposition Moire fringe
It is as follows up to formula:
S (ρ, θ)=A'(ρ, θ)+B'(ρ, θ) cos [2 π ρ (fc-f0)]
Wherein, A'(ρ, θ) be second order polar coordinates under background light intensity, B'(ρ, θ) be second order polar coordinates under contrast,
fc-f0For the line carrier frequency coefficient of low frequency moiré topography under second order polar coordinates；
Low frequency moiré topography under second order polar coordinates is recovered wave by Fourier transformation phase demodulating method by step 5
Face data w (ρ, θ)-w0(ρ, θ) (see reference document Radius Measurement of Spherical Surfaces With
Large Radii-of-Curvature Using Dual-Focus Zone Plates), and it is converted into cartesian coordinate
Wavefront differential data w (x, y)-w under system0(x, y) seeks the radius of curvature R of spherical surface 7 to be measured such as Fig. 5i:
w0The thickness of the airspace of (x, y) between cartesian coordinate system subscript director sphere and reference planes, w (x, y)
The thickness of airspace between spherical surface to be measured under cartesian coordinate system and reference planes.R0For the curvature half of standard spherical surface
Diameter, (x, y) are the coordinate at any point on the Newton ring interference figure of spherical surface 7 to be measured under cartesian coordinate system.
Step 6, by the radius of curvature R of spherical surface 7 to be measurediIt substitutes into sphere curvature radius nonzero digit detection ZEMAX model, asks
Take hysterisis error W_retracei, when the ball to be measured that 7 radius of curvature of spherical surface to be measured that this circulation obtains was recycled with last time
When being more than or equal to 50mm of 7 radius of curvature of face, return step 2, to W_retraceiIt updates；Otherwise circulation is terminated, is obtained to be measured
The radius of curvature R of spherical surface 7out.Radius of curvature result is 41307mm, the result and tested spherical surface mirror curvature half that simulation calculation obtains
Diameter nominal value 41400mm is compared, error 0.22%, such as Fig. 6.
The method precision that the experiment measures 7 radius of curvature of spherical surface to be measured is no less than existing deep camber measurement method, and big
Influence of the hysterisis error in larger radius of curvature spherical surface measurement is weakened greatly, is effective deep camber measurement method.
Claims (2)
1. a kind of spherical surface larger radius of curvature nonzero digit measurement method based on virtual Newton's ring, which is characterized in that spherical surface mirror curvature
Radius measurement detecting step are as follows:
Step 1, the Newton ring interference figure T (x, y) for acquiring spherical surface (7) to be measured；
Step 2 detects ZEMAX model emulation standard sphere curvature radius by sphere curvature radius nonzero digit as R0Backhaul miss
Poor W_retrace is simultaneously substituted into the emulation corrugated data of standard Newton ring interference figure, and emulation obtains standard Newton ring interference figure T0
(x, y):
T0(x, y)=A0(x,y)+B0(x,y)cos[2πf0(x2+y2)]
A0(x, y) is the background light intensity of standard Newton ring interference figure under cartesian coordinate, B0(x, y) is standard under cartesian coordinate
The intetference-fit strengthening of Newton ring interference figure, f0For the line carrier frequency coefficient of standard Newton ring interference figure under cartesian coordinate, (x,
It y) is the coordinate at any point on the Newton ring interference figure of spherical surface (7) to be measured under cartesian coordinate；
Step 3, Newton ring interference figure T (x, y) and standard Newton ring interference figure by the spherical surface to be measured (7) under cartesian coordinate system
T0(x, y) is converted to the interference pattern under second order polar coordinate system:
Newton ring interference figure to be measured: T (ρ, θ)=A (ρ, θ)+B (ρ, θ) cos (2 π fcρ)
Standard Newton ring interference figure: T0(ρ, θ)=A0(ρ,θ)+B0(ρ,θ)cos(2πf0ρ)
A (ρ, θ) is the background light intensity of Newton ring interference figure to be measured under second order polar coordinates, and B (ρ, θ) is ox to be measured under second order polar coordinates
The intetference-fit strengthening of ring interference pattern, fcFor the line carrier frequency coefficient of Newton ring interference figure to be measured under second order polar coordinates；(ρ,θ)
For the polar coordinates at any point on the Newton ring interference figure of spherical surface (7) to be measured under second order polar coordinate system；
A0(ρ, θ) is the background light intensity of standard Newton ring interference figure under second order polar coordinates, B0(ρ, θ) is standard under second order polar coordinates
The intetference-fit strengthening of Newton ring interference figure, f0For the line carrier frequency coefficient of standard Newton ring interference figure under second order polar coordinates；
Low frequency moiré topography is obtained by low-pass filtering after step 4, superposition Moire fringe, light intensity S (ρ, θ) expression formula is as follows:
S (ρ, θ)=A'(ρ, θ)+B'(ρ, θ) cos [2 π ρ (fc-f0)]
Wherein, A'(ρ, θ) be second order polar coordinates under background light intensity, B'(ρ, θ) be second order polar coordinates under contrast, fc-f0For
The line carrier frequency coefficient of low frequency moiré topography under second order polar coordinates；
Low frequency moiré topography under second order polar coordinates is recovered corrugated number by Fourier transformation phase demodulating method by step 5
According to, and the wavefront differential data being converted under cartesian coordinate system, seek the radius of curvature R of spherical surface to be measured (7)i:
w0The thickness of the airspace of (x, y) between cartesian coordinate system subscript director sphere and reference planes, w (x, y) are flute card
The thickness of airspace under your coordinate system between spherical surface to be measured and reference planes；R0For the radius of curvature of standard spherical surface, (x, y)
For the coordinate at any point on the Newton ring interference figure of spherical surface (7) to be measured under cartesian coordinate system；
Step 6, by the radius of curvature R of spherical surface to be measured (7)iIt substitutes into sphere curvature radius nonzero digit detection ZEMAX model, seeks
Hysterisis error W_retracei, when the ball to be measured that spherical surface to be measured (7) radius of curvature that this circulation obtains was recycled with last time
When being more than or equal to 50mm of face (7) radius of curvature, return step 2；Otherwise circulation is terminated, the curvature half of spherical surface to be measured (7) is obtained
Diameter Rout。
2. based on the device of the spherical surface larger radius of curvature nonzero digit measurement method described in claim 1 based on virtual Newton's ring,
It is characterized in that, the device for acquiring the Newton ring interference figure T (x, y) of spherical surface to be measured (7) is as follows in step 1:
Including polarization frequency stabilized He-Ne laser (1), convex lens (2), spatial filter (3), spectroscope (4), colimated light system (5),
Standard mirror (6), imaging system (8) and ccd detector (9), wherein common optical axis set gradually polarization frequency stabilized He-Ne laser (1),
Convex lens (2), spatial filter (3), spectroscope (4), colimated light system (5), standard mirror (6) and spherical surface to be measured (7), imaging system
(8) it is arranged on the reflected light path of spectroscope (4) with ccd detector (9) common optical axis；All optical elements are coaxial relative to substrate
It is contour；One monochromic beam is issued by polarization frequency stabilized He-Ne laser (1), planoconvex lens (2) are assembled, passed through spatial filter (3)
Filtering, is incident to spectroscope (4), is divided into transmitted light and reflected light through spectroscope (4), transmitted light is incident to colimated light system (5), shape
At collimated light beam, after collimated light beam enters standard mirror (6), part collimated light beam is reflected by the rear surface of standard mirror (6), is formed
Standard light, another part collimated light beam are incident to spherical surface to be measured (7) by standard mirror (6), and the front surface through spherical surface to be measured (7) is anti-
It penetrates, forms test light, standard light and test light are returned along input path, are reflected into imaging system by spectroscope (4)
(8), it is imaged on ccd detector (9) target surface, the image grayscale information recorded on ccd detector (9) target surface, ball as to be measured
The Newton ring interference figure T (x, y) in face (7).
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