CN106595529A - Measurement method and device for large-curvature-radius non-zero-digit interference based on virtual Newton's ring - Google Patents

Measurement method and device for large-curvature-radius non-zero-digit interference based on virtual Newton's ring Download PDF

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CN106595529A
CN106595529A CN201610147404.2A CN201610147404A CN106595529A CN 106595529 A CN106595529 A CN 106595529A CN 201610147404 A CN201610147404 A CN 201610147404A CN 106595529 A CN106595529 A CN 106595529A
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sphere
measured
curvature
newton ring
standard
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CN106595529B (en
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高志山
黄磊
杨忠明
王凯亮
赵彦
陈玥洋
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/24Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/255Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures for measuring radius of curvature

Abstract

The invention provides a measurement method and device for large-curvature-radius non-zero-digit interference based on a virtual Newton's ring. Circular carrier-frequency Newton's ring interferograms are converted into linear carrier-frequency interferograms via second-order polar coordinates, a low-frequency moire fringe graph after low-pass filtering is demodulated, wavefront differential data between a to-be-measured spherical surface and a standard spherical surface is extracted, and a calculation formula of the curvature radius is derived. On the basis of a model of a ZEMAX software based Fizeau spherical large-curvature-radium non-zero-digit detection system, a finite iteration method is used correct backhaul errors during Newton's ring interferogram collection in non-zero-digit detection. The Fizeau spherical large-curvature-radium non-zero-digit detection system is constructed, and verification for the spherical large-curvature-radium non-zero-digit measurement technology based on the virtual Newton's ring is completed.

Description

Larger radius of curvature nonzero digit interferometric method and device based on virtual Newton's ring
Technical field
The invention belongs to optical measuring technique, particularly a kind of larger radius of curvature nonzero digit interferometric method and device based on Newton's ring.
Background technology
Spherical mirror is a kind of optical element common in optical system, there is important application in all kinds of optical systems.For example, in Next Generation Lithographies projection objective system (Extreme Ultra-violet, abbreviation EUV), using 13.5nm total-reflection type lithographic objectives.Comprising 6 off-axis spheres or aspherical mirror in the system, the crudy of spherical reflector has the impact of key to the imaging effect of whole system.Radius of curvature (radius of curvature, ROC) is the Important Parameters for characterizing optical spherical surface mirror optical characteristics.Curvature radius of spherical reflector has very big impact to the image quality of optical system.In the process of spherical reflector, the radius of curvature for accurately measuring measurement spherical mirror is the important process of optical workshop inspection.
With the development of Large optical system, for the requirement also more and more higher of the radius of curvature measurement precision of larger radius of curvature aspherical elements.Calendar year 2001 Zhejiang University Yang Yongying et al. on the basis of various larger radius of curvature measuring methods are analyzed, it is proposed that Laser Newton Rings method.The measurable radius of curvature measurement scope of the method is 1~25m, and relative error is better than 0.3%.Foucault Knife-edge Shadow methods are the relatively common methods that larger radius of curvature aspherical elements are measured in optical workshop.The precision of the method depends on the precision of range-measurement system, can reach 0.05%, but the method is harsher to environmental requirement.Auto-collimating microscope method can measure convex surface and concave surface spherical optics element, the detection of suitable optical elements of large caliber, but the method certainty of measurement is limited to the error of focusing of human eye and the position error of length measurement system, and measurement range is limited by length measurement system and working distance of microscope.It is one of common method of spherical optics element curvature radius based on the differential confocal method of laser spherical interferometer.Aspherical elements to be measured are moved along guide rail direction, and part to be measured produces zero order interference fringe in opal and confocal position.The distance between opal and confocal position are the radius of curvature of sphere to be measured, and certainty of measurement depends on the distance between opal position and confocal position certainty of measurement, is limited to the restriction of test environment and rail length, and the measurement range of the method is limited.Graduate Hengyu Yi of Mianyang gongwu in 2011 et al. are proposed by design compensation device to reduce interference cavity length.Compensator constitutes a zooming system with mirror to be measured, and by adjusting test of the compensating glass realization to different curvature radius, relative error is better than 4.2 × 10-4.For the limitation of conventional confocal mensuration, 2014 American National Standard technical research institute (NIST) Quandou Wang et al. propose to replace the method for testing of standard spherical mirror using bifocal zone plate.The method is limited to the design of bifocal zone plate and machining accuracy, and measurement cost is higher.
The content of the invention
It is an object of the invention to provide a kind of larger radius of curvature nonzero digit interferometric method and device based on Newton's ring, in the case where experimental precision is ensured, correct the hysterisis error in sphere larger radius of curvature non-zero position detecting system using the method for finite iteration simultaneously, largely reducing the impact that hysterisis error is measured larger radius of curvature.
The technical solution for realizing the object of the invention is:A kind of sphere larger radius of curvature nonzero digit measuring method based on virtual Newton's ring, spherical mirror radius of curvature measurement detecting step is:
Step 1, Newton ring interference figure T (x, y) for gathering sphere to be measured.
Step 2, detect that ZEMAX model emulation standards sphere curvature radius is R by sphere curvature radius nonzero digit0Hysterisis error W_retrace and substitute into the emulation corrugated data of standard Newton ring interference figure, 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) be cartesian coordinate under standard Newton ring interference figure background light intensity, B0(x, y) be cartesian coordinate under standard Newton ring interference figure intetference-fit strengthening, f0For the line carrier frequency coefficient of standard Newton ring interference figure under cartesian coordinate, (x, y) is the coordinate of any point on the Newton ring interference figure of sphere to be measured under cartesian coordinate.
Step 3, by Newton ring interference figure T (x, y) of the sphere to be measured under cartesian coordinate system and standard Newton ring interference figure 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) be second order polar coordinates under Newton ring interference figure to be measured background light intensity, B (ρ, θ) be second order polar coordinates under Newton ring interference figure to be measured intetference-fit strengthening, 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 of any point on the Newton ring interference figure of sphere to be measured under second order polar coordinate system.
A0(ρ, θ) be second order polar coordinates under standard Newton ring interference figure background light intensity, B0(ρ, θ) be second order polar coordinates under standard Newton ring interference figure intetference-fit strengthening, f0For the line carrier frequency coefficient of standard Newton ring interference figure under second order polar coordinates.
Step 5, the low frequency moiré topography under second order polar coordinates is recovered into corrugated data by Fourier transformation phase demodulating method, and be converted into the wavefront differential data under cartesian coordinate system, ask for the radius of curvature R of sphere to be measuredi
w0(x, y) is the thickness of the airspace between cartesian coordinate system subscript director sphere and reference planes, and w (x, y) is the thickness of the airspace under cartesian coordinate system between sphere to be measured and reference planes;R0For the radius of curvature of standard sphere, (x, y) is the coordinate of any point on the Newton ring interference figure of sphere to be measured under cartesian coordinate system.
Step 6, by the radius of curvature R of sphere to be measurediIn substituting into sphere curvature radius nonzero digit detection ZEMAX models, hysterisis error W_retrace is asked fori, when the sphere curvature radius to be measured that the sphere curvature radius to be measured that this circulation is obtained is obtained with last time circulation is more than or equal to 50mm, return to step 2;Otherwise terminate circulation, obtain the radius of curvature R of sphere to be measuredout
A kind of device of the sphere larger radius of curvature nonzero digit measuring method based on virtual Newton's ring, in step 1, the device for gathering Newton ring interference figure T (x, y) of sphere to be measured is as follows:Including polarization frequency stabilized He-Ne laser, convex lens, spatial filter, spectroscope, colimated light system, standard mirror, imaging system and ccd detector, wherein, common optical axis sets gradually polarization frequency stabilized He-Ne laser, convex lens, spatial filter, spectroscope, colimated light system, standard mirror and sphere to be measured, and imaging system and ccd detector common optical axis are arranged on spectroscopical reflected light path;All optical elements are coaxially contour relative to substrate;One monochromic beam is sent by polarization frequency stabilized He-Ne laser, planoconvex lens is assembled, filtered by spatial filter, it is incident to spectroscope, Jing spectroscopes are divided into transmitted light and reflected light, transmitted light is incident to colimated light system, form collimated light beam, collimated light beam is entered after standard mirror, the surface reflection after standard mirror of part collimated light beam, formation standard light, another part collimated light beam is incident to sphere to be measured by standard mirror, the front surface reflection of Jing spheres to be measured, form test light, standard light is returned with test light along input path, imaging system is entered through dichroic mirror, it is imaged on ccd detector target surface, the gradation of image information recorded on ccd detector target surface, the Newton ring interference figure T (x of sphere as to be measured, y).
Compared with prior art, its remarkable advantage is the present invention:(1) experimentation is simple, and ensure that experimental precision.(2) impact that hysterisis error is measured sphere larger radius of curvature is greatly weakened.
Description of the drawings
Fig. 1 is flow chart of the present invention based on the sphere larger radius of curvature nonzero digit measuring method of virtual Newton's ring.
Fig. 2 is that the present invention realizes installation drawing based on the sphere larger radius of curvature nonzero digit measuring method of virtual Newton's ring.
Fig. 3 is Newton ring interference figure to be measured and standard Newton ring interference figure in the embodiment of the present invention:Wherein (a) is the Newton ring interference figure to be measured under cartesian coordinate, b () is the Newton ring interference figure to be measured under second order polar coordinates, c () is the standard Newton ring interference figure comprising hysterisis error under cartesian coordinate, be (d) the standard Newton ring interference figure comprising hysterisis error under second order polar coordinates
Fig. 4 is the Moire fringe in the embodiment of the present invention under second order polar coordinates:A () is the Moire fringe before filtering, (b) be filtered Moire fringe.
Fig. 5 is the wavefront differential data of sphere to be measured and standard sphere in the embodiment of the present invention:A () is the corrugated differential data under second order polar coordinates, be (b) the corrugated differential data under cartesian coordinate.
Fig. 6 is the radius of curvature measurement simulation result of sphere to be measured in the embodiment of the present invention.
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
The present invention Integral Thought be:Circle carrier frequency Newton ring interference figure is converted to into line carrier frequency interference pattern using second order polar coordinate transform, the Moire fringe to be formed is superimposed using the line carrier frequency Newton ring interference figure to be measured under second order polar coordinates and line carrier frequency standard Newton ring interference figure, low frequency moiré topography after by demodulating LPF, the wavefront differential data of sphere to be measured and standard sphere is extracted, the computing formula of radius of curvature is deduced.
With reference to Fig. 1, a kind of sphere larger radius of curvature nonzero digit measuring method based on virtual Newton's ring, spherical mirror radius of curvature measurement detecting step is:
Step 1, Newton ring interference figure T (x, y) for gathering sphere 7 to be measured.
Step 2, detect that ZEMAX model emulation standards sphere curvature radius is R by sphere curvature radius nonzero digit0Hysterisis error W_retrace and substitute into the emulation corrugated data of standard Newton ring interference figure, 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) be cartesian coordinate under standard Newton ring interference figure background light intensity, B0(x, y) be cartesian coordinate under standard Newton ring interference figure intetference-fit strengthening, f0For the line carrier frequency coefficient of standard Newton ring interference figure under cartesian coordinate, (x, y) is the coordinate of any point on the Newton ring interference figure of sphere to be measured 7 under cartesian coordinate.
Step 3, by Newton ring interference figure T (x, y) of the sphere to be measured 7 under cartesian coordinate system and standard Newton ring interference figure 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) be second order polar coordinates under Newton ring interference figure to be measured background light intensity, B (ρ, θ) be second order polar coordinates under Newton ring interference figure to be measured intetference-fit strengthening, 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 of any point on the Newton ring interference figure of sphere to be measured 7 under second order polar coordinate system.
A0(ρ, θ) be second order polar coordinates under standard Newton ring interference figure background light intensity, B0(ρ, θ) be second order polar coordinates under standard Newton ring interference figure intetference-fit strengthening, f0For the line carrier frequency coefficient of standard Newton ring interference figure under second order polar coordinates.
Low frequency moiré topography is obtained by LPF 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) for the background light intensity under second order polar coordinates, B'(ρ, θ) for the contrast under second order polar coordinates, fc-f0For the line carrier frequency coefficient of low frequency moiré topography under second order polar coordinates.
Step 5, the low frequency moiré topography under second order polar coordinates is recovered into corrugated data by Fourier transformation phase demodulating method, and be converted into the wavefront differential data under cartesian coordinate system, ask for the radius of curvature R of sphere to be measured 7i
w0(x, y) is the thickness of the airspace between cartesian coordinate subscript director sphere and reference planes, and w (x, y) is the thickness of the airspace under cartesian coordinate between sphere to be measured and reference planes.R0For the radius of curvature of standard sphere, (x, y) is the coordinate of any point on the Newton ring interference figure of sphere to be measured 7 under cartesian coordinate system.
Step 6, by the radius of curvature R of sphere to be measured 7iIn substituting into sphere curvature radius nonzero digit detection ZEMAX models, hysterisis error W_retrace is asked fori, when the radius of curvature of sphere to be measured 7 that the radius of curvature of sphere to be measured 7 that this circulation is obtained is obtained with last time circulation is more than or equal to 50mm, return to step 2, to W_retraceiUpdate;Otherwise terminate circulation, obtain the radius of curvature R of sphere to be measured 7out
With reference to Fig. 2, a kind of device of the sphere larger radius of curvature nonzero digit measuring method based on virtual Newton's ring, in step 1, the device for gathering Newton ring interference figure T (x, y) of sphere 7 to be measured is as follows: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 sets gradually polarization frequency stabilized He-Ne laser 1, convex lens 2, spatial filter 3, spectroscope 4, colimated light system 5, standard mirror 6 and sphere to be measured 7, and imaging system 8 and the common optical axis of ccd detector 9 are arranged on the reflected light path of spectroscope 4;All optical elements are coaxially contour relative to substrate;One monochromic beam is sent by polarization frequency stabilized He-Ne laser 1, planoconvex lens 2 is assembled, filtered by spatial filter 3, it is incident to spectroscope 4, 4 points of Jing spectroscopes are transmitted light and reflected light, transmitted light is incident to colimated light system 5, form collimated light beam, collimated light beam is entered after standard mirror 6, the surface reflection after standard mirror 6 of part collimated light beam, formation standard light, another part collimated light beam is incident to sphere to be measured 7 by standard mirror 6, the front surface reflection of Jing spheres 7 to be measured, form test light, standard light is returned with test light along input path, imaging system 8 is reflected into through spectroscope 4, it is imaged on the target surface of ccd detector 9, the gradation of image information recorded on the target surface of ccd detector 9, the Newton ring interference figure T (x of sphere 7 as to be measured, y).
Colimated light system 5 reaches the effect that incident beam is collimated outgoing using the simple combination mode of concave-convex lens.
Imaging system 8 is imaged on interference light light beam on CCD target surfaces by the way of lens group combination.
Compared with prior art, its remarkable advantage is the present invention:(1) experimentation is simple, and ensure that experimental precision.(2) impact that hysterisis error is measured sphere larger radius of curvature is greatly weakened.
Embodiment:
Feisuo type sphere curvature radius non-zero position detecting system is constructed, measured piece is the concave mirror that radius of curvature standard value is 41400mm, and effective aperture is 50mm;Canonical reference sphere curvature radius is 51000mm, and effective aperture is 50mm.
Step 1, Newton ring interference figure T (x, y) for gathering sphere 7 to be measured.
Step 2, detect that ZEMAX model emulation standards sphere curvature radius is R by sphere curvature radius nonzero digit0Hysterisis error W_retrace and substitute into the emulation corrugated data of standard Newton ring interference figure, 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) be cartesian coordinate under standard Newton ring interference figure background light intensity, B0(x, y) be cartesian coordinate under standard Newton ring interference figure intetference-fit strengthening, f0For the line carrier frequency coefficient of standard Newton ring interference figure under cartesian coordinate, (x, y) is the coordinate of any point on the Newton ring interference figure of cartesian coordinate subscript director sphere 7.
Step 3, by Newton ring interference figure T (x, y) of the sphere to be measured 7 under cartesian coordinate system and standard Newton ring interference figure 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 fcρ)
Standard Newton ring interference figure:T0(ρ, θ)=A0(ρ,θ)+B0(ρ,θ)cos(2πf0ρ)
A (ρ, θ) be second order polar coordinates under Newton ring interference figure to be measured background light intensity, B (ρ, θ) be second order polar coordinates under Newton ring interference figure to be measured intetference-fit strengthening, 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 of any point on the Newton ring interference figure of sphere to be measured 7 under second order polar coordinate system.
A0(ρ, θ) be second order polar coordinates under standard Newton ring interference figure background light intensity, B0(ρ, θ) be second order polar coordinates under standard Newton ring interference figure intetference-fit strengthening, f0For the line carrier frequency coefficient of standard Newton ring interference figure under second order polar coordinates.
Low frequency moiré topography, such as Fig. 4 are obtained by LPF 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) for the background light intensity under second order polar coordinates, B'(ρ, θ) for the contrast under second order polar coordinates, fc-f0For the line carrier frequency coefficient of low frequency moiré topography under second order polar coordinates;
Step 5, the low frequency moiré topography under second order polar coordinates is recovered into corrugated data w (ρ, θ)-w by Fourier transformation phase demodulating method0(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 wavefront differential data w (x, the y)-w under cartesian coordinate system0(x, y), such as Fig. 5 (wavefront differential data is colour picture, because Patent Law detailed rules for the implementation are required, can only provide artwork master, and such as auditor requires, it is possible to provide the corresponding colour picture of this picture), ask for the radius of curvature R of sphere to be measured 7i
w0(x, y) is the thickness of the airspace between cartesian coordinate system subscript director sphere and reference planes, and w (x, y) is the thickness of the airspace under cartesian coordinate system between sphere to be measured and reference planes.R0For the radius of curvature of standard sphere, (x, y) is the coordinate of any point on the Newton ring interference figure of sphere to be measured 7 under cartesian coordinate system.
Step 6, by the radius of curvature R of sphere to be measured 7iIn substituting into sphere curvature radius nonzero digit detection ZEMAX models, hysterisis error W_retrace is asked fori, when the radius of curvature of sphere to be measured 7 that the radius of curvature of sphere to be measured 7 that this circulation is obtained is obtained with last time circulation is more than or equal to 50mm, return to step 2, to W_retraceiUpdate;Otherwise terminate circulation, obtain the radius of curvature R of sphere to be measured 7out.Radius of curvature result is 41307mm, the result that simulation calculation is obtained is compared with tested sphere curvature radius nominal value 41400mm, error is 0.22%, such as Fig. 6, (the radius of curvature measurement simulation result of sphere to be measured should be colour picture, because Patent Law detailed rules for the implementation are required, artwork master can only be provided, such as auditor requires, it is possible to provide the corresponding colour picture of this picture).
The experiment measures the method precision of the radius of curvature of sphere 7 to be measured no less than existing deep camber measuring method, and largely reducing impact of the hysterisis error in larger radius of curvature spherical surface measurement, is effective deep camber measuring method.

Claims (2)

1. a kind of sphere larger radius of curvature nonzero digit measuring method based on virtual Newton's ring, it is characterised in that Spherical mirror radius of curvature measurement detecting step is:
Step 1, Newton ring interference figure T (x, y) for gathering sphere (7) to be measured;
Step 2, by sphere curvature radius nonzero digit detect ZEMAX model emulation standard sphere curvature radius For R0Hysterisis error W_retrace and substitute into the emulation corrugated data of standard Newton ring interference figure, emulation Obtain standard Newton ring interference figure T0(x,y):
T0(x, y)=A0(x,y)+B0(x,y)cos[2πf0(x2+y2)]
A0(x, y) be cartesian coordinate under standard Newton ring interference figure background light intensity, B0(x, y) is Descartes's seat The intetference-fit strengthening of the lower standard Newton ring interference figure of mark, f0For standard Newton ring interference under cartesian coordinate The line carrier frequency coefficient of figure, (x, y) is that the Newton ring interference figure of sphere (7) to be measured under cartesian coordinate is taken up an official post Anticipate the coordinate of a bit;
Step 3, by Newton ring interference figure T (x, y) and standard of the sphere to be measured (7) under cartesian coordinate system Newton ring interference figure 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 second order pole seat The intetference-fit strengthening of Newton ring interference figure to be measured, f under markcFor Newton ring interference to be measured under second order polar coordinates The line carrier frequency coefficient of figure;(ρ, θ) is that the Newton ring interference figure of sphere (7) to be measured under second order polar coordinate system is taken up an official post Anticipate the polar coordinates of a bit;
A0(ρ, θ) be second order polar coordinates under standard Newton ring interference figure background light intensity, B0(ρ, θ) is second order pole seat The intetference-fit strengthening of the lower standard Newton ring interference figure of mark, f0For standard Newton ring interference under second order polar coordinates The line carrier frequency coefficient of figure;
Step 5, by the low frequency moiré topography under second order polar coordinates by Fourier transformation phase demodulating method recover Go out corrugated data, and be converted into the wavefront differential data under cartesian coordinate system, ask for sphere to be measured (7) Radius of curvature Ri
R i = R 0 · ( x 2 + y 2 ) 2 R 0 · [ w ( x , y ) - w 0 ( x , y ) ] + ( x 2 + y 2 )
w0(x, y) for airspace between cartesian coordinate system subscript director sphere and reference planes thickness, w (x, y) For the thickness of the airspace under cartesian coordinate system between sphere to be measured and reference planes;R0For standard sphere Radius of curvature, (x, y) be cartesian coordinate system under sphere (7) to be measured Newton ring interference figure on any point Coordinate;
Step 6, by the radius of curvature R of sphere to be measured (7)iSubstitute into sphere curvature radius nonzero digit detection ZEMAX In model, hysterisis error W_retrace is asked fori, when sphere to be measured (7) radius of curvature that this circulation is obtained When being more than or equal to 50mm of sphere to be measured (7) radius of curvature obtained with last time circulation, return to step 2; Otherwise terminate circulation, obtain the radius of curvature R of sphere to be measured (7)out
2. based on the sphere larger radius of curvature nonzero digit measurement side based on virtual Newton's ring described in claim 1 The device of method, it is characterised in that in step 1, gathers Newton ring interference figure T (x, y) of sphere (7) to be measured Device is as follows:
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 sphere to be measured (7), imaging system (8) and ccd detector (9) Common optical axis is arranged on the reflected light path of spectroscope (4);All optical elements are coaxially contour relative to substrate; One monochromic beam is sent by polarization frequency stabilized He-Ne laser (1), planoconvex lens (2) is assembled, and is filtered by space Ripple device (3) is filtered, and is incident to spectroscope (4), and Jing spectroscopes (4) are divided into transmitted light and reflected light, transmission Light is incident to colimated light system (5), forms collimated light beam, and collimated light beam is entered after standard mirror (6), and part is accurate Collimated optical beam surface reflection after standard mirror (6), forms standard light, and another part collimated light beam is by mark Quasi- mirror (6) is incident to sphere to be measured (7), and the front surface reflection of Jing spheres to be measured (7) forms test light, Standard light is returned with test light along input path, and through spectroscope (4) imaging system (8) is reflected into, It is imaged on ccd detector (9) target surface, the gradation of image information recorded on ccd detector (9) target surface, Newton ring interference figure T (x, y) of sphere (7) as to be measured.
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