CN104048619B - It is a kind of to judge that axisymmetry aspheric surface adopt the method for directly interfering detection - Google Patents
It is a kind of to judge that axisymmetry aspheric surface adopt the method for directly interfering detection Download PDFInfo
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Abstract
The invention discloses a kind of judge that can axisymmetry aspheric surface using the method for directly interference detection, basis for estimation be：When directly interfering detection axisymmetry aspheric surface using digital wavefront interferometer, can the interference pattern of collection be differentiated completely by the detector of digital wavefront interferometer, i.e. on interference pattern, whether the corresponding wave aberration of an interference fringe of interference fringe thickness is less than the corresponding wave aberration of Nyquist frequencies of detector, it is that then axisymmetry aspheric surface directly interferes the method for detecting for digital wavefront interferometer can be adopted.Instant invention overcomes whether a certain axisymmetry aspheric surface of micro-judgment can adopt the inaccuracy for directly interfering detection for certain digital wavefront interferometer, the present invention provide can intuitively, be accurately used for judging that can axisymmetry aspheric surface adopt the method that directly interference be detected, it is theoretical reliable, accuracy of judgement, it is applied widely, the formulation time of axisymmetry Aspherical-surface testing scheme is saved, work efficiency is improved.
Description
Technical field
The invention belongs to advanced optics manufacture and detection technique field, and in particular to one kind judges axisymmetry aspheric surface
The method for directly interfering detection can be adopted.
Background technology
The detection of high-precision optical non-spherical element face shape is mainly adopted interferes detection technique, in the technology, without picture
Not good enough detection, zero compensation interfere detection and nonzero digit to interfere detection to be widely used to the face shape inspection in aspheric surface polishing stage
Survey.
Wherein, aberrationless point detection refers to that light is passed in addition a bit from a bit, through arbitrarily repeatedly according to Fermat's principle
Refraction is reflected, and its light path is maximum value or minimum value, that is to say, that light path is definite value, and optically such point is referred to as without picture
Almost, detect that aspheric method is referred to as the detection of aberrationless point using aberrationless point, what which utilized is quadric aberrationless
Dot characteristics, are made reference light be interfered with the reflected light with tested aspheric surface information, and are cut in aberrationless point with knife
Light path, observes due to interfering the echo for producing, by the interpretation to echo, determines aspheric face shape information.Aberrationless
Point detecting method has as a drawback that：Aberrationless point is detected mainly for detection of axisymmetry quadratic surface, it is impossible to detection rotation
The symmetrical high-order curved surface of rotating shaft；The greater experience of testing staff is relied on, qualitative detection can only be done.
Zero compensation interference detection technique is referred to and utilizes optical design software, and such as ZEMAX, CODE V etc. designs a kind of band
There are the optical system of specific wave aberration, referred to as zero compensation machine, the design of zero compensation machine is, based on desired aspheric, to examine
Via digital wavefront interferometer outgoing to compensator, through compensator, the tested aspheric surfaces of Jing reflect light beam optometry beam again, again Jing
Interferometer is returned to after overcompensation device, so as to realize the detection of non-spherical element face to be checked shape.Zero compensation interferes detection not only can
Axisymmetry secondary aspherical is detected enough, it is also possible to detect axisymmetry high order aspheric surface, but this detection method
Have the shortcomings that certain, be embodied in：For the non-spherical element of not coplanar shape, need to design different compensators, while being
The high-precision measurement result of acquisition, it is desirable in design compensation device, on the one hand enable correction asphere wavefront well
Difference, on the other hand requires the tolerance reasonable distributions such as the thickness of each element of compensator, radius of curvature, airspace, concentricity, so
The error of compensator easily produce ghost image, cause the appearance of diffraction ring, and due to some element reflection tubes in compensator and ginseng
Examine light to interfere, so as to occur some pseudo- interference fringes in image planes, due to these pseudo- interference fringes and detection light
There is phase shift simultaneously, therefore very big is affected on testing result.The precision of compensator is not only affected by design result, is also received
The impact debug, the detection of compensator itself precision is also a difficult problem, and it is complicated, time-consuming that compensation detects that light path is adjusted.
Directly interfere a kind of Aspherical-surface testing method that detection is nonzero digit, the Chinese invention that such as the present inventor applies a few days ago
Described in the real-time detection method of patent CN102937421B axisymmetry optical aspherical surface, which is by digital wave surface interferometry
Instrument（Feisuo type, Tai Man-Green's type etc.）Direct detection aspherical wavefront aberration, using Wavefront Fitting and wave-front subtracting technology,
With reference to some data processings obtaining aspheric surface error.This detection method simplifies aspheric detection process, is not required to
Zero compensation machine and other auxiliary optical components are wanted, detection time is shortened, aspheric manufacturing cost is reduced.Directly interfere
Detection in measurement range can carry out direct detection to the aspheric surface of different parameters, be that either shallow aspheric surface " generalization " is detected
Important means.
Due to the multiformity of aspheric surface parameter, there is presently no a kind of method and can judge a certain aspheric intuitively, exactly
Face whether certain digital wavefront interferometer can adopt the method for directly interfering detection, its main difficult point is " either shallow "
Without specific standard, lack intuitive and accurate basis for estimation.At present, for axisymmetry aspheric surface can be using direct
Interfere detection, more based on micro-judgment, certain difficulty is brought to the formulation of Aspherical-surface testing scheme.
The content of the invention
It is an object of the present invention to provide a kind of can judge that can axisymmetry aspheric surface using directly interference directly perceived, exactly
The method of detection.
To reach above-mentioned purpose, the technical solution used in the present invention is：One kind judges that can axisymmetry aspheric surface adopt
Method with detection is directly interfered, basis for estimation is：Directly interfere detection axisymmetry aspheric using digital wavefront interferometer
During face, can the interference pattern of collection be differentiated completely by the detector of digital wavefront interferometer, energy, then axisymmetry aspheric surface
For digital wavefront interferometer can adopt the method for directly interfering detection.
Wherein, can the interference pattern of collection by the basis for estimation that the detector of digital wavefront interferometer is differentiated completely be：
On interference pattern, whether the corresponding wave aberration of an interference fringe of interference fringe thickness is less than the Nyquist frequencies of detector
The corresponding wave aberration of rate, is that then interference pattern can be differentiated completely by detector, i.e., axisymmetry aspheric surface is for digital corrugated
Interferometer can adopt the method for directly interfering detection.
Further, on interference pattern, the corresponding wave aberration of an interference fringe of interference fringe thickness is less than detector
The corresponding wave aberration of Nyquist frequencies, by following steps derive：
（1）The spherical aberration letter being first depending on when third-order aberration theory derives that axisymmetry aspheric surface directly interferes detection
Number；
（2）Then according to wave aberration theory, according to the characteristics of optimal best-fitted sphere, it is determined that the curvature half of optimal best-fitted sphere
Footpath, it is determined that in optimal best-fitted sphere, the wavefront aberration function of detection light；
（3）According to the wavefront aberration function of detection light, the edge of the maximum in interference pattern of wave aberration slope is can determine whether out,
I.e., in the edge of axisymmetry aspheric surface bore, interference fringe is most close herein for the maximum of detection light wave aberration slope；
（4）Determine that the interference fringe at axisymmetry aspheric surface maximum caliber can be differentiated by detector, then using number
Word wavefront interferometer directly interferes all interference fringes produced during detection axisymmetry aspheric surface can be differentiated by detector,
Digital wavefront interferometer smoothly can be sampled；
（5）Requirement of the wave aberration corresponding with the Nyquist frequencies of detector to interference fringe be：One interference circle
4 pixels of occupancy detector, now corresponding wave aberration is half wavelength；
（6）" on interference pattern, the corresponding wave aberration of an interference fringe of interference fringe thickness is less than detection for foundation
The mathematical model of the corresponding wave aberration of Nyquist frequencies of device "：；
Wherein, D is axisymmetry aspheric surface bore, and k is quadratic surface constant, and f/# is axisymmetry aspheric surface F
Number, constant, pixel arrays of the M*N for detector, λ are digital wavefront interferometer inner light source wavelength；
（7）According to step（6）The judged result of middle mathematical model, you can judge axisymmetry aspheric surface for digital wave
Can face interferometer be detected using directly interfering.
Wherein, axisymmetry is aspheric directly interferes detection method to be autocollimation method, and its detection light path is as dry in sphere
The light path of detection is related to, any compensator or other auxiliary optical components, the light path for directly interfering detection during detection, is not needed
System includes digital wavefront interferometer and axisymmetry aspheric surface, and the digital wavefront interferometer is provided with standard spherical mirror
Head.
Wherein, the high-order curved surface on the basis of axisymmetry aspheric surface is mainly quadratic surface, or quadratic surface.
Wherein, the step（1）In, it is to simplify calculating, only considers quadric third-order aberration, Saden coefficient of spherical aberrationS 1
It is represented by：
Formula（1）
Wherein,hFor height of the axle glazed thread on each face,nWithnRefractions of the ＇ for light medium before and after reflecting surface
Rate,uWithu＇ is the angle of light light and optical axis before and after reflecting surface,RFor the curvature half of axisymmetry aspheric vertex of surface
Footpath,kFor quadratic surface constant；
Spherical aberration functionLA＇ with the relation of Saden coefficient of spherical aberration is,
Formula（2）
By formula（1）And formula（2）Can be calculated：
Formula（3）.
Wherein, the step（2）In, it is assumed that Δ is defocusing amount, then the radius of curvature of optimal best-fitted sphere can be written as：
Formula（4）
The later wave aberration of out of focus can be calculated by wave aberration formula is：
Formula（5）
In formulan′=-1,u′= y/2f′,yTo represent the variable of height of the axle glazed thread on each face, after arrangement：
Formula（6）
（1）When Δ=0, center band spherical aberration is zero,
Formula（7）
When, wave aberrationMaximum is,
Formula（8）
Optimal best-fitted sphere radius of curvature is：
Formula（9）；
（2）WhenWhen：
Formula（10）
WhenWhen, wave aberrationMaximum is,
Formula（11）
The radius of curvature of optimal best-fitted sphere is：
Formula（12）；
（3）When, boundary zone spherical aberration is zero,
Formula（13）
WhenyWhen=0, wave aberrationMaximum is
Formula（14）
The radius of curvature of optimal best-fitted sphere is：
Formula（15）；
For same axisymmetry aspheric surface, by formula（8）, formula（11）And formula（14）UnderstandMinimum, therefore work as
The focus of digital wavefront interferometer emergent light to the distance of axisymmetry aspheric vertex of surface isWhen, detection light
Wave aberration is minimum, and it is maximum that detector can measure the aspheric aspherical degree of axisymmetry；
The step（3）According to above-mentioned formula（11）, it is easy to judge the maximum of wave aberration slope on interferogram side
, in the edge of axisymmetry aspheric surface bore, interference fringe is most close herein for edge, the i.e. maximum of detection light wave aberration slope.
As above-mentioned technical proposal is used, the present invention has following advantages compared with prior art：
Instant invention overcomes whether a certain axisymmetry aspheric surface of micro-judgment can for certain digital wavefront interferometer
It is enough using the inaccuracy for directly interfering detection, present invention offer can intuitively, be accurately used for judging axisymmetry aspheric
Can face adopt the method for directly interfering detection, and theoretical reliable, accuracy of judgement is applied widely, saves axisymmetry aspheric
The formulation time of face detection scheme, improve work efficiency.
Description of the drawings
Fig. 1 is the direct detection light path schematic diagram for interfering detection in the present invention；
Interference pattern when Fig. 2 is sphere detection out of focus；
Fig. 3 is interference pattern when plane monitoring-network is inclined；
Fig. 4 is interference pattern when axisymmetry aspheric surface directly interferes detection.
Description of reference numerals：
1st, digital wavefront interferometer；
2nd, standard spherical mirror head；
3rd, axisymmetry aspheric surface.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described：
The aspheric direct interference detection method of axisymmetry is a kind of autocollimation method, and its detection light path is as dry in sphere
The light path of detection is related to, as shown in figure 1, including digital wavefront interferometer 1 and axisymmetry aspheric surface 3, the digital corrugated is done
Interferometer 1 is provided with standard spherical mirror head 2.
The aspheric mathematic(al) representation of axisymmetry is：, wherein,c
For axisymmetry aspheric surface vertex curvature（c=1/R）,RFor axisymmetry aspheric surface vertex curvature radius,kFor quadratic surface
Constant,a 1、a 2... for axisymmetry aspheric surface high order term coefficient.
Generally, some performance indications of interferometer in the description of digital wavefront interferometer, can be clearly indicated, than
Pixel array, discernmible maximum fringe number such as sampled detector etc..Axisymmetry aspheric surface directly interferes detection
The interference fringe of generation is different from evenly spaced concentric interference annulus during general sphere detection out of focus as shown in Figure 2；Also not
It is same as the interference fringe at equal intervals produced when plane monitoring-network as shown in Figure 3 is inclined；But non-homogeneous of as shown in Figure 4 one group
Every donut.Therefore, the discernmible maximum fringe number of detector that digital wavefront interferometer description is given, can not
It is directly used in and judges whether axisymmetry aspheric surface can adopt the side for directly interfering detection for the digital wavefront interferometer
In method.
In interferometry, the interference fringe that only can be differentiated by detector, digital wavefront interferometer could be sampled.Cause
This, will obtain the complete face shape error information of certain aspheric surface, when detection is directly interfered, it is desirable to which all of interference fringe is all necessary
Can be differentiated by detector.
Based on above-mentioned theory, can the present invention provide a kind of judgement axisymmetry aspheric surface and adopt and directly interfere detection
Method, basis for estimation is：When directly interfering detection axisymmetry aspheric surface using digital wavefront interferometer, the interferogram of collection
Can sample be differentiated completely by the detector of digital wavefront interferometer, can, then axisymmetry aspheric surface is for digital wave surface interferometry
Instrument can adopt the method for directly interfering detection.
Wherein, can the interference pattern of collection by the basis for estimation that the detector of digital wavefront interferometer is differentiated completely be：
Whether the corresponding wave aberration of one interference fringe of interference pattern up-sampling interference fringe thickness is less than detector
The corresponding wave aberration of Nyquist frequencies, is that then interference pattern can be differentiated completely by detector, i.e. axisymmetry aspheric surface pair
The method for directly interfering detection can be adopted in digital wavefront interferometer.
On interference pattern, the corresponding wave aberration of an interference fringe of interference fringe thickness is less than detector
The corresponding wave aberration of Nyquist frequencies, is derived by following steps：
（1）The spherical aberration letter being first depending on when third-order aberration theory derives that axisymmetry aspheric surface directly interferes detection
Number；
In order to simplify calculating, we only consider quadric third-order aberration, Saden coefficient of spherical aberrationS 1It is represented by：
Formula（1）
Wherein,hFor height of the axle glazed thread on each face,nWithnRefractions of the ＇ for light medium before and after reflecting surface
Rate,uWithu＇ is the angle of light light and optical axis before and after reflecting surface,RFor the curvature half of axisymmetry aspheric vertex of surface
Footpath,kFor quadratic surface constant.
Spherical aberration functionLA＇ with the relation of Saden coefficient of spherical aberration is,
Formula（2）
By formula（1）And formula（2）Can be calculated：
Formula（3）；
（2）Then according to wave aberration theory, according to the characteristics of optimal best-fitted sphere, it is determined that the curvature half of optimal best-fitted sphere
Footpath, it is determined that in optimal best-fitted sphere, the wavefront aberration function of detection light；
Hypothesis Δ is defocusing amount, then the radius of curvature of optimal best-fitted sphere can be written as：
Formula（4）
The later wave aberration of out of focus can be calculated by wave aberration formula is：
Formula（5）
In formulan′=-1,u′= y/2f′,yTo represent the variable of height of the axle glazed thread on each face, after arrangement：
Formula（6）
（1）When Δ=0, center band spherical aberration is zero
Formula（7）
When, wave aberrationMaximum is,
Formula（8）
Optimal best-fitted sphere radius of curvature is：
Formula（9）；
（2）WhenWhen：
Formula（10）
WhenWhen, wave aberrationMaximum is,
Formula（11）
The radius of curvature of optimal best-fitted sphere is：
Formula（12）；
（3）When, boundary zone spherical aberration is zero,
Formula（13）
WhenyWhen=0, wave aberrationMaximum is
Formula（14）
The radius of curvature of optimal best-fitted sphere is：
Formula（15）；
For same axisymmetry aspheric surface, by formula（8）, formula（11）And formula（14）UnderstandIt is minimum.Therefore work as
The focus of digital wavefront interferometer emergent light to the distance of axisymmetry aspheric vertex of surface isWhen, detection light
Wave aberration is minimum, and it is maximum that detector can measure the aspheric aspherical degree of axisymmetry.
（3）According to the wavefront aberration function of detection light, the edge of the maximum in interference pattern of wave aberration slope is can determine whether out,
I.e., in the edge of axisymmetry aspheric surface bore, interference fringe is most close herein for the maximum of detection light wave aberration slope；
Using formula（11）, it is easy to judge the maximum of wave aberration slope at interferogram edge, i.e. detection light wave aberration
, in the edge of axisymmetry aspheric surface bore, interference fringe is most close herein for the maximum of slope.
（4）Determine that the interference fringe at axisymmetry aspheric surface maximum caliber can be differentiated by detector, then using number
Word wavefront interferometer directly interferes all interference fringes produced during detection axisymmetry aspheric surface can be differentiated by detector,
Digital wavefront interferometer smoothly can be sampled；
（5）Requirement of the wave aberration corresponding with the Nyquist frequencies of detector to interference fringe be：One interference circle
4 pixels of occupancy detector, now corresponding wave aberration is half wavelength；
Known probes pixel array is N*M, and axisymmetry aspheric surface bore is D, D=2h, it is assumed that interferogram during sampling
Sample is just covered with whole detector, and now, the discernmible interference fringe of detector is most.The corresponding caliber size of one pixel
It is D/min (N, M)；When detector Nyquist frequency samplings are met, 4 pixel one interference circles of correspondence, corresponding aspheric
Face ring bandwidth is 2*D/min (N, M),
Formula（16）
In order to write conveniently, constant is madeβFor：
Formula（17）
I.e. most outer shroud interference fringe correspondence aspheric surface bore annulus width is
Formula（18）
Using formula（9）, the wave aberration that can write out most outer shroud interference fringe is：
Formula（19）
Wherein it is axisymmetry aspheric surface F number.
（6）" on interference pattern, the corresponding wave aberration of an interference fringe of interference fringe thickness is less than detection for foundation
The mathematical model of the corresponding wave aberration of Nyquist frequencies of device "：, λ is light in digital wavefront interferometer
Source wavelength；
The optical path difference of one annulus is equal to λ/2, and now striped can be differentiated, and interference pattern can be sampled, therefore, as long as full
Foot formula,
Formula（20）
Axisymmetry aspheric surface directly interferes the method for detecting to examine for digital wavefront interferometer can be adopted
Survey.
Embodiment one using above-mentioned determination methods is as follows：
In digital wavefront interferometer, the pixel array of sampled detector is 640*480, and optical source wavelength λ=0.6328 micron is right
Can adopt in several axisymmetry aspheric surfaces with different aspheric surface parameters directly interferes the judged result of detection to be shown in Table
1：
Table 1：
。
Embodiment two using above-mentioned determination methods is as follows：
In digital wavefront interferometer the pixel array of sampled detector be 1024*1024, optical source wavelength λ=0.6328 micron,
The judged result of detection is directly interfered to be seen for can several axisymmetry aspheric surfaces with different aspheric surface parameters adopt
Table 2：
Table 2：
。
Instant invention overcomes whether a certain axisymmetry aspheric surface of micro-judgment can for certain digital wavefront interferometer
It is enough using the inaccuracy for directly interfering detection, present invention offer can intuitively, be accurately used for judging axisymmetry aspheric
Can face adopt the method for directly interfering detection, and theoretical reliable, accuracy of judgement is applied widely, saves axisymmetry aspheric
The formulation time of face detection scheme, improve work efficiency.
The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art
For, on the premise of without departing from principle of the present invention, some improvement or replacement can also be made, these improve or replace
Should be regarded as protection scope of the present invention.
Claims (5)
1. it is a kind of to judge that can axisymmetry aspheric surface adopt the method for directly interfering detection, it is characterised in that basis for estimation
For：When directly interfering detection axisymmetry aspheric surface using digital wavefront interferometer, can the interference pattern of collection digital
The detector of wavefront interferometer is differentiated completely, can, then axisymmetry aspheric surface can be using direct for digital wavefront interferometer
The method for interfering detection；
Wherein, can the interference pattern of collection by the basis for estimation that the detector of digital wavefront interferometer is differentiated completely be：Interfere
On pattern, the corresponding wave aberration of an interference fringe of interference fringe thickness is corresponding less than the Nyquist frequencies of detector
Wave aberration；
Judge the corresponding wave aberration of an interference fringe of interference fringe thickness on interference pattern less than detector
The method of the corresponding wave aberration of Nyquist frequencies, including judging step as follows：
（1）The spherical aberration function being first depending on when third-order aberration theory derives that axisymmetry aspheric surface directly interferes detection；
（2）Then according to wave aberration theory, according to the characteristics of optimal best-fitted sphere, it is determined that the radius of curvature of optimal best-fitted sphere,
It is determined that in optimal best-fitted sphere, the wavefront aberration function of detection light；
（3）According to the wavefront aberration function of detection light, the edge of the maximum in interference pattern of wave aberration slope is can determine whether out, that is, is examined
, in the edge of axisymmetry aspheric surface bore, interference fringe is most close herein for the maximum of light-metering wave aberration slope；
（4）Determine that the interference fringe at axisymmetry aspheric surface maximum caliber can be differentiated by detector, then using digital wave
Face interferometer directly interferes all interference fringes produced during detection axisymmetry aspheric surface can be differentiated by detector, numeral
Wavefront interferometer smoothly can be sampled；
（5）Requirement of the wave aberration corresponding with the Nyquist frequencies of detector to interference fringe be：One interference circle takes
4 pixels of detector, now corresponding wave aberration is half wavelength；
（6）" on interference pattern, the corresponding wave aberration of an interference fringe of interference fringe thickness is less than detector for foundation
The mathematical model of the corresponding wave aberration of Nyquist frequencies "：；
Wherein, D be axisymmetry aspheric surface bore, k quadratic surface constants, f/# be axisymmetry aspheric surface F number, constant, pixel arrays of the M*N for detector, λ are digital wavefront interferometer inner light source wavelength；
（7）According to step（6）The judged result of middle mathematical model, you can judge that axisymmetry aspheric surface is dry for digital corrugated
Can interferometer adopt the method for directly interfering detection.
2. according to claim 1 to judge that can axisymmetry aspheric surface adopt the method for directly interfering detection, which is special
Levy and be, axisymmetry is aspheric directly to interfere detection method to be autocollimation method, directly interferes the light path system bag of detection method
Digital wavefront interferometer and axisymmetry aspheric surface are included, the digital wavefront interferometer is provided with standard spherical mirror head.
3. according to claim 1 to judge that can axisymmetry aspheric surface adopt the method for directly interfering detection, which is special
Levy and be, axisymmetry aspheric surface is quadratic surface or the high-order curved surface on the basis of quadratic surface.
4. according to claim 1 to judge that can axisymmetry aspheric surface adopt the method for directly interfering detection, which is special
Levy and be, the step（1）In, it is to simplify calculating, only considers quadric third-order aberration, Saden coefficient of spherical aberrationS 1Can represent
For：
Formula（1）
Wherein,hFor height of the axle glazed thread on each face,nWithnRefractive indexs of the ＇ for light medium before and after reflecting surface,u
Withu＇ is the angle of light light and optical axis before and after reflecting surface,RFor the radius of curvature of axisymmetry aspheric vertex of surface,k
For quadratic surface constant；
Spherical aberration functionLA＇ with the relation of Saden coefficient of spherical aberration is,
Formula（2）
By formula（1）And formula（2）Can be calculated：
Formula（3）.
5. according to claim 1 to judge that can axisymmetry aspheric surface adopt the method for directly interfering detection, which is special
Levy and be, the step（2）In, it is assumed that Δ is defocusing amount, then the radius of curvature of optimal best-fitted sphere can be written as：
Formula（4）
The later wave aberration of out of focus can be calculated by wave aberration formula is：
Formula（5）
N '=- 1 in formula, u '=y/2f ', y are the variable for representing height of the axle glazed thread on each face, after arrangement：
Formula（6）
（1）When Δ=0, center band spherical aberration is zero,
Formula（7）
When, wave aberrationMaximum is,
Formula（8）
Optimal best-fitted sphere radius of curvature is：
Formula（9）；
（2）WhenWhen：
Formula（10）
WhenWhen, wave aberrationMaximum is,
Formula（11）
The radius of curvature of optimal best-fitted sphere is：
Formula（12）；
（3）When, boundary zone spherical aberration is zero,
Formula（13）
WhenyWhen=0, wave aberrationMaximum is
Formula（14）
The radius of curvature of optimal best-fitted sphere is：
Formula（15）；
For same axisymmetry aspheric surface, by formula（8）, formula（11）And formula（14）UnderstandMinimum, therefore work as digital wave
The focus of face interferometer emergent light to the distance of axisymmetry aspheric vertex of surface isWhen, the wave aberration of detection light
Minimum, it is maximum that detector can measure the aspheric aspherical degree of axisymmetry；
The step（3）According to above-mentioned formula（11）, it is easy to the maximum of wave aberration slope is judged at interferogram edge, i.e.,
, in the edge of axisymmetry aspheric surface bore, interference fringe is most close herein for the maximum of detection light wave aberration slope.
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| CN104678554A (en) * | 2015-03-12 | 2015-06-03 | 南通大学 | Method for calculating most approximate comparing spherical surface curvature radius of full-aperture quadric surface |
| CN108895972A (en) * | 2018-06-27 | 2018-11-27 | 中国科学院光电技术研究所 | A kind of method and apparatus based on the optical element vertex radius measurement for calculating holography |
| CN109579738B (en) * | 2019-01-04 | 2020-08-28 | 北京理工大学 | Low-pass filtering characteristic measuring method of binary fringe defocusing projection system |
| CN110596893B (en) * | 2019-10-15 | 2022-05-03 | 南通大学 | Method for determining aspheric degree of quadric surface based on aberration theory |
| CN110703433A (en) * | 2019-10-15 | 2020-01-17 | 南通大学 | Method for calculating closest comparative spherical curvature radius of annular aperture quadric |
| CN110703434B (en) * | 2019-10-15 | 2024-04-12 | 南通大学 | Method for determining annular aperture quadric surface asphericity gradient |
| CN111351425B (en) * | 2020-03-10 | 2022-06-03 | 南通大学 | Method for determining dynamic range of interferometer during spherical defocus detection |
| CN111780686A (en) * | 2020-07-14 | 2020-10-16 | 南通大学 | Method for expanding aspheric surface direct interference detection dynamic range |
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| US4832489A (en) * | 1986-03-19 | 1989-05-23 | Wyko Corporation | Two-wavelength phase-shifting interferometer and method |
| US4818108A (en) * | 1987-12-14 | 1989-04-04 | Hughes Optical Products, Inc. | Phase modulated ronchi testing of aspheric surfaces |
| CN100580407C (en) * | 2005-10-31 | 2010-01-13 | 中国科学院光电技术研究所 | Deep aspherical mirror detection system with big bore |
| CN102997863B (en) * | 2012-11-05 | 2015-06-03 | 北京理工大学 | Direct detection system for surface-shape errors in full-aperture optical aspheric surfaces |
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2014
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