CN101975990B - A Design Method of Partial Compensation Lens with Slope as Optimum Objective - Google Patents
A Design Method of Partial Compensation Lens with Slope as Optimum Objective Download PDFInfo
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Abstract
The invention relates to a method for designing a partially compensatory lens by taking a slope as an optimization objective and belongs to the technical field of aspherical detection. The method comprises the following steps of: setting system parameters, namely setting entrance pupil diameter D and wavelength lambda as required by using ZEMAX optical design simulation software which is widely used in the field of photoelectron as a design platform; calculating the optical parameters of the partially compensatory lens; and arranging a reflected light path, and calculating structural parameters of a partially compensatory detection system to take the slope as the optimization objective. The method is simple and fast, is easy to implement, optimizes light rays in the full aperture range, performs comprehensive and reasonable analysis, realizes the detection and optimization of the maximum slope of residual wave aberration by using the radius of a confusion circle as the optimization objective, simplifies the design difficulty of the partially compensatory lens under the condition of ensuring distinguishable interference fringes, and can expend the detection scope for a compensator so as to reduce detection cost and improve detection speed.
Description
Technical field
The present invention relates to a kind of is the method for designing of the part offset lens of optimization aim with the slope, belongs to aspheric surface detection technique field.
Background technology
Traditional zero-compensation check is a kind of method of inspection of little residue wave aberration, needs the tested aspheric normal aberration of wavefront full remuneration through zero compensator, therefore needs usually to use complicated lens group as zero compensator, and design and difficulty of processing are bigger.It is the aspheric surface detection technique that a kind of new development is got up that the part compensation detects rule, is different from the zero-compensation check, and it does not require through the aspheric normal aberration of the light full remuneration behind the part offset lens.In actual optical interference circuit; Through the tested aspheric surface of the wavefront compensation behind the part offset lens, thereby obtain comprising the actual conoscope image of tested surface control information, in computing machine; According to actual optical interference circuit; The illusory one corresponding tested aspheric standard aspheric surface in the tested surface position, the part offset lens structural parameters that substitution is known obtain the theoretical interferogram of system with the method for ray tracing; With digital More's movable phase interfere technology actual interferogram of comparison process and theoretical interferogram, can obtain tested aspheric face shape error information.Therefore partly compensating detection method can realize aspheric interference compensation, and only need single element lens to realize under the situation of bigger residue wave aberration, has reduced the design and the difficulty of processing of compensator.
Yet; Because compensating detection method, part has bigger residue wave aberration; The maximum slope of residue wave aberration is relevant with the maximum spatial frequency and the detection accuracy of tested wavefront, and therefore the resolution to detector has proposed high requirement, can be surveyed by a certain detector in order to guarantee interference fringe; The maximum slope that in the application that partly compensates detection method, just must guarantee the residue wave aberration is not higher than a certain particular value, and this value is by the maximum spatial frequency and the detection accuracy decision of tested wavefront.Yet can not make the maximum slope of residue wave aberration too small again, otherwise design difficulty that will the augmenting portion offset lens.Therefore compensation detects most important the method for designing of part offset lens for implementation part.
Existing method of designing optical system and the method for designing that is used for the zero compensator of aspherical detection all adopt wave aberration as optimization aim; Usually the residue wave aberration after requirement optimization is accomplished is less than λ/100 even littler; But this optimization aim is not directly related with the greatest gradient of residue wave aberration; As be used to optimize the part offset lens; Can't judge then whether interference fringe can be differentiated, therefore can not adopt with the optical design method design part offset lens of wave aberration as optimization aim.
The patent of the patent No. 200410068823.4 has proposed a kind of interferometric method of realizing aspheric surface with the part offset lens in addition; It is provided with wave aberration as optimization aim; And since only controlled unified in the path of limited light control the maxima of waves front slope of residue wave aberration; Rather than unified light is optimized, so there is comprehensively problem reliably in Optimization result.
At last, existing optical design software like the ZEMAX optical design software, does not have the operand of direct optimization wavefront slope, therefore must could realize through special being provided with.
In order to solve the deficiency of prior art; The present invention adopts slope as optimization aim; And be optimized wavefront is unified, can under the situation that reduces part offset lens design difficulty as far as possible, satisfy the requirement that interference fringe can be surveyed; As far as a certain offset lens, can expand its measurement range simultaneously.
Summary of the invention
The objective of the invention is that optimization aim is provided with unreasonable when solving available technology adopting wave aberration method design part offset lens; Optimization result is unreliable comprehensively; And have the problem that optical design software can not directly be optimized wavefront slope now, proposing a kind of is the method for designing of the part offset lens of optimization aim with the slope, and unified light is optimized; Can under the detectable prerequisite of interference fringe, reduce the design difficulty of part offset lens as far as possible.
The objective of the invention is to realize through following technical scheme.
Of the present invention a kind of be the method for designing of the part offset lens of optimization aim with the slope, the ZEMAX optical design simulation software that adopts present optoelectronic areas widespread use is as design platform, known tested aspheric surface bore is that D ', vertex curvature radius are R
0And eccentricity is k; Design part offset lens in order to the concrete steps that detect tested aspherical mirror machining error is:
The first step: initialization system parameter
Set entrance pupil diameter D and wavelength X as required;
Second step: the optical parametric of calculating section offset lens
For most of aspheric surfaces, only need to use simple lens can meet the demands as the part offset lens.At first; Open ZEMAX optical design software Lens Data Editor formula bar, existing three faces are object plane OBJ in the formula bar; Diaphragm STO and image planes IMA; Diaphragm STO as first, is inserted a face as second after first, formed the part offset lens for first and second; After second, insert the 3rd then; The Glass type that is provided with the 3rd is that MIRROR makes the 3rd face become catoptron; And the quadric surface coefficient Conic and the bore that are provided with the 3rd be respectively known tested aspheric eccentricity k and bore D ', can represent tested aspheric surface for the 3rd.In the part compensation detected, the marginal ray of part offset lens should be incident to tested aspheric edge, and it is unified to guarantee to detect tested aspheric surface, so the logical light relative aperture D/f of part offset lens
1Should be not less than tested aspheric relative aperture D '/R at least
0, i.e. D/f
1>=D '/R
0, f
1Focal length for the part offset lens; Thereby can confirm the focal distance f of part offset lens
1≤(D * R
0)/D '.Last because tested aspheric surface exists mismachining tolerance therefore will depart from former incident ray from the light of tested aspheric surface reflection, thus the bore that the part offset lens need be set greater than entrance pupil diameter D, thereby guarantee that reflection ray can pass through the part offset lens once more.
The center thickness of setting between following first and second of the Thickness hurdle in the Lens Data Editor formula bar is d
1, the material refractive index under the Glass hurdle is n
1, the radius-of-curvature that the Radius hurdle is following first, second is R
1And R
2, these parameters all as optimization variable by ZEMAX software Automatic Optimal.
The 3rd step: reflected light path and calculating section compensation detection system structural parameters are set
Part offset lens two is set after tested aspheric surface; Accordingly first part offset lens is called part offset lens one; The parameter of setting section offset lens two is consistent with the parameter of part offset lens one, the reflection back passes through part offset lens two through the light behind the part offset lens one at tested aspheric surface place;
For the light that makes the reflection at tested aspheric surface place can pass through part offset lens two, in ZEMAX software, do some settings, concrete steps are following:
After tested aspheric surface, insert fourth face and the 5th, second and first of representing part offset lens one successively.Parameters R according to the part offset lens one that in second step, is provided with
1, R
2, d
1, n
1, the 4th, the 5th radius of curvature R at first is set in the Radius hurdle of Lens Data Editor
4=R
2, R
5=R
1, the material refractive index n between the 4th, the 5th is set in the Glass hurdle
2=n
1
It is following that part compensates detection system structural parameters computation process: according to the focal distance f of the part offset lens one that obtains in second step
1And tested aspheric surface vertex curvature radius R
0, be provided with second of part offset lens one to i.e. the 3rd the center thickness d of tested aspheric surface
2=f
1+ R
0, after the reflection of tested aspheric surface place, can pass through part offset lens two in order to make light, in the Thickness hurdle, the 3rd center thickness d to fourth face
3=-d
2, the center thickness d of five of the fourth faces to the of part offset lens two is set
4=-d
1
Thus, through the wavefront behind the part offset lens one after the tested aspheric surface of compensation, with being reflected onto the part offset lens two consistent, through the two also outgoing of part offset lens with the parameter of part offset lens one.
The 4th step: realize with slope as optimization aim
Because the operand that ZEMAX does not have direct optimization wavefront slope in order to realize with the slope being optimization aim, need carry out special setting:
At first; A perfect lens is inserted in part offset lens two backs that in the 3rd step, are provided with; Perfect lens can make directional light be imaged as an ideal image point; Because the tested aspheric surface of part offset lens one undercompensation, therefore the light after reflect and passes through part offset lens two at tested aspheric surface place forms a blur circle with parallel deviate light on the focal plane of perfect lens.The method to set up of perfect lens is: after the 5th, insert one side as the 6th, it is Paraxial that its face type type is set, and then can represent perfect lens for the 6th.Because available maxima of waves front slope K is by the resolution and the decision of wavefront spatial frequency of the used detector of reality, and blur circle radius r=f
2* K, f
2Therefore be the focal length of perfect lens, can realize the detection to the maxima of waves front slope through detecting the blur circle radius, wherein perfect lens only plays the effect of converging light, does not do specific (special) requirements to its focal length with to the 5th center thickness.
Then; In order to realize with wavefront slope as optimization aim; Need in Merit Function tabulation, do following setting: the optimization aim that Default Merit Function under the Merit Function menu Tools submenu is set is Spot Radius; Be the blur circle radius, it is RMS that type is set; Through above-mentioned setting, ZEMAX software can carry out analysis and Control to unified light, with optimization blur circle radius, rather than only controls the limited position of light on blur circle.
Secondly, the part operation number is provided with as follows: insert operand REAY as ray tracing, being arranged on the 3rd is the tested aspheric surface Py=1 of place; Optimization aim is-D '/2, makes to arrive tested aspheric surface lower limb through the coboundary light behind the part offset lens one, inserts same operand REAY again; Py=-1 is set; Optimization aim is D '/2, makes lower limb light reach tested aspheric surface coboundary, thereby control light detects aspheric surface is unified; MNCG controls as center thickness through operand, first to second center thickness d of setting section offset lens one
1Can not be beneficial to processing less than setting value; MNEG controls as edge thickness through operand; First to second edge thickness of setting section offset lens one can not be less than another setting value; Avoid edge thin excessively,, thereby also reached the effect of control section offset lens two because the parameter setting of part offset lens two is consistent with part offset lens one.
After being provided with more than the completion, first and second radius of curvature R of the part offset lens one of second step insertion is set
1, R
2, center thickness d
1And material refractive index n
1And the 3rd be provided with in the step second to aspheric center thickness d
2Be optimization variable, operation Optimization Automatic Optimal program can be optimized system, optimizes to accomplish the back and write down actual blur circle radius r ' size.
Confirm available maxima of waves front slope K according to system, according to perfect lens radius f
2, obtain available blur circle radius r=f
2* K; Judge the blur circle radius r that record obtains ' whether less than available blur circle radius r, if r '≤r, then interference fringe can be observed; And the part offset lens is suitable, otherwise interference fringe can not be observed, and need reset part offset lens parameter; Suboptimization again is till satisfaction.
Beneficial effect
Simple being prone to fast of the present invention realized, only need to adopt single element lens to design and get final product, and system's parameters is provided with simply, and majorized function is less; The present invention is optimized the light of unified scope, analyzes comprehensive and reasonable; The present invention adopts the blur circle radius as optimization aim, and is directly related with residue wave aberration maximum slope, thereby realized detection and the optimization to residue wave aberration maximum slope; Can guarantee under the distinguishable situation of interference fringe; Simplify the design difficulty of part offset lens,, can expand its sensing range for some compensators; Detect cost thereby reduce, improve detection speed.
Description of drawings
Fig. 1 is the input path figure of part compensation detection system;
Fig. 2 is the reflected light path figure of part compensation detection system;
Fig. 3 is the optical design process flow diagram of part offset lens;
Wherein, 1-is first; Second of 2-; The 3rd of 3-; The 4-fourth face; The 5th of 5-; The 6th of 6-; The 7-image planes; d
1-the first to second center thickness; d
2-the second to the 3rd center thickness; d
3Three center thicknesses of-Di to fourth face; d
4The center thickness that-fourth face to the is five; f
2The focal length of-perfect lens.
Embodiment
Below in conjunction with accompanying drawing and embodiment the present invention is further specified.
Embodiment
With the slope is the part offset lens method for designing of optimization aim, realizes by following mode:
Known tested aspheric surface bore is that D '=580mm, vertex curvature radius are R
0=1179.447mm, eccentricity are k=-0.499365, and design part offset lens is as shown in Figure 3 in order to the concrete steps that detect tested aspherical mirror machining error, comprising:
The first step: initialization system parameter
Set entrance pupil diameter D=80mm and wavelength X=550nm as required;
Second step: the optical parametric of calculating section offset lens
For most of aspheric surfaces, only need to use simple lens can meet the demands as the part offset lens.At first; Open ZEMAX optical design software Lens Data Editor formula bar, existing three faces are object plane OBJ in the formula bar; Diaphragm STO and image planes IMA; Diaphragm STO as first, is inserted a face as second after first, formed the part offset lens for first and second; After second, insert the 3rd then; The Glass type that is provided with the 3rd is that MIRROR makes the 3rd face become catoptron; And the quadric surface coefficient Conic and the bore that are provided with the 3rd be respectively known tested aspheric eccentricity k and bore D ', can represent tested aspheric surface for the 3rd.The logical light relative aperture D/f of part offset lens
1At least be not less than tested aspheric relative aperture D '/R
0, i.e. D/f
1>=D '/R
0, f
1Focal length for the part offset lens; Thereby can confirm the focal distance f of part offset lens
1≤(D * R
0)/D '=162.6823mm.The bore that the part offset lens is set is greater than entrance pupil diameter D, thereby the assurance reflection ray can pass through the part offset lens once more.
As shown in Figure 1, the center thickness of setting between following first and second of the Thickness hurdle in the Lens Data Editor formula bar is d
1=20mm, the Glass type between first and second is a F7 glass, following first radius-of-curvature in Radius hurdle is R
1, keep being defaulted as Infinity, set second radius of curvature R
2=-300mm, above-mentioned parameter can arbitrarily be provided with in the practical operation, needn't only need can be incident to tested aspheric surface place according to present embodiment through the light behind the part offset lens one, and center thickness d
1Not too small, satisfy processing request and get final product.
The 3rd step: reflected light path and calculating section compensation detection system structural parameters are set
Part offset lens two is set after tested aspheric surface, for the light that makes the reflection at tested aspheric surface place can pass through part offset lens two, in ZEMAX software, does some settings, concrete steps are following:
As shown in Figure 2, after tested aspheric surface, insert fourth face and the 5th, second and first of representing part offset lens one successively.The the 4th, the 5th radius of curvature R is set
4=R
2, R
5=R
1, material between the 4th, the 5th is set also for F7 glass in the Glass hurdle, make the material refractive index n of part offset lens two
2Equal the material refractive index n of part offset lens one
1
It is following that part compensates detection system structural parameters computation process: according to the focal distance f of the part offset lens one that obtains in second step
1And tested aspheric surface vertex curvature radius R
0, be provided with second of part offset lens one to i.e. the 3rd the center thickness d of tested aspheric surface
2=f
1+ R
0=1342.447mm can pass through part offset lens two in order to make light after the reflection of tested aspheric surface place, in the Thickness hurdle, and the 3rd center thickness d to fourth face
3=-d
2=-1342.447mm is provided with the center thickness d of five of the fourth faces to the of part offset lens two
4=-d
1=-20mm;
Thus, through the wavefront behind the part offset lens one after the tested aspheric surface of compensation, with being reflected onto the part offset lens two consistent, through the two also outgoing of part offset lens with the parameter of part offset lens one.
The 4th step: realize with slope as optimization aim
Because the operand that ZEMAX does not have direct optimization wavefront slope in order to realize with the slope being optimization aim, need carry out special setting:
At first; A perfect lens is inserted in part offset lens two backs that in the 3rd step, are provided with; The method to set up of perfect lens is: as shown in Figure 2, after the 5th, insert one side as the 6th, and the 5th to the 6th distance is not done specific (special) requirements; The face type type that is provided with the 6th is Paraxial, then can represent perfect lens for the 6th.Because available maxima of waves front slope K is by the resolution and the decision of wavefront spatial frequency of the used detector of reality, and blur circle radius r=f
2* K, f
2Be the focal length of perfect lens, therefore can realize the detection to the maxima of waves front slope through detecting the blur circle radius, in the present embodiment, available blur circle radius should be less than 350 μ m.
In Merit Function tabulation, do following setting: the optimization aim that Default Merit Function under the Merit Function menu Tools submenu is set is Spot Radius, i.e. blur circle radius, and it is RMS that type is set.
Secondly; The part operation number is provided with as follows: insert operand REAY as ray tracing, being arranged on the 3rd is the tested aspheric surface Py=1 of place, and optimization aim is-D '/2=-290mm; Insert same operand REAY again; Py=-1 is set, and optimization aim is D '/2=290mm, thereby control light detects aspheric surface is unified; MNCG controls as center thickness through operand, first to second center thickness d of setting section offset lens one
1Can not be beneficial to processing less than setting value 15mm, MNEG controls as edge thickness through operand, and first to second edge thickness of setting section offset lens one can not avoid edge thin excessively less than another setting value 5mm.Because the parameter setting of part offset lens two is consistent with part offset lens one, thereby also reached the effect of control section offset lens two.
After being provided with more than the completion, first and second radius of curvature R of the part offset lens one of second step insertion is set
1, R
2, center thickness d
1And the 3rd be provided with in the step second to aspheric center thickness d
2Be optimization variable, wouldn't be in the present embodiment to n
1Be optimized,,, then can add n as meeting the demands to adopt the glass trade mark commonly used as far as possible
1As optimization variable.Operation Optimization Automatic Optimal program, the result is after optimizing: R
1=R
5=343.0394mm, R
2=R
4=-158.1002mm, d
1=22.1015mm, d
2=1349.7645mm, d
3=-1349.7645mm, d
4=-22.1015mm, be r '=110.387mm in the blur circle maximum radius that the record of image planes 7 place's blur circles obtains this moment, much smaller than available blur circle radius r=350mm; Judge that interference fringe is distinguishable; This offset lens can be used, and the optimizer optimization time is merely 0.345s, rapid and convenient.
Claims (1)
1. one kind is the method for designing of the part offset lens of optimization aim with the slope, and the ZEMAX optical design simulation software that adopts present optoelectronic areas widespread use is as design platform, and known tested aspheric surface bore is that D ', vertex curvature radius are R
0And eccentricity is k; It is characterized in that concrete steps are:
The first step: initialization system parameter
Set entrance pupil diameter D and wavelength X as required;
Second step: the optical parametric of calculating section offset lens
At first; Open ZEMAX optical design software Lens Data Editor formula bar, existing three faces are object plane OBJ in the formula bar; Diaphragm STO and image planes IMA; Diaphragm STO as first, is inserted a face as second after first, formed the part offset lens for first and second; After second, insert the 3rd then, the Glass type that is provided with the 3rd is MIRROR, and the 3rd quadric surface coefficient Conic and bore is set is respectively known tested aspheric eccentricity k and bore D ', can represent tested aspheric surface for the 3rd; In the part compensation detected, the marginal ray of part offset lens was incident to tested aspheric edge, the logical light relative aperture D/f of part offset lens
1Be not less than tested aspheric relative aperture D '/R
0, i.e. D/f
1>=D '/R
0, f
1Focal length for the part offset lens; Thereby can confirm the focal distance f of part offset lens
1≤(D * R
0)/D '; The bore that the part offset lens is set is greater than entrance pupil diameter D;
The center thickness of setting between following first and second of the Thickness hurdle in the Lens Data Editor formula bar is d
1, the material refractive index under the Glass hurdle is n
1, the radius-of-curvature that the Radius hurdle is following first, second is R
1And R
2, these parameters all as optimization variable by ZEMAX software Automatic Optimal;
The 3rd step: reflected light path and calculating section compensation detection system structural parameters are set
Part offset lens two is set after tested aspheric surface; Accordingly first part offset lens is called part offset lens one; The parameter of setting section offset lens two is consistent with the parameter of part offset lens one, the reflection back passes through part offset lens two through the light behind the part offset lens one at tested aspheric surface place;
For the light that makes the reflection at tested aspheric surface place can pass through part offset lens two, in ZEMAX software, do some settings, concrete steps are following:
After tested aspheric surface, insert fourth face and the 5th, second and first of representing part offset lens one successively; Parameters R according to the part offset lens one that in second step, is provided with
1, R
2, d
1, n
1, the 4th, the 5th radius of curvature R at first is set in the Radius hurdle of Lens Data Editor
4=R
2, R
5=R
1, the material refractive index n between the 4th, the 5th is set in the Glass hurdle
2=n
1
It is following that part compensates detection system structural parameters computation process: according to the focal distance f of the part offset lens one that obtains in second step
1And tested aspheric surface vertex curvature radius R
0, be provided with second of part offset lens one to i.e. the 3rd the center thickness d of tested aspheric surface
2=f
1+ R
0, after the reflection of tested aspheric surface place, can pass through part offset lens two in order to make light, in the Thickness hurdle, the 3rd center thickness d to fourth face
3=-d
2, the center thickness d of five of the fourth faces to the of part offset lens two is set
4=-d
1
The 4th step: realize with slope as optimization aim
Because the operand that ZEMAX does not have direct optimization wavefront slope in order to realize with the slope being optimization aim, need carry out special setting:
At first; After the 5th, insert one side as the 6th, it is Paraxial that its face type type is set, as perfect lens; Light after reflect and passes through part offset lens two at tested aspheric surface place forms a blur circle with parallel deviate light on the focal plane of perfect lens; Blur circle radius r=f
2* K, f
2Focal length for perfect lens; K is available maxima of waves front slope;
Then, in Merit Function tabulation, do following setting: the optimization aim that Default Merit Function under the Merit Function menu Tools submenu is set is Spot Radius, i.e. blur circle radius, and it is RMS that type is set; Through above-mentioned setting, ZEMAX software can carry out analysis and Control to unified light, to optimize the blur circle radius;
Secondly, the part operation number is provided with as follows: insertion operand REAY is as ray tracing, and being arranged on the 3rd is the tested aspheric surface Py=1 of place, and optimization aim is-D '/2, inserts same operand REAY again, and Py=-1 is set, and optimization aim is D '/2; MNCG controls as center thickness through operand, first to second center thickness d of setting section offset lens one
1Can not be beneficial to processing less than setting value, MNEG controls as edge thickness through operand, and first to second edge thickness of setting section offset lens one can not be less than another setting value;
After being provided with more than the completion, first and second radius of curvature R of the part offset lens one of second step insertion is set
1, R
2, the center thickness d between first and second
1And material refractive index n
1And the 3rd be provided with in the step second to tested aspheric center thickness d
2Be optimization variable, operation Optimization Automatic Optimal program is optimized system, optimizes to accomplish the back and write down actual blur circle radius r ' size;
Confirm available maxima of waves front slope K according to system, according to the perfect lens focal distance f
2, obtain available blur circle radius r=f
2* K; Judge the blur circle radius r that record obtains ' whether less than available blur circle radius r, if r '≤r, then interference fringe can be observed; And the part offset lens is suitable, otherwise interference fringe can not be observed, and need reset part offset lens parameter; Suboptimization again is till satisfaction.
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| JP5767893B2 (en) * | 2011-08-08 | 2015-08-26 | Hoya株式会社 | Method for predicting molding difficulty of aspheric glass mold lens and design method of lens system including aspheric glass mold lens |
| CN103676149A (en) * | 2013-11-18 | 2014-03-26 | 四川星烁光电科技有限公司 | Design method of micro projection compound eye collimating collecting lens |
| CN105627944B (en) * | 2015-12-21 | 2018-01-05 | 中国科学院长春光学精密机械与物理研究所 | Method based on zero compensation optical system detection aspherical mirror shape |
| CN106871819B (en) * | 2017-01-12 | 2019-03-26 | 北京理工大学 | Aspherical vertex curvature radius error measurement method based on the optimal compensation position |
| CN110889200B (en) * | 2019-11-04 | 2023-06-02 | 天津大学 | Mould pressing forming pre-compensation method for aspherical glass lens |
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| CN1731232A (en) * | 2005-09-05 | 2006-02-08 | 长春理工大学 | A quasi-universal compensating mirror for optical aspheric surface detection |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1731232A (en) * | 2005-09-05 | 2006-02-08 | 长春理工大学 | A quasi-universal compensating mirror for optical aspheric surface detection |
Non-Patent Citations (3)
| Title |
|---|
| Liu Huilan,Hao Qun,Zhu Qiudong et.al..《A novel aspheric surface testing method using part-compensatin lens》.《Proceedings of the SPIE -The international society for optical engineering》.2005,第5638卷(第1期),324-329. |
| Liu Huilan,Hao Qun,Zhu Qiudong et.al..《A novel aspheric surface testing method using part-compensatin lens》.《Proceedings of the SPIE-The international society for optical engineering》.2005,第5638卷(第1期),324-329. * |
| 刘惠兰,郝群,朱秋东等.利用部分补偿透镜进行非球面面形测量.《北京理工大学学报》.2004,第24卷(第7期),625-628. * |
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| CN101975990A (en) | 2011-02-16 |
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