CN104932100B - Nonzero digit detects the part-compensating lens system and design method of concave paraboloid mirror - Google Patents
Nonzero digit detects the part-compensating lens system and design method of concave paraboloid mirror Download PDFInfo
- Publication number
- CN104932100B CN104932100B CN201510324738.8A CN201510324738A CN104932100B CN 104932100 B CN104932100 B CN 104932100B CN 201510324738 A CN201510324738 A CN 201510324738A CN 104932100 B CN104932100 B CN 104932100B
- Authority
- CN
- China
- Prior art keywords
- paraboloidal mirror
- compensating lens
- tested
- lens
- compensating
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000013461 design Methods 0.000 title claims abstract description 43
- 238000000034 method Methods 0.000 title claims abstract description 30
- 238000001514 detection method Methods 0.000 claims abstract description 26
- 238000005457 optimization Methods 0.000 claims description 32
- 230000003287 optical effect Effects 0.000 claims description 18
- 230000004075 alteration Effects 0.000 claims description 10
- 239000000463 material Substances 0.000 claims description 10
- 238000012545 processing Methods 0.000 claims description 7
- 230000007423 decrease Effects 0.000 claims description 6
- 239000004429 Calibre Substances 0.000 claims description 4
- 230000001427 coherent effect Effects 0.000 claims description 4
- 230000001447 compensatory effect Effects 0.000 claims description 4
- 230000000295 complement effect Effects 0.000 claims description 4
- 230000001351 cycling effect Effects 0.000 claims description 3
- 230000003252 repetitive effect Effects 0.000 claims description 3
- 238000005070 sampling Methods 0.000 claims description 3
- 239000000203 mixture Substances 0.000 claims description 2
- 238000009738 saturating Methods 0.000 claims 1
- 238000004458 analytical method Methods 0.000 abstract description 6
- 238000012360 testing method Methods 0.000 description 3
- GZPBVLUEICLBOA-UHFFFAOYSA-N 4-(dimethylamino)-3,5-dimethylphenol Chemical compound CN(C)C1=C(C)C=C(O)C=C1C GZPBVLUEICLBOA-UHFFFAOYSA-N 0.000 description 2
- 238000004441 surface measurement Methods 0.000 description 2
- 241000208340 Araliaceae Species 0.000 description 1
- 235000005035 Panax pseudoginseng ssp. pseudoginseng Nutrition 0.000 description 1
- 235000003140 Panax quinquefolius Nutrition 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 235000008434 ginseng Nutrition 0.000 description 1
- 239000011521 glass Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000004321 preservation Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0025—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for optical correction, e.g. distorsion, aberration
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Optics & Photonics (AREA)
- Lenses (AREA)
- Testing Of Optical Devices Or Fibers (AREA)
Abstract
The invention discloses the part-compensating lens system and design method that a kind of nonzero digit detects concave paraboloid mirror.The present invention is made up of some offset lens, total conventional tested paraboloidal mirror parameter of compensation range covering；Design method includes：It is less than 1.2 tested paraboloidal mirror calculating section offset lens initial configuration to F numbers；Constraints is set, part-compensating lens structural parameters are optimized in detection road model；Change tested paraboloidal mirror parameter, the distance between the tested paraboloidal mirror of adjustment and part-compensating lens determine tested paraboloidal mirror bound of parameter, make compensation range D R figures；To that F numbers can not be less than 1.2 tested paraboloidal mirror and design new part-compensating lens in compensating basin, until the conventional tested paraboloidal mirror parameter area of some offset lens covering；Screen some offset lens and build compensation ability database.The present invention solves the problems, such as the analysis of part-compensating lens compensation range and System Design, realizes the generalization detection of paraboloidal mirror.
Description
Technical field
The present invention relates to optical technical field, particularly a kind of nonzero digit detects the part-compensating lens body of concave paraboloid mirror
System and design method.
Background technology
When carrying out nonzero digit interference to aspherical mirror and detecting, part-compensating lens are by compensating most of method of tested surface
Line aberration, is reduced to distinguishable scope by the wavefront slope returned at interferometer detector image planes, system is collected
Clearly interference fringe, is the aspherical key element of part penalty method interference detection.Part-compensating lens are not required to tested surface
Complete zero compensation is carried out, if the wavefront slope at detector is in distinguishable scope, therefore a kind of part of parameter
Offset lens can be realized to the aspherical mirror in the range of certain parameter and detected.Nevertheless, a part-compensating lens institute energy
The tested aspherical mirror scope of compensation is still limited, it is difficult to realize that generalization is detected.In aspherical, concave paraboloid mirror is obtained extensively
General application, therefore, rationally designs and selects several part-compensating lens compositional systems, with less part-compensating lens quantity
The conventional tested paraboloidal mirror parameter area of covering, the compensation ability database of constructive system is thrown using part penalty method is recessed in fact
The prerequisite of object plane mirror generalization detection.
Design before part-compensating lens system, it is necessary to optimize design, constraints master to single part offset lens
There are three kinds：One kind such as document utilization part-compensating lens progress aspheric surface measurement (Beijing Institute of Technology's journal, 2004,
Described in Vol.24, No.7, P625~628), wave aberration curve greatest gradient is constrained in CODE V optical design softwares；Text
Offer for aspherical generalization detect part zero-bit lens (infrared and laser engineering, 2009, Vol.38, No.2, P322~
325) proposed in using the fringe density of detector plane as constraints, reason is identical.Second method such as document is based on
Optimization design (Acta Optica, 2011, Vol.31, No.6, the P0622002-1~0622002- of Zemax part-compensating lens
7) described in, constraints is the maximum radius of image planes blur circle.The third is used for the portion that aspherical generalization is detected such as document
Point zero-bit lens (infrared and laser engineering, 2009, Vol.38, No.2, P322~325) and document Design of partial
Nulls for testing of fast aspheric surfaces (Proc.Of SPIE, 2007, Vol.6671,
No.66710W, P66710W-1~66710W-8) described in, it regard the incidence angle of the incident tested surface of light as constraint control.But
It is that these constraintss only define that striped can be resolved at detector, can not ensure the machinability of lens during actual design,
The radial shear control errors of measurement result can not also be ensured in the detection in tolerance interval, therefore, such constraint is simultaneously
Imperfection, practicality is relatively low.
Although document utilization part-compensating lens progress aspheric surface measurement (Beijing Institute of Technology's journal, 2004,
Preliminary compensation range is carried out in Vol.24, No.7, P625~628) to the design examples of three part-compensating lens to analyze,
But simultaneously constituting portion point offset lens system and detailed compensation range database could not be set up, it is difficult to realize to special in certain limit
Determine the generalization detection of tested surface.In addition, the part compensating glass design in prior art uses multiple-piece construction mostly, processing and
Debug that cost is higher, also increase the difficulty of actually detected middle system calibration.Therefore need to design one chip part-compensating lens
System, is realized with simple and practical structures and methods and the generalization for commonly using concave paraboloid mirror is detected.
The content of the invention
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to detect that there is provided one kind for the generalization of concave paraboloid mirror
Nonzero digit detects the part-compensating lens system and design method of concave paraboloid mirror, and solves part-compensating lens in the prior art
If the relatively low technical problem of timing constraints imperfection, practicality.
Nonzero digit detects the part-compensating lens system of concave paraboloid mirror, including some offset lens, each part
Offset lens has respective compensable tested paraboloidal mirror parameter area, and the compensation range of all part-compensating lens can be held in the mouth
It is connected together, total compensation range of system is covered conventional tested paraboloidal mirror parameter；Each part is compensated in statistics system
The detailed compensation range border of lens, constructive system compensation range database makes the compensation range figure to being tested paraboloidal mirror；
According to compensation range figure, can the given tested paraboloidal mirror of intuitive judgment can be compensated by the part-compensating lens system；According to
The system compensation range database set up, can carry out more accurately judging, and therefrom select most to tested paraboloidal mirror
It is adapted to the prime offset lens that part compensation detection is realized to given tested paraboloidal mirror；To given tested paraboloidal mirror,
Without redesigning processing part-compensating lens, prime offset lens is selected to be used to detect directly from system.
A kind of part-compensating lens System Design method of nonzero digit detection concave paraboloid mirror is as follows：
Step 1, initial configuration are calculated
A tested paraboloidal mirror is selected, its F number is less than 1.2；Analyzed by geometric optical theory and primary aberration theory
Method, calculate to being tested the initial structure parameter of one chip part-compensating lens that paraboloidal mirror is compensated；
Described part-compensating lens, it is standard sphere close to the surface of tested surface, and the surface away from tested surface is set to
Plane, and it is incident by directional light；
The optimization of step 2, part-compensating lens
2-1. is in optical design software to the equivalent interference detection road modeling after simplification, the light channel structure of the equivalent model
To be incided after plane wave permeation parts offset lens on tested paraboloidal mirror, light wave is reflected by tested paraboloidal mirror, return
Light wave is interfered, shape at image planes with the standard flat ripple that is provided by optical design software again by part-compensating lens
Into interference fringe；
The structure of 2-2. part-compensating lens is by calculating obtained initial structure parameter, being tested the shape of paraboloidal mirror
The parameter that parameter is used when being the initial structure parameter of calculating part-compensating lens in step 1；
2-3. is to the distance between initial structure parameter, part-compensating lens and tested paraboloidal mirror of part-compensating lens
D is optimized, and object function is set up according to the constraints of restriction, and solution is optimized to initial structure parameter and apart from d；
Described initial structure parameter includes radius of curvature, thickness, bore and the material of part-compensating lens front and rear surfaces；
Described optical design software includes Zemax, Code V, ASAP, Light Tools and all with ray tracing
The software of function；
Described bound for objective function is as follows：
A. the caliber size of part-compensating lens, thickness and material meet optical design requirements and actual processing standard；
B. the greatest gradient value at image planes before coherent wave meets nyquist sampling law；
C. image planes wavefront is dull, and center light path is most long and radially successively decreases；
Step 3, the compensation range to optimization part-compensating lens are analyzed
3-1. uses the structural parameters after optimization in equivalent model, while the initial vertex of the tested paraboloidal mirror of initialization
Radius of curvature R and starting lowest calibre DMIN(typically taking 5mm), by the distance between part-compensating lens and tested paraboloidal mirror d
It is initialized as zero；The distance between part-compensating lens and tested paraboloidal mirror d is set to variable；
Wherein it is tested initial vertex radius of curvature R=- D of paraboloidal mirrorMIN× F, DMINIt is minimum for the starting of paraboloidal mirror
Bore, F is the F numbers of part-compensating lens；
3-2. optimizes solution according to the step 2-3 object functions set up, if the optimization time is asked beyond the most long of setting
Solution time TMAX(typically taking 10s) can not still meet constraints, then increase the vertex curvature of tested paraboloidal mirror according to step-length S
Radius R absolute value, then re-optimization is apart from d；So circulation is until meet constraints, then by the mouth of tested paraboloidal mirror
Footpath D and vertex curvature radius R are separately recorded in array a and array b；
3-3. increases the bore D of tested paraboloidal mirror according to step-length S1, and its vertex curvature radius R keeps last record
Value is constant, and solution is optimized according to the step 2-3 object functions set up, if the optimization time is beyond the most long solution time of setting
TMAX(typically taking 10s) can not still meet constraints, then the vertex curvature radius according to the tested paraboloidal mirror of step-length S increases is exhausted
To value, then re-optimization is apart from d；
3-4. repetitive cycling step 3-2 and 3-3, until the bore D of tested paraboloidal mirror reaches maximum set in advance
DMAX；
The bore D and vertex curvature radius R of corresponding tested paraboloidal mirror recorded in described array a and array b,
The compensable tested paraboloidal mirror parameter boundary of part-compensating lens is constituted, the compensation range of the part-compensating lens is drawn
D-R scheme, and mark can compensate for area with can not compensating basin；
Step 4, from compensation range D-R figures can not in compensatory zone selection F numbers be less than 1.2 tested paraboloidal mirror；Weight
Multiple step 1 designs new part-compensating lens to step 3, until the compensation ability for some offset lens designed is covered
The parameter area of the conventional tested paraboloidal mirror of lid；
Step 5, screen fraction offset lens
5-1. selects the complementary part-compensating lens part offset lens system of M compensation range, and statistics part is mended
The bore D and vertex curvature radius R that paraboloidal mirror is tested in lens system are repaid, and statistics is built to the compensation energy of the system
Force data storehouse；
5-2. carries out full border multinomial to the compensation range border of the part-compensating lens in part-compensating lens system
Fitting is compensated boundary curve, so as to realize that can the given tested paraboloidal mirror of quick judgement be compensated by the system；
5-3. carries out piecewise fitting and obtained to the compensation range border of the part-compensating lens in part-compensating lens system
The compensation range border of the system, realization more precisely compensates for judging；
5-4. selects the part-compensating lens corresponding away from the farthest border of tested paraboloidal mirror parameter to be used as the optimal compensation
Lens.
Compared with prior art, beneficial effects of the present invention：
The present invention proposes the part-compensating lens system that a kind of nonzero digit detects concave paraboloid mirror, substantially increases non-zero
The convenience of position detection, can really realize the nonzero digit generalization detection of concave paraboloid mirror；Propose to compensate part-compensating lens
The analysis method of scope, solves the problems, such as that nonzero digit detects the part-compensating lens System Design of concave paraboloid mirror, realizes and adopt
The prerequisite of concave paraboloid mirror generalization detection, and the pact of perfect proportions offset lens optimization design are carried out with part penalty method
Beam condition, improves the practicality of part-compensating lens design method, and then lift the precision of nonzero digit testing result.
Brief description of the drawings
Fig. 1 is nonzero digit interference detection concave paraboloid mirror index path；
Fig. 2 detects the modeler model index path on road for equivalent interference；
Fig. 3 is part-compensating lens compensation range analysis process figure；
Fig. 4 is the compensation range D-R figures of a part-compensating lens；
Fig. 5 schemes for the compensation range D-R of some offset lens；
Fig. 6 schemes for the full edge fitting D-R of compensation range of part-compensating lens system；
Fig. 7 schemes for the compensation range piecewise fitting D-R of part-compensating lens system.
Embodiment
The present invention will be further described with reference to the accompanying drawings and examples.
The part-compensating lens system of nonzero digit detection concave paraboloid mirror realizes that the generalization of parabola mirror surface-shaped is detected
Part is mended in prerequisite, part-compensating lens system reasonable combination some offset lens proposed by the invention, system
The compensation range for repaying lens is engaging one another, the parameter area of the conventional tested paraboloidal mirror of covering.To given tested paraboloidal mirror, nothing
Processing part-compensating lens need to be redesigned, select prime offset lens to be used to detect directly from system.This hair
Bright proposed part-compensating lens System Design method includes the single, design of one chip part-compensating lens, compensation range
The foundation of analysis, part-compensating lens System Design and system compensation range database, finally realizes part-compensating lens body
The foundation of system.In addition, optimization constraints during also perfect single part offset lens design, limitation wavefront is radially dull
It is incremented by, i.e., the light path at wavefront center is most long and radially successively decreases, and improves the practicality of part-compensating lens design method, so that
Lift the precision of testing result.
Nonzero digit detects the part-compensating lens system of concave paraboloid mirror, is made up of some offset lens；In system
Each part-compensating lens have respective compensable tested paraboloidal mirror parameter area, the compensation model of all part-compensating lens
Enclosing to be engaged togather, and total compensation range of system is covered conventional tested paraboloidal mirror parameter；It is each in statistics system
The detailed compensation range border of part-compensating lens, constructive system compensation range database makes the benefit to being tested paraboloidal mirror
Repay areal map；According to compensation range figure, can the given tested paraboloidal mirror of intuitive judgment can be by the part-compensating lens system
Compensation；According to the system compensation range database set up, tested paraboloidal mirror can be carried out more accurately to judge, and from
Middle selection is best suitable for realizing given tested paraboloidal mirror the prime offset lens of part compensation detection；To given tested throwing
Object plane mirror, without redesigning processing part-compensating lens, selects prime offset lens to be used to detect directly from system
.
The light path principle of part penalty method detection concave paraboloid mirror is as shown in figure 1, the angle pencil of ray that phase shifting interferometer (1) is sent
Single color plane ripple (2) incides tested paraboloidal mirror (4) by part-compensating lens (3), and light wave is anti-through tested paraboloidal mirror (4)
Penetrate, form detection ripple afterwards again by part-compensating lens (3)；Detection ripple meets with the reference wave inside interferometer to be occurred to do
Relate to, form interference pattern, image in image planes.Wherein, the primary spherical aberration that plane wave (2) permeation parts offset lens (3) is produced is mended
Repay most of normal aberration of tested paraboloidal mirror, thus a given part-compensating lens can be to certain parameter in the range of
Tested paraboloidal mirror realize compensation.As shown in figure 3, nonzero digit detects the part-compensating lens System Design side of concave paraboloid mirror
The step of method, is as follows：
Step 1, initial configuration are calculated
A tested paraboloidal mirror is selected, its F number is less than 1.2；Analyzed by geometric optical theory and primary aberration theory
Method calculate the initial structure parameters of the one chip part-compensating lens compensated to the tested paraboloidal mirror；
Described part-compensating lens, it is standard sphere close to the surface of tested surface, and the surface away from tested surface is set to
Plane, and it is incident by directional light；
The optimization of step 2, part-compensating lens
2-1. is in optical design software to the equivalent interference detection road modeling after simplification, such as Fig. 2, angle pencil of ray plane wave
(2) incided after permeation parts offset lens (3) on tested paraboloidal mirror (4), light wave is reflected by tested paraboloidal mirror (4), is returned
The light wave returned is again by part-compensating lens (3), at image planes (5) place and the canonical reference plane provided by optical design software
Ripple is interfered, and forms interference fringe；
The structure of 2-2. part-compensating lens (3) is by calculating obtained initial structure parameter, being tested paraboloidal mirror (4)
Form parameter be that the parameter used during the initial structure parameter of part-compensating lens is calculated in step 1；
2-3. is to the distance between initial structure parameter, part-compensating lens and tested paraboloidal mirror of part-compensating lens
D is optimized, and object function is set up according to the constraints of restriction, and solution is optimized to initial structure parameter and apart from d；
Described initial structure parameter includes radius of curvature, thickness, bore and the material of part-compensating lens front and rear surfaces；
Described optical design software includes Zemax, Code V, ASAP, Light Tools and all with ray tracing
The software of function；
Described bound for objective function is as follows：
A. the caliber size of part-compensating lens, thickness and material meet optical design requirements and actual processing standard, b.
Greatest gradient value at image planes before coherent wave meets nyquist sampling law, and c. image planes wavefront is dull, center light path most it is long simultaneously
Radially successively decrease；
Step 3, the compensation range to optimization part-compensating lens are analyzed, step such as Fig. 3
3-1. uses the structural parameters after optimization in equivalent model, while the initial vertex of the tested paraboloidal mirror of initialization
Radius of curvature R and starting lowest calibre DMIN(typically taking 5mm), by the distance between part-compensating lens and tested paraboloidal mirror d
It is initialized as zero；The distance between part-compensating lens and tested paraboloidal mirror d is set to variable；
Wherein it is tested initial vertex radius of curvature R=- D of paraboloidal mirrorMIN× F, DMINIt is minimum for the starting of paraboloidal mirror
Bore, F is the F numbers of part-compensating lens；
3-2. optimizes solution according to the step 2-3 object functions set up, if the optimization time is asked beyond the most long of setting
Solution time TMAX(typically taking 10s) can not still meet constraints, then increase the vertex curvature of tested paraboloidal mirror according to step-length S
Radius R absolute value, then re-optimization is apart from d；So circulation is until meet constraints, then by the mouth of tested paraboloidal mirror
Footpath D and vertex curvature radius R are separately recorded in array a and array b；
3-3. increases the bore D of tested paraboloidal mirror according to step-length S1, and its vertex curvature radius R keeps last record
Value is constant, and solution is optimized according to the step 2-3 object functions set up, if the optimization time is beyond the most long solution time of setting
TMAX(typically taking 10s) can not still meet constraints, then the vertex curvature radius according to the tested paraboloidal mirror of step-length S increases is exhausted
To value, then re-optimization is apart from d；
3-4. repetitive cycling step 3-2 and 3-3, until the bore D of tested paraboloidal mirror reaches maximum set in advance
DMAX；
The bore D and vertex curvature radius R of corresponding tested paraboloidal mirror recorded in described array a and array b,
The compensable tested paraboloidal mirror parameter boundary of part-compensating lens is constituted, the compensation range of the part-compensating lens is drawn
D-R schemes, and the bore D to being tested paraboloidal mirror, the vertex curvature radius absolute value for being tested paraboloidal mirror is exhausted more than corresponding border R
The equal of value can be compensated by the part-compensating lens, to can compensate for area, otherwise for can not compensating basin, be marked in D-R figures；
Step 4, from compensation range D-R figures can not in compensatory zone selection F numbers be less than 1.2 tested paraboloidal mirror；Weight
Multiple step 1 designs new part-compensating lens to step 3, until the compensation ability for some offset lens designed is covered
The parameter area of the conventional tested paraboloidal mirror of lid；
Step 5, screen fraction offset lens
5-1. selects the complementary part-compensating lens part offset lens system of M compensation range, and statistics part is mended
The bore D and vertex curvature radius R that paraboloidal mirror is tested in lens system are repaid, and statistics is built to the compensation energy of the system
Force data storehouse；
5-2. carries out full border multinomial to the compensation range border of the part-compensating lens in part-compensating lens system
Fitting is compensated boundary curve, so as to realize that can the given tested paraboloidal mirror of quick judgement be compensated by the system；
5-3. carries out piecewise fitting and obtained to the compensation range border of the part-compensating lens in part-compensating lens system
The compensation range border of system, realization more precisely compensates for judging；
5-4. selects the part-compensating lens corresponding away from the farthest border of tested paraboloidal mirror parameter to be used as the optimal compensation
Lens.
Embodiment 1：
The present invention detects that the example of the part-compensating lens System Design of concave paraboloid mirror is described as follows applied to nonzero digit.
Fig. 1 is the index path that concave paraboloid mirror is detected using phase shifting interferometer nonzero digit, a given portion as shown in Figure 1
Offset lens is divided to be compensated to the tested paraboloidal mirror in the range of certain parameter.Based on this principle, to generally applicableization
The part-compensating lens system of detection concave paraboloid mirror is designed.1) initial configuration is calculated --- and it is bent to bore 101mm, summit
Rate radius is 240mm tested paraboloidal mirror design part-compensating lens, and the F numbers of paraboloidal mirror are 1.19.Add for convenience of actual
Work and application, the bore for limiting designed part-compensating lens is 45mm, and laser wavelength lambda is 632.8nm.Calculate initial knot
It is standard close to the one side of tested paraboloidal mirror if side of the part-compensating lens away from tested paraboloidal mirror is plane during structure
Sphere, according to primary aberration theory, makes the primary spherical aberration coefficient of tested paraboloidal mirror and the primary spherical aberration system of part-compensating lens
Number sum is approximately zero, with reference to theory of geometric optics, calculates the part-compensating lens initial configuration for meeting above-mentioned condition, such as table
Shown in 1.
The part-compensating lens initial structure parameter of table 1
2) optimization of part-compensating lens --- road is detected to the equivalent interference after simplification in optical design software Zemax
Modeling, such as Fig. 2 is incided on tested paraboloidal mirror (4) after angle pencil of ray plane wave (2) permeation parts offset lens (3), light wave by
Tested paraboloidal mirror (4) reflection, the light wave of return is again by part-compensating lens (3), at image planes (5) place with being carried by Zemax
The canonical reference plane wave of confession is interfered, and forms interference fringe；Wherein, part-compensating lens (3) and tested paraboloidal mirror (4)
Use step 1) in parameter；The bore and material of holding part offset lens (3) are constant, by its front and rear surfaces radius of curvature,
The distance between thickness and part-compensating lens (3) and tested paraboloidal mirror (4) d are set to variable.Object function is set up, is constrained
Condition includes, and the bore of a. part-compensating lens is fixed as 45mm, and its edge minimum thickness is 1.8mm, and material immobilizes, b.
Greatest gradient value at image planes before coherent wave is most long per pixel λ/6, c. centers light path and radially successively decreases, specific practice be from
Wavefront center starts radially to take 8 sampled points at equal intervals and light path successively decreases, to control image planes wavefront dull.
Solution is optimized to variable by above-mentioned constraints in Zemax, until being met the structure of requirement.What optimization design was completed
Part-compensating lens parameter is as shown in table 2.
Part-compensating lens structural parameters of the table 2 Jing Guo optimization design
3) compensation range for optimizing part-compensating lens is analyzed --- part-compensating lens are to being tested paraboloidal mirror
The analysis process of compensation range such as Fig. 3, sets up equivalent detection road model as shown in Figure 2, is compensated using the part optimized in table 2
Lens parameter, the starting bore of the tested paraboloidal mirror of initialization is 5mm, the initial vertax curvature half of the tested paraboloidal mirror of initialization
Footpath R=-D × F, wherein D are the initial bore of paraboloidal mirror, and F is the F numbers of part-compensating lens, is mended for the part shown in table 2
Lens are repaid, the distance between part-compensating lens and tested paraboloidal mirror d is initialized as zero by Initial R=- 7.1544mm.Will
The distance between tested paraboloidal mirror and part-compensating lens d is set to variable, according in step 2) in the object function set up enter
Row 2 takes turns Optimization Solution, if the optimization time can not still meet constraints beyond 10s, tested paraboloidal mirror is increased by step-length 1mm
Vertex curvature radius absolute value, re-optimization is apart from variable d；So circulation is until meet constraints, and preservation is now tested
The bore D and vertex curvature radius R of paraboloidal mirror are respectively in array a and array b.After the completion of data are preserved, according to step-length
The bore D of the tested paraboloidal mirror of 0.5mm increases, the record value that its vertex curvature radius R remains the last time is constant, repeats above-mentioned
Optimization process, until the bore of tested paraboloidal mirror increases to maximum 200mm set in advance.The quilt preserved during this
Paraboloidal mirror bore D and its vertex curvature radius R array a and b is surveyed, is the compensable tested parabolic of the part-compensating lens
Face mirror boundary parameter, draws compensation range D-R figures accordingly.The part-compensating lens listed to table 2, its compensation range D-R schemes such as
Shown in Fig. 4, abscissa is tested paraboloidal mirror bore D, and ordinate is the absolute of the vertex curvature radius R of tested paraboloidal mirror
Value.Tested paraboloidal mirror to giving bore D, its vertex curvature radius absolute value can quilt more than corresponding R values on D-R curves
The part-compensating lens compensate, to can compensate for area, otherwise for can not compensating basin, be marked in D-R figures.
4) some offset lens are designed --- in compensatory zone tested surface F numbers can not be selected small from compensation range figure
In 1.2 paraboloidal mirror parameter, repeat step 1)~3), until have devised totally 14 part-compensating lens, its compensation ability
Cover tested paraboloidal mirror bore 5mm~200mm Common Parameters scope, compensation range D-R figure such as Fig. 5.Mend these parts
The design parameter for repaying lens is as shown in table 3, and the bore of part-compensating lens is 45mm, except 2#, 3# and 5# part-compensating lens
Material for outside Vd 1.5172, Nd 64.28, remaining is identical with the material in table 2.
14 part-compensating lens structural parameters designed by table 3
| Sequence number | Preceding surface curvature radius (mm) | Surface curvature radius (mm) afterwards | Thickness (mm) |
| 1# | 250.00 | -50.678 | 10.65 |
| 2# | 250.00 | -80.962 | 7.69 |
| 3# | 450.00 | -80.962 | 7.69 |
| 4# | 150.00 | -50.678 | 10.65 |
| 5# | 89.148 | -50.678 | 10.65 |
| 6# | 70.000 | -50.678 | 11.18 |
| 7# | 150.00 | -80.962 | 8.32 |
| 8# | 53.125 | -53.125 | 12.00 |
| 9# | 933.65 | -31.000 | 12.00 |
| 10# | 31.000 | -992.41 | 12.00 |
| 11# | 50.000 | -73.600 | 11.24 |
| 12# | 174.30 | -50.000 | 11.24 |
| 13# | 213.43 | -55.740 | 8.73 |
| 14# | 102.67 | -53.240 | 10.8 |
5) screen fraction offset lens --- analysis compensation range Fig. 5, selection compensation range is complementary and can cover maximum ginseng
Totally 9 part-compensating lens are renumbered as 1#~9#, composition portion by 4#~8#, 10# and 12#~14# in the table 3 of number scope
Divide offset lens system.The detailed compensation range parameter of part-compensating lens system is counted, i.e., each part-compensating lens can be mended
The tested paraboloidal mirror boundary parameter repaid, the compensation ability database of constructive system.Draw the compensation of part-compensating lens system
Scope D-R schemes, as shown in Figure 6 and Figure 7.Round and smooth full curve in Fig. 6 represents the bound of parameter to part-compensating lens system
Boundary curve is compensated after carrying out full border quadratic polynomial fitting, expression formula is R=0.0065D2+0.4151D+
42.9371, it can quickly judge that can given tested paraboloidal mirror be compensated by the system according to the curve, method is will be given
The bore D of tested paraboloidal mirror is brought into expression formula, if it is bent less than the actual summit of given tested paraboloidal mirror to calculate income value
Rate radius R absolute value, then can be compensated, instead then on the contrary.Such as Fig. 7, the compensation range border of the piecewise fitting system is adopted respectively
With quadratic polynomial fitting and linear fit, specific fitting result such as table 4, it can then realize more precisely compensate for judging accordingly.
Based on compensation ability database and compensation range figure, the farthest border of the given tested paraboloidal mirror parameter point of chosen distance is corresponding
Part-compensating lens be used as tested paraboloidal mirror prime offset lens.
The seriation offset lens compensation range piecewise fitting result of table 4
| Parabola bore D (mm) | Secondary term coefficient | Monomial coefficient | Constant term |
| 10~46 | -0.0260 | 2.8730 | 0.2543 |
| 46~47 | 0.0000 | 17.0000 | -704.3181 |
| 47~78 | -0.0183 | 2.6967 | 11.7937 |
| 78~79 | 0.0000 | 11.1650 | -655.3030 |
| 79~91 | -0.0035 | 0.7098 | 97.4717 |
| 91~92 | 0.0000 | 44.7030 | -3935.0190 |
| 92~114 | 0.0000 | 0.7360 | 169.1751 |
| 114~115 | 0.0000 | 43.0090 | -4725.4640 |
| 115~134 | -0.0012 | 0.3972 | 190.9348 |
| 134~135 | 0.0000 | 20.6100 | -2538.9790 |
| 135~144 | -0.0303 | 8.5515 | -358.811 |
| 144~145 | 0.0000 | 21.4200 | -2840.1090 |
| 145~163 | -0.0029 | 0.9924 | 183.7198 |
| 163~164 | 0.0000 | 262.0260 | -40812.4470 |
| 164~179 | -0.0028 | 1.0902 | 224.7282 |
| 179~180 | 0.0000 | 25.5670 | -4246.4930 |
| 180~188 | 0.0000 | 0.0000 | 355.5668 |
| 188~189 | 0.0000 | 30.1650 | -5315.453 |
| 189~200 | 0.0000 | 0.1399 | 359.5296 |
Claims (4)
1. the design method of the part-compensating lens system of nonzero digit detection concave paraboloid mirror, it is characterised in that including following step
Suddenly：
Step 1, initial configuration are calculated
A tested paraboloidal mirror is selected, its F number is less than 1.2；The side analyzed by geometric optical theory and primary aberration theory
Method, calculates the initial structure parameter to being tested the one chip part-compensating lens that paraboloidal mirror is compensated；
Described part-compensating lens, it is standard sphere close to the surface of tested surface, and the surface away from tested surface is set to plane,
And it is incident by directional light；
The optimization of step 2, part-compensating lens
2-1. is to the equivalent interference detection light path modeling after simplification in optical design software, and the light channel structure of equivalent model is flat
Incided after the ripple permeation parts offset lens of face on tested paraboloidal mirror, light wave is reflected by tested paraboloidal mirror, the light wave of return
Again by part-compensating lens, interfered at image planes with the standard flat ripple that is provided by optical design software, form dry
Relate to striped；
The structure of 2-2. part-compensating lens is by calculating obtained initial structure parameter, being tested the form parameter of paraboloidal mirror
The parameter used during the initial structure parameter for being calculating part-compensating lens in step 1；
2-3. enters to the distance between the initial structure parameters of part-compensating lens, part-compensating lens and tested paraboloidal mirror d
Row optimization, sets up object function according to the constraints of restriction, solution is optimized to initial structure parameter and apart from d；It is described
Initial structure parameter include radius of curvature, thickness, bore and the material of part-compensating lens front and rear surfaces；
Step 3, the compensation range to optimization part-compensating lens are analyzed
3-1. uses the structural parameters after optimization in equivalent model, while the initial vertex curvature of the tested paraboloidal mirror of initialization
Radius R and starting lowest calibre DMIN, the distance between part-compensating lens and tested paraboloidal mirror d is initialized as zero；By portion
The distance between offset lens and tested paraboloidal mirror d is divided to be set to variable；
Wherein it is tested initial vertex radius of curvature R=- D of paraboloidal mirrorMIN× F, DMINFor the starting lowest calibre of paraboloidal mirror,
F is the F numbers of part-compensating lens；
3-2. optimizes solution according to the step 2-3 object functions set up, if the optimization time is beyond the most long solution of setting
Between TMAXConstraints can not be still met, then increases the vertex curvature radius R of tested paraboloidal mirror absolute value according to step-length S, then
Re-optimization is apart from d；So circulation is until meet constraints, then by the bore D and vertex curvature of tested paraboloidal mirror half
Footpath R is separately recorded in array a and array b；
3-3. increases the bore D of tested paraboloidal mirror according to step-length S, and its vertex curvature radius R keeps the record value of last time not
Become, solution is optimized according to the step 2-3 object functions set up, if the optimization time is beyond the most long solution time T of settingMAX
Constraints can not be still met, then increases the vertex curvature radius absolute value of tested paraboloidal mirror, then re-optimization according to step-length S
Apart from d；
3-4. repetitive cycling step 3-2 and 3-3, until the bore D of tested paraboloidal mirror reaches maximum D set in advanceMAX；
The bore D and vertex curvature radius R of corresponding tested paraboloidal mirror recorded in described array a and array b, composition
Part-compensating lens compensable tested paraboloidal mirror parameter boundaries, draw the compensation range D-R of the part-compensating lens
Figure, and mark can compensate for area with can not compensating basin；
Step 4, from compensation range D-R figures can not in compensatory zone selection F numbers be less than 1.2 tested paraboloidal mirror；Repeat to walk
Rapid 1, to step 3, designs new part-compensating lens, until the compensation ability covering for some offset lens designed is normal
With the parameter area of tested paraboloidal mirror；
Step 5, screen fraction offset lens
5-1. selects the complementary part-compensating lens part offset lens system of M compensation range, and statistics part compensates saturating
The bore D and vertex curvature radius R of paraboloidal mirror are tested in mirror body system, and statistics is built to the compensation ability number of the system
According to storehouse；
5-2. carries out full border fitting of a polynomial to the compensation range border of the part-compensating lens in part-compensating lens system
Boundary curve is compensated, so as to realize that can the given tested paraboloidal mirror of quick judgement be compensated by the system；
5-3. carries out piecewise fitting and obtains the body to the compensation range border of the part-compensating lens in part-compensating lens system
The compensation range border of system, realization more precisely compensates for judging；
5-4. selects the part-compensating lens corresponding away from the farthest border of tested paraboloidal mirror parameter to be used as the optimal compensation lens.
2. the design method of the part-compensating lens system of nonzero digit detection concave paraboloid mirror as claimed in claim 1, it is special
Levy and be that described optical design software includes all softwares with ray tracing function.
3. the design method of the part-compensating lens system of nonzero digit detection concave paraboloid mirror as claimed in claim 1, it is special
Levy and be that described bound for objective function is as follows：
A. the caliber size of part-compensating lens, thickness and material meet optical design requirements and actual processing standard；
B. the greatest gradient value at image planes before coherent wave meets nyquist sampling law；
C. image planes wavefront is dull, and center light path is most long and radially successively decreases.
4. the design method of the part-compensating lens system of nonzero digit detection concave paraboloid mirror according to claim 2, its
It is characterised by that part-compensating lens system used in this method includes some offset lens, each part-compensating lens have
Respective compensable tested paraboloidal mirror parameter area, and the compensation range of all part-compensating lens can be engaged togather,
Total compensation range of system is set to cover conventional tested paraboloidal mirror parameter；By the detailed benefit of each part-compensating lens in system
Range boundary is repaid, constructive system compensation range database is made and can compensate for areal map to tested paraboloidal mirror.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510324738.8A CN104932100B (en) | 2015-06-12 | 2015-06-12 | Nonzero digit detects the part-compensating lens system and design method of concave paraboloid mirror |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510324738.8A CN104932100B (en) | 2015-06-12 | 2015-06-12 | Nonzero digit detects the part-compensating lens system and design method of concave paraboloid mirror |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104932100A CN104932100A (en) | 2015-09-23 |
| CN104932100B true CN104932100B (en) | 2017-08-15 |
Family
ID=54119337
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510324738.8A Active CN104932100B (en) | 2015-06-12 | 2015-06-12 | Nonzero digit detects the part-compensating lens system and design method of concave paraboloid mirror |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104932100B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110889200B (en) * | 2019-11-04 | 2023-06-02 | 天津大学 | Mould pressing forming pre-compensation method for aspherical glass lens |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102735187A (en) * | 2012-07-05 | 2012-10-17 | 北京理工大学 | Searching method for annular sub-aperture boundary splicing |
-
2015
- 2015-06-12 CN CN201510324738.8A patent/CN104932100B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102735187A (en) * | 2012-07-05 | 2012-10-17 | 北京理工大学 | Searching method for annular sub-aperture boundary splicing |
Non-Patent Citations (3)
| Title |
|---|
| 《Non-null interferometric aspheric testing with partial null lens and reverse optimization》;Dong Liu等;《Proc. of SPIE》;20091231;第7426卷;74260M1-7 * |
| 《利用部分补偿透镜进行非球面面形测量》;刘惠兰等;《北京理工大学学报》;20040731;第24卷(第7期);625-628页 * |
| 《用于非球面通用化检测的部分零位透镜》;刘东等;《红外与激光工程》;20090430;第38卷(第2期);摘要、323-325页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104932100A (en) | 2015-09-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Tonry et al. | Cosmological results from high-z supernovae | |
| CN102062677B (en) | Refractive index distribution measuring method and refractive index distribution measuring apparatus | |
| CN103776389A (en) | High-precision aspheric combined interference detection device and high-precision aspheric combined interference detection method | |
| CN107782254A (en) | A kind of mixed compensating mode sub-aperture stitching surface testing method | |
| CN103809290B (en) | A kind of mutual compensation optimizing method of optical system face shape error | |
| CN102183214A (en) | Light detection method for large-aperture aspherical mirror structure | |
| Davis | Fresnel lens solar concentrator derivations and simulations | |
| CN102997864A (en) | Detection system of large-aperture optical aspherical mirror | |
| CN104048619B (en) | It is a kind of to judge that axisymmetry aspheric surface adopt the method for directly interfering detection | |
| CN103389037A (en) | Device and method for detecting geometric technical parameters of lighting diffracting optical components | |
| CN103234480A (en) | Rapid surface shape detection method for circular convex aspheric surfaces | |
| CN104851106A (en) | CCD original image processing method | |
| CN104932100B (en) | Nonzero digit detects the part-compensating lens system and design method of concave paraboloid mirror | |
| CN112097745A (en) | Line structured light quality improvement method of vision measurement system | |
| CN114688963B (en) | Light path beam combination quality detection and calibration method and system for multi-wavelength point diffraction interferometer | |
| CN104048596B (en) | Compensator and the compensator control method coaxial with interferometer | |
| CN101975990B (en) | Method for designing partially compensatory lens by taking slope as optimization objective | |
| CN103196391A (en) | Quick surface shape detection method of annular concave aspheric surface near to paraboloid | |
| Kaisin et al. | Star Formation in Nearby Dwarf Galaxies | |
| CN107300419B (en) | A kind of Method of Adjustment and assembling ＆ adjusting system of spectrometer | |
| CN114185144B (en) | Mounting and adjusting method for mounting and adjusting large-caliber optical system based on small-caliber plane mirror | |
| CN106482732B (en) | A kind of round-the-clock high precision star anaclasis navigation stray light inhibition method | |
| CN201540198U (en) | Testing device for diffuse spot and color deviation of optical system | |
| CN103411896A (en) | Method for acquiring ultra-low dispersion spectral signature of low-orbit space debris | |
| CN103411535B (en) | A kind of Changeable weight picture point localization method for retro-reflective target |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |