CN109579739A - A kind of off-axis refraction-reflection type part compensator system and design method - Google Patents
A kind of off-axis refraction-reflection type part compensator system and design method Download PDFInfo
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract
The present invention relates to a kind of off-axis refraction-reflection type part compensator system and design methods, belong to photoelectric detection technology field.The compensator system includes two-stage compensator, system design optimization method establishes the unified spherical aberration of system, astigmatism relational expression using third-order aberration theory, the equation group about compensator structure parameter is established in conjunction with paraxial rays formula, genetic algorithm is combined to solve initial structure parameter and model in optical design software later, setting optimization aim, optimization operand and optimized variable optimize, and realize the detection to non-rotational symmetry non-spherical surface pattern.Structure is simple and easy to implement for present system, one-to-many surface testing can be achieved, reduce the design difficulty and processing cost of compensator, simultaneously, the design of Compensator method can effectively obtain initial configuration global optimum, the self-defect of existing optical design software is effectively avoided, non-rotational symmetry Aspherical-surface testing precision is improved.
Description
Technical field
The present invention relates to a kind of compensator system for being detected to non-rotational symmetry non-spherical element and design sides
Method belongs to photoelectric detection technology field.
Background technique
Aspherical is widely applied one kind optical element in contemporary optics system.It is aspherical, especially non-rotational symmetry
It is aspherical, a variety of aberrations can be corrected simultaneously, can be effectively improved system imaging quality, increase optical design freedom, improve system
The advantages such as the flexibility for design of uniting, make it play highly important role in various fields.But for non-rotating right
Claim aspherical detection then relative difficulty, its machining accuracy is caused to be difficult to ensure always, therefore, finds a kind of high-precision, structure
Simple non-rotational symmetry Aspherical-surface testing method, is the problem that field of photodetection is in the urgent need to address at this stage.
In existing non-rotational symmetry Aspherical-surface testing method, interferometry measurement is a kind of high-precision, high sensitivity
Detection means is broadly divided into two classes: zero-compensation interferometry and part compensating interferometer method.Wherein, zero-compensation interferometry is to compensate
The normal aberration of tested surface is fully compensated when device designs, to realize interferometry.Currently, common zero-compensation interferometry side
Method mainly has: computed hologram penalty method, Dall penalty method, Offner penalty method, etc..But the common spy of these methods
Point is: design of Compensator and difficulty of processing are higher, and a kind of compensator is only capable of compensating the aspherical of a certain special parameter,
Measurement dynamic range is small, poor universality.Part compensating interferometer method overcome zero-compensation interferometry there are the problem of, effectively increase
The versatility of compensator, and the design and difficulty of processing of compensator also relative reduction.But it is aspherical for non-rotational symmetry
Detection, because tested surface introduces such as astigmatism, coma non-rotational symmetry aberration, the aberration for needing to compensate is relative complex, this for
The calculating and design of compensator structure have extremely challenging.
In the existing part compensating interferometer method aspherical for non-rotational symmetry, Chinese invention patent
CN105352451B gives a kind of omnipotent compensating glass of standard and design method based on deformable mirror.But this method design knot
Fruit is very big to the design accuracy dependence of first order compensator, that is, lens or lens group, and second level compensator, that is, deformable mirror
Face type designs the optimization for the optical design software that places one's entire reliance upon, and optimization process easily falls into local optimum, leads to not obtain
Meet the compensator of design objective, and deformable mirror itself has the shortcomings that control difficulty is high, at high cost.
The aspherical interferometry difficult point of non-rotational symmetry is the calculating, design and processing of compensator.In order to solve
The deficiencies in the prior art, need to study that a kind of structure is simple, the higher compensator of detection accuracy, and carry out to its calculation method excellent
Change, design result is avoided to fall into local optimum in optimization process.
Summary of the invention
The purpose of the present invention is to solve structure is complicated existing for existing compensator, component is at high cost and optimum results
The problems such as easily falling into local optimum proposes a kind of off-axis refraction-reflection type part compensator system and design method, it is intended to utilize
The relatively simple lens of structure or lens group and spherical reflector constitute off-axis refraction-reflection type part compensator, realize to non-rotating right
Claim the compensation of aberration, can meet interference fringe it is detectable under the premise of, the aspherical inspection of raising non-rotational symmetry as far as possible
Survey precision.
The purpose of the present invention is what is be achieved through the following technical solutions.
A kind of off-axis refraction-reflection type part compensator system aspherical for non-rotational symmetry, comprising: ccd detector, at
As object lens, collimation laser, spectroscope, reference mirror, first order compensator, second level compensator, first order compensator and the second level
Compensator together constitutes off-axis refraction-reflection type part compensator.
Wherein, first order compensator is made of lens or lens group, for generating aberration (such as ball with rotational symmetry
Difference), realize the compensation to tested surface rotational symmetry aberration, meanwhile, by controlling the bias and inclination of first order compensator, generate
Non-rotational symmetry aberration, for compensating the low order non-rotational symmetry aberration of tested surface.Second level compensator is that off-axis spherical surface is anti-
Mirror is penetrated, by controlling its eccentric and inclination, realizes the compensation to non-rotational symmetry higher order aberratons.
The optical path that above-mentioned building block is constituted are as follows: collimation laser passes through spectroscope, and light beam reflects to form reference light, a branch of
Light transmission forms measurement light, measures light through reference mirror, first order compensator, second level compensator, non-rotational symmetry aspheric to be measured
It is reflected behind face, again passes by second level compensator, first order compensator, and penetrate reference mirror, formed and interfered with reference light
Striped is observed at ccd detector by image-forming objective lens.
The present invention proposes a kind of design optimization method for above system simultaneously.Firstly, based on third-order aberration theory,
Equation is analyzed whole system and established to paraxial rays theory etc., is derived and is calculated initial configuration.Later, with optical design
Software is design platform, and system initial structure parameter is arranged, and according to actual needs, initial optimization is carried out to initial system, with full
The geometrical relationship requirement of pedal system structure.Finally, carrying out two to system using the system after initial optimization as new initial configuration
Suboptimization, to obtain the system for meeting the aspherical face shape error detection of non-rotational symmetry.
Beneficial effect
1, the configuration of the present invention is simple is easily realized, only needs the relatively simple lens of structure, spherical reflector that non-rotation can be realized
Turn the detection of symmetric aspheres, the calibration and adjustment of system are relatively easy, and as part compensator, may be implemented one-to-many
Surface testing effectively reduces the design difficulty and processing cost of compensator；
2, the design method of the compensator fully considers the characteristics of non-rotational symmetry aberration, and combines genetic algorithm, obtains
The global optimum of initial structure parameter effectively avoids that design result is caused to fall into part most because of optical design software self-defect
The figure of merit and the problem of be unable to satisfy design objective.
Detailed description of the invention
Fig. 1 is application schematic diagram example of the part compensator of the present invention in fizeau interferometer；
Fig. 2 is compensator detection method flow chart in part of the present invention；
Wherein, 1- collimation laser, 2- spectroscope, 3- reference mirror, 4- first order compensator, the second level 5- compensator, 6- at
As object lens, 7-CCD detector, 8- non-rotational symmetry to be measured is aspherical.
Specific embodiment
It elaborates with reference to the accompanying drawings and examples to the present invention.
As shown in Figure 1, a kind of off-axis refraction-reflection type part compensator system aspherical for non-rotational symmetry, comprising: quasi-
Straight laser 1, spectroscope 2, reference mirror 3, first order compensator 4, second level compensator 5, image-forming objective lens 6 and ccd detector 7.The
First-order compensators 4 and second level compensator 5 together constitute off-axis refraction-reflection type part compensator.
Wherein, first order compensator 4 is made of lens or lens group, for generating the aberration with rotational symmetry (such as
Spherical aberration), realize the compensation of 8 rotational symmetry aberration aspherical to non-rotational symmetry to be measured, meanwhile, by controlling first order compensator
4 bias and inclination generates non-rotational symmetry aberration, the low order non-rotational symmetry picture for non-rotational symmetry to be measured aspherical 8
Difference.Second level compensator 5 is off-axis spherical reflector, by controlling its eccentric and inclination, is realized to non-rotational symmetry high-order
The compensation of aberration.
The optical path that above-mentioned building block is constituted are as follows: collimation laser 1 passes through spectroscope 2, and light beam reflects to form reference light, and one
Beam light transmission forms measurement light.Light is measured through reference mirror 3, first order compensator 4, second level compensator 5, non-rotational symmetry to be measured
It is reflected after aspherical 8, second level compensator 5, first order compensator 4 is again passed by, and penetrate reference mirror 3, with reference light
Interference fringe is formed, is observed at ccd detector 7 by image-forming objective lens 6.
A kind of off-axis refraction-reflection type part compensator system design method, specifically includes the following steps:
Step 1: determining the basic parameter of system.
Basic parameter, including Entry pupil diameters D and wavelength X are set based on system structure.
Step 2: establishing the equation group about system structure parameter.
Firstly, establishing the aberration coefficients relational expression of whole system by third-order aberration theory.In order to simplify design, consider
Not with the spherical aberration S of off-axis amount variationⅠAnd non-rotational symmetry aberration astigmatism SⅢ, to realize the benefit of non-rotational symmetry aspherical aberration
It repays.Spherical aberration SⅠAnd astigmatism SⅢExpression formula be respectively as follows:
SI=∑ hP+ ∑ h Δ P (1)
Wherein:
J=n (uhz-uzh) (7)
In formula, h is the first auxiliary light i.e. height of incidence of rim ray, hzIt is the incidence height of the second auxiliary light
Degree, i are incidence angles, and i' is the angle of emergence, and u is object space angular aperture, and u' is image space angular aperture, and n and n' respectively indicate the refraction of incidence side
Rate and transmission or reflection side's refractive index, k are secondary aspherical coefficient, R0For the vertex curvature radius of tested surface, uzIt is the second auxiliary
Angle of incidence of light.
Secondly as light passes through off-axis refraction-reflection type part compensator twice, and on non-rotational symmetry to be measured is aspherical
Only reflection is primary, and the aberration governing equation established between system and tested surface is as follows:
2SI is mended+SI is non-=0 (8)
2SIII mends+SIII is non-=0 (9)
Wherein, SI mendsIt is the spherical aberration of off-axis refraction-reflection type part compensator, SI is non-It is the ball of the aspherical generation of non-rotational symmetry to be measured
Difference.SIII mendsIt is the astigmatism of off-axis refraction-reflection type part compensator, SIII mendsIt is the astigmatism of the aspherical generation of non-rotational symmetry to be measured.It is establishing
When aberration relational expression, to consider off-axis refraction-reflection type part compensator and tested surface it is unified between aberration relationship, sufficiently to examine
Consider the aberration introduced due to system non-rotational symmetry.
Again, using paraxial rays expression formula, each refraction, reflecting surface image side angular aperture are established about radius of curvature
Equation:
Wherein, r is each refraction, the corresponding radius of curvature of reflecting surface.To sum up, by formula (8), (9), (10) establish about from
The equation group of axis refraction-reflection type part compensator structure parameter.
Step 3: utilizing Mathematical tool, solve above-mentioned equation group, obtain off-axis refraction-reflection type part compensator and initially tie
Structure parameter.
According to priori knowledge and the design requirement of real system, be arranged lens (group) vertex to spherical reflector vertex it
Between distance d1And spherical reflector vertex is to the distance d between non-rotational symmetry aspheric vertex of surface to be measured2.It is asked based on genetic algorithm
Off-axis refraction-reflection type part compensator initial structure parameter is solved, the overall situation of off-axis refraction-reflection type part compensator initial structure parameter is obtained
Optimal value is iterated calculating on this basis, obtains the off-axis refraction-reflection type part compensator initial configuration eventually for modeling
Parameter.
Step 4: utilizing optical design software, system structure is modeled and is optimized.
Firstly, the initial structure parameter obtained according to step 3 models system in optical design software, avoid
The problem of causing design result to fall into local optimum because of optical design software self-defect.
Secondly, the bias of initial structure parameter and off-axis refraction-reflection type part compensator that setting acquires and inclination are optimization
Variable carries out initial optimization to system using wavefront PV as optimization aim, with overcome because it is paraxial it is approximate caused by rim ray without
Method enters the problem of system.If there is light occlusion issue in system, by combining ZPL instruction to control ray position, and
Using the system after initial optimization as new initial system.
System after the completion of initial optimization can guarantee that rim ray enters system and dull thread occlusion issue.In this base
On plinth, double optimization is carried out to system, optimized variable and optimization aim are identical as initial optimization, interfere at image planes to obtain
Striped is relatively sparse as a result, the remaining wavefront of record at this time.
Step 5: judging whether design result is feasible.
The maximum wavefront slope K for calculating remaining wavefront, judges whether interference fringe at this time is detectable.In general, selected CCD
The pixel number of detector is 1024 pixels × 1024 pixels, and the maximum spatial frequency of corresponding detectable interference fringe is about 0.45
When λ/pixel, i.e. K≤0.45 λ/pixel, interference fringe is detectable, and otherwise, interference fringe is not detectable, the structural parameters of system
Design objective is not met, return step 4 is needed to re-start system parameter settings, and optimizes and is up to meeting design objective
Only.
Embodiment
The aspherical non-rotational symmetry of this example measurement is the relatively simple off axis paraboloid mirror of structure, and bore is
76.2mm, vertex curvature radius 889mm, asphericity coefficient are -1, and off-axis amount is 10mm.Design off-axis refraction-reflection type part compensation
Device detection system, it is as shown in Figure 2 to the detailed process of non-rotational symmetry aspheric surface error-detecting to realize.
Step 1: determining system basic parameter.
Based on system structure, the Entry pupil diameters D=81mm of system, wavelength X=532nm are set.
Step 2: establishing the equation group about system structure parameter.
The equation group of system initial structure parameter is established according to third-order aberration theory, paraxial rays formula, wherein astigmatism and
Spherical aberration relational expression need to consider it is unified, to fully consider the influence of the introduced aberration of non-rotational symmetry tested surface.
Step 3: solving above-mentioned equation group using Mathematical tool, solve off-axis refraction-reflection type part compensator initial configuration
Parameter.
According to priori knowledge and the design requirement of real system, be arranged lens (group) vertex to spherical reflector vertex it
Between distance d1=100mm and spherical reflector vertex are to the distance d between non-rotational symmetry aspheric vertex of surface to be measured2=-500mm.
Solve the global optimum of off-axis refraction-reflection type part compensator initial configuration based on genetic algorithm, and in this, as iterative initial value,
Solution obtains the initial structure parameter for system modelling, i.e. the radius of curvature r of two optical surfaces of lens1=-8.5787mm,
r2=-8.2617mm, the radius of curvature r of spherical reflector3=-323.0668mm
Step 4: utilizing optical design software, system structure is modeled and is optimized.
The present embodiment selects ZEMAX as optical design software.In ZEMAX, the initial configuration that is obtained according to step 3
Parameter models system, and optimized variable, optimization aim and optimization operand is arranged, and unites to system and carries out initial optimization,
To guarantee that light is able to enter system and dull thread circumstance of occlusion.On this basis, double optimization is carried out to system, finally obtained
System optical parameter be r1=168.217619mm, r2=-1030.439322mm, r3=-89.718106mm, spherical surface are anti-
Penetrate aperture of mirror D3=9.375m3m3,2d1=291.980398mm, d2=-843.885967mm, lens and spherical reflector it is inclined
The heart and inclination are respectively L1decenter=1.173455mm, L1tilt=0.005740054 °, M1decenter=-0.038789mm,
M1tilt=-10 °.
Step 5: judging whether design result is feasible.
Read the system spare wavefront after the completion of optimization, calculate residue wavefront maximum wavefront slope K=0.373 λ 8 as/it is plain,
Maximum 0.45 λ of the wavefront slope/pixel for meeting the detectable interference fringe of detector then can determine whether to obtain in the embodiment and interfere item
Line can be detected, and designed off-axis refraction-reflection type part compensator is suitble to.
Claims (3)
1. a kind of off-axis refraction-reflection type part compensator system, which is characterized in that including collimation laser (1), spectroscope (2), reference
Mirror (3), first order compensator (4), second level compensator (5), image-forming objective lens (6) and ccd detector (7)；First order compensator
(4) and second level compensator (5) together constitutes off-axis refraction-reflection type part compensator；
Wherein, first order compensator (4) is made of lens or lens group, for generating aberration (such as ball with rotational symmetry
Difference), realize the compensation of (8) rotational symmetry aberration aspherical to non-rotational symmetry to be measured, meanwhile, by controlling first order compensator
(4) bias and inclination generate non-rotational symmetry aberration, and the low order for non-rotational symmetry to be measured aspherical (8) is non-rotating right
Claim aberration；Second level compensator (5) is off-axis spherical reflector, by controlling its eccentric and inclination, is realized to non-rotating right
Claim the compensation of higher order aberratons；
The optical path that above-mentioned building block is constituted are as follows: collimation laser (1) passes through spectroscope (2), and light beam reflects to form reference light, and one
Beam light transmission forms measurement light；Light is measured through reference mirror (3), first order compensator (4), second level compensator (5), non-rotation to be measured
Turn symmetric aspheres (8) to reflect afterwards, again passes by second level compensator (5), first order compensator (4), and through reference
Mirror (3) forms interference fringe with reference light, is observed at ccd detector (7) by image-forming objective lens (6).
2. a kind of off-axis refraction-reflection type part compensator system design method, which comprises the following steps:
Step 1: determining the basic parameter of system；
Basic parameter, including Entry pupil diameters D and wavelength X are set based on system structure；
Step 2: establishing the equation group about system structure parameter；
Firstly, establishing the aberration coefficients relational expression of whole system by third-order aberration theory；Consider not with off-axis amount variation
Spherical aberration SⅠAnd non-rotational symmetry aberration astigmatism SⅢ, to realize the compensation of non-rotational symmetry aspherical aberration, spherical aberration SⅠAnd astigmatism SⅢ
Expression formula be respectively as follows:
SI=∑ hP+ ∑ h Δ P (1)
Wherein:
J=n (uhz-uzh) (7)
In formula, h is the first auxiliary light i.e. height of incidence of rim ray, hzIt is the height of incidence of the second auxiliary light, i is
Incidence angle, i' are the angles of emergence, and u is object space angular aperture, and u' is image space angular aperture, and n and n' respectively indicate incidence side's refractive index and thoroughly
It penetrates or reflection side refractive index, k is secondary aspherical coefficient, R0For the vertex curvature radius of tested surface, uzIt is that the second auxiliary light enters
Firing angle；
Secondly, the aberration governing equation established between system and tested surface is as follows:
2SI is mended+SI is non-=0 (8)
2SIII mends+SIII is non-=0 (9)
Wherein, SI mendsIt is the spherical aberration of off-axis refraction-reflection type part compensator, SI is non-It is the spherical aberration of the aspherical generation of non-rotational symmetry to be measured；
SIII mendsIt is the astigmatism of off-axis refraction-reflection type part compensator, SIII mendsIt is the astigmatism of the aspherical generation of non-rotational symmetry to be measured；Establishing picture
When poor relational expression, to consider off-axis refraction-reflection type part compensator and tested surface it is unified between aberration relationship, to fully consider
Due to the introduced aberration of system non-rotational symmetry；
Again, using paraxial rays expression formula, each refraction, equation of the reflecting surface image side angular aperture about radius of curvature are established
Formula:
Wherein, r is each refraction, the corresponding radius of curvature of reflecting surface；To sum up, it is established by formula (8), (9), (10) about off-axis folding
The equation group of trans- part compensator structure parameter；
Step 3: utilizing Mathematical tool, solve above-mentioned equation group, obtain off-axis refraction-reflection type part compensator initial configuration ginseng
Number；
According to priori knowledge and the design requirement of real system, the distance between setting lens apex to spherical reflector vertex
d1And spherical reflector vertex is to the distance d between non-rotational symmetry aspheric vertex of surface to be measured2；Off-axis folding is solved based on genetic algorithm
Trans- part compensator initial structure parameter obtains the global optimum of off-axis refraction-reflection type part compensator initial structure parameter,
It is iterated calculating on this basis, obtains the off-axis refraction-reflection type part compensator initial structure parameter eventually for modeling；
Step 4: utilizing optical design software, system structure is modeled and is optimized；
Firstly, the initial structure parameter obtained according to step 3 models system in optical design software, avoid because of light
Learn the problem of design software self-defect causes design result to fall into local optimum；
Secondly, the bias of initial structure parameter and off-axis refraction-reflection type part compensator that setting acquires and inclination become for optimization
Amount carries out initial optimization to system using wavefront PV as optimization aim, with overcome because it is paraxial it is approximate caused by rim ray can not
The problem of into system；If there is light occlusion issue in system, by combining ZPL instruction to control ray position, and will
System after initial optimization is as new initial system；
System after the completion of initial optimization can guarantee that rim ray enters system and dull thread occlusion issue；On this basis,
Double optimization is carried out to system, optimized variable and optimization aim are identical as initial optimization, to obtain the interference fringe at image planes
It is relatively sparse as a result, record remaining wavefront at this time；
Step 5: judging whether design result is feasible；
The maximum wavefront slope K for calculating remaining wavefront, judges whether interference fringe at this time is detectable；If interference fringe can not be visited
It surveys, illustrates that the structural parameters of system do not meet design objective, need return step 4 to re-start system parameter settings, and carry out excellent
Change until meeting design objective.
3. a kind of off-axis refraction-reflection type part compensator system design method as claimed in claim 2, which is characterized in that step 5
In, judge the whether detectable method of interference fringe are as follows:
If the pixel number of selected ccd detector (7) is 1024 pixels × 1024 pixels, the maximum of corresponding detectable interference fringe
Spatial frequency is about 0.45 λ/pixel, i.e., when maximum wavefront slope K≤0.45 λ/pixel of remaining wavefront, interference fringe can be visited
It surveys, otherwise, interference fringe is not detectable.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113409256A (en) * | 2021-06-08 | 2021-09-17 | 沈阳化工大学 | Axial size detection method for pipeline corrugated compensator |
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