CN103234480A - Rapid surface shape detection method for circular convex aspheric surfaces - Google Patents
Rapid surface shape detection method for circular convex aspheric surfaces Download PDFInfo
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Abstract
The invention discloses a rapid surface shape detection method for circular convex aspheric surfaces. The method includes: simulating wave aberration of a convex aspheric surface relative to a most approximate hyperbolic surface by optical design software based on a spherical surface auto-collimating method, fitting the wave aberration by Zernike polynomial under polar coordinates, and converting a wave aberration equation under the polar coordinates into an equation under rectangular coordinates; measuring the wave aberration of the aspheric surface relative to the hyperbolic surface by a digital wavefront interferometer, unifying a matrix of the actual wave aberration and a matrix of a theoretical wave aberration to the same coordinate system, allowing pixels in the two wave aberrations to be in one-to-one correspondence, and subjecting rise of the two wave aberrations to differential operation to obtain residual distribution of the actual surface shape and theoretical surface shape of the aspheric surface. Detection on the maximum asphericity and asphericity gradient of the aspherical surface by the method depends on the size and number of CCD (charge coupled device) array elements in the digital wavefront interferometer as well as the parameters of the selected most approximate hyperbolic surface. The method has the advantages of rapidity, accurateness, wide detection range and the like, and has promising market prospect.
Description
Technical field
The invention belongs to optical design and optical detective technology field.
Technical background
The aspheric equation of annular can be expressed as
C is the aspheric surface vertex curvature in the formula, K=-e
2Be quadric surface constant, a
1, a
2Be aspheric surface high-order term coefficient.The convex annular aspheric surface only is the part (annular region) of unified convex aspheric surface, and interior ring is the blind area with in.
The interference detection technique is mainly adopted in the detection of high-precision optical non-spherical element face shape.In this technology, the face shape that aberrationless point detects, zero compensation interferes detection technique to be widely used in the aspheric surface polishing stage is detected.
To on the other hand being the propagated of extreme value along light path, namely light is minimum, greatly or the propagated of constant along light path to light from a bit.No aberration point detects and refers to: if the equivalent optical path of all light of propagating at this point-to-point transmission calls the aberrationless point to such point on the optics.Utilize aberrationless point to detect aspheric method and be called the detection of aberrationless point.
This type of aberrationless point detecting method has certain disadvantages, and is in particular in that aberrationless point detects mainly for detection of turning axle symmetry quadric surface, can not detect turning axle symmetry high order curved surface; In protruding quadric surface, have only protruding hyperboloid that the aberrationless point is just arranged, therefore can not adopt aberrationless point detection method to other protruding quadric detection.
Zero compensation interferes detection technique to refer to utilize optical design software, and as ZEMAX, CODE V etc. design a kind of optical system that has the certain wave aberration, are referred to as zero compensation machine, and its design is based on desirable aspheric.To compensator,, get back to interferometer through behind the compensator again, thereby realize the detection of non-spherical element face shape to be checked again through tested aspheric surface reflection through compensator by light beam via the digital wavefront interferometer outgoing for the check light beam.
This type of zero compensation detection not only can detect turning axle symmetry secondary aspherical also can detect turning axle symmetry high order aspheric surface.But this detection method also has certain shortcoming, be in particular at the non-spherical element of coplanar shape not, need the different compensator of design, simultaneously in order to obtain high-precision measurement result, requirement is when the design compensation device, on the one hand enable correction asphere wavefront difference well, require the tolerances such as thickness, radius-of-curvature, airspace, concentricity of each element of compensator to distribute rationally on the other hand.Otherwise the error of compensator very easily produces ghost image, and cause the appearance of diffraction ring, and because wherein reflected light and the reference light generation interference mutually of some element of compensator, thereby in image planes some pseudo-interference fringes appear, because it is these pseudo-interference fringes with detection light phase shifts take place simultaneously, therefore very big to the testing result influence.The precision of compensator not only is subjected to the influence of design result, and the also influence that can be debug, the detection of compensator self precision also are difficult problems.Compensation detects light path and adjusts complicated, consuming time.
Summary of the invention
The object of the present invention is to provide a kind of convenience, the aspheric quick face shape detection method of convex annular accurately.
The technical solution adopted for the present invention to solve the technical problems is:
The aspheric quick face shape detection method of a kind of convex annular, it is characterized in that: utilize optical design software, as ZEMAX, CODE V etc., go out spherical wave by optimization Simulation and incide aspheric surface, when with heavy caliber standard spherical reflector the light collimation being returned, obtain the convex annular aspheric surface with respect to a certain approaching protruding bi-curved wave aberration, be aspheric surface with respect to bi-curved theoretical wave aberration, with this wave aberration, under polar coordinates, utilize the Zernike polynomial expression, get preceding 36 or preceding 37 and carry out match, make x=rcos θ, y=rsin θ is converted into form under the rectangular coordinate with the Zernike equation under the polar coordinates; Use digital wavefront interferometer, utilize the sphere camera lens to build sphere autocollimation light path and measure aspheric surface with respect to bi-curved wave aberration, be that aspheric surface is with respect to this bi-curved actual wave aberration, this actual wave aberration discrete matrix (x, y, z) expression, x, y represents locations of pixels, and z represents the rise of respective pixel position wave aberration; According to actual wave aberration matrix, determine the valid pixel on actual corrugated, on this basis theoretical wave aberration (Zernike polynomial repressentation under the rectangular coordinate system) being carried out pixel under rectangular coordinate system divides, to be converted into matrix (x' with the theoretical wave aberration of Zernike polynomial repressentation, y', z') form, guarantee identical with the distribution of actual wave aberration valid pixel, with the matrix unification of the matrix of actual wave aberration and theoretical wave aberration under the same coordinate system, make the pixel of two wave aberrations corresponding one by one, then the rise of two wave aberrations is done poor method computing, be Δ z=z'-z, the residual error that can obtain the actual face shape of aspheric surface and theoretical face shape distributes, thereby realizes that the aspheric quick face shape of convex annular is detected.
For the satisfied the ratio of obstruction requirement for the treatment of microscopy, and make the bore of standard spherical mirror as much as possible little, the position of standard spherical mirror, the size of center pit are had certain requirement, the relation between them satisfies:
In the formula: h
kBe half of standard sphere center pit (blind hole) diameter, h
1For treating half of microscopy effective aperture, h
2For treating in the microscopy half of ring (being the blind area, center) diameter, l
1=-(a+b)=-r/ (1-e), l
2=a-b=r/ (1+e), a, b are respectively semi-major axis and the semi-minor axis of approaching protruding bi-curved meridian cross section curve (hyperbolic curve), and r is vertex point radius-of-curvature to be checked, l
3Arrive the distance on aspheric surface to be checked summit for the center of standard spherical reflector.The radius-of-curvature of standard spherical reflector
Standard sphere aperture of a mirror is D=2h
2(β+1)/(α β+1), wherein α=h
2/ h
1, β=l
1/ l
2Can know h only in these equations according to top description
1, h
2Be definite value, this also is not enough to determine fully other parameter, and therefore the parameter that satisfies condition has a lot of groups.Because the heavy caliber standard spherical mirror is made difficulty, therefore generally can at first select the existing standard spherical mirror, determine its parameter, come to determine l again
1, l
2, l
3Thereby, determine the protruding bi-curved parameter that approaches with convex aspheric surface to be measured.
Digital wavefront interferometer is measured aspheric surface with respect to bi-curved wave aberration, needs to remove translation and droop error.
This detection method detects size and the number that aspheric maximum aspherical degree and aspherical degree gradient not only depend on ccd array pixel in the digital wavefront interferometer, also depends on selected near bi-curved parameter.
Beneficial effect: the present invention has not only overcome aberrationless point method can not detect turning axle symmetry high order aspheric surface, shortcomings such as also having overcome compensator specificity in the check of traditional zero compensation, debug complexity, be consuming time, only need a standard spherical mirror, have advantages such as quick, accurate, that sensing range is wide, especially obvious for medium caliber (diameter 100 millimeter) the aspheric detection cost performance of convex annular, have vast market prospect.
Description of drawings
The invention will be further described below in conjunction with accompanying drawing and example.
Fig. 1 is fundamental diagram of the present invention.
Fig. 2 is that convex annular aspheric surface of the present invention detects index path.
Fig. 3 is convex annular aspheric surface of the present invention with respect near bi-curved theoretical wave aberration figure.
Fig. 4 is convex annular aspheric surface of the present invention with respect near bi-curved actual wave aberration figure.
Fig. 5 is the residual error distribution plan of the actual annular convex aspheric surface of the present invention and theoretical face shape.
Wherein, 1. digital wavefront interferometer, 2. interferometer standard spherical mirror head is 3. treated microscopy, 4. standard spherical mirror.
Embodiment
Below in conjunction with accompanying drawing the specific embodiment of the present invention is described in further details.
The aspheric quick face shape detection method of a kind of convex annular.Fig. 1 is fundamental diagram of the present invention.
According to the parameter of existing related elements and equipment, calculate near bi-curved parameter, determine l
1, l
2And l
3For example detect certain effective clear aperture and be Φ=8～100 millimeter, vertex curvature radius r=236.2 millimeter, the convex paraboloid of excentricity K=-1, existing standard spherical mirror radius of curvature R=557.01 millimeters, h
k=22 millimeters, the D=550 millimeter calculates as can be known according to top formula: h
1=4 millimeters, h
2=50 millimeters, α=0.08, β=8.03, l
1=830.42 millimeters, l
2=103.42 millimeters, l
3=464.96 millimeters, e=1.284, i.e. K=-1.649.
According to top initial configuration parameter, utilize optical design software, as ZEMAX, CODE V etc., the aspheric autocollimation of convex annular detected carry out emulation and optimization, detect light path as shown in Figure 2, obtain aspheric surface with respect near bi-curved theoretical wave aberration as shown in Figure 3.
Thereby obtain aspheric surface to be measured 3 with respect near bi-curved actual wave aberration, remove translation, the inclination equal error, as shown in Figure 4.
With the matrix unification of the matrix of actual wave aberration and theoretical wave aberration under the same coordinate system, make the pixel of two wave aberrations corresponding one by one, then the rise of two wave aberrations is done poor method computing, be Δ z=z'-z, the residual error that can obtain the actual face shape of aspheric surface and theoretical face shape distributes, as shown in Figure 5.
Fig. 3 is theoretical wave aberration gray-scale map, and Fig. 4 is that actual wave aberration gray-scale map, Fig. 5 are the gray-scale map of the residual error distribution of the actual face shape of aspheric surface to be measured and theoretical face shape.True origin (0 among the figure, 0) is aspheric center to be measured, horizontal ordinate and ordinate have been determined the position of putting on the aspheric surface to be measured, and the unit of coordinate axis is millimeter, and the difference of ordinate or horizontal ordinate maximal value and minimum value equals effective clear aperture of non-ball sphere to be measured.The size of gray scale chart oscillography picture, unit is wavelength.
Claims (4)
1. aspheric quick face shape detection method of convex annular, it is characterized in that: utilize optical design software, as ZEMAX, CODE V etc., go out spherical wave by optimization Simulation and incide aspheric surface, when with heavy caliber standard spherical reflector the light collimation being returned, obtain the convex annular aspheric surface with respect to a certain approaching protruding bi-curved wave aberration, be aspheric surface with respect to bi-curved theoretical wave aberration, with this wave aberration, under polar coordinates, utilize the Zernike polynomial expression, get preceding 36 or preceding 37 and carry out match, make x=rcos θ, y=rsin θ is converted into form under the rectangular coordinate with the Zernike equation under the polar coordinates; Use digital wavefront interferometer to utilize the sphere camera lens to build sphere autocollimation light path and measure aspheric surface with respect to bi-curved wave aberration, be that aspheric surface is with respect to this bi-curved actual wave aberration, discrete three-dimensional matrice (the x of this actual wave aberration, y, z) expression, x, y represents locations of pixels, z represents the rise of respective pixel position wave aberration; Three-dimensional matrice according to actual wave aberration, determine the valid pixel on actual corrugated, on this basis theoretical wave aberration (Zernike polynomial repressentation under the rectangular coordinate system) being carried out pixel under rectangular coordinate system divides, to be converted into matrix (x' with the theoretical wave aberration of Zernike polynomial repressentation, y', z') form, guarantee identical with the distribution of actual wave aberration valid pixel, with the matrix unification of the matrix of actual wave aberration and theoretical wave aberration under the same coordinate system, make the pixel of two wave aberrations corresponding one by one, then the rise of two wave aberrations is done poor method computing, be Δ z=z'-z, the residual error that can obtain the actual face shape of aspheric surface and theoretical face shape distributes, thereby realizes that the aspheric quick face shape of convex annular is detected.
2. the aspheric quick face shape detection method of a kind of convex annular according to claim 1, it is characterized in that: in order to satisfy the ratio of obstruction requirement for the treatment of microscopy, and make the bore of standard spherical mirror as much as possible little, the position of standard spherical mirror, the size of center pit are had certain requirement, and the relation between them satisfies:
In the formula: h
kBe half of standard sphere center pit (blind hole) diameter, h
1For treating half of microscopy effective aperture, h
2For treating in the microscopy half of ring (being the blind area, center) diameter, l
1=-(a+b)=-r/ (1-e), l
2=a-b=r/ (1+e), a, b are respectively semi-major axis and the semi-minor axis of approaching protruding bi-curved meridian cross section curve (hyperbolic curve), and r is vertex point radius-of-curvature to be checked, l
3Arrive the distance on aspheric surface to be checked summit for the center of standard spherical reflector; The radius-of-curvature of standard spherical reflector
Standard sphere aperture of a mirror is D=2h
2(β+1)/(α β+1), wherein α=h
2/ h
1, β=l
1/ l
2Can know h only in these equations according to top description
1, h
2Be definite value, this also is not enough to determine fully other parameter, and therefore the parameter that satisfies condition has a lot of groups; Because the heavy caliber standard spherical mirror is difficult to make, and therefore generally can at first select the existing standard spherical mirror, determines its parameter, comes to determine l again
1, l
2, l
3Thereby, determine the protruding bi-curved parameter that approaches with convex aspheric surface to be measured.
3. the aspheric quick face shape detection method of a kind of convex annular according to claim 1, it is characterized in that: digital wavefront interferometer is measured aspheric surface with respect to bi-curved wave aberration, needs to remove translation and droop error.
4. the aspheric quick face shape detection method of a kind of convex annular according to claim 1, it is characterized in that: this detection method detects size and the number that aspheric maximum aspherical degree and aspherical degree gradient not only depend on ccd array pixel in the digital wavefront interferometer, also depends on selected near bi-curved parameter.
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Cited By (9)
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| CN104075668A (en) * | 2014-07-01 | 2014-10-01 | 中国科学院长春光学精密机械与物理研究所 | High-accuracy geographic sense measuring method in convex hyperboloid Hindle detection |
| CN105917190A (en) * | 2013-12-19 | 2016-08-31 | 卡尔蔡司Smt有限责任公司 | Method for measuring a spherical-astigmatic optical area by fizeau interferometry |
| CN106871819A (en) * | 2017-01-12 | 2017-06-20 | 北京理工大学 | Aspherical vertex curvature radius error measurement method based on the optimal compensation position |
| CN109946044A (en) * | 2019-03-11 | 2019-06-28 | 中国科学院上海技术物理研究所 | A kind of catadioptric lens group examines the optical system of super large caliber convex paraboloid reflecting mirror |
| CN111024053A (en) * | 2019-11-22 | 2020-04-17 | 武汉大学 | Method for acquiring and resolving laser scanning data reflected by convex spherical mirror |
| CN111122121A (en) * | 2020-01-07 | 2020-05-08 | 中国科学院上海光学精密机械研究所 | Method for constructing small-F-number convex hyperboloid reflector detection light path |
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| CN105917190A (en) * | 2013-12-19 | 2016-08-31 | 卡尔蔡司Smt有限责任公司 | Method for measuring a spherical-astigmatic optical area by fizeau interferometry |
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| CN111122121A (en) * | 2020-01-07 | 2020-05-08 | 中国科学院上海光学精密机械研究所 | Method for constructing small-F-number convex hyperboloid reflector detection light path |
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| CN112378367B (en) * | 2020-11-05 | 2021-10-22 | 天津大学 | Method for measuring surface shape and position of multi-free-form surface reflector distributed in inner cavity |
| CN112378367A (en) * | 2020-11-05 | 2021-02-19 | 天津大学 | Method for measuring surface shape and position of multi-free-form surface reflector distributed in inner cavity |
| CN112629436A (en) * | 2020-11-20 | 2021-04-09 | 西安交通大学 | High-order aspheric surface detection method and system based on adaptive optical wavefront correction |
| CN112629436B (en) * | 2020-11-20 | 2021-11-19 | 西安交通大学 | High-order aspheric surface detection method based on adaptive optical wavefront correction |
| CN113570578A (en) * | 2021-07-29 | 2021-10-29 | 歌尔光学科技有限公司 | Lens ghost phenomenon detection method and device |
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Application publication date: 20130807 |