CN103017681B - Real time detecting method for rotary shaft symmetrically concave aspheric surfaces approximate to paraboloids - Google Patents
Real time detecting method for rotary shaft symmetrically concave aspheric surfaces approximate to paraboloids Download PDFInfo
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- CN103017681B CN103017681B CN 201210521650 CN201210521650A CN103017681B CN 103017681 B CN103017681 B CN 103017681B CN 201210521650 CN201210521650 CN 201210521650 CN 201210521650 A CN201210521650 A CN 201210521650A CN 103017681 B CN103017681 B CN 103017681B
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Abstract
The invention discloses a real time detecting method for rotary shaft symmetrically concave aspheric surfaces approximate to paraboloids. A plane auto-collimation method is adopted to simulate wave aberration of the concave aspheric surfaces relative to most approximate paraboloids, a Zernike polynomial is utilized to perform fitting under a polar coordinate to convert a Zernike equation under the polar coordinate into an equation under a rectangular coordinate. A digital wavefront interferometer is used to measure the wave aberration of the concave aspheric surfaces relative to the paraboloids, an actual wave aberration matrix and a theoretical wave aberration matrix are unified under the same coordinate system to enable pixels of two wave aberrations to be correspond in one-to-one mode, then arc rise of the two wave aberrations is subjected to difference method operation to obtain residual error distribution of actual surface shapes and theoretical surface shapes of the concave aspheric surfaces. The real time detecting method for rotary shaft symmetrically concave aspheric surfaces approximate to the paraboloids has the advantages of being quick, accurate, wide in detection range and the like and has wide market prospect.
Description
Technical field
The invention belongs to the advanced optical length of schooling makes and the detection technique field.
Technical background
The recessed aspheric surface of nearly paraboloidal axisymmetry mainly refers to that approaching paraboloidal concave ellipsoidal surface or recessed hyperboloid and take concave ellipsoidal surface or recessed hyperboloid is basic high-order curved surface.The detection of high-precision optical non-spherical element face shape mainly adopts the interference detection technique.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.
So-called aberrationless point detects and refers to according to Fermat principle, light passes to more in addition from a bit, through repeatedly refraction or reflection arbitrarily, its light path is maximum value or minimum value, that is to say that light path is definite value, on optics, such point is become to the aberrationless point, utilize aberrationless point to detect aspheric method and be called the aberrationless detection.
This type of aberrationless point detecting method has certain disadvantages, and is in particular in that aberrationless point detects mainly for detection of the axisymmetry quadric surface, can not detect the axisymmetry high-order curved surface.
Zero compensation interference detection technique refers to utilizes optical design software, as ZEMAX, CODE V etc., design a kind of optical system with the certain wave aberration, be referred to as zero compensation machine, the design of zero compensation machine wherein is based on desirable aspheric, the check light beam via the digital wavefront interferometer outgoing to compensator, light beam, is again got back to interferometer, thereby is realized the detection of non-spherical element face shape to be checked again through tested aspheric surface reflection through compensator after compensator.
This type of zero compensation detection not only can detect the axisymmetry secondary aspherical and also can detect the axisymmetry high order aspheric surface.But this detection method also has certain shortcoming, be in particular in for the non-spherical element of coplanar shape not, need the different compensator of design, simultaneously in order to obtain high-precision measurement result, requirement, when the design compensation device, enables correction asphere wavefront difference well on the one hand, requires on the other hand the thickness of each element of compensator, radius-of-curvature, the tolerances such as airspace, concentricity are distributed rationally.The error of compensator very easily produces ghost image like this, and cause the appearance of diffraction ring, and wherein reflected light and the reference light of some element occur mutually to interfere due to compensator, thereby some pseudo-interference fringes appear on image planes, because phase shifts occurs for these pseudo-interference fringes and detection light simultaneously, therefore very large on the testing result impact.The precision of compensator not only is subject to the impact of design result, the impact that also can be debug, and the detection of compensator self precision is also a difficult problem.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 recessed aspheric real-time detection method of nearly paraboloidal axisymmetry accurately.
Technical solution of the present invention is:
The recessed aspheric real-time detection method of a kind of nearly paraboloidal axisymmetry, it is characterized in that: utilize optical design software, as ZEMAX, CODE V etc., simulate recessed aspheric surface (quadric surface or high-order curved surface) with respect to approaching most paraboloidal wave aberration with the plane autocollimation method, be called aspheric surface with respect to paraboloidal theoretical wave aberration, by this wave aberration, under polar coordinates, utilize the zernike polynomial expression (get front 36 or front 37 all can) carry out matching, make x=rcos θ, y=rsin θ, zernike equation under polar coordinates is converted into to the form under rectangular coordinate, using digital wavefront interferometer (as zygo, wyko, fisba, esdi etc.) to utilize the sphere camera lens to build plane autocollimation light path measures aspheric surface with respect to paraboloidal wave aberration, is called aspheric surface with respect to paraboloidal actual wave aberration.This is discrete three-dimensional matrice (x, y, z) expression for actual wave aberration, x, and y means the position of pixel, z means the rise of respective pixel position wave aberration.Three-dimensional matrice according to actual wave aberration, determine the valid pixel on actual corrugated, to theoretical wave aberration, the zernike polynomial expression under rectangular coordinate system carries out the pixel division on this basis, the theoretical wave aberration of zernike polynomial repressentation is converted into to matrix (x', y', z') form, guarantee identical with the distribution of actual wave aberration valid pixel, by 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 to poor method computing, be Δ z=z '-z, can obtain the residual distribution of the actual face shape of aspheric surface and theoretical face shape, thereby realize the recessed aspheric real-time detection of nearly paraboloidal axisymmetry.
The standard flat aperture of mirror is not less than aspheric mirror bore to be measured, and center pit is opened at standard flat mirror center, and the size of center pit is not more than the size of recessed aspheric surface center blind zone.
Digital wavefront interferometer can be measured optical aspherical surface to be measured with respect to approaching most paraboloidal unified wave aberration by enough autocollimation methods, and needs to remove translation (piston), and (tilt) equal error tilts.
The present invention has not only overcome the aberrationless point can not detect the axisymmetry high order aspheric surface, also overcome compensator specificity in traditional zero compensation check, debug the shortcomings such as complicated, consuming time, only need to be more than or equal to the standard flat mirror of aspheric mirror bore to be checked, there is the advantages such as quick, that accurate, sensing range is wide, there are wide market outlook.This detection method aspheric maximum aspherical degree of detection and aspherical degree gradient depend on size and the number of ccd array pixel in digital wavefront interferometer.
The accompanying drawing explanation
Below in conjunction with drawings and Examples, the invention will be further described.
Fig. 1 is fundamental diagram of the present invention.
Fig. 2 is that hyperboloid of the present invention is with respect to approaching most paraboloidal theoretical wave aberration figure.
Fig. 3 is that hyperboloid of the present invention detects index path.
Fig. 4 is that hyperboloid of the present invention is with respect to approaching most paraboloidal actual wave aberration figure.
Fig. 5 is the residual distribution figure of the present invention's actual hyperboloid face shape and theoretical face shape.
Embodiment
The recessed aspheric real-time detection method of a kind of nearly paraboloidal axisymmetry, it is characterized in that: utilize optical design software, as ZEMAX, CODE V etc., simulate recessed aspheric surface (quadric surface or high-order curved surface) with respect to approaching most paraboloidal wave aberration with the plane autocollimation method, be called aspheric surface with respect to paraboloidal theoretical wave aberration, by this wave aberration, under polar coordinates, utilize zernike polynomial expression (get front 36 or 37 all can) to carry out matching, make x=rcos θ, y=rsin θ, zernike equation under polar coordinates is converted into to the form under rectangular coordinate, using digital wavefront interferometer (as zygo, wyko, fisba, esdi etc.) to utilize the sphere camera lens to build plane autocollimation light path measures aspheric surface with respect to paraboloidal wave aberration, is called aspheric surface with respect to paraboloidal actual wave aberration.This is discrete three-dimensional matrice (x, y, z) expression for actual wave aberration, x, and y means the position of pixel, z means the rise of respective pixel position wave aberration.Three-dimensional matrice according to actual wave aberration, determine the valid pixel on actual corrugated, to theoretical wave aberration, the zernike polynomial expression under rectangular coordinate system carries out the pixel division on this basis, the theoretical wave aberration of zernike polynomial repressentation is converted into to matrix (x', y', z') form, guarantee identical with the distribution of actual wave aberration valid pixel, by 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 to poor method computing, be Δ z=z '-z, can obtain the residual distribution of the actual face shape of aspheric surface and theoretical face shape, thereby realize the recessed aspheric real-time detection of nearly paraboloidal axisymmetry.
The standard flat aperture of mirror is not less than aspheric mirror bore to be measured, and center pit is opened at standard flat mirror center, and the size of center pit is not more than the size of recessed aspheric surface center blind zone.
Digital wavefront interferometer can be measured optical aspherical surface to be measured with respect to approaching most paraboloidal unified wave aberration by enough autocollimation methods, and needs to remove translation (piston), and (tilt) equal error tilts.
Utilize optical design software, as ZEMAX, CODE V etc., carry out plane autocollimation detection to the recessed aspheric surface of nearly paraboloidal axisymmetry and carry out emulation, detects light path as shown in Figure 2, obtains aspheric surface with respect to connecing most paraboloidal theoretical wave aberration as shown in Figure 3.
Utilize digital wavefront interferometer 1 to detect aspheric surface to be checked, 2 is the interferometer camera lens, and 3 is aspheric mirror to be checked, and 4 is the standard flat mirror.The standard flat mirror is placed between interferometer camera lens and aspheric mirror to be checked, the scope apart from being less than rd/ (2D) to interferometer camera lens focus all can, the vertex curvature radius that wherein r is aspheric mirror to be checked, the diameter that d is standard flat mirror center pit, D is aspheric mirror bore to be checked, for before the convenience of adjusting is placed in interferometer camera lens focus by the standard flat mirror usually, as shown in Figure 2.Thereby obtain aspheric surface 3 to be measured with respect to approaching most paraboloidal actual wave aberration, remove translation (piston), (tilt) equal error that tilts, as shown in Figure 4.
By 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 to poor method computing, be Δ z=z '-z, can obtain the residual distribution of the actual face shape of aspheric surface and theoretical face shape, as shown in Figure 5.
Claims (1)
1. the recessed aspheric real-time detection method of nearly paraboloidal axisymmetry, it is characterized in that: with the plane autocollimation method, simulate recessed aspheric surface with respect to approaching most paraboloidal wave aberration, be that aspheric surface is with respect to paraboloidal theoretical wave aberration, by this wave aberration, utilize the zernike polynomial expression under polar coordinates, get first 36 or first 37 and carry out matching, make x=rcos θ, y=rsin θ, be converted into the form under rectangular coordinate by the zernike equation under polar coordinates, use digital wavefront interferometer to utilize the sphere camera lens to build plane autocollimation light path and measure aspheric surface with respect to paraboloidal wave aberration, be that aspheric surface is with respect to paraboloidal actual wave aberration, discrete three-dimensional matrice (x for this actual wave aberration, y, z) mean, x, y means the position of pixel, z means the rise of respective pixel position wave aberration, three-dimensional matrice according to actual wave aberration, determine the valid pixel on actual corrugated, to theoretical wave aberration, the zernike polynomial expression under rectangular coordinate system carries out the pixel division on this basis, the theoretical wave aberration of zernike polynomial repressentation is converted into to matrix (x', y', z') form, guarantee identical with the distribution of actual wave aberration valid pixel, by 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 to poor method computing, be Δ z=z'-z, can obtain the residual distribution of the actual face shape of aspheric surface and theoretical face shape, thereby realize the recessed aspheric real-time detection of nearly paraboloidal axisymmetry, it is that the standard flat mirror is placed between interferometer sphere camera lens and aspheric mirror to be checked that described use digital wavefront interferometer utilizes the sphere camera lens to build plane autocollimation light path, the standard flat mirror is less than rd/ (2D) to the distance of interferometer camera lens focus, the vertex curvature radius that wherein r is aspheric mirror to be checked, the diameter that d is standard flat mirror center pit, D is aspheric mirror bore to be checked.
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| CN 201210521650 CN103017681B (en) | 2012-12-07 | 2012-12-07 | Real time detecting method for rotary shaft symmetrically concave aspheric surfaces approximate to paraboloids |
| CN201310413646.8A CN103471522B (en) | 2012-12-07 | 2012-12-07 | The recessed aspheric real-time detection method that sensing range is wide |
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| CN 201210521650 Expired - Fee Related CN103017681B (en) | 2012-12-07 | 2012-12-07 | Real time detecting method for rotary shaft symmetrically concave aspheric surfaces approximate to paraboloids |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103234480A (en) * | 2013-04-16 | 2013-08-07 | 北京理工大学 | Rapid surface shape detection method for circular convex aspheric surfaces |
| CN103196391A (en) * | 2013-04-16 | 2013-07-10 | 北京理工大学 | Quick surface shape detection method of annular concave aspheric surface near to paraboloid |
| CN103791854A (en) * | 2014-01-23 | 2014-05-14 | 中国科学院长春光学精密机械与物理研究所 | Method for splicing sub-apertures high in spatial resolution |
| DE102015119274B4 (en) * | 2015-11-09 | 2018-07-12 | Björn Habrich | Method and device for determining the spatial position of an object by means of interferometric length measurement |
| CN106907991B (en) * | 2017-02-24 | 2019-06-07 | 湖北航天技术研究院总体设计所 | A kind of off-axis aspheric mirror zero testing alignment methods based on compensator |
| CN108227186B (en) * | 2018-01-16 | 2020-03-20 | 南通大学 | Method for determining closest comparison spherical curvature radius of annular caliber quadric surface of optical system |
| CN110703434B (en) * | 2019-10-15 | 2024-04-12 | 南通大学 | Method for determining annular aperture quadric surface asphericity gradient |
| CN112697398B (en) * | 2020-12-10 | 2023-09-19 | 中国科学院光电技术研究所 | Calculation method for detecting wave aberration residual error twice before and after spatial position change |
| CN117091532A (en) * | 2023-08-25 | 2023-11-21 | 同济大学 | Absolute measurement device and method for aspheric surface high-precision interferometer |
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| CN1731232A (en) * | 2005-09-05 | 2006-02-08 | 长春理工大学 | An optical aspheric surface detection qausi-universal compensating mirror |
| US7276717B2 (en) * | 2004-11-05 | 2007-10-02 | Canon Kabushiki Kaisha | Measuring apparatus, exposure apparatus and device manufacturing method |
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| CN102155926A (en) * | 2011-03-09 | 2011-08-17 | 浙江大学 | Aspherical mirror vertex curvature radius measurement system and method |
| CN102175150A (en) * | 2011-01-27 | 2011-09-07 | 南京理工大学 | Infrared interference detection device with pint aligning and detecting double detectors |
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| JP2008256517A (en) * | 2007-04-04 | 2008-10-23 | Hoya Corp | Aberration measurement method |
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Patent Citations (5)
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| US7276717B2 (en) * | 2004-11-05 | 2007-10-02 | Canon Kabushiki Kaisha | Measuring apparatus, exposure apparatus and device manufacturing method |
| CN1731232A (en) * | 2005-09-05 | 2006-02-08 | 长春理工大学 | An optical aspheric surface detection qausi-universal compensating mirror |
| CN101650157A (en) * | 2009-09-18 | 2010-02-17 | 中国科学院长春光学精密机械与物理研究所 | Detecting method and detecting device of surface-shape error of double curved surface convex reflecting mirror |
| CN102175150A (en) * | 2011-01-27 | 2011-09-07 | 南京理工大学 | Infrared interference detection device with pint aligning and detecting double detectors |
| CN102155926A (en) * | 2011-03-09 | 2011-08-17 | 浙江大学 | Aspherical mirror vertex curvature radius measurement system and method |
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| CN103017681A (en) | 2013-04-03 |
| CN103471522A (en) | 2013-12-25 |
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