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Compensation of misalignment error on testing aspheric surface by subaperture stitching interferometry
Abstract
For the purpose to decrease the misalignment error from a testing aspheric surface by Subaperture Stitching Interferometry(SSI), a translated error compensation method is proposed to subtract the misalignment error from each phase detum and to stitch multi-subapertures precisely. The basic principle and process of the method are researched, and a compensation mode is established based on the mode search algorithm. The experiment is carried on for an off-axis SiC aspheric mirror with a clear aperture of 230 mm×141 mm, the phase data of the whole aperture are stitched precisely and the figure error is compensated by eliminating the misalignment error. For the comparison and validation, the asphere mirror is also tested by null compensation method, and the relative errors of PV and RMS are 0.57% and 2.74%, respectively.
In the process of an asphere fabricating, the part with large mapping distortion in the large caliber off-axis asphere may not be measured by an interferometer due to larger interferometric fringe density. To solve this problem, the parameter named related distortion was used to describe the mapping distortion quantitatively, and a Computer Generated Hologram (CGH) with higher freedom and stronger compensation ability was designed. By taking the mapping distortion distribution into account, the method selected a proper path and allowed all the aspheric surface to have smaller mapping distortion in the design of the CGH. With the method, a CGH with proper paths was designed for testing the 1.45 m off-axis asphere, by which the full map distortion of the system is less than that of the traditional null-lens compensator. The test experiment shows that the designed CGH can test the full map error of the off-axis asphere, which verifies the validity and practicability of the proposed CGH design method and demonstrates that designed CGH with considering test mapping distortion has solved the problem as mentioned above. By this method, the map errors of 1.45 m diameter off-axis asphere are 0.374λ PV and 0.023λ RMS now.
An error compensation algorithm was proposed by introducing a position correction compensator into general stitching algorithm to reduce the relative location errors between subapertures due to poor positioning accuracy in a subaperture stitching interferometry. The working principle of the algorithm was introduced and the accuracy of the fitted translation and rotation coefficients was analyzed in theory. Then a simulation experiment by using MetroPro software and Matlab software was implemented, and the influence of positioning accuracy on the stitching results was analyzed. The simulation result shows that the accuracy of rotation coefficient is less than that of the translation coefficient and is consistent with the theoretical analysis. Moreover, the algorithm is more robust than the general stitching algorithms. For the purpose of experimental verifying mechanical error compensation algorithm, a Φ150 mm flat mirror was tested by a subaperture stitching interferometer and a full aperture interferometer. The test results indicate that the peak-to-valley(PV) and root-mean-square(RMS) of the phase distribution residue are 0.015 30λ and 0.001 570λ, respectively as compared with the stitching results from the directly measured full aperture, which means that the optimal algorithm is stable and reliable and effectively compensates positioning system errors.
In order to satisfy all-frequency error quality controlling and high-precision test during the process of the convex asphere, double laps with polar coordinate polishing technique and the measuring poles method used for the alignment of Hindle test are proposed. Firstly, the double laps with polar coordinate polishing technique for manufacturing the aspheric mirror and the numerical control machine for processing aspheric surface are presented. Then, the measuring poles method used to control the distances between vertex of the standard sphere and the vertex and focus of the tested asphere is introduced, and the controlling precision is analyzed. Finally, for a convex asphere with the aperture of Φ158 mm, the test results and precision of the Hindle test are described. The results indicate that the double laps polishing technique can make the low-frequency surface error convergence quickly, and the mid-frequency surface error is restrained at the same time. The controlling precision of the low-frequency surface error is about λ/30 (λ=633 nm). The limit error using the measuring poles to control the distance is ±0.065 mm, and the tolerances of the two space parameters are ±0.22 mm and ±0.30 mm, respectively. The fast manufacture and all-frequency controlling of the convex asphere are realized by the double laps with polar coordinate polishing technique, and the test result of low-frequency surface error is 0.022λ (RMS, @633 nm) in the Hindle test, which satisfies the specification requirements of the optical design.
The influence of polarization direction orthogonality on Polarization Phase Shifting Interferometry (PPSI) was analyzed to improve its measurement precision. Based on the analysis of PPSI principle, it points out that the measurement error is a function of Optical Path Difference (OPD) and the PV of measurement error is proportional to the non-orthogonality and the ratio of amplitudes of test beam to reference beam. The polarization non-orthogonality can be introduced by the reflection or refraction on a surface. Then several approaches were recommended to depress the non-orthogonality, such as proper coatings, incident angles and polarization directions. A configuration of Skip-Flat test with incident angle of 45° was set up. It shows that the distribution of measurement error is coincident with that of OPD. Moreover, the measurement error is 0.1741λ (PV), which is in agreement with that of the theoretical analysis. Finally, the paper suggests that it is necessary to analyze individually each of the component under the test for making sure the measurement precision.
To improve the accuracy of Ritchey-Common test for a flat mirror, a new method to use the relationship between the system pupil coordinate and the test mirror coordinate to interpolate and fit the test mirror surface was proposed. On the basis of the least square method, the system defocus error and surface error in two test angles were detached to gain a more actual flat surface error. The simulation analysis shows that the test error can be controlled under λ/100(λ=632.8 nm). A flat mirror with a diameter of 40 mm was tested. In the test process, the test flat mirror was rotated with different angels and the wavefront was reconstructed through the relationship between coordinate mapping and amplitude conversion. The obtained results show that the RMS of the test mirror surface is 0.018 6 λ after detaching the defocus error of the system. As compared with the test RMS of 0.021λ from an interferometer, the residual error is 0.002 4 λ. Experiment results indicate that this error detaching method is valid and accurate in the Ritchey-Common test for flat mirrors.
In this paper, several aspheric testing methods for different fabrication steps and their new research progresses are introduced. Especially, we emphasis on the testing methods for precision polishing step, in which subaperture stitching interferometric testing and non-null partial compensating testing method are described in detail. Moreover, several combined interferometric testing methods which perform well in measuring large and steep aspherics are introduced. In addition, we provide a general description of free-form surface testing. The further development of aspheric surface testing methods is also prospected.
On the basis of the asymmetric distortion from asphere measurement by a Computer-generated Hologram (CGH), three basic distortion models were analyzed, and an effective correction method for asymmetric distortion was proposed. By using a few fitted parameters, the method can correct the asymmetric distortion accurately, reduce data point pairs needed by distortion correction and can avoid over-fitting effect. Furthermore, the distortion of whole interferometric system was simulated, and its distortion was corrected by the proposed method. The simulating result shows that the relative residual of the correction is less than 0.2%. Finally, an off-axis CGH was designed and fabricated to verify the reliability of the correcting method and an asphere surface was tested with this CGH. Then, the correcting method mentioned above was used to correct the testing result, and the correcting result was taken to fabricate the asphere iteratively. The experiments show that the aspheric surface figure converges at 1.8 nm RMS (Root Mean Square) eventually. These results verify the reliability of the correction method.
Optical testing of a large convex aspheric surface, such as the secondary of a Ritchey-Chretien telescope, can be performed with a Fizeau interferometer that utilizes subaperture aspheric reference plates, each providing a null test of a subaperture of the larger mirror. The subaperture data can be combined or stitched together to create a map of the full surface. The region of the secondary mirror surface under test in each sub-aperture is an off-axis segment of the parent aspheric surface, therefore, the Fizeau reference requires a non-axi-symmetric aspheric surface to match it. Misalignment of the Fizeau reference relative to the parent in each sub-aperture will then result in aberrations in the measurements other than the ordinary terms of piston and tilt. When stitching sub-aperture measurements together, the apparent aberrations due to the null lens misalignment need to be fitted and subtracted. This paper presents an algorithm to perform this particular type of stitching.
This paper introduces the developing trends of QuickBird, WorldView-1, WorldView-2 satellites from DigitaleGlobe Inc(USA) and the IKONOS, GeoEye-1, GeoEye-2 satellites from GeoEye Inc(USA), and then analyzes and reviews the specifications and characteristics of these high resolution earth imaging commercial satellites and their space cameras at different launch schedules. It points out that the development of earth imaging commercial satellites will trend towards small volumes and smart performance. Therefore, the next research should focus on the attitude control of satellites precisely, exploration of TDICCD with small pixel sizes and high integrated orders, design of optical systems in small related apertures and digital image processing technology for image enhancement.
A subaperture stitching interferometric method was introduced, and the basic principle was analyzed. A reasonable mathematical model and an effective stitching algorithm were established based on homogeneous coordinates transformation, least square method and Zernike polynomial fitting. Meanwhile the computer simulation experiment was carried out with five subapertures for a parabolic mirror, the phase map after stitching is consistent to the inputted map, the difference of the PV and RMS of the full aperture surface error is -0.0092 λ and 0.0013 λ after stitching, and the relative error of PV and RMS is -0.39% and 0.44% respectively. The results show that the method is feasible and accurate, and can test large aspheric surfaces without compensators and other auxiliary null optics.
This paper overviews the development of the single diamond machines used in weapons and commercial fields, and introduces nowadays widely-used commercial ultra-precision diamond turning machines. Then, it analyzes the key techniques to achieve nanometer-level precision machining, such as air bearing work spindles, oil hydrostatic bearing X/Z slides, work piece measurement & error compensation, optical tool setters, Linear Variable Differential Transformer(LVDT) tool setters and adaptive control systems. Finally, it summarizes the materials suitable for diamond turning, and introduces the fast tool servo and slow slide servo used in the manufacturing of opto-mechanical components. By taking drop-in assembly of a Cassegrain telescope and an fine optical system for examples, this paper shows the important effort of the ultra-precision diamond turning in photoelectric products.
With the large applications of the two-mirror optical system with hyperboloidal secondary mirror to astronomical and spacial fields, the aperture and relative aperture of the mirror grow larger and larger, which demands the measurement techniques to be improved greatly. According to the parameters of internationally typical hyperboloidal secondary mirrors, the basic specification and developing trends of secondary mirror is analyzed. The surface measurement method in overseas for the secondary mirror is emphatically introduced, and the corresponding key techniques and applicability are analyzed. In addition, the status of surface measurement method in our country for the mirror is also introduced. Finally, the developing trends of surface measurement technology for the secondary mirror are summarized and prospected, it points out that the research on measurement method in future should focus on the transmission materials with high homogeneity, high precision and large aperture auxiliary components and the measurement methods and data processing based on sub-aperture stitching.
This paper summarizes some of QED Technologies" latest developments in the field of high-precision polishing and metrology. Magneto-Rheological Finishing (MRF) is a deterministic sub-aperture polishing process that overcomes many of the fundamental limitations of traditional finishing. MRF has demonstrated the ability to produce optical surfaces with accuracies better than 30 nm peak-to-valley (PV) and surface micro-roughness less than 0.5 nm rms on a wide variety of optical glasses, single crystals, and glass-ceramics. The MR fluid forms a polishing tool that is perfectly conformal and therefore can polish a variety of shapes, including flats, spheres, aspheres, prisms, and cylinders, with either round or rectangular apertures. QED"s Sub-aperture Stitching Interferometer (SSI) complements MRF by extending the effective aperture, accuracy, resolution, and dynamic range of a phase-shifting interferometer. This workstation performs automated sub-aperture stitching measurements of spheres, flats, and mild aspheres. It combines a six-axis precision stage system, a commercial Fizeau interferometer, and specially developed software that automates measurement design, data acquisition, and the reconstruction of the full-aperture map of figure error. Aside from the correction of sub-aperture placement errors (such as tilts, optical power, and registration effects), our software also accounts for reference-wave error, distortion, and other aberrations in the interferometer"s imaging optics. By addressing these matters up front, we avoid limitations encountered in earlier stitching work and significantly boost reproducibility beyond that of the integrated interferometer on its own.
The fabrication and metrology of astronomical optics are very demanding tasks. In particular, the large sizes needed for astronomical optics and mirrors present significant manufacturing challenges. One of the long-lead aspects (and primary cost drivers) of this process has traditionally been the final polishing and metrology steps. Furthermore, traditional polishing becomes increasingly difficult if the optics are aspheric and/or lightweight. QED Technologies (QED(r)) has developed two novel technologies that have had a significant impact on the production of precision optics. Magnetorheological Finishing (MRF(r)) is a deterministic, production proven, sub-aperture polishing process that can enable significant reductions in cost and lead-time in the production of large optics. MRF routinely achieves surface figure accuracy of better than 30 nm peak-to-valley (better than 5 nm rms) and microroughness better than 1 nm rms on a variety of glasses, glass ceramics and ceramic materials. Unique characteristics of MRF such as a comparatively high, stable removal rate, the conformal nature of the sub-aperture tool and a shear-mode material removal mechanism give it advantages in finishing large and lightweight optics. QED has, for instance, developed the Q22-950F MRF platform which is capable of finishing meter-class optics and the fundamental technology is scalable to even larger apertures. Using MRF for large optics is ideally partnered by a flexible metrology system that provides full aperture metrology of the surface to be finished. A method that provides significant advantages for mirror manufacturing is to characterize the full surface by stitching an array of sub-aperture measurements. Such a technique inherently enables the testing of larger apertures with higher resolution and typically higher accuracy. Furthermore, stitching lends itself to a greater range of optical surfaces that can be measured in a single setup. QED's Subaperture Stitching Interferometer (SSI(r)) complements MRF by extending the effective aperture, accuracy, resolution, and dynamic range of a standard phase-shifting interferometer. This paper will describe these novel approaches to large optics finishing, and present a variety of examples.
A new method combined subaperture stitching with interferometry(SSI) is introduced. It can test large and off-axis aspheric surfaces without the aid of other null optics. In this paper the basic principle and theory of the technique are analyzed. The synthetical optimization stitching model and effective stitching algorithm are established based on homogeneous coordinates transformation and simultaneous least-squares method. The software of SSI is devised and the prototype for testing of large aspheres by SSI is designed and developed. An off-axis asphere with the aperture of 376mm×188mm is tested by this method. For comparison and validation, the asphere is also tested by null compensation.The synthesized surface profile is consistent to that ofthe entire surface from null test; and the difference of PV and RMS error between them is 0.047 lambda and 0.006 lambda, respectively. So it provides another quantitative measurement for testing large aspheric surfaces and off-axis aspheres besides null-compensation.
A new method for testing aspheric surfaces by annular subaperture stitching interferometry is introduced. It can test large-aperture and large-relative-aperture aspheric surfaces at high resolution, low cost, and high efficiency without auxiliary null optics. The basic principle of the method is described, the synthetical optimization stitching model and effective algorithm are established based on simultaneous least-square fitting. A hyperboloid with an aperture of 350 mm is tested by this method. The obtained peak-to-valley (PV) and root-mean-square (RMS) values of the surface error after stitching are 0.433'lambda' and 0.052'lambda' ('lambda' is 632.8 nm), respectively. The reconstructed surface map coincides with the entire surface map from null test, and the difference of PV and RMS errors between them are 0.031'lambda' and 0.005'lambda', respectively. This stitching model provides another quantitive method for testing large aspheric surfaces besides null compensation.