Ligong Zheng

Experimental study on subaperture testing with iterative triangulation algorithm

Applying the iterative triangulation stitching algorithm, we provide an experimental demonstration by testing a Φ120 mm flat mirror, a Φ1450 mm off-axis parabolic mirror and a convex hyperboloid mirror. By comparing the stitching results with the self-examine subaperture, it shows that the reconstruction results are in consistent with that of the subaperture testing. As all the experiments are conducted with a 5-dof adjustment platform with big adjustment errors, it proves that using the above mentioned algorithm, the subaperture stitching can be easily performed without a precise positioning system. In addition, with the algorithm, we accomplish the coordinate unification between the testing and processing that makes it possible to guide the processing by the stitching result.

The Talbot effect of plasmonic nanolenses

The Talbot effect of an Ag nanolens with five periodic concentric rings that are illuminated by the radially polarized light was numerically studied by means of rigorous finite-difference and time-domain (FDTD) algorithm. It was found that the Talbot effect occurs only when the incident wavelength is at the scale of less than half of period of the grating structures of the nanolenses. Specifically, in this work, the nanolenses with a 500 nm period grating structures has five focal points due to Talbot effect for the incident wavelength of λ = 248 nm. The diameter of the first focal spot after the exit plane in free space is 100 nm. In contrast, we analyzed the corresponding focal points on the basis of Talbot self-imaging by scalar diffraction theory. It was found that the scalar Talbot effect cannot interpret the Talbot effect phenomenon for the metallic nanolenses. It may attribute to the paraxial approximation applied in the Talbot effect theory in far-field region. However, the approximation does not hold in our nanolenses structures during the light propagation. In addition, the Talbot effect appears at the short-wavelength regime only, especially in the ultraviolet wavelength region.

Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology

Wavefront coding technology can extend the depth of focus of a well-corrected three-mirror anastigmatic optical system by about ten times, but the image obtained directly by charge-coupled devices blurs at the same time. An effective image restoration must be applied to these blurred images. This paper describes an innovative method that restores the blurred image, which combines the optical design software and mathematical software. The point spread function of system with wavefront coding technology is quite different from the usual and difficult to simulate by a disk function or other simple function in most cases. The commercial optical design software is applied to obtain the point spread function. If a 1×1-pixel image with brightness 255 is set as the point source of a optical system, the result of calculation software using a ray tracing algorithm will itself be the digital point spread function. This is proven to be a simple and effective way to acquire the complicated point spread functions of unusual optical systems such as those using wavefront coding technology. A regularization factor and contrast-adjusting factors are introduced into the classical Wiener filter, which achieves good restored images: the root-mean-square error is less than 0.0193, while the peak signal-noise ratio is higher than 23.7. Some parameters of the filter can be adjusted so that the restored image is more suitable for evaluation by eye. It is also shown that a single filter can restore all the images within the extended depth of focus.

Annular sub-aperture stitching interferometry for testing of large aspherical surfaces

Annular subaperture stitching interferometric technology can test large-aperture, high numerical aperture aspheric surfaces with high resolution, low cost and high efficiency without auxiliary null optics. In this paper, the basic principle and theory of the stitching method are introduced, the reasonable mathematical model and effective splicing algorithm are established based on simultaneous least-squares method and Zernike polynomial fitting. The translation errors are eliminated from each subaperture through the synthetical optimization stitching mode, it keeps the error from transmitting and accumulating. The numerical simulations have been carried on by this method. As results, the surface map of the full aperture after stitching is consistent to the input surface map, the difference of PV error and RMS error between them is -0.0074 λ and -0.00052 λ (λ is 632.8nm), respectively; the relative error of PV and RMS is -0.53% and -0.31%; and the PV and RMS of residual error of the full aperture phase distribution is 0.027 λ and 0.0023 λ, respectively. The results conclude that this splicing model and algorithm are accurate and feasible. So it provides another quantitive measurement for test aspheric surfaces especially for large aperture aspheres besides null-compensation.

Belt-MRF for large aperture mirrors

With high-determinacy and no subsurface damage, Magnetorheological Finishing (MRF) has become an important tool in fabricating high-precision optics. But for large mirrors, the application of MRF is restricted by its small removal function and low material removal rate. In order to improve the material removal rate, shorten the processing cycle, we proposed a new MRF concept, named Belt-MRF to expand the application of MRF to large mirrors and made a prototype with a large remove function, using a belt instead of a very large polishing wheel to expand the polishing length. A series of experimental results on Silicon carbide (SiC) and BK 7 specimens and fabrication simulation verified that the Belt-MRF has high material removal rates, stable removal function and high convergence efficiency which makes it a promising technology for processing large aperture optical elements.

Design and fabrication of CGH for aspheric surface testing and its experimental comparison with null lens

Computer-generated hologram (CGH) is an effective way to compensate wavefront in null test of aspheric surfaces and freeform surfaces. Our strategies of CGH design and fabrication for optical testing are presented, and an experiment demonstrating the compensation results of CGH and null lens is also reported. In order to design complex CGH, software was developed, with which we can design a CGH including three sections: main section for compensating wavefront in null test, alignment section for adjusting the relative position between CGH and interferometer, and fiducial section for projecting fiducial marks around the optics under test. The design result is represented in GDS II format file which could drive a laser-direct-writer-machine to fabricate a photomask. Then, a 1:1 replication process is applied to duplicate the patterns from photomask to a parallel optical substrate whose surface is error better than λ/60 rms. Finally, an off-axis aspheric surface was tested with CGH and null lens respectively. The test result with CGH (0.019λ;rms) is almost the same as the result with null lens (0.020λ rms). This experiment also demonstrated that fiducial marks projected by CGH can be used to guide the alignment of the optics and measurement of its off-axis distance.

Swing arm profilometer: high accuracy testing for large reaction-bonded silicon carbide optics with a capacitive probe

A feasible way to improve the manufacturing efficiency of large reaction-bonded silicon carbide optics is to increase the processing accuracy in the ground stage before polishing, which requires high accuracy metrology. A swing arm profilometer (SAP) has been used to measure large optics during the ground stage. A method has been developed for improving the measurement accuracy of SAP using a capacitive probe and implementing calibrations. The experimental result compared with the interferometer test shows the accuracy of 0.068 μ m in root-mean-square (RMS) and maps in 37 low-order Zernike terms show accuracy of 0.048 μ m RMS, which shows a powerful capability to provide a major input in high-precision grinding.

Design of an off-axis three-mirror anastigmatic optical system with wavefront coding technology

Wavefront coding (WFC) technology can extend the depth of focus of an optical system, which makes the application of this technology to space cameras extremely attractive. This paper introduces the application of wavefront coding to three-mirror anastigmatic optical systems. A transition model is established, in which the secondary mirror is regarded as the wavefront coding element and redesigned according to mathematical calculation. A comparison of modulation transfer function (MTF) behavior between the traditional system and the innovative system with wavefront coding technology is provided. The MTF behavior of both on-axis and off-axis field-of-view points remains the same in spite of the extended depth of focus. It is also observed that the system becomes very insensitive to aberration related to defocus through WFC technology. Errors in optical design and its improvement are discussed. The linear transition model is proven to be an acceptable one. Finally, an extension factor for the depth of focus is defined, and its effect is presented graphically.

Manufacturing and testing SiC aspherical mirrors in space telescopes

Reaction Bonded (RB) SiC mirrors due to their excellent specific stiffness and thermal properties have been widely used in space telescopes. However, polishing large SiC aspherical mirrors is difficult compared to other materials such as fused silica or Zerodu. In addition, surface roughness of the polished SiC mirrors is limited by the defects of the materials and needs to be improved by means of surface coating technique. This paper introduces the current progress of large SiC aspherical mirrors manufacturing and testing in CIOMP. In particular, the procedures of making large off-axis aspherical mirrors were discussed in detail. A proprietary computer controlled optical surfacing (CCOS) technique was utilized to grind and polish the mirrors and the computer aided null test was used to measure the surface figure. As results, a 600mm class off-axis SiC aspherical mirrors was demonstrated with figure error less than 13nm rms.

Fabrication of large off-axis asymmetry aspherics using stressed lap with orbital tool motion

The stressed-lap technique has been proven to be an effective method to meet the challenge of polishing large mirrors with highly aspheric figures. It has the advantage of high material removal and strong natural smoothing tendency over a wide range of spatial frequencies, only round mirrors could be processed with this technology. A solution is put forward in this paper by applying the CCOS (Computer controlled optical surfacing) removing strategy into the stressed lap technology, employing the stressed lap as the removing tool but moving the lap in the CCOS fashion, naming the stressed lap with orbital motion. With the new technology, almost any shape of mirror could be processed, the figuring ability could be improved and the changing rate of the force imposed on the lap turn out to be only 1/6 of the stressed lap with spinning motion based on simulation results, which conducing a lower response requirement of the lap with orbital motion.