Testing Aspheric Surfaces Research Articles

用于高精度非球面面形检测的计算全息图的设计

用于高精度非球面面形检测的计算全息图的设计

低空间频率组合计算全息元件检测深度非球面

低空间频率组合计算全息元件检测深度非球面

大口径光学非球面元件拼接优化及精度验证

大口径光学非球面元件拼接优化及精度验证

Correction for mapping errors in non-null test of aspheric surface

The non-null testing methods have the potential to allow measurement of aspheric surfaces with large departures from a reference sphere. In a non-null configuration, the ray will return along a different path and interfere with a different reference ray. This difference in “mapping” between the test and reference rays creates an additional optical path difference (OPD) contribution, which causes test part errors to be mapped to the wrong location. To correct the mapping errors in non-null test of aspheric surface, correction method are proposed by ray trace and wave-front analysis. Experiments are carried out to illustrate the effectiveness of this approach. The methods can work well, despite large deviation between the theoretic value of the aspheric and the reference wave-front.

<i>In Situ</i> Measurement and Compensation Turning Technique of Deep MgF<sub>2</sub> Conformal Dome

The adoption of conformal optics system can evidently improve the synthetical performance of infrared missiles. Hot-pressing poly-crystal magnesium fluoride (MgF2) is an ideal material for conformal optics dome. But many problems about machining and surface test of deep aspheric surface have not been solved at present, and there is not much research about the machining characteristics of MgF2 material. In this paper, in-situ measurement system is designed, so positional errors that introduced by repeating installation can be avoided. Then, machining process of MgF2 material by single point diamond turning is studied, and optimized diamond turning process is proposed by experiments in order to obtain low surface roughness. Furthermore, surface accuracy is tested by on-machine measurement system. Based on the result, error compensation process of conformal dome is carried out. Finally, the shape error of the dome is less than 0.8μm PV.

A New Method for Testing the Asphere Surface with a Liquid Crystal Spatial Light Modulator

Due to the special properties of asphere lens, the testing of it is more difficult than that of spherical lens. In this paper, the development of a new method using the liquid crystal spatial light modulator (SLM) to measure the accuracy of an aspheric surface is presented. The surface form was measured using a new component as the compensator lens in conjunction to provide an interferogram representing the aspheric form deviation from the nominal. Interferograms are decoded using a spatial-carrier phase shifting technique. The interferometric data is compared to data obtained using a contact stylus profilometer. The system can be mounted over a polishing machine and used for on-line testing of aspheric mirror surfaces.

Autocollimating compensator for controlling aspheric optical surfaces. I

A compensator (null-corrector) for testing aspheric optical surfaces is proposed, which enables (1) independent verification of optical elements and assembling of the compensator itself, and (2) ascertaining the compensator position in a control layout for a specified aspheric surface. The autocollimating design allows significant reducing difficulties associated with practical use of lens compensators.

Mathematical Model and Simulation for Testing Aspheric Surface Using the Digital Moiré Patterns by Circular Sub-Region Stitching Method

sub-region stitching measurement of asphere by using the combination of digital moire patterns without compensator, auxiliary mirror and other assistant modules. This paper illustrated the principal theory. And use of digital filtering, phase shifting, the least square method and Zernike polynomial fitting to establish the reasonable mathematical model. Meanwhile the computer simulation experiment was carried on. the PV and RMS of the full aperture phase distribution residual error are 0.058λand 0.0087λ After this method processing.

Measurement of aspheric surfaces using an improved annular subaperture stitching interferometry (IASSI)

An improved annular subaperture stitching interferometry (IASSI) is proposed for testing aspheric surfaces in the stage of precision polishing. It includes a reasonable stitching model and an automatic positioning operation. In the testing process, a series of optical path difference (OPD) data of annular subapertures is obtained as the interferometer is gradually shifted relative to the tested aspheric surface. Then these OPD data can be analyzed by the automatic positioning operation to get the key stitching parameters, and can be stitched together based on a reasonable mathematical model. To verify its validity, we study the applicability of the method to subaperture stitching tests of two conic aspheric surfaces. The stitching results agreed with the full-aperture test results.

Optimization stitching model for subaperture test of aspheric surfaces

Annular subaperture stitching interferometry (ASSI) is increasingly used for precision metrology of aspheric surfaces. The stitching model is a critical factor for stitching algorithms in ASSI. An optimized stitching model is proposed, which describes the alignment errors of adjacent subapertures based on an off-axis model and wave aberration theory. To keep the stitching errors from transmitting and accumulating, a simultaneous optimization algorithm is presented. The residual difference of overlapped regions of adjacent subapertures is utilized to evaluate the stitching accuracy. Finally, the comparative numerical simulations and experiments are carried out. It shows that the optimized stitching model has a better performance and validity.

Autocollimating compensator for controlling aspheric optical surfaces

A compensator (null-corrector) for testing aspheric optical surfaces is proposed, which enables i) independent verification of optical elements and assembling of the compensator itself, and ii) ascertaining the compensator position in a control layout for a specified aspheric surface. The compensator consists of three spherical lenses made of the same glass. In this paper, the scope of the compensator expanded to a surface speed ~f/2.3; a conceptual example for a nominal primary of Hubble Space Telescope is given. The autocollimating design allows significant reducing difficulties associated with practical use of lens compensators.

Aspheric surface reconstruction for scanning interference

A simplified reconstructing method for the aspheric surface testing based on scanning interference technology is presented. The aspheric normal intersects the optical axis at different points with different angles, which is called normal congruence; a normal congruence can identify an aspheric surface. In this method, the test aspheric surface is shifted along the optical axis to scan the tested aspheric surface; meanwhile a series of interferograms and phase maps are obtained. The angles between the normal lines and the aspheric axis are obtained using the positions of zero-phase points, according to the image-forming principle of the camera. Here, Zernike polynomials are applied to analyze the phase maps and extract the zero-phase points. Finally, the absolute coordinates of the test surface is rebuilt through iterative integration. Because both the system deformation and amplification do not affect the reconstruction result, this method can avoid complicated stitching algorithm in the subaperture stitching interferometric method. Experimental results show that the method has high accuracy and reliability.

非球面光学元件的面形检测技术

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.

Error correction of a phase-only computer-generated hologram for an aspheric surface

When applying phase-only computer-generated hologram (CGH) as a standard model of optical measurement in computer-generated holography for aspheric surface testing, it has the advantage of simplifying optical path configuration and improving the diffraction efficiency of the incoming light. However, errors always exists during the encoding process of fabricating multiphase level CGHs and this kind of errors will be amplified level by level in the measurement. According to the analysis of the encoding error, the error of CGH increases linearly when its quantified period increases. For example, if the quantified period is 32, the maximum of encoding error is 16.46 which can lead wave-front aberration 0.085λ of a secondary parabolic surface with 512×512 sampling pixels. In this article, an optimization method based on deviation of minimum boundary value has been used to eliminate the encoding error of CGH. In the experiment, we use a liquid crystal spatial light modulator to generate CGHs and measure residuals of reconstructed wave-front of a secondary parabolic surface. The measurement results show that average decrease of the RMS values of the residuals is 0.07 when their periods range from 3 to 6, which indicates the optimization method is effective.

用于非球面检验的激光直写高精度计算全息图制作

用于非球面检验的激光直写高精度计算全息图制作

Aspheric surface measurement based on sub-aperture stitching interferometry

In order to test convex aspheric surfaces without the aid of other null optics, a novel method combined sub-aperture stitching and interferometry called SSI (sub-aperture stitching interferometry) is introduced. In this letter, the theory, basic principle, and flow chart of SSI are researched. A synthetical optimization stitching mode and an effective stitching algorithm are established based on homogeneous coordinate's transformation and simultaneous least-squares fitting. The software of SSI is devised, and the prototype for testing of large aspheres by SSI is designed and developed. The experiment is carried out with five subapertures for a convex silicon carbide (SIC) aspheric mirror with a clear aperture of 130 mm. The peak-to-valley (PV) and root-mean-square (RMS) error are 0.186 \lambda and 0.019 \lambda, respectively. For the comparison and validation, the TMA system which contained the convex asphere is tested by interferometry. The wavefront error of the central field of the optical system is 0.068 \lambda RMS which approaches to diffraction limitation. The results conclude that this technique is feasible and accurate. It enables the non-null testing of aspheric surfaces especially for convex aspheres.

非球面检测中最佳入射球面波和最佳参考球面波的确定

To test an aspheric surface with an interference way in high-precision,a new method for determining the optimum positions of incident spherical wave source and reference spherical wave source are proposed.The optimal position of incident spherical wave source is determined by calculating the interferometric fringe density between incident spherical wave and aspherical reflective wave and that of the reference spherical wave source is obtained from calculating the interferometric fringe density on a CCD.On the theoretical basis of this research,the specific strategies of selecting CCDs and optical components can be determined and the interferogram can be fully analyzed to get much information about tested aspheric surfaces.It is shown that the research results can be used for theoretically guiding the debugging process of testing aspheric surfaces.

用于凹非球面的计算全息设计及其误差分析

用于凹非球面的计算全息设计及其误差分析

Measurement accuracy verification of aspheric surface test with computer-generated hologram

A convex aspheric surface using a computer-generated hologram (CGH) test plate fabricated with novel techniques and equipment is tested. However, the measurement result is not verified via comparison with other methods. To verify the accuracy of the measurement, a perfect sphere surface is measured by the following. The measurement result is quantified into four parts: the figure error from the tested spherical surface; the figure error from the reference spherical surface; the error from the hologram; and the adjustment error from misalignment. The measurement result, removed from the later three errors, shows agreement to 4-nm RMS with the test by Zygo interfermeter of the same surface. Analysis of the CGH test showed the overall accuracy of the 4-nm RMS, with 3.9 nm from the test plate figure, 0.5 nm from the hologram, and 0.74 nm from other sources, such as random vibration, various second order effects, and so on. Thus, the measurement accuracy using the proposed CGH could be very high. CGH can therefore be used to measure aspheric surfaces accurately.

A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface

To solve the best-fit sphere (BFS) accurately is one of the technological keys for the generating and testing of optical aspherical surfaces. This paper presents a new algorithm for solving the BFS of aspherical surfaces to suppress some deficiencies in the existing BFS algorithms. In the proposed approach, a BFS is constructed, which passes through both sides of endpoints in the section of the aspherical surfaces, the center of the BFS is shifted along the x-axis, and its radius of curvature is automatically computed. The variable step size method is proposed to speed up the convergence of the iteration. Through numerically solving the BFS of conic and cubic surface, the advantages of the proposed approach are verified. The results show that the proposed approach is of rapid convergence, and high accuracy; it is not only suitable for the conic surface, but also for higher order aspheres. The obtained asphericity and material removal function is more suitable for the machining and test.