In AR and VR devices, freeform surfaces are widely used to improve system performance. The manufacture of freeform surfaces is limited to the measurement. In order to guide the manufacturing process, we have proposed a real-time interferometric measurement system. In the system, an accurate, automatic and fast description method is needed to describe complex freeform surface. In order to improve this situation, a description method with automatically configurable Gaussian radial basis function (AC-GRBF) has been proposed. The key parameters of AC-GRBF, the number of subapertures N, coefficient A and the base number of GRBFs affect the fitting accuracy and speed, and they are analyzed by numerical simulation in the paper. The analysis in this paper can provide reference for the description method of GRBF, especially AC-GRBF, and the description of complex freeform surfaces in the design.
Aspheric surfaces are widely used in advanced optical instrument. Measuring aspheric surface parameter errors (SPEs) in high accuracy is of vital importance in manufacturing and aligning optical aspheric surfaces. A simulation to prove the effectiveness and accuracy of an interferometric measurement method for high-order aspheric SPEs is carried out based on the ideal situation that there is no error of the BCD. The relative accuracy of vertex radius of curvature error, conic constant error and fourth order aspheric coefficient error can reach 5.58×10-8 %, 1.36×10-4 % and 0.02%. The influence of the BCD error is analyzed to prove the feasibility of this method and provide a theoretical guidance for real measurement configurations. This method can measure all kinds of aspheric surface parameter errors mentioned above simultaneously in high accuracy.
Accuracy and correctness are significant to the entire measurement. The measurement results of new methods are usually compared with the results of mature measurement methods aiming at evaluating the consistency of the two methods, which can estimate the feasibility of new methods. Two criteria are usually utilized to evaluate the consistency of surface measurements. One criterion is to compare the Peak-Valley (PV) value and Root-Mean-Square (RMS) value directly. However, lots of surfaces which are not similar or even completely different share the same PV and RMS values. The other criterion is to analyze the point-to-point difference. But this criterion still utilizes the PV value and RMS value as the consistency evaluation of the point-to-point difference. Surface Error Consistency Coefficient (SECC) is proposed as a criterion in this paper. In this criterion, the principle of cross-correlation is introduced to evaluate the consistency of two measurement results and all the data are utilized. This criterion can evaluate the consistency of two surfaces by a percentage and is not susceptible to some special single points. In this paper, some surfaces are evaluated in simulations, and the consistency of surface maps by Coordinate-transform method and Fourier-transform method is evaluated.
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