Deformable mirror (DM) is a flexible wavefront modulator with a changeable surface. It is traditionally adopted in adaptive optical system for aberration correction. Recently applications in zoom imaging system and interferometer for freeform measurement have been proposed because the improvement in fabrication technique makes larger stroke amount and faster response possible. The order and accuracy of aberration correction are typical wavefront correction characteristics of DMs. Due to the non-linearity, hysteresis and creep characteristic of piezoelectric ceramics, accurate control of piezoelectric type DM remains a challenge. Generally, the surface shape of a DM is changed by altering the voltages applied to different actuators below the DM film. And the shape of the DM can be fitted with Zernike polynomial to better characterize the aberration. So accurate control of the DM surface shape requires a relationship between the control voltage vector and the Zernike coefficients of the surface shape. We adopt neural network for the foundation of the relationship. 3000 set of control-voltage-vector and Zernike-coefficient pairs are experimentally collected based on the data measured with an interferometer and fitted with Zernike polynomials. The neural network is constructed and trained, and the control voltage vectors of new surface shapes can be retrieved with the network. The accuracy of shape realization is finally demonstrated by comparison between measured and predicted voltages.
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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