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.
Freeform surfaces have drawn intensive attention in optical imaging and illumination field because of its great flexibility in optical design. However, the fabrication and testing of freeform surfaces remain a great challenge due to the arbitrary shape. Interferometry is among the high-accuracy testing method of optical surfaces. How to generate a non-rotationally symmetric wavefront similar with the surface under test and retrieve the phase from dense interferogram are hotspot issues. In this paper, we introduce two key technologies in non-null interferometry to solve the above-mentioned problems. The first is the design method of an off-axis catadioptric non-null compensator including a deformable mirror. The second is phase retrieval of single dense interferogram with digital moiré phase shifting interferogram and wavelet analysis. Simulations demonstrate the feasibility of the proposed method.
Optical freeform surfaces have been widely used in optical systems owing to their design degrees of freedom, which can simplify the structure and improve the performance of optical systems. High accuracy testing for freeform surface is needed due to the improvement of machining accuracy. However, it is still a challenge to achieve high measuring accuracy because freeform surfaces lack rotational symmetry. In this paper, an off-axis catadioptric partial compensator (OACPC) design for non-null interferometric method is proposed to measure freeform surface. The design of OACPC consists of two parts: constructing initial structure and optimizing. The initial structure is obtained by the vector aberration theory and PW method. Based on the initial structure, the OACPC is generated by modelling and optimizing in the optical design software. In order to verify the feasibility, universality and effectiveness, a design example is given. Theoretical analysis and simulation results demonstrate that the design can realize the measurement of freeform surfaces.
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.
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