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.
Wavefront modulation devices are of great significance in optical information processing systems. These devices capable of phase modulation are used in a variety of optical applications: wavefront correction, optical metrology, adaptive optics, aberration compensation, etc. The liquid crystal spatial light modulators (LC-SLMs) and deformable mirrors (DMs) have been regarded as the promising device for their flexibility and programmability on wavefront modulations. This paper presents applications of LC-SLMs and DMs when they are used as aberration compensators in testing of aspheric and freeform. Besides, a pixel-wise method based on analysis of the phase maps obtained by a Fizeau interferometer for calibrating the phase modulation characteristics of the LC-SLM is proposed. A PLUTO-VIS-020 LC-SLM produced by the Holoeye Company is employed in the calibrating experiment. A Zygo interferometer based on Fizeau interference theory is also employed. The experimental results demonstrate that the phase modulation characteristics of LC-SLM and a specific lookup table (LUT) for every pixel of the LC-SLM aperture can be obtained by utilizing the proposed method with convenience and high efficiency. The device calibrated in this paper provides a high phase shift up to 6π at 632.8nm wavelength and has a linearized phase distribution. It coincides well with the average modulation curve offered in the manual of the device. This paper provides a simple and accurate method for pixel-wise phase modulation characteristics calibration.
With no necessity of compensating the whole aberration introduced by the aspheric surfaces, non-null test has the advantage over null test in applicability. However, retrace error, which is brought by the path difference between the rays reflected from the surface under test (SUT) and the incident rays, is introduced into the measurement and makes up of the residual wavefront aberrations (RWAs) along with surface figure error (SFE), misalignment error and other influences. Being difficult to separate from RWAs, the misalignment error may remain after measurement and it is hard to identify whether it is removed or not. It is a primary task to study the removal of misalignment error. A brief demonstration of digital Moiré interferometric technique is presented and a calibration method for misalignment error on the basis of reverse iteration optimization (RIO) algorithm in non-null test method is addressed. The proposed method operates mostly in the virtual system, and requires no accurate adjustment in the real interferometer, which is of significant advantage in reducing the errors brought by repeating complicated manual adjustment, furthermore improving the accuracy of the aspheric surface test. Simulation verification is done in this paper. The calibration accuracy of the position and attitude can achieve at least a magnitude of 10-5 mm and 0.0056×10-6rad, respectively. The simulation demonstrates that the influence of misalignment error can be precisely calculated and removed after calibration.
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