The phase retrieval hybrid algorithm based on gradient search algorithm and GS algorithm is designed for surface testing of the high dynamic range error beyond one wavelength after the rough polish process. Phase retrieval is a wave front sensing method that uses the intensity distribution to reconstruct the phase distribution of optical field. In the rough polish process of optical surface testing, there is the problem of phase wrapping caused by the high dynamic range error, which makes it hard to be measured by interferometers. In this condition, infrared interferometers are widely used for optical testing, but the operation of infrared interferometer is complicated because of the invisibility of infrared light and it’s very sensitive to the temperature, vibration and turbulence. The phase retrieval hybrid algorithm derives from gradient search algorithm and GS algorithm, aiming to solve the problem of phase wrapping caused by the high dynamic range error. Firstly, phase distribution is described by Zernike polynomials and the coefficients of Zernike polynomials are optimized by the gradient search algorithm to retrieve the low frequency error beyond one wavelength. Then GS algorithm is used to retrieve the high frequency error of small value. In the simulated calculation, the hybrid algorithm is used for surface testing of a spherical mirror with PV 2.42λ , RMS 0.41λ . The retrieved surface is PV 2.53λ , RMS 0.42λ .The simulation result shows that the hybrid algorithm is effective and accurate for optical surface testing of high dynamic range error.
The pendulum type processing technique is a manufacture way that the workpiece is rotating actively and the lap is slave
drive from the workpiece under its gravity force and the pressure which comes from the pressure head. The rotational
speed of lap is varied. Because the aperture size of the lap can be selected in the processing. So the processing efficiency
is high. And this technique is commonly used in the grinding stage to remove a large margin, sub-surface damage layer and to smooth the mirror surface in the stage of polishing. Shown in the Preston equation, the removal function of lap is
connected to the relative speed of lap_workpiece. Based on moment-equilibrium principle, a theoretical model is
established about the lap which associated with the coherent parameters. Under the condition of the lap and the workpiece at different relative positions, the rotational speed of the lap and correspondence between the parameters is summarized and derived. The speed ratio of lap_workpiece increases with the increment of the eccentricity, and the
actual rotational speed is determined by the workpiece’s rotational speed, the size of lap and the force acting on the lap. The relationship of speed ratio between the lap and workpiece which impacts on the removal function is given at the last
of the paper.
In order to test the high dynamic range error beyond one wavelength after the rough polish process, we design a phase retrieval hybrid algorithm based on diffraction angular spectrum theory. Phase retrieval is a wave front sensing method that uses the intensity distribution to reconstruct the phase distribution of optical field. Phase retrieval is established on the model of diffractive propagation and approach the real intensity distribution gradually. In this paper, we introduce the basic principle and challenges of optical surface measurement using phase retrieval, then discuss the major parts of phase retrieval: diffractive propagation and hybrid algorithm. The angular spectrum theory describes the diffractive propagation in the frequency domain instead of spatial domain, which simplifies the computation greatly. Through the theoretical analysis, the angular spectrum in discrete form is more effective when the high frequency part values less and the diffractive distance isn’t far. The phase retrieval hybrid algorithm derives from modified GS algorithm and conjugate gradient method, aiming to solve the problem of phase wrapping caused by the high dynamic range error. In the algorithm, phase distribution is described by Zernike polynomials and the coefficients of Zernike polynomials are optimized by the hybrid algorithm. Simulation results show that the retrieved phase distribution and real phase distribution are quite contiguous for the high dynamic range error beyond λ.