Phase Interferometry Theoretical Analysis

Inertial Confinement Fusion (ICF), one of present significant research fields in the frontier of basic science, is of great scientific and practical meaning in national defense and exploitation of new energy resources. As the driver of ICF, the high power solid-state laser facility employs a lot of large aperture optical components, which must be characterized with a high degree of accuracy over low and middle frequency components of phase errors. However, our testing method and apparatus for such frequency components of phase information is far from meeting the requirement of SG-III laser system at present. Therefore, in this dissertation, an information-theoretic model of phase-measurement interferometry has been developed to analyze the transfer characteristics of phase information, optimize the interferometric system and provide a guide to measurement of low-middle frequency components of large optics. Some meaningful results are obtained as follows.Firstly, an information-theoretic model of wavefront deformation of optical components is presented on the basis of Wigner distribution function. In this model, the degree of freedom of wavefront deformation is characterized by space-bandwidth product (SBP), and the tolerance of wavefront deformation is specified with power spectral density function (PSD) and Wigner distribution function.So it provides a comprehensive characterization and specification of wavefront deformation and a concrete guide to optical fabrication.Secondly, the theoretical model of information capacity in interferometric imaging system is proposed by means of information theory. The model shows that the information capacity of the system depends on its space-bandwidth product (SBP) and signal-to-noise ratio (SNR). As an evaluating parameter of the system's performance, information capacity is more effective than system transfer function (STF) because the latter fails to express any information of SNR. Furthermore, the theoretical model of SNR in interferometric imaging system is derived according to statistical optics. By maximizing the objective function of SNR, optimization is employed to some key components such as rotating diffuser, ring source and CCD. According to the results of theoretical calculations and experiments, some conclusions are drawn as follows. (1) An increasing in fill factor and exposure time of CCD leads to an increasing in SNR of system. (2) To obtain high SNR, the rotating diffuser should be well controlled so that the rotating period is not longer than the exposure time of CCD, and the coherent length of optical intensity is about 2～5 times as long as the optical path difference (OPD) between reference and test beams. (3)By utilizing the ring source, the average SNR of the system increases from 5.2dB (tranditional point source) to 8.6dB because of the effect of source's area. Howerver, if given the equivalent area, the ability of ring source in reducing coherent noise is improved by increasing of the ratio of the inner and outer radii.Thirdly, the relationship between the precision of phase estimation and the Fisher information of its correspondent intensity data is given on the basis of Cramer-Rao lower bound (CRLB). According to the relationship, the precisions of the existing algorithms are analyzed, including temporal phase-shifting method (TPS), spatial carrier phase shifting method (SCPS) and Fourier transform method (FFT). To obtain higher precision of phase estimation, a series of algorithms based on least-squares iteration are designed to deal with the problems of phase-shift miscalibration (including random translational errors and tilt-shift errors for TPS and random spatial carrier frequency for SCPS) and high-order harmonics (including multiple-beam Fizeau interferograms and multiple-surface interferograms with random phase shifts). The results of numerical simulations and experiments demonstrate that the proposed algorithms exhibit higher precision than the existing algorithms. With the proposed algorithm, the large aperture interferometer could provide the ability of precision metrology in dynamic environments, thus the accurate phase-shifting devices and the high performance optical platform are no longer required for large aperture interferometer, which greatly reduces the cost.Fourthly, a 100-mm-aperture interferometer has been developed under the guidance of information capacity. The interferometer's test results indicate the one-dimension SBP and the average SNR are higher than 100mmx2.5mm"1 and 4dB, respectively. To measure mid spatial period error of large aperture optical components, sub-aperture measurement is adopted and the full-aperture PSD is estimated by weighted average of sub-aperture PSD. Considering that the system is not shift-invariant, the Wigner distribution of the system is calibrated to obtain accurate sub-aperture and full-aperture PSD.To sum up, this dissertation presents a comprehensive analysis of phase measurement interferometry from the viewpoint of information theory. Thus, it offers us a better understanding of the transfer characteristic of phase information.The results mentioned above provide certain guiding value to interferometer design and measurement of mid-spatial period error of large-aperture optical components. Moreover, the optimized interferometers, the 500-mm aperture wavelength-tuning phase-shifting interferometer and the 100-mm-aperture high lateral resolution interferometer, whose measurement accuracy satisfies the requirement of the high power solid-state laser facility, will offer technical support and guarantee for optical measurement in SG-III laser system.