Continuous Fourier transform method and apparatus

An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications

System calibration method for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently proposed quantitative phase imaging technique with high resolution and wide field-of-view (FOV). In current FPM imaging platforms, systematic error sources come from the aberrations, LED intensity fluctuation, parameter imperfections and noise, which will severely corrupt the reconstruction results with artifacts. Although these problems have been researched and some special methods have been proposed respectively, there is no method to solve all of them. However, the systematic error is a mixture of various sources in the real situation. It is difficult to distinguish a kind of error source from another due to the similar artifacts. To this end, we report a system calibration procedure, termed SC-FPM, based on the simulated annealing (SA) algorithm, LED intensity correction and adaptive step-size strategy, which involves the evaluation of an error matric at each iteration step, followed by the re-estimation of accurate parameters. The great performance has been achieved both in simulation and experiments. The reported system calibration scheme improves the robustness of FPM and relaxes the experiment conditions, which makes the FPM more pragmatic.Comment: 18 pages, 9 figure

Improvement of Fourier Polarimetry for applications in tomographic photoelasticity

The use of the Fourier Polarimetry method has been demonstrated to extract the three characteristic parameters in integrated photoelasticity. In contrast to the phase-stepping method, it has been shown that the Fourier method is more accurate. However, the Fourier method isn't very efficient as it requires that a minimum of nine intensity images be collected during a whole revolution of a polarizer while the phase-stepping method only needs six intensity images. In this paper the Fourier transformation is used to derive the expression for determination of the characteristic parameters. Four Fourier coefficients are clearly identified to calculate the three characteristic parameters. It is found that the angular rotation ratio could be set arbitrarily. The angular rotation ratio is optimized to satisfy the requirements of efficiency and proper data accuracy, which results in data collection about three times faster than the methods suggested by previous researchers. When comparing their performance in terms of efficiency and accuracy, the simulated and experimental results show that these angular rotation ratios have the same accuracy but the optimized angular rotation ratio is significantly faster. The sensitivity to noise is also investigated and further improvement of accuracy is suggested