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
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