Phase detection of equidistant fringes for highly sensitive optical sensing I Principle and error analyses

Abstract

A method for detecting a phase of equidistant and straight fringe patterns is presented that is based on an arctangent calculation of Fourier cosine and sine integrals of the fringe profile. In the phase calculation, phase errors caused by a spatial truncation, nonlinearity, and sampling of the light intensity and by a random noise are analyzed theoretically. From the analyses, it is concluded that (1) the phase error due to the truncation of data decreases as the frequency of the fringes increases, (2) the Hanning windowing makes the error small, and (3) the phase fluctuation due to the random noise depends mainly on the signal-to-noise ratio (SNR) of the fringe and the number of sample points. The total accuracy of the phase measurement is determined by the sum of three phase errors due to the calculation of a phase, a random noise, and a frequency deviation of a laser light. The total error is reduced to one thousandth of the wavelength of the laser light when the number of sample points is 256, the SNR is 100, and the frequency stability of the laser light is 1 × 10−7.