Scale factor calibration method for integrating-bucket sinusoidal phase shifting interferometry

Abstract

In order to recover the phase map φ(x, y) from sinusoidally phase-shifted interferograms obtained with the integrating-bucket method, two images Ψs and Ψc should be calculated first which are proportional to sin(φ) and cos(φ) respectively, and one of them needs to be scaled by a scale factor before they are used to solve the phase with the arctangent function. Because parameters deciding the scale factor such as the sinusoidal phase modulation amplitude and initial phase are difficult to be set accurately, miscalibration of it can always happen and result in significant error in the phase demodulation. Therefore, in this paper we propose a simple scale factor calibration method which performs the calibration directly with the phase-shifted interferograms and avoids the need for accurate parameter setting. First, we introduce high-density fringes to the interferograms; then, we construct a new image variable Γ with the squares of Ψs and Ψc; last, we find the value of the scale factor by minimizing the second harmonic amplitude in Γ’s spatial spectrum. Simulation results show that the proposed method is robust against noise and fringe distortion, and it was tested in a fiber-optic fringe projection profilometer.