Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

Abstract

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements.To find an algorithm which will satisfy the requirements, I extract individual terms (I j m I k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I j is light intensity just after the j-th phase shift. Using computer simulations, I 1 search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.

Fundamental aspects of resolution and precision in vertical scanning white-light interferometry

“…As representative examples of PSI algorithms the five point phase estimation algorithm introduced by Schwider and Hariharan [4,5]:…”

Phase modulation with micromachined resonant mirrors for low-coherence fiber-tip pressure sensors

“…(3a) and (3b)), the common background noise of LCI output is eliminated and thus the fluctuation of light source power does not affect the result. As compared to the linear demodulation method and the phase shifting method [13][14][15][16][17]21], this algorithm offers some additional advantages, for instance, it does not rely on the time information of the waveform and thus avoids the needs of synchronization and time control. As both 0 φ′ and A can be determined simultaneously, it does not require a pre-calibration of the modulation depth and thus tolerates modulation signal drift during the operation.…”

“…However, the linear demodulation method requires the sensor to be operated at a quadrature point and thus real-time stabilization of the operating condition is needed. The phase shifting method introduces additional phase changes in a controllable manner, usually a linear phase ramp [15] or several well-defined phase steps [16][17][18][19][20][21]. It requires sophisticated control of the phase steps and strict synchronization between the modulation and sampling [13][14][15][16][17][18][19][20][21].…”