In order to measure the optical distance of the object that changes rapidly over time, Fourier transform method
is appropriate because it requires only a single interferogram. In the measurements of such fast phenomena, the
thermal noise by the camera to record the interferogram results in a significant error and the signal becomes
weak owing to the short exposure time of the camera. When the noise level is high, a process to denoise wrapped
phase should be added before phase unwrapping in order to obtain an optical distance distribution. The thermal
noise has a uniform spatial distribution; however, the signal depends on a profile of the incident wave to the
interferometer. This means that the signal to noise ratio has a spatial distribution. This paper proposes the
denoising method that can take account of the weight of the data that depends on the signal intensity distribution.
In order to determine the denoised phase, two cost functions are examined. One is a complex-valued cost function
that can ensure convergence of iterative method to obtain the stationary point; however, it is not proved that
both the real part and the imaginary part are minimized at the stationary point. The other is a real-valued
cost function that cannot ensure the convergence but it minimizes the cost function at the stationary point.
The numerical simulation demonstrates the validity of the weighted denoising and the applicability of the cost
"Weighted denoising for phase unwrapping", Proc. SPIE 9019, Image Processing: Algorithms and Systems XII, 90190M (25 February 2014); doi: 10.1117/12.2039390; https://doi.org/10.1117/12.2039390