Fourier description of digital phase-measuring interferometry

Design of phase-shifting algorithms by fine-tuning spectral shaping

“…In the book of Malacara et al [3] an encyclopedic number of PSI algorithms are presented, including the motivation behind many of them; their spectral plots are also shown according to Freischlad and Koliopoulos (F&K) [4]. Spectral analysis of PSAs was popularized only after the F&K paper [4] was published. Nowadays, spectral analysis is the gold-standard reference to compare among several PSAs.…”

“…Nowadays, spectral analysis is the gold-standard reference to compare among several PSAs. Most people uses this spectra to visualize and gauge among several promising PSAs, and choose the best one for their needs [4][5][6][7][8]11,12].…”

“…Then, Surrel proposed the CP-diagram, to visualize some properties of a PSA based on the (discrete) angular location over the unit circle of these zeroes and their multiplicities [9]. Surrel proposed no continuous spectral plot to gauge his x-polynomials [9], as the F&K spectral plot does provide [4]. He did not follow the standard continuous spectral analysis of z-transformed digital filters [10].…”

“…In 2010, Burke [11] efficiently combined both perspectives: the discrete CP-diagram [9], and the continuous F&K spectral analysis [4]. Burke did this to point-out the importance of fine-tuning the zeroes of a x-polynomial of symmetric PSAs.…”

“…Burke did this to point-out the importance of fine-tuning the zeroes of a x-polynomial of symmetric PSAs. That is, Burke generated a new visualizing-gauging technique, by combining the discrete CP-diagram [9], with the F&K continuous spectrum [4,11], while finely tuning the PSA' symmetric spectral zeroes.…”