Spectral analysis for the generalized least squares phase-shifting algorithms with harmonic robustness

Gamma correction in simultaneously dual fringe projection moiré profilometry

“…The N-step least-squares PSA, with nominal 2𝜋 𝑁 ⁄ , has the best harmonic rejection capability so that 𝐾 = 𝑁 − 1 13 , moreover, the unrejected harmonics are ∀𝑘 ∈ 𝒦 = {… − 3𝑁 + 1, −2𝑁 + 1, −𝑁 + 1, 𝑁 + 1, 2𝑁 + 1, 3𝑁 + 1, … }; refer to 14 . Particularly, it is plausible to consider that only harmonic 𝜅 = (−𝑁 + 1) has enough energy to not be negligible, whereas we can neglect all the others.…”

Colored digital Moire technique for self-occluding shading in fringe projection profilometry

“…From Eq. ( 2), we aim to determine the sinusoidal signal, namely the interference term, and so we can recover it by calculating the anality signal utilizing the least-squares phase-shifting algorithm (LS-PSA) as 5 ,…”

“…Whereas, in real-time applications, the aim is to measure the UUT's surface, which can be moving in a given direction or experimenting a transformation over the time (for example a beating heart); hence, FPP techniques for realtime applications usually require a single shot. Since the FPP signal's nature has three variables -or more for distorting harmonics-the phase recovery from a single fringe pattern is an ill-posed problem in the Hadamard sense 5 . In order to overcome this issue, real-time applications need to introduce prior information like spatial phase carriers and/or color encoding as well as using two video projectors 3,[6][7][8][9][10][11][12][13][14] and references therein.…”

The Moore–Penrose inverse: a hundred years on a frontline of physics research

“…An everlasting interest in the least squares method is well reflected by a immutable stream of articles, in which the method is utilized and most often plays a relevant role. Regarding recent research within broadly understood physics, exemplary applications of the method can be encountered in the following articles: Chou et al (2018) proposing a framework for privacy preserving compressive analysis (which exploits formulae for the Moore-Penrose inverse of columnwise partitioned matrices), Gaylord and Kilby (2004) specifying a procedure of measuring optical transmittance of photonic crystals, Huang et al (2006) introducing the extreme learning machine algorithm, Le Bigot et al (2008) presenting high-precision energy level calculations in atomic hydrogen and deuterium, Ordones et al (2019) deriving frequency transfer function formalism for phase-shifting algorithms, Sahoo and Ganguly (2015) optimizing the linear Glauber model to analyse kinetic properties of an arbitrary Ising system, Stanimirović et al (2013) introducing a computational method of the digital image restoration, Wang et al (1993) identifying sources of neuronal activity within the brain from measurements of the extracranial magnetic field, Wang and Zhang (2012) deriving an online linear discriminant analysis algorithm (which exploits formulae for the Moore-Penrose inverse of modified matrices), and White et al (2014) elaborating a method for computing the initial post-buckling response of variable-stiffness cylindrical panels (even though the least squares method was not explicitly mentioned in the paper, we conclude it was exploited from remarks on pp. 141 and 143 stating that the systems of equations solved were overdetermined).…”