We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.

/pdf/complex-wave-retrieval-from-a-single-off-axis-hologram-4xkjxab0oj.pdf

Complex-wave retrieval from a single off-axis hologram.

Many optical measurement techniques provide fringe patterns as their results. The decodification processes that employ one or several fringe patterns to automatically retrieve the phase are generally designated as phase-evaluation methods. In this work, an overview of these methods will be schematically presented. Their particular performances will be compared, stressing their main advantages and drawbacks. An important group of these methods employs the well-known phase-shifting algorithms as a tool for calculating the phase. In the general form of these algorithms, the principal value of the optical phase is computed by an inverse trigonometric function whose argument is a combination of phase-shifted intensity values, provided by the modulation of one or several fringe patterns. These algorithms will be also studied in the general context of the phase-evaluation methods.

https://iopscience.iop.org/article/10.1088/0957-0233/10/3/005/pdf

Phase-evaluation methods in whole-field optical measurement techniques

Interferogram Analysis For Optical Testing, Second Edition

Fringe analysis: Premise and perspectives

Wavelength-scanning interferometry permits the simultaneous measurement of variations in surface shape and optical thickness of a nearly parallel plate. Interference signals from both surfaces of the test plate can be separated in frequency space; however, these frequencies are shifted from the expected frequency by the refractive-index dispersion of the test plate and any nonlinearity that is due to wavelength scanning. Conventional Fourier analysis is sensitive to this detuning of the signal frequency and suffers from multiple-beam interference noise. We propose new wavelength-scanning algorithms that permit a large tolerance for dispersion of the test plate and nonlinearity of scanning. Two 19-sample algorithms that suppress multiple-interference noise up to the second order of the reflectance of the test plate are presented. Experimental results show that the variation in surface shape and optical thickness of a glass parallel plate of 250-mm diameter was measured with a resolution of 1–2 nm rms.

Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer

In phase-shifting interferometry spatial nonuniformity of the phase shift gives a significant error in the evaluated phase when the phase shift is nonlinear. However, current error-compensating algorithms can counteract the spatial nonuniformity only in linear miscalibrations of the phase shift. We describe an error-expansion method to construct phase-shifting algorithms that can compensate for nonlinear and spatially nonuniform phase shifts. The condition for eliminating the effect of nonlinear and spatially nonuniform phase shifts is given as a set of linear equations of the sampling amplitudes. As examples, three new algorithms (six-sample, eight-sample, and nine-sample algorithms) are given to show the method of compensation for a quadratic and spatially nonuniform phase shift.

http://nontrivialzeros.net/KGL_Papers/26_Hibino_Phase_Nonlinear_JOSAA_1997.pdf

Kenichi Hibino

Papers

Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts