Abstract

One of the most relevant tasks in modern optics is to synthesize phase objects from amplitude objects. Currently, there are different arrangements and technologies to perform this task. This thesis proposes a versatile double-aperture common path interferometer with a liquid crystal spatial light modulator at the input of the system. The purpose of this proposal is to synthesize phase pro les from amplitude objects and perform different optical operations obtained by the superposition phenomenon.

In this thesis, for the superposition of amplitude objects, an interferometer based on the 4f Fourier optical processor is proposed. A liquid crystal spatial light modulator working in amplitude modulation is placed in the input plane. In the modulator, two windows are displayed with the amplitude objects to be superposed. In the Fourier plane, a Ronchi grid is placed with an appropriate frequency to achieve superposition of the windows displayed at the entrance. A camera is positioned on the exit plane to capture the fringe patterns generated by the system. With this arrangement, phase objects were synthesized even though the modulator does not work with this configuration type.

Analytically, it is shown that the amplitude objects displayed in the modulator in the two input interferometer’s windows are additively and multiplicatively superposed in moiré patterns. Thus, by processing the resulting moiré patterns, it is possible to recover it into the encoding phase. Also, it was found that when an object with the same phase is placed in both windows at the system input, the result will be a moiré pattern with the spatial derivate of the phase. Results are presented that execute the derivative operation manipulating the phase information from the input windows. Showing the reconstruction of the phase of these results.

Analysis of fringe patterns requires appropriate phase extraction algorithms. In this thesis, some of the most used phase shifting algorithms in the literature were studied. Results were obtained by implementing basic algorithms where it is required to know the phase shift, to more advanced algorithms where it is not necessary to know the phase shift. The results of this research were published in the paper entitled How do phase shifting algorithms work? in the indexed journal European Journal of Physics.

Keywords: Fourier optical processor, liquid crystal spatial light modulator, phase shifting, Ronchi grating, moiré patterns, spatial amplitude derivative, spatial derivative phase.

Contributions

Rigoberto Juarez-Salazar, Ceciibet Mendoza-Rodriguez, Jose E Hernandez-Beltran, and Carlos Robledo-Sanchez, “How do phase-shifting algorithms work?,” European Journal of Physics, Vol. 39(6), pp. 065302, 2018.