An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing a polarizing phase-shifting cyclic shear interferometer coupled to a 4-f Fourier imaging system with crossed high-frequency Ronchi gratings. This system can obtain nine interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, it is only analyzed using four patterns obtained in a single shot, and applying the classical method of phase extraction.

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In this study, an optical system capable of simultaneously grabbing three phase-shifted interferometric images was developed for dynamic temperature field measurements of a thin flame. The polarization phaseshifting technique and a Michelson interferometer that is coupled to a 4-f system with a Ronchi grating placed at the frequency plane are used. This configuration permits the phase-shifted interferograms to be grabbed simultaneously by one CCD. The temperature field measurement is based on measuring the refraction index difference by solving the inverse Abel transform, which requires information obtained by the fringe order localization. The phase map is retrieved by a three-step algorithm. Experimental results of a dynamic thin flame are presented.

In order to recover the holographic object information, a method based on the recording of two digital holograms, not only at different planes but also in a slightly off-axis scheme, is presented. By introducing a -phase shift in the reference wave, the zero-order diffracted term and the twin image are removed in the frequency domain during the processing of the recorded holograms. We show that the zero-order elimination by the phase-shifted holograms is better than working with weak-order beam and average intensity removal methods. For recording experimentally two-shifted holograms at different planes slightly off-axis, a single cube beam splitter is used. Computer simulations and experimental results, carried out to validate our proposal, show a high accuracy of /14 that can be comparable with phase-shifting digital holography. For high fringe spacing, our proposal could be applied in electron holography, avoiding high voltage in a biprism.

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