Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.

The interference of four noncoplanar beams (IFNB) is analyzed. It is shown that all 14 Bravais lattices can be formed by a holographic method of IFNB. The relationship among the three basis vectors of the lattice that are to be produced, the required wavelength, and the geometric arrangement of the four beams is derived. This analysis may lay the foundation for fabrication of three-dimensional photonic crystals by holographic lithography.

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N > or = 3) and for both smooth and diffusing objects, as is verified by a series of computer simulations.

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.

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