Based on the quotient of inner products, a simple and rapid algorithm is proposed to retrieve the measured phase from two-frame phase-shifting interferograms with unknown phase shifts. Firstly, we filtered the background of interferograms by a Gaussian high-pass filter. Secondly, we calculated the inner products of the background-filtered interferograms. Thirdly, we extracted the phase shifts by the quotient of the inner products then calculated the measured phase by an arctangent function. Finally, we tested the performance of the proposed algorithm by the simulation calculation and the experimental research for a vortex phase plate. Both the simulation calculation and the experimental result showed that the phase shifts and the measured phase with high accuracy can be obtained by the proposed algorithm rapidly and conveniently.

To perform the visual measurement of the evaporation process of a sessile droplet, a dual-channel simultaneous phase-shifting interferometry (DCSPSI) method is proposed. Based on polarization components to simultaneously generate a pair of orthogonal interferograms with the phase shifts of π/2, the real-time phase of a dynamic process can be retrieved with two-step phase-shifting algorithm. Using this proposed DCSPSI system, the transient mass (TM) of the evaporation process of a sessile droplet with different initial mass were presented through measuring the real-time 3D shape of a droplet. Moreover, the mass flux density (MFD) of the evaporating droplet and its regional distribution were also calculated and analyzed. The experimental results show that the proposed DCSPSI will supply a visual, accurate, noncontact, nondestructive, global tool for the real-time multi-parameter measurement of the droplet evaporation.

Phase shifts extraction is an important research field of phase-shifting interferometry. In this paper, based on Gram-Schmidt orthonormalization of two vectors, a novel algorithm for phase shifts extraction is proposed. This algorithm can determine the phase shifts by using only two-frame phase-shifting interferograms, as well as the phase shifts among a sequence of interferograms by a loop program. To verify the performance of the proposed algorithm, we have employed this algorithm to the simulation fringe patterns and experimental interferograms to extract the phase shifts, both of the results prove that this algorithm can obtain the phase shifts with high precision rapidly. Comparing with other algorithms, it shows that the proposed algorithm is suitable for phase shifts extraction, especially in the situation of only two-frame interferograms.