Single-frame double-grating interferometry with two inherent-phase-shifted interferograms

In this work we introduce a novel self-referencing, common-path, double-grating interferometry method for studying slowly varying phase samples. Two plane wave diffraction orders of the gratings, namely (0,+1) and (+1,0), with a certain phase difference, interfere with each other in a single frame. When a phase sample is applied in the middle of the impinging beam, two simultaneous inherent phase-shifted interferograms are generated on either side of the interference pattern. In one interferogram, the sample phase is added to (0,+1), while in the second one, the sample phase is added to (+1,0). Consequently, the phase of the first interferogram increases by the amount of the sample phase, while in the second interferogram, it decreases by the same amount. In the absence of a phase sample, both interferograms have uniform intensity and value, since the two interfering beams have the same phase difference in both patterns. We observe that the intensity changes in the two interferograms due to the phase sample, depending on the initial phase difference between the two interfering beams, can be equal or even complementary. By precisely controlling the separation between two diffraction gratings, we introduce a specific phase difference between the interfering orders. This allows us to extract the phase information of the sample from the resulting pair of interferograms. This setup enables us to obtain the phase of the sample without applying an additional phase shift(s) between the interfering beams. The method was applied to a thermal lens induced in a nonlinear liquid sample containing absorbent nanoparticles. The proposed method is characterized by its simplicity, accuracy, and insensitivity to vibrations, making it well-suited for analyzing dynamic samples with millimeter scales, such as nearly transparent organisms. The theory, simulations, and experimental results presented in this paper are found to be consistent. Unlike conventional methods, our approach does not necessarily require a reference interferogram. Additionally, when the absolute value of phase changes over the sample area and time is less than π, the raw phase pattern precisely matches the reconstructed phase pattern of the sample, eliminating the need for a phase-reconstructing algorithm. The phase pattern can be accurately calculated from the interferograms using an arcsine function, without the need for a fast Fourier transform. In comparison to Fourier-based methods, the phase extraction process for each frame in our approach is 60 times faster. As a result, this technique operates in real-time for |φ(x,y;t)|<π.