Quantitative Phase Factor Retrieval from Single-Shot Off-Axis Interferograms for Object Reconstruction

In the far-field approximation, an object’s diffraction field can be expressed as its Fourier transform multiplied by a phase factor. Here, we present a simple method with which to directly retrieve this phase factor from a single-shot off-axis interference pattern. By exploiting and adjusting its unique two-dimensional quadratic form, the quadratic contribution from the object’s Fourier transform can generally be neglected, particularly for amplitude-only objects and slowly varying phase objects. The phase factor is extracted by fitting a quadratic surface to the unwrapped phase obtained via Fourier-transform-based phase retrieval. Removing this factor enables precise reconstruction through a straightforward inverse Fourier transform, without requiring iterative computations. Compared with conventional far-field diffraction setups, our approach reduces system length and allows the use of smaller CCD sensors. Experimental validation using a modified Mach–Zehnder interferometer demonstrates high reconstruction accuracy and robustness. Overall, this method provides an efficient, practical, and real-time solution for object reconstruction, with the potential to simplify and miniaturize optical setups, offering an alternative approach to standard coherent diffraction imaging techniques.