Optimal spatial bandwidth capacity in multiplexed off-axis holography for rapid quantitative phase reconstruction and visualization

We present new methods for optimizing the spatial bandwidth capacity in off-axis holography using spatial multiplexing. We use optimal spatial multiplexing of off-axis holograms to fill the entire spatial frequency domain, including the space previously occupied by the intensity of the sample. Our approach enables spatial digital compression of eight offaxis holograms into a single real-valued multiplexed hologram, having the same number of pixels as each of the input holograms, but still allowing their full reconstruction without resolution or magnification loss in the reconstructed complex wave fronts. This new method allows 33% improvement in usage of the spatial bandwidth capacity compared to the best available off-axis holography real-value multiplexing method. Since the output multiplexed hologram contains only real values, it can be used for rapid display of eight wave front reconstructions at once, which is useful for real-time visualization, when the hologram display device is slower than the acquiring camera. We further generalize this technique to digital multiplexing of 16 real-valued holograms into a single complex-valued hologram by simple arithmetic operations in the hologram domain. Then, the extraction of the 16 wave fronts includes a single 2-D discrete Fourier transform to access the spatial frequency domain, allowing fast reconstruction, which is useful for real-time processing of off-axis holograms, with improved processing rate compared to current hologram processing algorithms. These new approaches allow the full reconstruction of all compressed data without loss of resolution or magnification, even though the samples are dense such that their frequency content employs the entire range. 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