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A new hybrid diffractive optical element (HDOE) was designed by randomly multiplexing an axicon and a Fresnel zone lens. The HDOE generates two mutually coherent waves, namely a conical wave and a spherical wave, for every on-axis point object in the object space. The resulting self-interference intensity distribution is recorded as the point spread function. A library of point spread functions are recorded in terms of the different locations and wavelengths of the on-axis point objects in the object space. A complicated object illuminated by a spatially incoherent multi-wavelength source generated an intensity pattern that was the sum of the shifted and scaled point spread intensity distributions corresponding to every spatially incoherent point and wavelength in the complicated object. The four-dimensional image of the object was reconstructed using computer processing of the object intensity distribution and the point spread function library.

Randomly Multiplexed Diffractive Lens and Axicon for Spatial and Spectral Imaging