Theory of diffraction effects in spatial frequency-modulated imaging

An analytic theory describing the effects of diffraction and aberrations on single-pixel imaging performed by temporally modulating illumination light is presented. This method encodes spatial information using sinusoidal temporal modulations that are chirped in frequency across the extent of an illumination line focus. With some approximations, a point spread function relationship as a function of defocus or other aberrations is found for both spatially coherent and incoherent cases. The theory is validated through experiments and simulations, including measurement of the transverse and longitudinal optical transfer function, and confirmation of insensitivity to aberrations and significant optical scattering after encoding of spatial information through temporal modulation.