Fourier imaging with a single-pixel correlation

Abstract

Fourier spectrum plays a crucial role in many applications such as optical microscopy, Fourier telescopy, quantitative phase imaging, etc. The Fourier spectrum, in general, a complex quantity, comprises the amplitude and phase part of the signal. However, direct measurement of the phase or argument of the Fourier signal is not possible. Interferometry and phase retrieval (PR) techniques are commonly used methods to quantitatively acquire the complex Fourier spectrum. Moreover, the presence of random scattering and turbulence in the propagation channel further complicates the situation and direct recovery of the complex Fourier spectrum becomes a difficult task. In this paper, we present a new technique to acquire the complex Fourier spectrum from a single-pixel analysis of the second-order intensity correlation and present some initial experimental results. This technique is free from the interferometry and PR approach. Here we apply active structured illumination to acquire the complex information in the spatial frequency space and use spatial averaging rather than temporal averaging. Information retrieval in the spatial frequency domain, rather than in the space domain, is found to be useful in conditions such as diffraction-limited imaging through severe scattering and atmospheric turbulence. We believe that our method may find applications in Fourier microscopy and telescopy. © 2025 SPIE.