Lensless imaging through thin scattering layers under broadband illumination

Lensless scattering imaging is a prospective approach to microscopy in which a high-resolution image of an object is reconstructed from one or more measured speckle patterns, thus providing a solution in situations where the use of imaging optics is not possible. However, current lensless scattering imaging methods are typically limited by the need for a light source with a narrowband spectrum. Here, we propose two general approaches that enable single-shot lensless scattering imaging under broadband illumination in both noninvasive [without point spread function(PSF) calibration] and invasive(with PSF calibration) modes. The first noninvasive approach is based on a numerical refinement of the broadband pattern in the cepstrum incorporated with a modified phase retrieval strategy. The latter invasive approach is correlation inspired and generalized within a computational optimization framework. Both approaches are experimentally verified using visible radiation with a full-width-at-half-maximum bandwidth as wide as 280 nm(Δλ∕λ = 44.8%) and a speckle contrast ratio as low as 0.0823. Because of its generality and ease of implementation, we expect this method to find widespread applications in ultrafast science,passive sensing, and biomedical applications.