Noninvasive wavelength estimation through scattering media using recovered point-spread functions

Recovering color objects concealed behind scattering media remains a major challenge due to wavelength-dependent decorrelation of speckle patterns and the requirement for invasive calibration in conventional methods. We propose a noninvasive technique for estimating the central wavelength of a speckle image by recovering point-spread functions (PSFs) from speckle-correlation imaging (SCI) and analyzing their spectral cross-correlation characteristics. A lensless optical system consisting of a monochrome camera and a broadband LED source is used to acquire speckle images filtered by a liquid-crystal tunable filter. SCI reconstructs the object image through hybrid input–output and error-reduction phase-retrieval algorithms, and the corresponding PSF is recovered using Lucy–Richardson deconvolution. The central wavelength of an unknown speckle image is estimated from the fitted peak of the cross-correlation between its recovered PSF and reference recovered PSFs. Experiments demonstrate 1-nm-level wavelength discrimination without direct PSF measurement.