Incoherently illuminated or luminescent objects give rise to a low-contrast speckle-like pattern when observed through a thin diffusive medium, as such a medium effectively convolves their shape with a speckle-like point spread function (PSF). This point spread function can be extracted in the presence of a reference object of known shape. Here it is shown that reference objects that are both spatially and spectrally separated from the object of interest can be used to obtain an approximation of the point spread function. The crucial observation, corroborated by analytical calculations, is that the spectrally shifted point spread function is strongly correlated to a spatially scaled one. With the approximate point spread function thus obtained, the speckle-like pattern is deconvolved to produce a clear and sharp image of the object on a speckle-like background of low intensity.

A wavelength-depth-matching method based on speckle correlation is proposed to achieve an ultra-large depth of field (DOF) of 90.5 mm experimentally on one side in imaging through a thin scattering layer. By making rational use of chromatic aberrations to compensate for the effects of depth differences, we determine the depth information of a target object using a incoherent wavelength-tunable light source. A random matrix that satisfies the distribution with a root mean square of 1 μm and a correlation length of 100 μm is generated to simulate the varying heights of the scattering surfaces which is used to demonstrate that larger DOF can be attained theoretically. This method, with its improved depth detection capability and ultra-large DOF, makes 3D dynamic imaging through scattering media possible.

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