Imaging with Local Speckle Intensity Correlations: Theory and Practice

Abstract

Recent advances in computational imaging have significantly expanded our ability to image through scattering layers such as biological tissues by exploiting the auto-correlation properties of captured speckle intensity patterns. However, most experimental demonstrations of this capability focus on the far-field imaging setting, where obscured light sources are very far from the scattering layer. By contrast, medical imaging applications such as fluorescent imaging operate in the near-field imaging setting, where sources are inside the scattering layer. We provide a theoretical and experimental study of the similarities and differences between the two settings, highlighting the increased challenges posed by the near-field setting. We then draw insights from this analysis to develop a new algorithm for imaging through scattering that is tailored to the near-field setting by taking advantage of unique properties of speckle patterns formed under this setting, such as their local support. We present a theoretical analysis of the advantages of our algorithm and perform real experiments in both far-field and near-field configurations, showing an order-of magnitude expansion in both the range and the density of the obscured patterns that can be recovered.

Enhancing Speckle Statistics for Imaging inside Scattering Media

“…In realistic biomedical imaging applications one is usually interested in detecting fluorescent illumination sources located inside the tissue rather than far beyond it. As analyzed in [11], and the correlation between S i 1 , S i 2 only holds for very small displacements ∆ = i 2 − i 1 . In Fig.…”

“…18 translating interferometry modulations are superior over 54 random modulations. No modulation [11] u We note that the translating interferometry measurements used here are similar to those used in shearing interferometry [23]. However shearing interferometry usually uses smaller displacements to obtain the local gradient of the wave, while the displacements we use here are larger than the speckle grain size so that we obtain independent speckles.…”

“…For example, while in realistic biomedical imaging scenarios fluorescent sources of interest are located inside the scattering sample rather than far behind it, many earlier demonstrations of speckle correlation based see-through algorithms considered sources located a few centimeters beyond the sample rather than inside it. This is due to the fact that speckle correlations have been shown [11] to be stronger when the sources are further than the scattering layer, and hence they span a smaller range of angles relative to the sample. Also, the contrast of the observed speckle pattern decays as more independent emitters are present, and hence, mostly simple and sparse emitter layouts were recovered.…”

“…To further maximize the amount of information we can extract from speckle data, we follow an idea recently proposed by [11], which argue that when light sources are located inside the sample rather than far behind it, the speckles from each source have a limited support and do not spread over the full sensor. Thus, rather than computing a global auto-correlation, they compute local auto-correlations in the form of a Ptychogra- phy algorithm [12][13][14][15][16].…”

“…Thus, rather than computing a global auto-correlation, they compute local auto-correlations in the form of a Ptychogra- phy algorithm [12][13][14][15][16]. As shown in [11] these local correlations can boost the signal to noise ratio of the detect correlation by a few orders of magnitude.…”