With applications from photonics to seismology, wave scattering is ubiquitous in physics. Yet, to study scattering in highly heterogeneous materials, evidence must be obtained from theoretical approximations and surface measurements. Numerical approaches can offer an insight into the wave behavior deep within a complex structure; however, the large scale, with respect to the short wavelength of light, of most systems of interest makes photonic simulations some of the most challenging numerical problems. Memory and time constraints typically limit coherent light scattering calculations to the micrometer scale in 2D and to the nanoscale in 3D. The study of large photonic structures, or scattering in biological samples larger than a few cells, remains out of reach of conventional computational methods. Here, we highlight a connection between the wave equation that governs light-scattering and the structure of a recurrent network. A one-to-one correspondence enables us to leverage efficient machine learning infrastructure and address coherent scattering problems on an unprecedented scale.
Its subcellular resolution and minimal sample exposure make light-sheet microscopy the ideal tool to study biological specimen during their early development. A light-sheet microscope scans the sample with a plane of light and collects fluorescence with an objective orthogonal to the illumination. However, tightly focused Gaussian light-sheets suffer from a shallow depth of focus and are susceptible to scattering-induced aberrations. Light-sheets created by non-diffractive Airy beams can overcome this to yield isotropic sub-cellular resolution over a ten-fold larger field-of-view. Airy beam light-sheets have a characteristically curved structure and a broad transverse structure with side-lobes. Digital deconvolution of the raw data is thus essential to obtain high-fidelity images. Provided that the scan is along the direction of the detection axis, and all recorded data fits within working memory, a simple and efficient Wiener filter can recover accurate 3D images. However, multi-millimeter sized samples must be scanned with a light-sheet that is diagonal to the sample surface. The diagonal movement prevents the use of standard Wiener filtering. Moreover, the associated data sets can become too large to fit within the working memory of a consumer-grade GPU. This demands slow off-line processing, thus breaking a rapid experimental feedback-loop. Here, we investigate the potential of on-the-fly deconvolution of diagonally-scanned Airy light-sheet microscopy.
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