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1. Determination of size and complex index of refraction of single particles with elastic light scattering

   https://doi.org/10.1364/AO.413675  

   Waez, Mir_Seliman; Eckels, Steven_J; Sorensen, Christopher_M (January 2021, Applied Optics)

   We show that for spherical particles greater than ca. 5 µm, the differential scattering cross section is only weakly dependent on the real and imaginary parts of the refractive index ( $m=n+i\mathrm{\kappa <\#comment/>}$) when integrated over angle ranges near $37\pm <\#comment/>5^{\circ <\#comment/>}$and $115\pm <\#comment/>5^{\circ <\#comment/>}$, respectively. With this knowledge, we set up an arrangement that collects scattered light in the ranges $37\pm <\#comment/>5^{\circ <\#comment/>}$, $115\pm <\#comment/>5^{\circ <\#comment/>}$, and $80\pm <\#comment/>5^{\circ <\#comment/>}$. The weak functionality on refractive index for the first two angle ranges simplifies the inversion of scattering to the particle properties of diameter and the real and imaginary refractive indices. Our setup also uses a diamond-shaped incident beam profile that allows us to determine when a particle went through the exact center of the beam. Application of our setup to droplets of an absorbing liquid successfully determined the diameter and complex refractive index to accuracies ranging from a few to ten percent. Comparisons to simulated data derived from the Mie equations yielded similar results. 

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2. Universal parameter to describe the reduction of refraction effects in the scattering of absorbing spheres

   https://doi.org/10.1364/JOSAA.394401  

   Maughan, Justin_B; Sorensen, Christopher_M (August 2020, Journal of the Optical Society of America A)

   The scattered intensity from large spheres with a real part of the refractive index of $n=1.33,1.5,2.0$is investigated as the radius $R$and an imaginary part of the refractive index $\mathrm{\kappa <\#comment/>}$are varied. It is shown that the product of $\mathrm{\kappa <\#comment/>}$and the size parameter $kR$, $\mathrm{\kappa <\#comment/>}\text{kR}$, is a universal parameter describing the quenching of the refraction phenomenon of the scattered light: the refraction hump, the generalized rainbows, and the glory. The physical reason for this is that $\mathrm{\kappa <\#comment/>}\text{kR}$is the inverse of the relative skin depth of light penetration into the sphere, which is demonstrated by calculations of the internal fields that darken universally as $\mathrm{\kappa <\#comment/>}\text{kR}$increases. 

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3. Refractive index dispersion measurement in the short-wave infrared range using synthetic phase microscopy

   https://doi.org/10.1039/d3cp03158f  

   Nyakuchena, Melisa; Juntunen, Cory; Shea, Peter; Sung, Yongjin (August 2023, Physical Chemistry Chemical Physics)

   Refractive index is an optical property explored in the light scattering measurement of micro- and nano-particles as well as in label-free imaging of cells and tissues. Because the refractive index value is a major input to the characterization and quantification of the analyzed specimens, various methods have been developed targeting at different sample types. In this paper, we demonstrate a technique for the refractive index measurement of homogeneous microspheres and liquids in the short-wave infrared (SWIR) range. We use synthetic phase microscopy (SPM), which records a scattering-corrected projection of the 3D refractive index distribution, in combination with a least-squares fitting to a theoretical model of a sphere. Using the method, we determine the refractive index dispersion of two polymer microspheres (polymethyl methacrylate and polystyrene), two glass microspheres (silica and soda lime), and three microscopy mounting media (glycerol, FluorSave, and Eukitt) in the SWIR range of 1100–1650 nm. 

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4. Quantitative 3D refractive index tomography of opaque samples in epi-mode

   https://doi.org/10.1364/OPTICA.410135  

   Ledwig, Patrick; Robles, Francisco_E (December 2020, Optica)

   Three-dimensional (3D) refractive index (RI) tomography has recently become an exciting new tool for biological studies. However, its limitation to (1) thin samples resulting from a need of transmissive illumination and (2) small fields of view (typically $\sim <\#comment/>50\text{µ<\#comment/>}\mathrm{m}\times <\#comment/>50\text{µ<\#comment/>}\mathrm{m}$) has hindered its utility in broader biomedical applications. In this work, we demonstrate 3D RI tomography with a large field of view in opaque, arbitrarily thick scattering samples (unsuitable for imaging with conventional transmissive tomographic techniques) with a penetration depth of ca. one mean free scattering path length ( $\sim <\#comment/>100\text{µ<\#comment/>}\mathrm{m}$in tissue) using a simple, low-cost microscope system with epi-illumination. This approach leverages a solution to the inverse scattering problem via the general non-paraxial 3D optical transfer function of our quantitative oblique back-illumination microscopy (qOBM) optical system. A theoretical analysis is presented along with simulations and experimental validations using polystyrene beads, and rat and human thick brain tissues. This work has significant implications for the investigation of optically thick, semi-infinite samples in a non-invasive and label-free manner. This unique 3D qOBM approach can extend the utility of 3D RI tomography for translational and clinical medicine. 

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5. Single-molecule orientation localization microscopy for resolving structural heterogeneities between amyloid fibrils

   https://doi.org/10.1364/OPTICA.388157  

   Ding, Tianben; Wu, Tingting; Mazidi, Hesam; Zhang, Oumeng; Lew, Matthew_D (June 2020, Optica)

   Simultaneous measurements of single-molecule positions and orientations provide critical insight into a variety of biological and chemical processes. Various engineered point spread functions (PSFs) have been introduced for measuring the orientation and rotational diffusion of dipole-like emitters, but the widely used Cramér-Rao bound (CRB) only evaluates performance for one specific orientation at a time. Here, we report a performance metric, termed variance upper bound (VUB), that yields a global maximum CRB for all possible molecular orientations, thereby enabling the measurement performance of any PSF to be computed efficiently ( $\sim <\#comment/>1000\times <\#comment/>$faster than calculating average CRB). Our VUB reveals that the simple polarized standard PSF provides robust and precise orientation measurements if emitters are near a refractive index interface. Using this PSF, we measure the orientations and positions of Nile red (NR) molecules transiently bound to amyloid aggregates. Our super-resolved images reveal the main binding mode of NR on amyloid fiber surfaces, as well as structural heterogeneities along amyloid fibrillar networks, that cannot be resolved by single-molecule localization alone. 

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