Tomographic reconstruction of the cross‐sectional refractive index distribution in semi‐transparent, birefringent fibres

Abstract

Summary Optical diffraction tomography (ODT) is used to reconstruct the complex refractive index distribution in cross‐sections of semi‐transparent, birefringent fibres. The selected fibres were polymer and animal fibres of either circular or non‐circular cross‐section with average thicknesses in the range 8–110 μm. This choice of samples was made to illustrate the imaging capabilities of ODT, and also to demonstrate some potential applications of the technique. The images representing the reconstructed refractive index distributions have a spatial resolution of about 2 μm, and show noticeable image contrast for refractive index variations of about 0·001. The ODT reconstructions compare well with refractive index information provided with the samples, and with scanning electron micrographs of cross‐sections of the same fibre samples. From these results it appears that ODT can be used to reconstruct the complex refractive index distribution in cross‐sections of semi‐transparent, birefringent fibres.

Tomographic diffractive microscopy: Towards high-resolution 3-D real-time data acquisition, image reconstruction and display of unlabeled samples

“…Published work on TDM [17][18][19]27,[41][42][43][44]53,54,[86][87][88][89][90][91] have clearly demonstrated the usefulness of accessing the index of refraction distribution at microscopic scale, for biological research as well as work on artificial samples. But note that absorption is often not discussed, while it has been shown that refraction and absorption indeed provides complementary information [25,26,32,37,38,[45][46][47]. This dual imaging capability should be further investigated, as absorption measurements may probably also contribute to diagnostic tools.…”

“…Note that the index of refraction is a complex quantity, related to the refraction and to the absorption. This dual imaging capability has not yet found applications for biological studies, but could used to distinguish organelles from their refraction/absorption properties [14,25,26,32,37,38,46,47], and not from their refraction only, as usually performed. shows a Betula pendula pollen grain, attached to a photopolymer tip for manipulation, displaying refraction and absorption images.…”

Comparison of reconstruction algorithms for optical diffraction tomography

“…We will employ the standard ODT experimental configuration [1][2][3][4] where a semitransparent object is mounted in such a way that it can achieve varying orientations relative to the direction of propagation of an illuminating plane wave as illustrated in Fig. 1.…”

“…In optical diffraction tomography (ODT) a semitransparent object is interrogated in a set of scattering experiments employing coherent incident waves, and the amplitude and phase of the resulting scattered optical waves are recorded and used to reconstruct the internal complex index-of-refraction distribution of the object. [1][2][3][4] The standard reconstruction algorithms employed in ODT are based on the well-known Born or Rytov approximation 5,6 and require that the object being studied be embedded in a uniform constant-index-of-refraction background medium whose (constant) index of refraction is closely matched to that of the object. In addition, these algorithms are usually based on the so-called generalized projection-slice theorem 5,7 of diffraction tomography (DT), which requires that the experiments employ a large set of incident plane waves whose directions of incidence are closely packed over the unit sphere.…”

<title>Diffraction effects in laser-computed tomography and time-resolved imaging in random media</title>

“…9, we can find the diffracted field in a similar manner as in section 4.1. To that end we first consider the field from the complementary slit, which according to the Kirchhoff diffraction theory is given by ': (10) where the amplitude function g(x) and the phase function 1(x) are given by 9(x)=v/;;:LsR (11) f(x)= R5+Rd-, (12) with Rd and R5 being the distances between the integration point Q(x, 0) and the observation point P(xd, Zd) and the source point S(0, -z), respectively (Fig. 9), i.e.…”