Perturbation correction for refraction in interferometric tomography

Reconstruction of an axisymmetric refractive index distribution with non-negligible refraction

“…It is seen that, contrary to Vest's assertion [9], the error is minimjzed by focusing slightly in front of the test section rather than at its centre. This fact has been noted before (see [l] and [14]), although in the former reference it was attributed to a computational artifact. Figure 3 shows the results of straight-line Abel inversion with L = 0 (chain curve)…”

“…It is concluded that, provided the observation plane's position is accurately known, there is no advantage in ignoring refraction: the reconstruction formula, equation (14), is easily programmed and, for smoothly varying distributions, it yields excellent results.…”

“…The earliest references to these equations appears to be as follows: reference [4] for equation (12), [9] for equation ( 13) and [51 and 181 for equation (14). @ = A@ +2,/qip 2p tan@+noL(l -sec@) ( 15) and y = ys cos $ -L sin @.…”

“…For both cases angle q 6 was obtained as a function of ys from equation (17) using the plus sign. This angular distribution was reassigned to the y coordinates using equation ( 16) and then submitted tc the reconstruction algorithm, equation (14).…”

<title>Tomographic reconstruction of strongly refracting fields and identification of light rays simultaneously</title>

“…To solve the Eikonal equation (2) ( or (1) ), the method of characteristics'0 is used to reduce the nonlinear Eikonal equation to the following system of linear differential equations dx p 3 ds n dy q (4 ds n dz r ds n dS (6) dp an (7) ds ax dq an (8) ds ay dr an 9 ds az ____________________ where x , y , z are the ray path coordinates, ds =s[ix)2 + (dy)2 + (dz)2 . Therefore, we can obtain the digitized form of ray tracing formulae: where j and j+1 enumerate successive increments along the ray path, and As is the numerical integration step size.…”