Daniel Vazquez, Eva Acosta, George Smith, and Leon Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. A 23, 2551-2565 (2006)
In the first part of this paper we presented a tomographic method to reconstruct the refractive index profile of spherically symmetrical lenses. Here we perform the generalization to lenses that are rotationally symmetrical around the optical axis, as is the ideal human lens. Analysis of the accuracy and versatility of this method is carried out by performing numerical simulations in which different magnitudes of experimental errors and two extreme case scenarios for the likely shape of the refractive index distribution of the human lens are considered. Finally, experimental results for a porcine lens are shown. Conceptually simple and computationally swift, this method could prove to be a valuable tool for the accurate retrieval of the gradient index of a broad spectrum of rotationally symmetrical crystalline lenses.
Alberto de Castro, Judith Birkenfeld, Bianca Maceo Heilman, Marco Ruggeri, Esdras Arrieta, Jean-Marie Parel, Fabrice Manns, and Susana Marcos Biomed. Opt. Express 10(7) 3622-3634 (2019)
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Peak–valley difference between the retrieved and theoretical gradient indices.
Rms of the difference between the original optical path distributions and those obtained by propagating rays through the retrieved gradient index.
Table 3
Accuracy of the Monopolynominal and Bipolynomial Retrievals of the Porcine Lens Gradient Index
and are the rms and peak–valley values of the difference between the reproduced and experimental exit angle sine distributions in all rows. is the rms value of the difference between the reproduced and experimental optical path distributions in all rows.
Table 4
Retrieved Coefficients , Eccentricities, and of the Monopolynomial and Bipolynomial Refractive Index Distributions of the Porcine Lens
Retrieved Gradient Parameters
Monopolynomial Gradient
Bipolynomial Gradient
Anterior
Posterior
1.366
1.278
1.361
0.0382
0.0766
0.0394
0.569
0.780
0.484
Tables (4)
Table 1
Coefficients of the Weak (Monopolynomial) and Strong (Bipolynomial) Gradients for Fourth-Order Polynomials
Gradient Coefficients
Weak Gradient
Strong Gradient
Anterior
Posterior
1.386
1.371
1.4171
Table 2
Results of the Tomographic Retrieval for the Weak and Strong Gradients When Using Data from 0°, 20°, and 40° Projections
Peak–valley difference between the retrieved and theoretical gradient indices.
Rms of the difference between the original optical path distributions and those obtained by propagating rays through the retrieved gradient index.
Table 3
Accuracy of the Monopolynominal and Bipolynomial Retrievals of the Porcine Lens Gradient Index
and are the rms and peak–valley values of the difference between the reproduced and experimental exit angle sine distributions in all rows. is the rms value of the difference between the reproduced and experimental optical path distributions in all rows.
Table 4
Retrieved Coefficients , Eccentricities, and of the Monopolynomial and Bipolynomial Refractive Index Distributions of the Porcine Lens