A method for three-dimensional 3-D optical distortion (refraction) correction on anterior segment Optical Coherence Tomography (OCT) images has been developed. The method consists of 3-D ray tracing through the different surfaces, following denoising, segmentation of the surfaces, Delaunay representation of the surfaces, and application of fan distortion correction. The correction has been applied theoretically to realistic computer eye models, and experimentally to OCT images of: an artificial eye with a Polymethyl Methacrylate (PMMA) cornea and an intraocular lens (IOL), an enucleated porcine eye, and a human eye in vivo obtained from two OCT laboratory set-ups (time domain and spectral). Data are analyzed in terms of surface radii of curvature and asphericity. Comparisons are established between the reference values for the surfaces (nominal values in the computer model; non-contact profilometric measurements for the artificial eye; Scheimpflug imaging for the real eyes in vivo and vitro). The results from the OCT data were analyzed following the conventional approach of dividing the optical path by the refractive index, after application of 2-D optical correction, and 3-D optical correction (in all cases after fan distortion correction). The application of 3-D optical distortion correction increased significantly both the accuracy of the radius of curvature estimates and particularly asphericity of the surfaces, with respect to conventional methods of OCT image analysis. We found that the discrepancies of the radii of curvature estimates from 3-D optical distortion corrected OCT images are less than 1% with respect to nominal values. Optical distortion correction in 3-D is critical for quantitative analysis of OCT anterior segment imaging, and allows accurate topography of the internal surfaces of the eye.

We present an optimization method to retrieve the gradient index (GRIN) distribution of the in-vitro crystalline lens from optical path difference data extracted from OCT images. Three-dimensional OCT images of the crystalline lens are obtained in two orientations (with the anterior surface up and posterior surface up), allowing to obtain the lens geometry. The GRIN reconstruction method is based on a genetic algorithm that searches for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens. Computer simulations showed that, for noise of 5 μm in the surface elevations, the GRIN is recovered with an accuracy of 0.003 and 0.010 in the refractive indices of the nucleus and surface of the lens, respectively. The method was applied to retrieve three-dimensionally the GRIN of a porcine crystalline lens in vitro. We found a refractive index ranging from 1.362 in the surface to 1.443 in the nucleus of the lens, an axial exponential decay of the GRIN profile of 2.62 and a meridional exponential decay ranging from 3.56 to 5.18. The effect of GRIN on the aberrations of the lens also studied. The estimated spherical aberration of the measured porcine lens was 2.87 μm assuming a homogenous equivalent refractive index, and the presence of GRIN shifted the spherical aberration toward negative values (-0.97 μm), for a 6-mm pupil.

We address the measurement and correction of fan distortion in optical coherence tomography (OCT). This effect arises from the scanning system configuration and prevents one, in general, from obtaining quantitative topographic data from OCT. Computer simulations allowed us to quantify the effect and evaluate its dependence on the scanning mirror separation and design of the collimating lens, as well as to estimate the optimal axial position of that lens to minimize the fan distortion. We also developed a numerical algorithm based on 3-D ray propagation for the correction of the residual fan distortion. The effect was studied experimentally using a custom developed time-domain OCT in a Michelson configuration provided with a confocal channel, and the accuracy of the fan distortion correction algorithm tested on samples of known dimensions (flat surfaces and spherical lenses). With a proper calibration of the system with use of an onfocal channel, this algorithm makes it possible for time-domain OCT devices to be used as topographers.