Crystalline lens gradient refractive index and posterior surface shape from multiple orientations OCT imaging: towards a reconstruction in vivo?

Abstract

Purpose: The gradient index (GRIN) plays a key role in the crystalline lens optical properties, yet most current estimations are in vitro. We provide computational and experimental evidence to extend a method previously applied in vitro and reconstruct both the GRIN and posterior lens surface using optical coherence tomography (OCT) images obtained from multiple projections.

Methods: Optical path difference (OPD) between anterior and posterior surface of a simulated 4-variable (nucleus/surface refractive indices nN/nS; axial/meridional decay pa/pm) GRIN lens were calculated for different angles of the entry rays (0 and 30 deg in air). Gaussian error (σ=10 μm) was added to the data to simulate experimental error. A global search algorithm was used to search the GRIN variables and the posterior surface shape that best matched the OPD data. The reconstruction error using different projections was compared. As a demonstration, four in vitro cynomolgus monkey lenses were imaged using the probe of a commercial OCT system (ENVISU R4400, Bioptigen, Inc.) mounted on a rotational stage at different angles from -45 to 45 deg (5-deg steps). The anterior surface was used for registration purposes. The OPD of the rays passing through the lens was used to reconstruct the GRIN variables and the posterior surface shape, as described. The lens was flipped up and imaged for a direct measurement of the posterior lens surface.

Results: While on axis OCT images alone provided a poor reconstruction of the GRIN variables and the posterior surface shape, using input data from multiple angles (0 and 30 deg) allowed high accuracy in the estimated parameters on the simulations: mean errors of 0.007 and 0.004 for nS and nN, and near 1 for axial and meridional exponential decay; and 0.3 mm and 0.1 for posterior surface shape R and Q, respectively. Mean GRIN estimates from experimental data in the monkey lenses were: nS =1.371; nN =1.422; pa =5.4; pm =7.7. The experimental accuracy in the estimation of the posterior surface shape was 0.55 mm for R and 1.0 for Q.

Conclusions: Simultaneous reconstruction of lens GRIN and the posterior surface shape is possible from multiple projection OCT imaging, suggesting that in vivo GRIN reconstruction may be possible using optimization methods.

Keywords: 630 optical properties • 421 anterior segment • 552 imaging methods (CT, FA, ICG, MRI, OCT, RTA, SLO, ultrasound)