Abstract
Purpose :
A Shack-Hartmann wavefront sensor has been widely used to characterize ocular optics. Despite its popularity, it offers a limited lateral resolution imposed by the lenslet size. To overcome the limitation, we propose a phase retrieval technique based on the Transport of Intensity Equation (TIE) that extracts phase information by analyzing spatial intensity variation along the light propagation. The goal of this study is to demonstrate the feasibility of quantifying ocular aberration at a high spatial resolution.
Methods :
The experiment was performed using a phase plate fabricated with known aberrations for aperture of 3 mm diameter. A 4-F system was used to create two pupil conjugate planes. We placed the phase in the first pupil conjugate and recorded the intensity of the sample at two separate image planes including the second pupil conjugate using a collimated 635 nm laser beam. The sample's phase profile was estimated directly from the intensity images by solving TIE, a two-dimensional Poisson equation revealing relationship between intensity derivative and phase. A fast Fourier transform-based computational approach was utilized to solve TIE under uniform light distribution, circular aperture, and noise conditions to mimic the ocular optics.
Results :
We first verified the TIE solver algorithm through simulation for a test wavefront created using Zernike coefficients (up to 4th order) with mean square deviation of 0.44 µm. The intensity was assumed uniform with added white noise. Two intensity images collected at the pupil conjugate and 1 mm away from it were numerically modeled by applying Fresnel propagation. From these images, the wavefront was retrieved with a mean square error (MSE) of 0.003 µm. In the experiment conducted with the 4-F system, intensity distributions of the phase sample were recorded using a CCD camera with a pixel pitch 5.5 µm. From the pair of intensity images with 600×600 pixels, the phase distribution was reconstructed using the TIE and MSE was 0.24 µm.
Conclusions :
Our results demonstrated the feasibility of estimating phase profiles from light field propagation using TIE. TIE directly retrieves light phase at each camera pixel and a significantly higher sampling resolution than a Shack-Hartmann sensor can be achieved. However, for the real eye application, further optimizing TIE solver algorithm will be needed to take intraocular light scatter and non-uniform intensity distribution.
This abstract was presented at the 2023 ARVO Annual Meeting, held in New Orleans, LA, April 23-27, 2023.