Zernike Wavefront Reconstruction of In Vitro Crystalline Lenses From Laser Ray Tracing Spot Patterns

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The goal of this thesis project is to develop a method to perform direct wavefront reconstruction of in vitro crystalline lenses from spot diagrams measured using a Laser Ray Tracing (LRT) system. The LRT system is combined with a commercial Spectral-Domain OCT system to deliver laser rays sequentially onto the in vitro crystalline lens.

The spot position for each ray is recorded at different axial positions using a camera. A MATLAB  program was developed to calculate the slope of the rays from the spot positions. The  ray slopes were used to calculate the Zernike wavefront coefficients using a least square curve  fitting algorithm. The method was tested on glass lenses, on cynomolgus monkey lenses, and on human lenses.


The Optics of the Crystalline Lens:

The crystalline lens of human eyes continuously grows throughout life. The continued growth of the crystalline lens changes the shape and gradient refractive index of the lens, which  causes changes in the optical power and aberrations. The  effects of these changes on the optical quality of the human eyes in general and their implications for the development of refractive error, the development of presbyopia, and the long term outcomes for vision  correction procedures are not well understood (Smith, 2003; Kasthurirangan et al., 2008).

In Vitro Wavefront Aberration Measurement Overview:

The three common approaches for the measurement of wavefront aberrations of in vitro crystalline lens are Point Diffraction Interferometry (PDI) (Smartt, 1975,Acosta  et  al.,2009), Hartmann-Shack  wavefront  sensors (H-S)(Liang et  al.,4 1994, Liang & Williams, 1997), and Laser Ray Tracing (LRT)(Navarro & Losada, 1997).

Schematic of Interferometer with HDI Plate in Focus.

Schematic of Interferometer with HDI Plate in Focus.

Laser Ray Tracing System Developed at OBC:

At the Ophthalmic Biophysics Center (OBC) in Bascom Palmer Eye Institute, a laser ray tracing (LRT) system combined with an optical coherence tomography (OCT) system has been developed to  measure lens power and spherical aberration directly on in vitro crystalline lens.


Zernike Polynomials:

Zernike polynomials are a set of continuous orthogonal functions defined on a unit circle and  they have been broadly applied to characterize the aberration of optical instruments and of the eye (Born&Wolf, 1980, Malacara, 1992).

Implementation in MATLAB:

The aim of this project is to develop a MATLAB program to determine the Zernike coefficients of in vitro crystalline lenses measured using the LRT system. The MATLAB program was designed to calculate the first 28 Zernike polynomial terms, up to the 6thorder.

The developed MATLAB program was separated into several steps to obtain the Zernike coefficients.

  • Input x and y sampling positions
  • Determine matrix V
  • Input the local wavefront slopes from LRT system experiments to determine matrix S.
  • Calculation of Zernike coefficients though matrix manipulation.


Experimental Setup:

The invitro experimental set up of the LRT system. During the experiments, the LRT system uses the OCT delivery system to deliver input beams sequentially on the crystalline lenses and the spot positions for each ray are recorded on a camera at different vertical positions. The  recorded spot positions along the vertical axis for each ray can be used to represent the trajectory of the ray, which will be applied for x and y slope determination and Zernike coefficients calculations.

Data Analysis:

Calculation of Spot Centroid Positions

Examples of Spot Images Recorded from the LRT System.

Examples of Spot Images Recorded from the LRT System.

The camera recorded spot position images during the LRT experiments. In this experiment, for each camera position, there are a total of 621 laser rays passing through the crystalline lens sequentially and 621 images were formed containing spot position information. The combination  of all 621 spots positions forms a 23 by 27  matrix. In  order to find the input sampling  geometry of the LRT system, an experiment without crystalline lens nor chamber was performed. The camera was placed at the position where the chamber would be.



In this thesis project, A MATLAB program was developed to reconstruct the Zernike coefficients from the LRT spot patterns to study the aberrations of the crystalline lens. The developed program was tested on glass lenses, human lenses, and cynomulgus lenses. The results show the  feasibility of using LRT spots patterns acquired at different axial positions to calculate  Zernike coefficients.

Future studies will focus on correcting for the effects of distortions on the calculated  Zernike coefficients of in vitro crystalline lens in the LRT system, determining the optimal  sampling geometry related to the number of spots and the spots spacing, and studying the  optimal number of axial positions that are used for the slope calculations. Future studies will also focus on investigating the accuracy of centroids, further validating the Zernike  coefficients, evaluating the effects of input beam geometry, and improving the  MATLAB  program for easier data input and output.

Source: University of Miami
Author: Yue Yao

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