Feasibility of Using Backscattered

Light to Recover Refractive Index

Gradient in Biological Samples

PAYMAN RAJAI

Supervised by

Dr. REJEAN MUNGER

Visual Optics Lab, The Eye Institute

The Eye

The Crystalline Lens

• A: single layer of epithelial cells at the anterior surface

• E: Cells in the equatorial section

• P:The posterior surface has no epithelial cells

• IC: Inner Cortex

• N: Nucleus

• Gradient index along vertical and horizontal axes• Gradient index along vertical and horizontal axes

• Circular symmetric in Equatorial plane.

Physiology of the Lens, GEORGE DUNCAN and I. MICHAEL WORMSTONE

Equatorial Plane

Stating the Problem

• The variation in the gradient is still the challenging question

• No direct measurement has been done

• All previous techniques detected and analyzed the transmitted

light.

• All previous studies needed the lens to be in laboratory • All previous studies needed the lens to be in laboratory

situation, out of the eye

• All previous techniques are valid in equatorial plane

Foundation of Previous Studies:

Ray Tracing Approach

•Laser beam

•Equatorial plane

•circular symmetry

Cynthia Wilson Thesis 2010

The Goals of my Project

• Direct measurement of the index profile

• Detect and analyze the backscattered light

• Utilize the commercially available FD-OCT as a

high precision tool to extract depth high precision tool to extract depth

information

The Benefits of the Project

• Enabling measurement in real situation

• Enabling individual measurement, individual

eye modelling

• Enabling more precise refractive surgery• Enabling more precise refractive surgery

• Extendable to other areas

Optical Coherence Tomography

Time Domain OCT Fourier Domain OCT

Fercher, Rep. Prog. Phys. 66 (2003) 239–303

Conventional TD-OCT signal

Conventional FD-OCT signal

Assumptions in conventional OCT

� δ-like object’s structure

� Uniform and homogeneous refractive index

for the whole sample

� Reflectivity of each layer does not depend on � Reflectivity of each layer does not depend on

the refractive index

Possible Approaches to Solve for

Inhomogeneous Refractive Index

• Plane Wave Approach• Plane Wave Approach

• Diffraction Tomography Approach

Plane Wave Approach

z0

z1

z2

z3

n0

n1

n2

n3

Possible Solutions

• Oblique illumination in two different angles: difficult to

implement

Possible Solutions

• Oblique illumination in two different angles: difficult to

implement

• Employing two sources with different spectrums

• Simulation based on Matrix method of EM wave propagation

Diffraction Tomography Approach

Helmholtz eq.

Scattering Potential

Born Approximation

Using the angular spectrum representation yields

Born approximation is valid

just for very small objects

Direct application to the OCT

Rytov Approximation

Rytov approximation is valid for

smooth fluctuations in phasesmooth fluctuations in phase

Direct application to the OCT