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 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
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
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
Born Approximation
Using the angular spectrum representation yields
Born approximation is valid
just for very small objects
Rytov Approximation
Rytov approximation is valid for
smooth fluctuations in phasesmooth fluctuations in phase