Fourier Domain Optical Coherence Tomography (FD-OCT)

1

Fourier Domain Optical

Coherence Tomography (FD-OCT)

PAYMAN RAJAI

1

References:

•Fercher 1995, Measurement of intraocular distances by

backscattering spectral Interferometry, Optics Communications 117

(1995) 43-48

•Wolf 1969, Three dimensional structure determination of semi

transparent objects from holography data, Optics Communications,

1,4,153-156

•Born and Wolf, Principles of Optics, Seventh Edition

•Izatt, Theory of Optical Coherence Tomography

2

• FD-OCT Overview

• Born Approximation

• Back Scattered light

• Measurement by Backscattering spectral

Interferometry

• Sample Calculation for δ-like Scattering Potential

• Removing Noises from FDOCT by Phase Shifting

2

3

3

4

Born approximation

4

5

5

Helmholtz eq.

Scattering Potential

6

Green’s function for

Helmholtz equation

6

Subtract two eqs and use Green’s Theorem.

Integral over r’ bounded by a large sphere, when R → infinity

Free space green’s function

7

7

First Born approximation makes it easy to compute. For weakly scattering sites,

n≈1 and F(r) would be very small. Hence U(r’) inside the integral is the same as

U(incident).

Scattering Amplitude

8

Back Scattered light

8

9

9

Suppose the object illuminated by a plane monochromatic wave

Using the first Born approximation

Scattering Potential

10

10

Origin of x,y,z

“P(r)” observation point

located on the z-axis, a

distance D outside of the

object

PZ axis

Thickness of the sample

If D ›› T then r-r’ ≈ D

11

11

Integration over x’ and y’ can be replaced by a constant W chosen proportional to the

cross section of the beam waist.

When the detector is placed at θ=π

three dimensional Fourier transform is replaced the by a one dimensional.

12

12

Back Scattered light at the point “P” located on the z-axis in D

distance from the the object

It can be done if the phase and amplitude of the scattered field are known for a

range of k-values

These describe why we have to use a multi wavelength source of illumination.

13

Measurement by Backscattering

spectral Interferometry

13

14

14

We have obtained auto correlation function of the scattering potential not the potential itself !

15

How to obtain F(z)

• 1) if we interfere an additional singular light at the distance L

from the object (Reference Mirror)

• 2) if the object itself contains one interface with large

reflectivity to act as a reference mirror

15

Photodiode ArrayBroadband light source

Spectrometer

Diffraction

Grating

16

16

Actual object potential

auto correlation

function of the

sample

structure

centered at Z=0

complex

conjugate of

sample potential

centered at Z=zR

true

reconstruction of

the potential

centered at Z=-zR .

additional peak at

the origin of the

reconstructed

sample space

Intense light

background noise at

center caused by the

mirror

Weak background noise

at center caused by

different objects sites

Symmetric mirror images

17

Sample Calculation for δ-like Scattering

Potential

17

18

18

19

19

20

20

21

Sample Data Looks like:

21

22

Removing Noises from FDOCT by

Phase Shifting

22

23

23

DC Terms removed

To eliminate the mirror image, we need to acquire interferogram with 2φ differs

from π, for example 3π/2 and π/2. In this case the subtracting interferogram results

24

Combining all phase shifted interferogram yields

24

25

25

Standard FD-OCT images Mirror image and DC

terms removed images

the anterior chamber

of the human eye

a three-day-old

chicken embryo.

http://spie.org

26

26

Standard FD-OCT images Mirror image and DC

terms removed images

the palm skin

finger nail near the

nail fold region of a

human

http://spie.org