Coherence and OCT

Question 1

What is OCT

Answer 1

a 3d imaging technique with high spatial resolution and large penetration depth even in highly scattering media

Question 2

What principles is OCT based on

Answer 2

• on measurements of the reflected light from tissue discontinuities
• on the interference between the reflected light and the reference beam, using it as a coherence gate to isolate light from a specific depth

Question 3

What are some of the uses for OCT

Answer 3

• functional imaging
• guided surgery
• embryology, endoscopy, dermatology, opthalmology

Question 4

What does interferometry measure in OCT

Answer 4

small time delays of scattered photons

Question 5

Describe the set up for OCT

Answer 5

• low coherence light source travels through beam expander then beam splitter
• some beams are reflected onto the sample, others are reflected off the moveable reference mirror
• the beams recombine and the signals are processed

Question 6

What are the characteristics of coherent sources

Answer 6

• monochromatic
• definite and constant phase relation

Question 7

What are two methods for obtaining two coherent sources

Answer 7

• wavefront splitting
• amplitude splitting

Question 8

What can be said about photon sources of light

Answer 8

• radiate wavetrains of finite length
• more than one wavelength (spectral bandwidth)
• fixed phase relation only within individual wavetrain

Question 9

Define coherence

Answer 9

correlation of light wave at two points in space-time : 𝚪 (𝒓𝟏, 𝒕𝟏; 𝒓𝟐, 𝒕𝟐) =< 𝑬 (𝒓𝟏, 𝒕𝟏) 𝑬 (𝒓𝟐, 𝒕𝟐) >

Question 10

Define temporal coherence

Answer 10

correlation of light wave along the light propagation direction : 𝚪 =< 𝑬𝒂 (𝒕) 𝑬𝒃
∗ (𝒕) >=< 𝑬 (𝒕 + 𝒕𝒃𝒂) 𝑬∗ (𝒕) >

Question 11

Define coherence length

Answer 11

the length of the wavetrain where there is definite phase relation

Question 12

Define coherence time

Answer 12

the time for the elementary wavetrain to pass a single point

Question 13

what is the relationship between the coherence length and time

Answer 13

𝐿𝑐 = 𝑐 𝜏𝑐

Question 14

What is temporal coherence a measure of

Answer 14

spectral bandwidth

Question 15

How does temporal coherence relate to the spectral bandwidth

Answer 15

• high temporal coherence gives a narrow spectral bandwidth
• they are a fourier transform pair
• 1/delta nu = 𝜏𝑐

Question 16

what is the effect if the path length difference is much less than the coherence length

Answer 16

the same wavetrain overlap and an interference fringe is observable

Question 17

what happens if the path length difference is much greater than the coherence length

Answer 17

different wavetrain overlap and no interference fringe is observable

Question 18

describe a partially coherent source

Answer 18

• a broad spectrum band (like incoherent sources)
• definite phase relation within coherence length

Question 19

What is the phase change for interference with partially coherent light sources

Answer 19

2𝜋Δ𝐿𝜈

Question 20

What is the interference for light with continuous spectra

Answer 20

Γ (Δ𝐿) ≈ 2𝐼0 integral from 0 to ∞ of 𝑆(𝜈) cos (2𝜋Δ𝐿𝜈𝑖)
where S(v) is the spectral density

Question 21

How are the source spectrum and coherence function related for interference with a partially coherent light source

Answer 21

they are linked by the fourier transform

Question 22

What is the intensity formula for interference of partially coherent sources

Answer 22

𝐼 = 𝐼1 + 𝐼2 + 2 sqrt(𝐼1𝐼2) exp[−4 ln 2 (Δ𝐿/𝐿𝑐)^2]cos(2𝜋Δ𝐿𝜈)

Question 23

What are the conditions for seeing interference fringes with partially coherent sources

Answer 23

optical path length are matched within the coherence length of the source
broader bandwidth = shorter Lc and higher resolution

Question 24

What are the common light sources for OCT

Answer 24

• pulsed lasers
• scanning sources

Question 25

What are the advantages of scanning sources for OCT

Answer 25

the reference arm is not scanned and fast scanning is feasible

Question 26

How is an OCT image constructed

Answer 26

scanning - contrast comes from refractive index variations

Question 27

What is spectral domain OCT

Answer 27

• no scanning
• depth intensity profile calculated from spectra due to fourier transform relationship between the autocorrelation and the spectral power density

Question 28

What is swept source OCT

Answer 28

• no scanning of reference arm but wavelength of source changes