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In Optical Coherence Tomography, Broader bandwidth/low coherence light sources are used. Is it only because to increase the resolution or are there any other reasons? What will happen if we use a high coherence source ?

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You're right. OCT is working a little like radar, but whereas radar works out the depth i.e. distance to a reflector by measuring time of flight, OCT achieves the same thing by correlation: as you seem to be aware, really constructive interference can only happen with light of low coherence length when the delays through the interferometer arms are the same to within the light's coherence length. The Wikipedia article on OCT explains this well. With a fixed reference arm length, the system is most sensitive to scattering that happens at the particular depth in the imaged sample that matches the optical path in the two interferometer arms. So by scanning the reference arm length, you are changing the depth that the system is imaging at.

Another way to put this: by scanning the reference arm length, you are measuring the light's autocorrelation function $R(\Delta x)$. By the Wiener-Khinchin theorem, the light's power spectral density as a function of wavenumber $k = \omega/c$ is the Fourier transform of $R(\Delta x)$. So, for a resolution $\Delta x$ of $1{\rm \mu m}$, we must have $\Delta k \approx 1{\rm (\mu m)^{-1}}$, and, given $\Delta k = 2\pi \Delta \lambda/\lambda^2$, this means a source of breadth $\Delta \lambda \approx 0.16 \mu m$, or approximately 160nm linewidth when $\lambda = 1000nm$.

It is wholly a question of imaging depth. The system is working like a confocal microscope (see my description here) and this is your answer for when high coherence light is used. However, to image deeply into samples, for example, the retina of an eye, one can generally only use very low numerical aperture, owing to the high wavefront aberration imparted by the eye ("high" in confocal microscope terms - we're still only talking a wave or a few waves of aberration) on the signal as it travels to and fro through the eye and retina. The higher the numerical aperture of a confocal microscope, the finer its depth resolution, but unfortunately the tolerance to wavefront aberration becomes swiftly less with bigger NA. To image deep into tissue, we are therefore restricted to numerical apertures of 0.1 or less, which translates to a depth resolution of roughly $100{\rm \mu m}$ to $200{\rm \mu m}$. The use of OCT restores the depth resolution in an otherwise poorly depth resolving confocal microscope system.

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