1 Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation

In OCT, dispersion compensation is usually performed by matching the optical materials and path lengths in the two interferometer arms. Dispersion can also be compensated by using numerical techniques.

Principle of SD-OCT:

The sample is illuminated with broadband light. Backreflected or backscattered light signals from different depths that correspond to different delays are brought to interference with light from a reference path with a known delay. The interference produces fringes, which are detected by a spectrometer using a high-speed multi-element CCD or photodiode array detector. The delay and magnitude of the optical reflections from the sample can be detected by Fourier transforming the spectral interference signal.

Frequency and delay-dependent phase:

`S_{\text {int }}(\omega)=2 \operatorname{Re}\left\{E_{R}(\omega)^{*} E_{S}(\omega)\right\}=2 \operatorname{Re}\left\{\sum_{n} \sqrt{I_{n}(\omega) I_{r}(\omega)} \exp \left[i\left(\omega \tau_{n}+\Phi\left(\omega, \tau_{n}\right)\right)\right]\right\}`

`I_n`

is the intensity of light reflected from the n-th layer in the sample, `I_r`

is the intensity of light reflected from the reference arm, and `τ_n`

is the optical group delay of the n-th reflection, relative to the reference light path. __ Φ(ω,τ_n) is a general frequency and delay-dependent phase that includes higher order dispersive terms.__

Theoretical axial resolution:

`\Delta z=\frac{2 \ln 2}{\pi} \frac{\lambda_{0}^{2}}{\Delta \lambda}`

where `∆λ`

is the full width half maximum (FWHM) of the light source and `λ_0`

is the center wavelength.

How to choose a proper bandwidth or spectral range of a spectrometer?

To be read: Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation