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The Fourier-domain OCT technique was first presented in 1995 by Fercher [50]. It provides equivalent imaging of structural information as time-domain OCT with the same spatial

resolution [165]; it also features improved sensitivity and elimination of depth scanning of both interferometer arms. Instead of time-dependent interferograms acquired in time-domain OCT, the signal data obtained in a Fourier domain system are spectra, in which the spectral density intensity is plotted as a function of wavelength or frequency. Whereas in standard OCT both depth and lateral scans have to be performed, only the lateral-scan is necessary in the Fourier-domain techniques [3].

Based on the channelled spectra technique (spectral modulation), Fourier-domain OCT has been implemented into mainly two schemes; one is called spectral domain OCT with a spectrometer to detect spectrum; the other is called swept-source OCT with a tuneable laser source and a photodetector to extract spectral information over a wide bandwidth. Both methods are based on spectrums (spectral A-scan signals) acquired at the interferometer exit [50, 165]. The depth-dependent A-scan signals can be obtained by an inverse FT of the path difference modulation of OCT spectrums [4].

a. Theoretical Formulae

Considering the Wiener-Khintchine theorem [174], the spectral density (power spectrum) function of a light wave can be represented by the FT (FT{...}) of its autocorrelation (self- correlation) denoted byΓ(τ):

S(ν) =FT{Γ(τ)}. (2.15)

E_s(t)andE_r(t,τ)are still defined the wave fields of sample and reference beams (τ is the time delay between the two waves), the power spectrum at the interferometer exit can be expressed as [174]:

S_out(ν,τ) =Ss(ν) +Sr(ν) +2

p

S_s(ν)Sr(ν)ℜ[µsr(ν)e−iφ(ν,τ)] (2.16)

=Ss(ν) +Sr(ν) +2ℜ[Wsr(ν)]cos(φ(ν,τ)) (2.17)

In Equation 2.16,S_s(ν)andSr(ν)are the spectral densities at frequencyν of sample and reference beams respectively; µsr(ν)denotes the spectral degree of coherence at frequency ν; the spectral phase is computed byφ(ν,τ) =2π ν τ. In Equation 2.17, the spectral density function of two waves is obtained as:

However, following the Wiener-Khintchine theorem in Equation 2.15, the spectral density functionW_sr(ν)is also in relation of the mutual coherence functionΓsr(τ)by:

Wsr(ν) =FT{Γsr(τ)}. (2.19) The depth-dependent interferogram and the cross-spectral intensity are FT pairs of each other [175]. Hence the depth-dependent A-scan signal can be obtained from the path difference modulated part of the interferometer exit spectrum:

Gsr(z) =2ℜ{FT−1{Wsr(ν)}}. (2.20) where FT−1is the inverse FT. The spectral densityWsr(ν)plays essential role of a spectral A-scan signal [4].

b. Spectral Interferometry Fourier-domain OCT

This technique is known as spectral-domain OCT, in which spectra of the backscattered light are obtained at the exit of the interferometer using a spectrometer. As explained in equation 2.19 to 2.20, the inverse FT of the spectral density intensity yields the same depth-scan signal as obtained by time-domain OCT [176], since a given path difference generates a unique wavelength-dependent signature of phase difference [4]. Hence, the time-consuming mechanical OCT depth-scan is replaced by a spectrometric measurement. A typical spectral-domain OCT scheme using a spectrometer at the interferometer exit is shown in Fig. 2.8.

A broadband light source and the lateral scanning are common with the standard OCT system. Lateral scans are performed to acquire sequential depth signals along the lateral direction, allowing cross-sectional images of sample sections to be obtained. Simultaneously, all spectral components are captured at the output of a spectrometer [50, 53, 56]. The spectral information can also be extracted by distributing different optical frequencies onto a photo detector array via a diffraction grating component.

A phase modulator in the reference arm is used for the introduction of a variable single- pass phase delay. Then a set of spectral interferograms may be acquired with different phase delays, and combined in signal processing to eliminate the undesired artefacts [177]. The phase shifting technique has been important to resolve the A-scan signal for both time-domain OCT and Fourier-domain OCT. The 4-step phase shifting approach is the most common way to remove artefacts and oscillations.

Fig. 2.8 Schematic diagram of spectral interferometry Fourier-domain OCT. PS: Phase Shifter. Spectral interferogram can be recorded instantaneously with no OCT depth scans. The A-scan signal is extracted from inverse FT of combined spectral interferograms, which are acquired under different phase delays. The B-scan image is the combination of a series of A-scan signals acquired after each OCT lateral scan.

c. Wavelength Tuning Fourier Domain OCT

Fourier-domain OCT can also be performed using a tuneable light source and detecting the intensity due to component frequencies [51]. This technique is known as optical frequency domain reflectometry, it has only recently been applied in tomography. This type of Fourier-domain OCT is called wavelength tuning Fourier-domain OCT or swept- source OCT. Whereas spectral-domain scheme simultaneously records the spectrum at the interferometer exit by a spectrometer, the wavelength-resolved intensity components are captured sequentially by a single detector during the synchronous wavelength sweeping of a narrowband swept-laser source [52, 178, 179]. However, both Fourier-domain OCT schemes are based on the same fundamental principle of optical interferometric imaging.

As shown in Fig. 2.9, a time encoded (square-law) photodetector is used at the interferometer exit in common with the time-domain OCT. Both arm path lengths are held constant as no depth scan is required, similar with the spectral-domain OCT. A tuneable light source is the key system component, the wavelength sweeping allows successive registration of all spectral components at once with short exposure time [180]. In addition, there is no further phase shifting measurements required to eliminate OCT artefacts as in spectral-domain OCT. Together with superior sensitivity over time-domain OCT [58, 60],

swept-source OCT enables high speed imaging, which is important for real-time acquisition and reduces image-blurring motion artefacts [156].

Fig. 2.9 Schematic diagram of wavelength tuning Fourier-domain OCT. Wavelength resolved intensities are recorded sequentially by a photodetector during the wavelength sweeping of a tuneable laser source. The A-scan signal is extracted through the inverse FT of the integrated spectral intensity. The B-scan image is the combination of a series of A-scan signals performed after each OCT lateral scan.

The key advantages of Fourier-domain OCT include its high sensitivity and the detection scheme does not require depth scans. It also inherits time-domain OCT’s properties of the depth and the transverse resolutions (dependent on coherence length and probe beam NA). The spectral-domain OCT scheme features high speed data acquisition, whereas the swept-source OCT scheme features high speed imaging, comparing to the conventional time-domain OCT. However, the use of phase shifting method could result in the artefact reduction at the cost of increased acquisition time in spectral-domain OCT. There has been many studies on the sensitivity advantage of Fourier-domain OCT approaches over the time-domain OCT [58, 60, 181, 182].