## OCT Fundamentals

Optical coherence tomography (OCT) is a 3-D imaging technique that can provide high resolution (up to few micrometers) and deep penetration (up to few millimeters) in a scattering media. Applications include medical diagnosis, biological imaging and material inspection.

OCT relies on back-scattered light from different regions of a sample to generate a 3-D map. It uses different localization techniques to obtain the information in the axial direction (along the optical beam, z-axis) and the transverse direction (plane perpendicular to the beam, x-y axes). The information in the axial direction is obtained by estimating the time delay of light reflected from structures or layers in the sample. This technique is similar to that used for generating an ultrasound image, but light is used instead of sound. Given the high speed of light, it is not easy to perform a direct measurement of the time delay for the back-scattered light. OCT systems indirectly measure the time delay using what is called low-coherence interferometry. In low-coherence interferometers, a light sources with a broad optical bandwidth is used for illumination (see Figure 1). The light coming out of the source is split by a beam splitter into two paths called the reference and sample arms of the interferometer. The light from each arm is reflected back and combined at the detector. An interference effect (fast modulations in intensity) are seen at the detector only if the time travelled by light in the reference and sample arms is nearly equal. Thus the presence of interference serves as a relative measure of distance travelled by light. OCT uses this concept by replacing the mirror in the sample arm with the sample to be imaged. The reference arm is then scanned in a controlled manner and light intensity is recorded on the detector. The interference pattern shows up when the mirror is nearly equidistant to one of the reflecting structures in the sample. The distance between two mirror locations where the interference occurs corresponds to the optical distance between two reflecting structures of the sample in the path of the beam. Even though the light beam passes through different structures in the sample, the low-coherence interferometry described above, helps to separate out the amount of reflections from individual structures in the path of the beam.

The transverse or x-y localization of the sample structure is simpler. The broadband light source beam that is used in OCT is focused to a small spot (on the order of a few microns) and scanned over the sample.

### Fourier-Domain

Fourier-Domain

Fourier-domain OCT provides an efficient way to implement low-coherence interferometry described above. Instead of recording intensity at different locations of the reference mirror, the intensity is recorded as a function of wavelengths or frequencies of the light. The intensity modulations when measured as function of frequency are called spectral interference. The rate of variation of intensity over different frequencies is indicative of the location of the different reflecting layers in the samples. It can be shown that a Fourier transform of spectral interference data provides information equivalent to the one obtained by moving the reference mirror *(Figure 2)*.

There are two common methods of obtaining spectral interference in OCT: Spectral-Domain and Swept-Source. In Spectral-Domain OCT, the light is split into different wavelengths and uses a spectrometer as the detector. In Swept-Source OCT, The light source sweeps through a range of wavelengths and the temporal output of the detector is converted to spectral interference.

Fourier-domain allows for much faster imaging since all the back reflections from the sample are being measured simultaneously. This speed increment introduced by Fourier-domain OCT opened a whole new arena of applications. Live video OCT imaging can be easily obtained using commercial systems.

### Key parameters for OCT Systems

#### Resolution

The axial and transverse resolution of an OCT system are independent. The axial resolution is related to the bandwidth, or the coherence-length, of the source. For a Gaussian spectrum, the axial resolution (*l*_{c}) is given by:

*l*_{c} = 0.44*l^{2}/Dl

where l is the central wavelength and Dl is the bandwidth of the source. It should be noted that this is the spectrum measured at the detector and may differ from the spectrum of the source, due to the response of optical components and the detector itself. The above equation holds only for Gaussian spectra. For spectrum of arbitrary shape the axial spread function should be estimated to understand the achievable resolution and any artifacts like side lobes. Plots of the axial resolution equation for three different central wavelengths is found in figure 3.

The imaging depth of OCT is primarily limited by the depth of penetration of the light source in the sample. Additionally, in Fourier-domain OCT, the depth is limited by the finite number of pixels and optical resolution of the spectrometer. As previously mentioned, the image in FD-OCT is obtained after Fourier transformation of the spectral interference data. The total length or depth after Fourier transform is limited by the sampling rate of the spectral data, and is governed by Nyquist theorem. A total bandwidth (Dl) sampled by *N* pixels gives us the wavelength sampling rate of *d*l = Dl /*N*. Since Fourier transform relates frequency to time, we convert wavelength to frequency, dn = c*Dl /l^{2}. Nyquist theorem indicates the maximum time delay in the Fourier transformed data will be *t*_{max} = 1/2* dn, and maximum depth in the data will be *l*_{max} = c** t*_{max}. By combining these, the maximum imaging depth in FD-OCT is:

*l*_{max} = 1/2*(l^{2} /(D l /N))

#### Loss of sensitivity with depth

In Fourier domain OCT, theoretical sensitivity is dependent on the location of the reflector. The maximum sensitivity is around the zero delay difference point and goes down as we move away from the zero delay. This loss is result of finite pixel size and finite optical resolution of the spectrometer. It can be shown that sensitivity is related to depth by:

**R( z) = sin(p*z)/( p*z)*exp( –z^{2}/(w*p))**

Where w is equal to dl/Dl and depends on the optical resolution of spectrometer elements. The first term representing a sin function on left hand side of the equation is the result of finite pixels in the spectrometer. The second term relates to the finite optical resolution of the spectrometer that results in ‘leakage’ of a given wavelength into multiple pixels.

#### Signal to Noise Ratio (SNR)

Signal to noise ratio is generally defined as ratio of signal power to the power of noise. Being a statistical quantity, noise power is defined by its variance. There are three main sources of noise that dominate OCT. (1) The detector noise resulting mainly from thermal fluctuations in the electronics, (2) Shot noise due to inherent variance in arrival and detection of photons on the detector, and (3) Relative intensity noise (RIN) in the light source. An ideal system has minimal detector and intensity noise and operates in the shot-noise domain. The performance of such a system is limited by number of photons arriving at the detector.

### Sensitivity in OCT

Sensitivity in OCT refers to the ability of the system to detect the faintest amount of back-reflection from the sample under observation. Numerically it is the attenuation in the signal that results in a signal to noise ratio (SNR) of 1.

#### Measurement in dB

Signal to noise ratio or sensitivity is often defined in decibels (dB). In general the dB unit of a physical quantity corresponds to 10*log(P_{a}/P_{b}). When dealing with optical light measurements the power in question should be carefully considered. The light power (*P*) is proportional to the current output of a photodetector (*I*), however the electrical power is proportional to *I*^{2} hence the SNR and sensitivity measurements in OCT when considering optical power are given by 20*log(P_{a}/P_{b}). In general, while stating values in dB clear distinction should be made if the quantity in consideration is optical or electrical power.

#### Speed

The speed of an OCT system depends on several factors. The first being the amount of light received on the detector. Speed is directly related to the time the system needs to accumulate enough photons for a good signal to noise ratio. . The other limitations on speed are the system parameters themselves. For a spectrometer based spectral-domain OCT system the speed of the camera sensor and electronics are usually the limiting factor. For swept-source Fourier-domain OCT the speed of the swept source laser is often the limiting speed.