Biophotonics_Concepts_to_Applications

Analogous to the monochromatic source case, the rightmost term in square brackets
in Eq. (10.10) has a peak value when the length zrof the reference arm matches the
distance zsto the backscattering interface at a particular sample depth.
The coherence lengthlcdetermines the broadness of the peak interference signal.
In order to have a narrow width of the interference signal, which will allow a
well-defined position of the backscattering interface, it is desirable for the light
source to have a short coherence length or, equivalently, a broad spectral band-
width. Thus, by examining the various peaks of the interference envelopes during a
scan of the sample, the location and backscattering strength of interfaces within the
sample can be determined.

Example 10.3Recall from Eq. (2.36) that the coherence length for a spectral

widthΔλat a center wavelengthλ 0 is given bylc= [(4 ln 2)/π](λ 0 )^2 /Δλ.

Suppose an OCT setup for ophthalmology tests uses the following

super-luminescent diodes: (1) an 850-nm peak wavelength with a 50-nm

spectral bandwidth and (2) a 1310-nm peak wavelength with an 85-nm

spectral bandwidth for the posterior segment and the anterior segment of the

eye, respectively. What are the coherence lengths of these two sources?

Solution: From Eq. (2.36) the coherence length at 850 nm is

lcð 850 Þ¼½ð4ln2Þ=pŠð850 nmÞ^2 =ð50 nmÞ¼ 12 : 7 lm

At 1310 nm,lc(1310) = [(4 ln 2)/π] (1310 nm)^2 /(85 nm) = 17.8μm

If a pulsed light source is used, an interference signal can only occur at the
detector when the pulses returning from the two arms of the interferometer arrive at
the detector at the same time. Therefore, as the spectral bandwidth becomes
broader, the interference pulses become sharper, thereby enabling a more precise
location of the backscattering interface being examined for a particular setting of
the reference mirror.
Several important characteristics of an OCT system can be derived if the sample
arm is treated as a reflection-mode scanning confocal microscope. In this case the
SMF acts as a pinhole aperture for both the illumination and the collection of light
from the sample. Then the expressions for both the lateral and the axial intensity
distributions are given by the expressions for an ideal confocal microscope with a
small pinhole aperture. A summary of the resulting expressions is given in Fig.10.6
in which the OCT system is taken to be cylindrically symmetric [ 6 ].
The image resolution is an important parameter for characterizing an OCT system.
The lateral and axial resolutions of OCT are decoupled from each other and thus can be
examined independently. Thelateral resolutionis a function of the resolving power of
the imaging optics, as is discussed in Sect.8.2.Theaxial resolutionΔz is derived from
the coherence length of the source. If anOCT system uses a broadband light source with
acenterwavelengthλ 0 , the standard equation for the axial resolution is

298 10 Optical Imaging Procedures