Only a portion of the fluence rate F at the collection fiber successfully couples into the fiber. The collection fiber has an area of collection, A [cm2]. The power that enters the fiber equals the product FA = PoTA.
Fig. 2: Diagram of the possible return paths of light in a 2-fiber configuration. Light that reach the fiber face with an angle smaller than the half angle of the acceptance cone will be guided through the fiber to the detector (Rcore). Light that reach the fiber face with an angle greater than the half angle of the acceptance cone will escape through the fiber cladding (Rclad). Rair is the light that leaves the tissue outside the fiber and rsp is the Fresnel reflection due to the fiber/tissue index of refraction mismatch. Light can also be absorbed by the tissue.
The collection fiber also has a cone of collection within which photons must enter the fiber, or else the photons will not be properly guided and will escape the fiber and not reach the detector. Let the fraction of photons that enter the fiber that are successfully guided by the fiber be called the "collection efficiency" ec [dimensionless]. Hence the power that enters the collection fiber is calculated:
The value of ec is dependent on the size of the fiber and the optical properties of the tissue at each wavelength of measurement. For a low scattering coefficient and narrow fiber, many of the photons that enter the fiber originate distant from the fiber and enter the fiber relatively close to perpendicular to the fiber face. Hence the value of ec is relatively high. If the scattering coefficient is high, then fiber is large, then the photons that enter the fiber originate close to the fiber and hence the angle of entry can be quite large. Consequently, many photons enter the fiber oustide the cone of collection and the value of ec is relatively low. Figure 2 shows the behavior of ec as a function of tissue optical properties and fiber size.
Fig. 2: Collection efficiency determined by Monte Carlo simulations as a function of optical fiber separation for the multiple fiber probe with a central source fiber surrounded by an annular detection ring placed on the surface of a semi-infinite medium with air/medium boundary. Fig. A is the special case of a single fiber used as source and detector. Drawings on top of the figures represent a front view of the face of the probes. The y-axis is ec. The x-axis is the tissue reduced scattering coefficient. The three symbols denote different tissue absorption coefficients. [from PR Bargo, SL Jacques, R Sleven, T Goodell, Optical properties effects upon the collection efficiency of multifiber probe configurations, IEEE J. Selected Topics in Quantum Electronics (2003)]
The key lesson:
The transfer function through a tissue from a source fiber to a collection fiber involves both the transport T through the tissue and the collection efficiency ec at the collector fiber, and both are functions of the tissue optical properties.
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