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Light Transport in Tissue Experimental apparatus The goniophotometer used at Wellman Laboratory is shown in Figure 5.2. The interior of the tank was painted flat black and filled with saline to minimize internal reflections from the box and within the sample. A helium-neon laser delivered a 1mW beam normal to the sample which was sandwiched between glass microscope slides. The beam diameter was 1mm. The 3mm diameter detecting fiber located at the end of an 8.5cm long arm was attached to a computer-controlled stepping motor. The stepping motor made 1.8$^\circ$ steps throughout a full 360$^\circ$ circle. A 1.17mm aperture was placed over the end of the detecting fiber to increase the resolution of the goniophotometer. Light collected by the fiber was measured with a photomultiplier tube whose output was connected to the computer. Figure 5.1: Correction factor as a function of angle required to convert measurements of reflection and transmission into phase function measurements. These correction factors are for an optical depth of unity and an albedo of one-half. The solid line is the correction factor required for transmitted light and the dashed line is that needed for reflected light. Figure 5.2: The goniophotometer apparatus. Helium-neon laser light enters the saline filled tank through a glass port on the side. The light strikes the sample and is scattered. The light is detected by a fiber attached to an arm driven by a computer controlled stepper motor. The fiber is connected to a photomultiplier tube which is monitored by a computer. The angular resolution $(\alpha_{\mathrm{resolution}})$ of the goniophotometer depends on several different factors: the width of the detector (Wdetector), the acceptance angle of the detector $(\alpha_{\mathrm{acceptance}})$, the width of the beam on the sample (Wbeam), and the distance from the sample to the detector (D). The angle subtended by the beam is approximately (Figure 5.3A) $$\alpha_{\mathrm{spot}} = {W_{\mathrm{beam}}\over D}$$ (5.5) Any light leaving the sample at angles larger than this will not reach the detector. The angle subtended by the detector is approximately (Figure 5.3B) $$\alpha_{\mathrm{detector}} = {W_{\mathrm{detector}}\over D}$$ (5.6) Again any light leaving the sample at angles larger than this will not reach the detector. The angular resolution of the goniophotometer is usually determined by the larger of $\alpha_{\mathrm{beam}}$ and $\alpha_{\mathrm{detector}}$ since the acceptance angle of the detector is usually much larger than the other angles. Thus, the larger of diameters of the beam and the detector determine the resolution of the goniophotometer. The angular resolution of the goniophotometer used for these experiments was about 0.8$^\circ$. Figure 5.3: Angular resolution of the goniophotometer is determined by the relative size of the detector and the spot size when the detector is sufficiently far from the sample. This figure defines the angles subtended by the spot and the detector.

S. A. Prahl."Light Transport in Tissue," PhD thesis, University of Texas at Austin, 1988.