Obtaining the Bidirectional Transfer Distribution Function of Isotropically Scattering Materials Using an Integrating Sphere

This paper demonstrates a method to determine the bidirectional transfer distribution function (BTDF) using an integrating sphere. Information about the sample's angle dependent scattering is obtained by making transmittance measurements with the sample at different distances from the integrating sphere. Knowledge about the illuminated area of the sample and the geometry of the sphere port in combination with the measured data combines to an system of equations that includes the angle dependent transmittance. The resulting system of equations is an ill-posed problem which rarely gives a physical solution. A solvable system is obtained by using Tikhonov regularization on the ill-posed problem. The solution to this system can then be used to obtain the BTDF. Four bulk-scattering samples were characterised using both two goniophotometers and the described method to verify the validity of the new method. The agreement shown is great for the more diffuse samples. The solution to the low-scattering samples contains unphysical oscillations, but still gives the correct shape of the solution. The origin of the oscillations and why they are more prominent in low-scattering samples are discussed.