New Optical Systems For The Measurement Of Diffuse Reflectance

AbstractA new class of two -stage optical systems are proposed for the measurement of diffusereflectance. The proposed systems consist of a single ellipsoidal or dual paraboloidalprimary mirror and a nonimaging compound parabolic concentrator (CPC) as the secondarymirror. When operated in the direct mode, the CPC's larger aperture is occupied by thereflectometer's detector, the CPC's smaller aperture resides at the focus of the primarymirror, and the CPC half -angle is chosen so as to minimize the angular dependence of thedetector's response. The resultant uniformity of the detector /CPC response over the hemi-sphere overcomes a major disadvantage of using ellipsoid and paraboloid -type reflectometersin the direct mode, at the expense of a slightly larger detector area. In the reciprocalmode, the CPC's larger aperture is occupied by a high temperature source, with the CPC'sfield of view chosen so as limit the variation in the source's directional emissivity toless than one percent. This source design offers less stray radiation than a cavity -typesource with comparable Lambertian properties. The emissivity and wavelength dependence ofthe CPC source is determined by the high temperature surface. An analysis of the designtradeoffs for CPC /conic section reflectometers is given including ray tracing.Introduction and backgroundThe optical systems used for measuring diffuse reflectance can be groupedl into threebroad categories according to the type of optics employed: collecting mirrors, integratingspheres, and heated cavities (holraums). Collecting mirrors attempt to gather all theradiation scattered from a sample with a minimal number of reflections and direct it onto adetector. The throughput of a collecting mirror can be orders of magnitude higher than anintegrating sphere, however, their sensitivity to flux losses and misalignment errors isconsiderably worse. The three primary collecting mirrors are the hemisphere2, theparaboloid3 and the ellipsoid4.Low eccentricity oblate ellipsoids are preferred over the hemisphere because of theirsmaller aberrations5. In the direct mode of operation, one focus of such an ellipsoid isoccupied by a sample and the other focus by a detector. The sample is then irradiatedeither through a hole in the ellipse or by using a small mirror suspended in the ellipsoid.The diffusely scattered radiation is then collected by the ellipsoid and directed onto thedetector. The two major sources of systematic error in such a device are overfilling ofthe detector and variations of the detector response with angle. Paraboloidal mirrorssuffer from these errors also.The overfilling problem comes about because the ellipsoid is designed for point, ratherthan finite sized sources. For finite sized sources the image spot size can be considerablylarger then the object size, leading to overfilling of the reflectometer's detector. Over-filling can be eliminated by choosing a very low eccentricity ellipse and oversizing thedetector slightly. In the following section we develop upper bounds for the magnificationof an ellipsoid in terms of its eccentricity and verify these results with ray tracing.The angular response of the detector is more difficult to eliminate, particularly if oneis interested in absolute measurements at large incidence angles or in relative measurementsas a function of angle. One could measure the angular dependence of the detector, howeverin order to back this response out of a diffuse reflectance measurement one would have toknow the bi- directional properties of sample's reflectance a priori. This is not practicaland to the author's knowledge has not been attempted for anything other then specular ornearly specular samples.The traditional solution to this problem has been to either 1)replace the integratingmirror with an itegrating sphere6 or 2)place a small integrating sphere at the detectorfocus7 and mount the detector on the sphere wall. As discussed in an accompanying paper8,the detector field of view must be restricted from observing direct beam radiation and firstreflections off the sphere wall. It is difficult to envision a collimator or baffle whichpermits proper integration of the radiation entering a sphere placed at an ellipsoid's focusfor all incidence angles. A double sphere system might work but the throughput penalty ofsuch a system would negate the original advantage of the collecting mirror. A recentattempt at NBS9 to use a gold integrating sphere at the focus of an ellipsoid /FTS system