On the limited validity of reciprocity in measured BRDFs

Bidirectional reflectance distribution functions (BRDFs) of natural surfaces which are best represented by measured biconical reflectance factors (BRDFs) frequently do not fulfill the Helmholtz reciprocity requirement, although theory does not permit deviations. A new set of measured radiance data has been used to derive the BCRF by two different techniques to investigate the validity of the reciprocity requirement in measured data. Both techniques consider sky radiance. The interpolation technique replaces missing measurements by interpolated values. The resulting BRDFs show deviations from reciprocity but reproduce the measured radiances perfectly. This technique has been previously used. The new reciprocity technique replaces missing measurements by the requirement of reciprocity. The resulting BRDFs fulfill reciprocity completely but partly fail to reproduce the measurements. A discussion is given on the differences between the two sets of BRDFs, which are mostly small, and their possible reasons. The conclusion is that the truth is not known but may be in between the results obtained from the two techniques.