Aperture size effects on backscatter intensity measurements in Earth and space remote sensing

Most materials show a peaked intensity versus phase (light-source-target-detector angle) curve. For nonnegligible angular apertures of the source and/or the detector, the measured intensity at and near zero phase (backscatter) is lower than the real one. We derive an averaging aperture integral that represents this effect, and with it we invert measured intensity values to obtain the actual intensity curve. We also give a practical formula for estimating the magnitude of the aperture effect in zero-phase intensity measurements and show that only two such measurements made at different apertures are sufficient for deriving the real intensity. These corrections are needed in the comparison of measured reflectances in an increasing number of validation efforts for remote sensing applications requiring ground truth measurements.