Incidence- and acceptance-angle effects on soiled solar mirror reflectance

The reflectance of a soiled solar mirror depends not only on the soiling level, but also on the angle of incidence and on the acceptance half-angle of the detector or of the receiver. This hinders the comparison of different reflectometers and the translation of field readings into system-relevant optical losses. We measured full-hemisphere bidirectional reflectance distributions of second-surface glass mirrors soiled with desert dust from Australia, Kuwait and Spain, and of mirrors soiled naturally outdoors in Spain, for incidence angles 8 ∘ – 65 ∘ and acceptance half-angles 12.5 -- 145 mrad. Soiling broadens the specular lobe into a forward-scattered halo whose characteristic angular width ( 48 -- 54 mrad) is almost independent of dust type, whereas its amplitude is specific to the dust and to the dust loading. On this basis we developed a compact physical model that separates the reflected flux into a non-interacting specular core, described by a generalised Beer–Lambert law, and a scattered halo with explicit angular redistribution. The model uses five dust-specific parameters and one cleanliness parameter, the effective optical depth ( 0.012 -- 0.224 ), which can be inferred from a single routine reflectometer reading. It reproduces all measured acceptance curves with a mean deviation of 0.005 in absolute reflectance and a median coefficient of determination of 0.993 . Reflectometers operating near normal incidence with wide acceptance cones overestimate the receiver-relevant reflectance by 5 to 7 percentage points at 90 % cleanliness, and by 3 to 19 percentage points across a central-receiver field, depending on the soiling level and on the position of the heliostat. The model thus converts a single field reading into system-relevant reflectance for any geometry.