Automated spectro-goniometer: A spherical robot for the field measurement of the directional reflectance of snow

Abstract

We describe an automated spectro-goniometer (ASG) that rapidly measures the spectral hemispherical-directional reflectance factor (HDRF) of snow in the field across the wavelength range 0.4⩽λ⩽2.5 μm. Few measurements of snow’s HDRF exist in the literature, in part caused by a lack of a portable instrument capable of rapid, repeatable sampling. The ASG is a two-link spherical robot coupled to a field spectroradiometer. The ASG is the first revolute joint and first automated field goniometer for use over snow and other smooth surfaces. It is light enough (∼50 kg) to be portable in a sled by an individual. The ASG samples the HDRF at arbitrary angular resolution and 0.5 Hz sampling rate. The arm attaches to the fixed-point frame 0.65 m above the surface. With vertical and oblique axes, the ASG places the sensor of the field spectroradiometer at any point on the hemisphere above a snow target. In standard usage, the ASG has the sun as the illumination source to facilitate in situ measurements over fragile surfaces not easily transported to the laboratory and to facilitate simultaneous illumination conditions for validation and calibration of satellite retrievals. The kinematics of the ASG is derived using Rodrigues’ formula applied to the 2 degree-of-freedom arm. We describe the inverse kinematics for the ASG and solve the inverse problem from a given view angle to the necessary rotation about each axis. Its two-dimensional hemispheric sampling space facilitates the measurement of spectral reflectance from snow and other relatively smooth surfaces into any direction. The measurements will be used to validate radiative transfer model results of directional reflectance and to validate/calibrate directional satellite measurements of reflectance from these smooth surfaces.