The orientation of remote objects can be easily measured optically and very accurately using optical technologies. In this paper, we address the accuracy of a roll angle estimation technique that is based on the estimation of the polarization of a retroreflected beam and is applied in a long-range measurement task. Over long transmission ranges, the optical power decreases significantly leading to severe SNR deterioration. As a result, the measurement accuracy decreases. In this study, the estimation is carried out using a maximum-likelihood estimator and its performance is evaluated using the analytical Cramer-Rao bound.

Remote measurement of object orientation is used in various scientific fields, such as robotics, optics, and biology (e.g., optical tweezers). Roll angle is one of the three angles that describe the orientation of an object in space. A common method to measure the roll angle is based on analyzing the polarization of the backreflection of a beam. The accuracy of the measurement is degraded by low signal-to-noise ratio (SNR). The low SNR is the result of the large distance between the measurement device and the object, or due to the small backreflection cross section. We perform a laboratory experiment and derive a mathematical model for the probability density function of the measured roll angle and its expectation value. This model makes it possible to calculate the accuracy of the roll angle measurement at low SNRs. Experiments and theoretical analysis using our model were performed and good agreement between the two approaches has been found.