Statistics of remote roll angle measurement

Abstract

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.

Metrology and Measurement Systems

“…Dynamic angle measurement (DAM) is an important part of geometric measurement [1][2][3][4]. The real-time online measurement technology with dynamic angular quantity has been paid more and more attention, and plays an important role in the fields of precision machining, aerospace, military and artificial intelligence [3,[5][6][7].…”

A high-precision measurement of small roll angular displacements based on AOMs and its error impact analysis

“…Roll angular displacement is difficult to measure in the geometric error detection of numerical control (NC) machine tools due to the low resolutions of the conventional methods, whose sensitive directions are orthogonal to the plane of angular displacement [1]. To overcome that problem, many methods have previously been proposed, such as diffraction gratingsbased methods [1,2], polarization intensity variation methods [3][4][5], geometric relation transformation methods [6][7][8][9], collimator methods [10][11][12], polarization phase detection methods [13][14][15][16][17][18][19] and so on [20][21][22][23][24]. The polarization phase detection methods have been adopted by many researchers because of their advantages of having a simple structure and high resolution.…”