# Improved Autocollimator for Roll Angle Measurement with an Enlarged Measuring Range
## 1 Introduction  
An angle is a basic physical quantity, and many other parameters can be converted to angles; thus, angle measurement is of great significance in the fields of aerospace, optical processing, equipment manufacturing, etc. [1, 2]. Compared with laser interferometer [3, 4, 5], polarization detection [6, 7], and internal reflection methods [8, 9], the autocollimator is more frequently employed owing to the advantages of a simple architecture and high accuracy [10, 11, 12]. Over the years, the performance of the autocollimator has been greatly enhanced with the continuous development of component materials and fabrication technologies. However, its fundamental structure and measuring principle have not changed [13]. The autocollimator perceives the deflection of the reflected beam, but can only give the pitch angle and yaw angle of a planar mirror rather than the roll angle around the optic axis. To address this issue, many scholars have carried out relevant studies. [PERSON] et al. [14] aligned a laterally placed autocollimator with a planar mirror that could translate along a guideway. Thus, the roll angle of this mirror around the guideway was equivalent to the pitch angle for the autocollimator, and its measurement error was within \(\pm 0.9\) arcsec. [PERSON] et al. [15] built an autocollimation system that utilized a grating instead of a planar mirror to generate two diffracted beams. The roll angle of the grating could be computed through the beam spot displacements on two position-sensitive detectors, and a measuring accuracy of \(\pm 0.2\) arcsec over a range of \(250\) arcsec was achieved. [PERSON] et al. [16] proposed a dual-collimator method where one emitted a light beam with a dot-array pattern, while the other admitted this beam. The roll angle of the admitting collimator was solved in terms of dot distribution parameters, and the measurement error was better than \(\pm 1\) arcsec within \(\pm 150\) arcsec. [PERSON] et al. [17] designed a pyramidal prism which was equivalent to a pair ofright-angle prisms and could produce two reflected beams. Then, a goniometric algorithm allowed roll angle calculation based on the beam spot positions, but the calculation error was significantly affected by collimation angles. [PERSON] et al. [18] devised a cylindrical corner cube prism to form a cross-line image on a CMOS camera. By detecting the image obliquity, the roll angle of the prism was determined, and a measuring accuracy of \(\pm\)6.1 arcsec over a range of \(\pm\)20\({}^{\circ}\) was realized. [PERSON] et al. [19] adopted a right-angle prism (RAP) as a reflector of a goniometric system to create two reflected beams. The roll angle of the RAP could be acquired by dividing the difference in the vertical displacements of the two beam spots by the spacing between both beams. The measurement error ranged from \(-\)1.5 to 2.2 arcsec within \(\pm\)100 arcsec. [PERSON] et al. [20] incorporated the moire technique into an autocollimation system to generate a group of fringes. Subsequently, they worked out the roll angle of a RAP based on the variation in fringe width, and attained a root-mean-square error of 5 arcsec within 1000 arcsec. [PERSON] et al. [21] proposed an autocollimator that used an optical wedge working in reflective mode rather than a planar mirror. The roll angle of the optical wedge was solved according to the \(y\)-directional displacement of the light spot reflected from its rear face, and the measurement error did not exceed \(\pm\)35 arcsec within \(\pm\)2\({}^{\circ}\). [PERSON] et al. [22] presented an autocollimation system using a cooperated reflector. A collimated beam carrying a crosshair image was projected onto the reflector and then returned. The roll angle of the reflector was determined by sensing the rotation angle of the crosshair image. Although the above autocollimation methods materialize the roll angle measurement, there are still some deficiencies.