A Method for Rapid Measurement of the Deformation and Spatial Attitude of Large Radar Antennas Inside Radomes

It is challenging to measure, analyze, and control the deformation and space attitude of antennas in narrow radomes through geometric measurement to ensure the accuracy of phased array radar application. In this manuscript, a method for rapid measurement of antennas by adopting the combination of photogrammetry system, laser tracker and total station was proposed. The photogrammetric method was used with a homemade auxiliary tool to measure and calculate the antenna’s deformation under different temperatures and pitch angles. Mapping relations between the instrumental coordinate systems of photogrammetry system, laser tracker and total station were established through common points, including target balls and reflectors. Coordinates of mark points on antenna surface were converted from photogrammetric coordinate system to laser tracker’s and total station’s coordinate system. Thus, antenna’s pitch angles relative to the local horizontal plane and deflection angles relative to the north of the engineering coordinate system were calculated. Planar fitting, coordinate transformation and space attitude calculation were all carried out in the Spatial Analyzer (SA) software. The photogrammetric method detected the antenna’s gravitational deformation sensitively, the maximum Root Mean Square Residual (RMSR) of the reference length was
$54~\mu \text{m}$
, and that of the mark points was
$59~\mu \text{m}$
, which was stably in line with its nominal accuracy. Deviations caused by coordinate transformation had no significant effect on the calculation of antenna’s spatial attitude, for the maximum deviation between the converted and measured coordinates in laser tracker’s coordinate system was 0.139 mm, and that in total station’s coordinate system was 1.037 mm, both of which were within reasonable limits of the derived theoretical maximum deviations between different instruments. As a result, the maximum deviation between the calculated value and servo system’s nominal value of antenna’s pitch angle was
$59.4''$
, and that of antenna’s deflection angle was
$91.87''$
. This method’s efficiency was greatly improved by about ten times compared with traditional methods through statistics and estimates.