Planar-Symmetric Fore-Afocal Lens Mapping for Residual Motion Compensation Error Suppression in Backscanning Step-and-Stare Imaging

Fore-afocal lenses with axisymmetric and linear angular magnifications are widely used for ray-beam compression before retrace compensation in backscanning step-and-stare imaging. However, the axisymmetric nature of the fore-afocal lens mapping introduces differences in the motion characteristics of off-axis rays relative to the central field, thereby leading to residual motion compensation errors and motion blur at off-axis positions within the instantaneous field of view (IFOV). To overcome this limitation, we derive a planar-symmetric fore-afocal lens mapping that ensures uniform rotational behavior of the output rays during scanning. Combined with image-space retrace compensation, this mapping theoretically enables residual motion compensation error suppression across the full IFOV. We further present an optical design implementation method for this mapping using a freeform field lens group and validate the theory and method through comprehensive optical simulations and comparative analyses, using a mid-wave infrared backscanning step-and-stare imaging system as a case study. Under operating conditions of a 400°/s scanning speed and a 5 ms exposure time in a simulation environment, the maximum motion blur caused by the residual motion compensation error is reduced from 607 µm to 3.1 µm compared with the axisymmetric case, confirming the effectiveness of the theory and methodology. The proposed planar-symmetric fore-afocal lens mapping is broadly applicable to backscanning step-and-stare imaging systems with a wide IFOV, substantially enhancing their off-axis imaging performance.