Calculation of the light intensity distribution reflected by a spherical cube corner retroreflector array

Because the light intensity distribution (LID) reflected by a spherical cube corner retroreflector array (SCCRA) is of great significance for the detection of the remote laser ranging to receive laser pulse echo precisely and to accomplish the function outstandingly, it is vital to find a method to calculate the LID reflected by SCCRAs with different structural parameters for the SCCRA design. Besides, considering that the reflected light goes through a complex optical system (COS) described by ABCD matrix before it reaches the detector, the method to calculate the LID should be suitable for the COS. This article derives formulae to calculate LID reflected by a SCCRA based on the lens-system diffraction formula of S.A. Collins. In the process of deriving, coordinate transformation matrixes and vector formulations are applied and the dihedral offsets are taken into account. Because the structural parameters of the SCCRA and the expression of the ABCD matrix of the COS are not limited in the deriving process, these formulae are suitable for calculation of the LID reflected by different SCCRA and going through different COS. In addition, computer simulations are applied to explain clearly how to get the LID of a SCCRA by the formulae derived in this paper.