The Fourier transform infrared microspectroscopy (FTIRm) system of the Australian Synchrotron has a unique optical configuration with a peculiar beam profile consisting of two parallel lines. The beam is tightly focused using a 36× Schwarzschild objective to a point on the sample and the sample is scanned pixel by pixel to record an image of a single plane using a single pixel mercury cadmium telluride detector. A computational stitching procedure is used to obtain a 2D image of the sample. However, if the imaging condition is not satisfied, then the recorded object’s information is distorted. Unlike commonly observed blurring, the case with a Schwarzschild objective is unique, with a donut like intensity distribution with three distinct lobes. Consequently, commonly used deblurring methods are not efficient for image reconstruction. In this study, we have applied a recently developed computational reconstruction method called the Lucy–Richardson–Rosen algorithm (LRRA) in the online FTIRm system for the first time. The method involves two steps: training step and imaging step. In the training step, the point spread function (PSF) library is recorded by temporal summation of intensity patterns obtained by scanning the pinhole in the x-y directions across the path of the beam using the single pixel detector along the z direction. In the imaging step, the process is repeated for a complicated object along only a single plane. This new technique is named coded aperture scanning holography. Different types of samples, such as two pinholes; a number 3 USAF object; a cross shaped object on a barium fluoride substrate; and a silk sample are used for the demonstration of both image recovery and 3D imaging applications.