## 5 Summary and Conclusions  
The online FTIRm system of the Australian Synchrotron uses an IR beam with a peculiar intensity distribution in the shape of two lines, which results in a complicated  
Figure 5: Experimental imaging results. (**a**) Image of the \(I_{PSF}\), and (**b**) recorded intensity image of the two-plane objects. Reconstruction results using (**c**) matched filter, (**d**) phase-only filter, (**e**) NLR (\(\alpha\) = 0, \(\beta\) = 0.7), (**f**) LRA (\(n\) = 100), (**g**) LRRA (\(\alpha\) = 0.4, \(\beta\) = 1 and \(n\) = 10) and (**h**) Weiner filter (\(\sigma\) = 1000). The scale bar is 50 \(\upmu\)m.  
Figure 6: Simulation results. (**a**) Test object. (**b**) \(I_{PSF}\). (**c**) \(I_{O}\). Reconstruction results using (**d**) matched filter, (**e**) phase-only filter, (**f**) NLR (\(\alpha\) = 0, \(\beta\) = 0.5), (**g**) LRA (\(n\) = 100) and (**h**) LRRA (\(\alpha\) = 0, \(\beta\) = 0.95, \(n\) = 9). optical configuration. As it is known, the development of a detector in the wavelength region of MIR is challenging, unlike in the visible region where megapixels of information can be detected with high-resolution sensors. The online FTIRm system at the Australian Synchrotron is equipped with two image sensors: single pixel and FPA detectors made of mercury cadmium telluride, both cooled by liquid nitrogen. As the FPA has only 64 \(\times\) 64 pixels, a single shot recording with that detector results in a low-resolution image. Therefore, the single pixel detector is used for pixel-by-pixel scanning of the sample followed by a computational stitching procedure to record a 2D image of the object with a better resolution. Even though in most of the measurements with FTIRm a thin slice of the sample is used, with a strong (36\(\times\)) objective, an axial aberration or thickness variation of a few micrometres can significantly affect the imaging results. The running cost of the Australian Synchrotron is quite high, with most of the user projects awarded with limited beamtime hours ranging from 48 h to 96 h and valued at -AUD 100 K. Therefore, it is crucial to avoid aberrations during measurements and to utilize the beamtime efficiently. The focusing elements used in FTIRm are not regular refractive lenses but reflective Schwarzschild objectives, which have a unique spatial aberration in the form of a donut with three distinct intensity lobes. When there is an axial aberration, the images are highly distorted. Consequently, existing deblurring methods are not suitable for deblurring the images. In this study, a recently developed computational reconstruction method called the LRRA has been applied to realise CASH. Both standard samples, such as USAF objects and pinholes, and biochemical samples such as silk were studied. The LRRA method was able to reconstruct not only 2D but also 3D information from the object. One of the challenges with the LRRA is that it is not possible to know the values of \(\alpha\), \(\beta\) and \(n\) beforehand, and they can only be predicted by an expert user from the outcomes of NLR and the LRA. However, in the future, we plan to address this problem. We believe that the proposed and demonstrated method is a significant step forward for the FTIRm system of the Australian Synchrotron. The impact of the study is high, as the developed technique will enable rapid imaging, aberration correction, and 3D imaging, benefiting the users of the Australian Synchrotron. The proposed method is not limited only to applications in the FTIRm system of the Australian Synchrotron but can be applied to other advanced imaging systems with complicated optical configurations. Recently, single shot phase imaging has been demonstrated at the Australian Synchrotron [22]. Scanning holography is a milestone in the history of holography [10]. We believe that the CASH developed in this study and the recent phase imaging demonstration will lead to further developments and wider applications of FTIRm.