## 3 Results  
The simplified optical configuration of the FTIRm system is shown in Figure 1. The spectral range of the MIR beam from the synchrotron is 899-3845 cm\({}^{-1}\) with 765 channels. The MIR beam from the synchrotron is extracted using a special mirror, with a gold coating and a central slit to reject X-rays, and enters the FTIRm system. The size of the beam at the entrance port of the FTIR spectrometer is 12 mm \(\times\) 12 mm [20]. A visible light source is collinearly aligned with the MIR beam and used as a reference for preliminary studies and alignment of the MIR beam. Extensive information on the calibration of the FTIRm system and the resolution limits are presented in [20; 21]. For the 36\(\times\) SOL, the spatial resolution is \(\sim\)8 um at 1600 cm\({}^{-1}\) and varies with the wavelength. After the matching 36\(\times\) SOL, a pinhole was used to define the spot size measured at the sample plane. Consequently, in this computational imaging method, the wavelength dependent spatial resolution limit is changed to the wavelength independent spatial resolution limit. For each recorded image, the condenser and objective were aligned in free space or an equivalent blank substrate before the pinhole (25 um pinhole, Thorlabs Inc.) or sample was placed onto the sample stage. Each point spectra were taken with a 4 cm\({}^{-1}\) resolution and averaged over four scans per point. The pinhole discussed throughout the manuscript is the one that is mounted on the sample stage. During scanning, the stage moved the sample such that the static IR beam was aligned over each measurement point. For the \(I_{PSF}\)s, a 40 \(\times\) 40 grid with 5 um grid spacing was selected totalling a 200 \(\times\) 200 um scan area. A 5.6 um beam spot was used to ensure a slight overlap between scans. A 40 \(\times\) 40, 15 um grid and 16.7 um beam size were used for the silk fibre in Figure 3. The above spot sizes are the built-in scanning options of the Bruker system and do not match with the actual spot sizes. The FTIRm system uses the OPUS software (Version 8.0) for recording and processing information. The data structure of OPUS is the spectral information for every pixel. This data structure is converted into spectral-wise images using a MATLAB linking code. The images are then averaged over the entire spectrum to obtain noise free images. This process is conducted for both the \(I_{PSF}\) and \(I_{O}\). Figure 2: Schematic of LRRA. ML—maximum likelihood; OTF—optical transfer function; \(n\)—number of iterations; NLR—non-linear reconstruction; \(\otimes\)—2D convolutional operator; \(O\)—object; \(I_{O}\)—object intensity; \(I_{O}\)’—estimated object intensity; \(3\)—Fourier transform; \(3\)’—complex conjugate operation following a Fourier transform; \(3\)’—inverse Fourier transform. \(I_{R}\)\({}^{n}\) and I\({}_{R}\)\({}^{(n+1)}\) are the \(n\)th and (\(n+1\))th solutions. \(I_{O}\) was used as the initial guess solution. \(R\)\({}^{1}\), -Fourier transform of a variable. \(\alpha\) and \(\beta\) are tuned between \(-1\) and \(+1\) to obtain the optimal reconstruction. A silk fibre is mounted on the sample plane held by a pinhole with a size of 400 \(\upmu\)m. As the silk fibre is in 3D space, the focus changes with the depth as shown in Figure 3a (\(\Delta z\) = 100 \(\upmu\)m) and Figure 3e (\(\Delta z\) = 200 \(\upmu\)m). When the plane of interest is changed along \(z\), a different region in (\(x\),\(y\)) appears sharp and intense. The \(I_{PSF}\) has a unique donut shaped intensity distribution with three lobes arising from the support structure consisting of three spokes in the SOL, as shown in the inset in Figure 1. A similar structure with four spokes in a Cassegrain objective lens has been investigated in [14]. Using the \(I_{PSF}\) similar to the one shown as an inset in Figure 3, the images Figure 3a,e were reconstructed as shown in Figure 3b,f, respectively, with \(\alpha\) = 0.5, \(\beta\) = 1 and eight iterations. As seen from the figure, the out of focus features are in focus after reconstruction.