## 3 Results
A single fibre strand can be clearly seen in both cases. The magnified versions of Figure 3a,b,e,f are shown in Figure 3c,d,g,h, respectively. The normalised absorbance spectrum was obtained, which is plotted as shown in Figure 3i which shows a distinct absorbance peak at 1600 cm\({}^{-1}\). By choosing an \(I_{PSF}\) recorded at a different distance, different parts of the images at different depths can be reconstructed. The high-intensity regions seen in the reconstructed images correspond to the axial plane of the pinhole when the \(I_{PSF}\) was recorded. When an \(I_{PSF}\) of another axial plane was used for reconstruction, it increased the intensity of the region that corresponded to that plane. To further evaluate the method, a two-plane object was constructed using two pinholes in one plane and the digit '3' from the USAF resolution target separated by a distance of 300 \(\upmu\)m. This was achieved by summing the corresponding intensity distributions from the two planes. Since the synchrotron beam is spatially incoherent, there is only intensity addition between light from two points and not a complex addition as in spatially coherent light sources. In this case, there was a slight misalignment, which is indicated by the intensity difference in one of the three lobes of the \(I_{PSF}\). The images of the \(I_{PSF}\) recorded intensity distribution and the reconstructed images are shown in Figure 4a-c, respectively. It can be seen that the reconstructed image shows the two pinholes and distorts the digit '3' which was focused. The distortion also follows the nature of the \(I_{PSF}\) bringing more reconstructed intensity to the middle. The above digital refocusing shows the possibility of 3D imaging in the IR synchrotron beam. The reconstruction conditions of the LRRA are quite similar to the previous case, with \(\alpha\) = 0.4, \(\beta\) = 1 and seven iterations. Figure 3: Experimental 2D imaging results. Recorded image of silk fibre (**a,e**). Reconstructed images of (**a,e**) are (**b,f**). Magnified versions of sections of (**a,b,e,f**) are shown in (**c,d,g,h**), respectively. The image of the \(I_{PSF}\) is given as an inset in left most part of the figure. (**i**) The normalised absorbance of the silk fibre. The scale bar is 100 \(\upmu\)m.  
In Figure 4b, it is seen that the digit '3' is well focused, but the two pinholes were blurred indicating that the two objects are in different planes. When Figure 4b is reconstructed using the \(I_{PSF}\) shown in Figure 4a using the LRRA, as the \(I_{PSF}\) corresponds to the plane of the two pinholes, the information of the two pinholes is deblurred, while the other object digit '3' is blurred. The blurring and deblurring behaviours depend upon the nature of the \(I_{PSF}\). The \(I_{PSF}\) of the SOL is quite different from the commonly seen blurring with a lens. Consequently, unusual distributions such as the 'hot spots' seen in Figure 4c are obtained during blurring. Considering the fundamental concepts of image formation and image reconstruction, the above behaviour can be clearly understood. The physical meaning of the convolution operation which yields the object information \(I_{O}\) is that every object point in \(O\) is replaced by the \(I_{PSF}\) and in the overlapped regions there is an addition. This can be seen in Figure 4b, as there are two points, each point is replaced by Figure 4a and the overlapped region has a higher intensity, indicating an addition. The image reconstruction or deblurring from the \(I_{O}\) and the \(I_{PSF}\) is achieved by pattern recognition, where the \(I_{PSF}\) is scanned over the \(I_{O}\) and a peak is generated whenever there is a pattern matching. Consequently, when Figure 4a is scanned over Figure 4b, two peaks are generated for the two pinholes as there is perfect pattern matching in those locations. Further, there is some similarity between the structure of the digit '3' and Figure 4a which gives rise to hot spots.