Figure 6 Reconstruction of back-to-back objects from a two-dimensional hologram: (a) and (b) Two simulated, planar, back-to-back objects.
One such application is reconstruction of back-to-back objects from in-line Fresnel holograms [14].
Figure 5 Reconstruction of back-to-back objects from a 1-D hologram: (a) Filter SCR mask that selects the lower, longer horizontal line in Figure 4d.
Figure 4a shows a simulated hologram of two back-to-back objects having one-dimensional (1-D) variation like a long thin wire.
Figure 4 Reconstruction of back-to-back objects from a 1-D hologram: (a) A simulated two-depth 1-D hologram.
Thus, linear tracks associated with back-to-back objects overlap in the space-frequency (SF) domain, making it tedious to design SF filter mask functions to resolve such objects.
In Figure 6d, two back-to-back objects are represented by two pairs of lines with opposite slopes that intersect on the spatial axis (zero-frequency axis) at the common object coordinate n0 = 130.
The article shows that it is easier to design filter masks in the TCR domain than in the time-frequency domain for recovering downsampled cubic phase signals and resolving back-to-back objects from in-line holograms.
The proposed TCR filter intends to ease the filter design task for some applications where it is more convenient to design the filter mask function in the TCR domain than in the TF domain; such as reconstruction of back-to-back objects from in-line holograms for which SF masks have to overlap, whereas SCR masks do not.
Simulations illustrate the proposed filtering in recovery of undersampled cubic phase signals and in resolving back-to-back objects from in-line holograms for which cases it is easier to design filter masks in the TCR domain than in the time-frequency domain.
The two filter output images are summed, and then a Fourier synthesis algorithm [14] is applied to the resulting image, to recover the square shaped object as shown in Figure 7c. Figure 7 Reconstruction of back-to-back objects from a two-dimensional hologram: (a) and (b) Filter SCR masks that select horizontal traces in Figure 6e,f, respectively, to recover the square shaped object in Figure 6a.
