2 1) As shown in Fig. 1 below, a lensless Fourier transform hologram is made by placing an object and a point source in front of a photographic plate. The point source has two purposes. First, it is...

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2 1) As shown in Fig. 1 below, a lensless Fourier transform hologram is made by placing an object and a point source in front of a photographic plate. The point source has two purposes. First, it is used to generate the fields scattered from the object which is denoted as the object beam O. Secondly, it is used as the reference beam R which interferes with the object beam on the photographic plate surface consequently forming a fringe pattern on this surface. Assume the point source is to be a distance zo from the photographic plate. Furthermore, assume that the hologram is fabricated from only one object slice positioned a distance z1 in front of the plate ozz1 . In order to reconstruct the image, the hologram is illuminated by a reconstructing beam P generated by a point source positioned a distance z~ in front of the transparency and displaced along the x-axis distance x~ as shown in Fig. 2 below. Assuming the distance z~ between the point source generating the reconstructing beam and the hologram can be varied, determine the position of the point source so to generate the true image. Find the location of the reconstructed true image. You must show all work and all details for credit. zo R z1 O xf z Object Point Source Hologram Fabrication Figure 1. Lensless hologram fabrication 3 z P xf z Point Source Image Reconstruction ~ x~ Figure 2 Image reconstruction of a lensless Fourier transform hologram.