For the volumetric holographic recording, data capacity is increased by superimposing multiple holograms using Bragg selectivity. Consequently, requirements for optical design are mainly imposed by the Bragg selectivity. Figure 1(a) shows a schematic of the volumetric holographic recording system. Since the archiving is the primary purpose of far-field recording, we consider removable media system, i.e., recording and retrieval is employed at different disc drive platforms. For example, once information is recorded at platform 1, recording media is removed and retrieved later at the platform 2. At platform 1, a spatial light modulator (SLM) is placed at the front focal point of the lens 1 (L1) and is coherently illuminated. The image bearing beam at the back focal plane of the lens L1 interferes with a reference beam (R), and forms a Fourier transform hologram. We assume that holograms are multiplexed by employing angular multiplexing by changing the angle of incidence of R with respect to recording media [
9]. Upon retrieval of the data, the recording medium is transferred to the platform 2, and is illuminated by reconstructions reference beam (R′) while varying the angle of incidence with respect to the media. The reconstructed Fourier hologram is inversely Fourier transformed by the second lens (L2), and is detected by a two-dimensional sensor array such as a charge coupled device (CCD). From the viewpoint of geometrical optics, the interchangeable media system is equivalent to a time delayed imaging system with forward and inverse Fourier transforms. By examining Fig. 1(b), we notice that there are two kinds of imaging are involved, the object imaging and pupil imaging. For the object imaging, the SLM and CCD are conjugates, i.e., object and image. Whereas for the pupil imaging, an object located at negative infinity with respect to L1 is imaged at the location of positive infinity with respect to the second lens L2. In other words, the pupil imaging is focusing of the collimated beam on the recording medium followed by re-collimation of the focused light by the second lens L2. For volume holographic imaging, the pupil imaging is especially important in two aspects, 1) mapping of SLM images to CCD and 2) performing exact Fourier transform [
10]. The accuracy of the mapping is crucial, especially for volume holographic recording system without employing quasi phase conjugate readout [
11]. Although for holographic recording as far as the mapping of SLM pixel image to the CCD is well defined, there is no physical significant requirement on the mapping. Also, exact Fourier transform of the SLM image is not necessary either. However, assuring the media transfer capability among platforms requires well-defined mapping. Consequently, the mapping of
h =
f sin
θ, where
h is the marginal ray height for pupil imaging, and is also height of the chief-ray for objet imaging,
θ is the angle of the ray at Fourier plane, and
f is the focal length of the lens, the most appropriate mapping if we consider the relations of objects and pupil aberrations [
12,
13].