Fig. 1. System configuration without proposed method. Only single diffraction term is passed by the filter of the 4-f system to form the eyebox.

Fig. 2. System configuration with proposed eyebox expansion. Vertical high order diffraction terms are passed by the filter to expand the eyebox vertically. Also, the HOE functioning as three concave mirrors duplicates horizontal eyebox.

Fig. 3. Comparison with previous eyebox expansion techniques. 3 × 3 diffraction orders in the SLM Fourier plane are shown. (a) Multiple apertures technique [8], (b) horizontal scanning technique [10], and (c) proposed technique.

Fig. 4. Angular spectrum wrapping concept. [Left column] When the desired frequency band coincides with the integer multiple of the base frequency band supported by the CGH. [Center column] When the desired band is at the boundary between the neighboring replicated base frequency band and the angular spectrum is simply shifted. [Right column] The same as the center column but when the angular spectrum is properly wrapped. In all columns, each row represents (a) the ideal angular spectrum over the CGH bandwidth, (b) the angular spectrum calculated at the desired reconstruction frequency band, (c) the angular spectrum wrapped into the CGH bandwidth, (d) the repeated angular spectrum by the SLM high order diffractions or the HOE, (e) the same as (d) but highlighted at the desired reconstruction frequency band, and (f) the same as (a) but highlighted.

Fig. 5. On-axis configuration of the proposed system. The HOE is represented by two functional blocks, i.e. vertical linear grating for horizontal replication and a focusing lens.

Fig. 6. Angular spectrums in each plane of the on-axis configuration shown in Fig. 5. (a) Horizontal direction, (b) vertical direction.

Fig. 7. (a) Schematic diagram of HOE recording process and recorded HOE. (b) Schematic diagram and picture of the hologram observing setup.

Fig. 8. (a) Simple schematic diagram of our system and the position of the camera (b) Amplitude of the angular spectrum |G_CGH(f_x, f_y)| of the CGH loaded in the SLM when range is narrow (left) and fully used (right) (c) Captured photos by positioning a diffuser at the eyebox plane. Expanded eyebox and replicated angular spectrum of the hologram can be seen.

Fig. 9. (a) Schematic diagram of the camera position and movement in hologram observing setup. (b) Position of the camera and observed hologram when the CGH for the base eyebox is maintained regardless of the camera position (Visualization 1). The camera is focusing the rear teapot hologram (3.45D)

Fig. 10. Observed hologram with the angular spectrum wrapping method (Visualization 2). The camera is focused at the rear teapot hologram (3.45D)

Fig. 11. Captured holograms from Visualization 3 and Visualization 4 when camera is focusing (a) 4.34D and (b) 3.45D at the horizontal eyebox boundary. Left and right ones were captured without and with the developed angular spectrum wrapping method, respectively.

Fig. 12. (a) Calculated diffraction efficiency distribution in the Fourier plane of the SLM. Dots represent the centers of diffraction orders. Red rectangle represents the aperture in the 4-f optics used in the experiment. (b) Relative power density measured at 3 × 3 positions in the expanded eyebox