## 3 Diffusive Markers Based Compensation  
The micromirrors are fabricated as computer generated holograms (CGH) on a photopolymer sheet. While calculating the CGH, small diffuse areas were added to the top-left corner of each micromirror. The diffuse area consists of random dots of size 0.6 \(\upmu\)m occupying an area of 150 \(\times\) 150 \(\upmu\)m. The dot size of 0.6 \(\upmu\)m is the result of each pixel of the SLM (size 6 \(\upmu\)m) being de-magnified 10\(\times\) on the photopolymer. The dimensions of the diffuse area were experimentally determined so that they could be detected by the dedicated calibration procedure but remain invisible during the reconstruction. Each elemental micromirror in the array is rectangular in shape and is 1 mm \(\times\) 0.5 mm in dimension. The size of each elemental micromirror was also determined experimentally, so that the best diffraction, resolution, and view-angle was achieved, given the limitation of the fabrication setup. The ratio of length to width of each micromirror was determined in accordance with the aspect ratio of the SLM. The array contains 100 \(\times\) 200 elemental micromirrors and the whole DDHOE screen is of size 10 cm \(\times\) 10 cm. The optical axis of each elemental micromirrors are tilted a bit towards the center, in-order to obtain maximum field-of-view [11]. The hologram pattern was generated on the computer, phase wrapping a summation of two terms, (i) a quadratic phase term (that corresponds to the focal length of the lens) and (ii) a linear phase term (that corresponds to the tilt to optical axis) which results in a Fresnel-zone like pattern as shown in Figure 3. A detailed explanation to the hologram computation procedure can be found in [11]. These computed digital data are then converted into light modulations by displaying them on a spatial light modulator (SLM) and illuminating it with a laser beam. The light pattern generated by the SLM is then optically de-magnified and transferred to a photopolymer film. The photopolymer used was Bayfol HX-102 manufactured by Covestro. This fabrication process is called as \"wave-front printing\" and is explained in detail by [PERSON] et al. [12]. Figure 4a shows the photograph of a fabricated micro mirrorarray sheet when illuminated with white light from a projector. Since a green laser of wavelength 532 nm was used for fabricating the volume hologram, and only green light reflects back even illuminated with white light (due to the property of wavelength selectivity of a Bragg hologram). The fabricated Bragg holograms had a diffraction efficiency of 60%. It is worth noting here that a wave-optics based treatment is used to define and execute the hologram computation and fabrication process [11], whereas the calibration process to follow will be treated using geometric optics principles. Due to the light diffusing property, the marker itself is hard to see with the naked eye, as can be observed from Figure 4a. Even when it is fully lit by the projector, it does not interfere with the reconstructed light field: it only reflects a small amount of light towards the observer, compared to the rest of the mirror. This clearly shows that the presence of diffuse areas does not create any effect during reconstruction. A small drawback of this approach is that the viewpoints in one of the corners of the viewing zone will not be reconstructed; however, an observer usually does not reside in these corners of the viewing zone due to practical reasons: the regions are located too high or low for a pleasant viewing experience, as well as the scene that starts to disappear at the border of the viewing zone. The diffuse areas are visible as tiny spots on the bottom-right corner of each mirror-array. Figure 3: Illustration of the interference pattern used by the wavefront printer. The randomness in the lower-right corner introduces a diffusing area in the final micromirror. In order to use the markers for the calibration, we need to detect them first.