Find out more about holograms and real time translation respectively .
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Explanation:
Relighting is an important technique in photography which enables the optical properties of a picture to be modified without retaking it again. However, different from an optical image, a digital hologram cannot be relit by simply varying the value of individual pixel, as each of them is representing holistic information of the entire object scene. In this paper, we propose a fast method for the relighting of a digital hologram. First, the latter is projected to a virtual wavefront recording plane (WRP) that is located close to the object scene. Next, the WRP is relit, and subsequently expanded into a full hologram. Experiment results have demonstrated that our proposed method is capable of relighting a 2048x2048 hologram at a rate of over 50 frames per second. To the best of our knowledge, this is the first time relighting is considered in the context of holography.
©2012 Optical Society of America
1. Introduction
In traditional photography, it is often necessary to modify a picture to enhance its visual quality, or to create special effects that are absent in the image acquisition process. Amongst different techniques, relighting is perhaps one of the most popularly practiced methods as it allows the optical properties (such as illumination), which may be difficult to control in the real world environment, to be synthesized. Nowadays, relighting can now be conducted by both professional and novice users through a comprehensive choice of commodity photo-editing software. In brief, a picture is relit by modifying the value of each pixel according to a given criteria, an operation commonly referred to as the 'point' process. For example, the effect of a spotlight can be simulated by modulating the luminance of each pixel with the spatial distribution of the illumination. Apparently, it will be desirable if the relighting mechanism can be applied to digital holograms to enhance their impact to the observers. The problem is, rendering a digital hologram with the point process is erroneous, as each pixel is representing the holistic information from the entire object scene. Until now, research on hologram relighting has not been investigated. A straightforward solution is to render the original object scene, if it is still available, whenever a relighting task is required, and then regenerate the hologram afterwards.
2. Hologram relighting The concept of the proposed hologram relighting can be illustrated with Fig. 1 . To start with, we insert a hypothetical diffraction plane, known as the wavefront recording plane (WRP), between the digital hologram and the scene. Given an arbitrary object point, its optical wave will propagate by diffraction to the entire hologram. Other object points in the scene are contributed to the hologram in a similar manner. Hence, modifying a hologram pixel will affect the diffracted waves contributed by the entire scene image, instead of localizing in the region around the pixel of interest. However, as shown in the diagram, an object point will only cover a small area on the WRP (the dotted region). The closer the distance between the object point and the WRP, the smaller will be the coverage (a.k.a. the support) of the diffraction pattern on the latter. As such, relighting a pixel in the WRP will only affect the diffraction pattern of a small cluster of object points that share the same support. Our proposed relighting method is realized in 3 stages. First, we derive the WRP based on the mathematical framework in [1] that described the relationship between the object points in a 3D scene, the field distribution on WRP (,), and the hologram (,). These three entities are assumed to have the same horizontal, as well as vertical extents of X and Y units.-The complex wavefront contributed by the object points on the WRP is given by (Eq. (1).
where 0<< and 0<< are the horizontal and vertical positions of the jth object point. and =(−)2+(−)2+2−−−−−−−−−−−−−−−−−−−−−√ are the amplitude of the 'jth' object point and its distance from the WRP, respectively. is the perpendicular distance from the jth object point to the WRP and is the wavelength of the reference light. As the object scene is very close to the WRP, the diffracted beam of each object point only covers a small square window of size × (the dotted window in Fig. 1). As such, Eq. (1) can be rewritten as (Eq. (2).
where =⎧⎩⎨exp(2)0if|−|and|−|<12ℎ.
figure: Fig. 1