# Recording a Hologram Transmitted over a Communication Channel on One Sideband
## 1 Introduction  
The problems related to holographic TV infringe on the interests of experts both in the area of holography and in image coding. For this reason, the Joint Photographic Experts Group (JPEG) has announced a competition of the proposals in holographic coding [1, 2, 3]. In its standard ISO/IEC 21794 [4], JPEG proposed solutions for coding more complete light field data [5] through creating a 4D array of the data on the light wave, with subsequent purely mathematical elimination of redundancy, similar to Huffman codes, for an increase in the entropy of an encoded message. High requirements in terms of the amount of information processed in this manner and the processing rate are also mentioned. This is due to the fact that each frame, which is a 3D array of the object holographic data, should change at a frame rate accepted by the major TV standards. This approach is implemented at present within the technologies of point cloud [6, 7], polygonal [8, 9] and voxel [10, 11] representation of 3D images. Transmission of the real-time 3D images requires not only high computer productivity, but also the immense throughput capacity of the communication channel. Indeed, the density of holographic data records is limited by diffraction effects and is proportional to the spatial frequencies in a frame, inversely proportional to the size of the Airy spot [12, 13, 14]. In other words, the number of points on a hologram is inversely proportional to the size of the Airy spot, and for the focused image holograms, their number is inversely proportional by the order of magnitude to the wavelength. Within the visible range, for a hologram of a portrait image of A4 size (210 mm \(\times\) 297 mm), which corresponds to a television screen of 14 inches diagonal,at \(\lambda\) = 0.63 \(\upmu\)m, the number of points on the hologram reaches \(n\) = 1.6 \(\times\) 10\({}^{11}\). For the binary record, this corresponds to the same amount of information measured in data bits. This is approximately \(n\) = 2 \(\times\) 10\({}^{10}\) bytes \(\approx\) 20 GB, which is equivalent to the information contained in an hour-long film of the Full HD standard. For transmission along a radio channel with a frame rate of 25 frames/s, this will take a bandwidth of about 500 GHz and will overlap the whole radio range available for mankind, pushing out all other radio and television channels. A way out of the formed contradiction is either a substantial decrease in the size of the holographic image, which does not correspond to the requirements of augmented reality, or the compression of the holographic information so that its amount would not exceed reasonable limits--that is, the possibilities of the modern communication channels 3G and 4G. To solve this problem, we chose another method of transmitting the holographic information, as presented in [14; 15] and covered by RF Patent [16]. The essence of this method is in recognizing that it is not necessary to transmit the whole amount of holographic information for the creation of a 3D holographic image at the receiver end of the communication channel; it is sufficient to only transmit the part responsible for carrier modulation. In spite of the fact that the modulation in holography is more complicated, this is very similar to the SSB method, because the spatial frequencies of the carrier are already input at the receiving end of the communication channel. The difference between the proposed method and the SSB is the fact that the side spatial frequencies are not transmitted, but are still created at the receiving end of the communication channel on the basis of the two transmitted image modes: depth map + surface texture of the 3D holographic object. So, a 4D file of the holographic content considered in [4; 5], which is a time-base sweep of 3D images, is replaced by the time-base sweep of two 2D images, to which JPEG compression has already been applied. The first of these two images is the surface texture of the 3D object, similar to a common photographic image or a series in a video.