Linear Canonical Transformations are phase space deformations that can be used to describe linear optical systems. In geometric optics they correspond to the transformations of the light rays during propagation in arbitrary media, while in wave optics they describe the evolution of the space-frequency components. Although their meaning is non-ambiguous in the former case, in the latter it depends on the specific space-frequency decomposition of the wavefield. In this paper we gather several results from theoretical time-frequency analysis with Gabor Frames and provide a preliminary analysis on the implementation of phase space deformation for linear optical systems.
In this paper, we investigate the application of Gabor Frames (GFs) as an effective Time-Frequency (TF) analysis tool for compressing digital holograms. Our choice of GFs stems from their notable flexibility and accuracy in TF decomposition. Unlike some other techniques, GFs offer the advantage of accommodating both overcomplete and orthonormal signal representations. Furthermore, GFs have a robust mathematical foundation, opening doors to a broad spectrum of potential applications beyond compression. First, we provide an overview of essential concepts in GFs theory like dual GFs, analysis and synthesis operators. Second, we illustrate how GFs can be employed for digital holograms representation in the phase space domain. For compression purpose, we substitute the Short-Time Fourier Transform (STFT) used in the JPEG-PLENO Holography codec by tight GFs, and compare their encoding performance. We present and thoroughly discuss the rate-distortion graphs, shedding light on the efficacy of GFs in digital hologram lossy compression.
Digital holography is an emerging technology for 3D visualization which is expected to dethrone conventional stereoscopic devices in the future. Aside from their specific signal properties, high quality holograms with broad viewing angles contain massive amount of data. For a reasonable transmission time, efficient scalable compression schemes are needed to bridge the gap between the overwhelming volume of data and the limited bandwidth of the communication channels. The viewpoint scalability is a powerful property since it allows to encode and transmit only the information corresponding to the observer’s view. However, this approach imposes an online encoding at the server which may increase the latency of the transmission chain. To overcome this hurdle, we propose a scalable compression framework based on Gabor-wavelets decomposition, where the whole hologram is encoded offline. First, the observer plane is divided into spatial blocks. Then, the Gabor atoms are assigned to these blocks by exploiting the duality between Gabor wavelets and light rays. The atoms of each block are then classified into different layers according to their importance for the reconstruction and encoded in packets. At the decoder side, the atoms’ packets are progressively decoded based on the viewer’s position. Then, the corresponding sub-hologram is generated using a GPU implementation. Results show that our approach enables a practical progressive streaming of digital holograms with a low latency.
In this paper we investigate the suitability of Gabor Wavelets for an adaptive partial reconstruction of holograms based on the viewer position. Matching Pursuit is used for a sparse light rays decomposition of holographic patterns. At the decoding stage, sub-holograms are generated by selecting the diffracted rays corresponding to a specific area of visualization. The use of sub-holograms has been suggested in the literature as an alternative to full compression, by degrading a hologram with respect to the directional degrees of freedom. We present our approach in a complete framework for color digital holograms compression and explain, in details, how it can be efficiently exploited in the context of holographic Head-Mounted Displays. Among other aspects, encoding, adaptive reconstruction and selective degradation are studied.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.