The advantage of optics is its capability of providing highly parallel operations in a three-dimensional space. In this paper, we propose optical architectures to execute various image compression techniques. We optically implement the following compression techniques: transform coding, vector quantization, video coding. We show many generally used transform coding methods, for example, the cosine transform, can be implemented by a simple optical system. The transform coding can be carried out in constant time. Most of this paper is concerned with an innovative optical system for vector quantization using holographic associative matching. Limitations of conventional vector quantization schemes are caused by a large number of sequential searches through a large vector space. Holographic associative matching provided by multiple exposure holograms can offer advantageous techniques for vector-quantization-based compression schemes. Photorefractive crystals, which provide high-density recording in real time, are used as our holographic media. The reconstruction alphabet can be dynamically constructed through training or stored in the photorefractive crystal in advance. Encoding a new vector can be carried out by holographic associative matching in constant time. An extension to interframe coding using optical block matching methods is also discussed.>

Optical computing has recently become a very active research field. The advantage of optics is its capability of providing highly parallel operations in a three dimensional space. The authors propose optical architectures to execute various image compression techniques. They optically implement the following compression techniques: transform coding; vector quantization; and interframe coding; They show many generally used transform coding methods, for example, the cosine transform, can be implemented by a simple optical system. The transform coding can be carried out in constant time. Most of this paper is concerned with a sophisticated optical system for vector quantization using holographic associative matching. Holographic associative matching provided by multiple exposure holograms can offer advantageous techniques for vector quantization based compression schemes. Photorefractive crystals, which provide high density recording in real time, are used as the holographic media. The reconstruction alphabet can be dynamically constructed through training or stored in the photorefractive crystal in advance. Encoding a new vector can be carried out by holographic associative matching in constant time. An extension to interframe coding is also discussed.>

The ray-tracing problem is considered for optical systems consisting of a set of refractive or reflective surfaces. It is assumed that the position and the tangent of the incident angle of the initial light ray are rational. The computability and complexity of the ray-tracing problems are investigated for various optical models. The results show that, depending on the optical model, ray tracing is sometimes undecidable, sometimes PSPACE-hard, and sometimes in PSPACE.>