Karl-Heinz Brenner

Digital optical computing with symbolic substitution.

Symbolic substitution logic is based on optical pattern transformations. This space-invariant mechanism is shown to be capable of supporting space-variant operations. An optical implementation is proposed. It is based on splitting an image, shifting the split images, superimposing the results, regenerating the superimposed image with an optical logic array, splitting the regenerated image, shifting the resulting images, and superimposing the shifted images. Experimental results are presented. Examples demonstrate how symbolic substitution logic can be used to implement Boolean logic, binary arithmetic, cellular logic, and Turing machines.

The wigner distribution function and its optical production

Abstract An optical signal (image etc.) can be described by its complex amplitude u (x, y), or by its spatial frequency spectrum. Both descriptions are complte and also equivalent, because one can be derived from the other by a Fourier transformation. Neither the complex amplitude nor the spatial frequency spectrum is suitable for answering a question like “what is the spatial frequency in a certain part of the image?”. Here the term “local spectrum” is adequate. A rigorous definition of the “local spectrum” can be based on the Wigner distribution function. We developed optical methods for producing this “local spectrum” and we applied these methods to the investigation of sound patterns.

Optical implementations of the perfect shuffle interconnection

The concept of a perfect shuffle is reviewed. Holographic approaches based on implementing a point spread function equivalent to the sum of two shifted delta functions are suggested. Interferometric approaches based on splitting an image and then combining them in a shifted manner are also suggested.

The ambiguity function as a polar display of the OTF

Abstract It is shown that the Ambiguity function of the generalized pupil function of an optical system, is a polar display of the optical transfer function with the focus error as variable. This geometrical interpretation allows one to obtain the OTF for any given amount of defocus.

Wigner distribution function display of complex 1D signals

Abstract Three optical methods are proposed for the production of the Wigner distribution function (WDF). This function offers an alternative way of representing signals. The WDF depends simultaneously on time (or space) and on frequency. For the production of the WDF we distinguish between real signals, holograms of complex signals and truly complex signals. An important special class of signals are pure-phase functions. The WDF of such phase functions is very useful for testing optical phase structures. Our setups can also be employed for the production of the ambiguity function.

Diffractive–reflective optical interconnects

We have demonstrated the feasibility of diffractive-reflective optical interconnects. These interconnects consist of a sandwich of a holographic plane and a reflective plane. Various possibilities like beam relaying, connection switching, and broadcasting are discussed.

New implementation of symbolic substitution logic

Symbolic substitution is a spatial logic for digital optical computers that utilizes the specific advantages of optical signal processing. Previous implementations used the optical intensity for coding the binary values. In this implementation we are using polarization for coding, and we show how a complete recognition–substitution processor can be implemented. The advantages of this type of coding are: better utilization of the device area, an equal distribution of intensity, and symmetry between the two logic states.

Ambiguity function and Wigner distribution function applied to partially coherent imagery

The mutual intensity function is conveniently replaced by the ambiguity function or the Wigner distribution function. This allows us to treat optical systems under partially coherent illumination in a simple fashion. Many optical set-ups can be described on a geometrical basis, as is illustrated with some examples.

Compact photorefractive correlator for robotic applications.

We design, implement, and test a multichannel photorefractive optical joint transform correlator that is capable of performing sorting tasks for robotic applications. The use of mini-YAG lasers and liquid-crystal spatial light modulators, in conjunction with updatable holographic BSO crystals, results in a compact correlator (600 mm x 300 mm x 300 mm) with real-time capabilities (100-ms recognition speed). Flexibility is a built-in feature, and correlation is demonstrated for various applications. Electronic and optical preprocessing and postprocessing for improving demonstrator performances are also discussed.

Optical symbolic substitution: system design using phase-only holograms

Symbolic substitution is a method for manipulating binary data that depends on both the value of the data and its spatial location to realize logical operations. A substitution system requires only a pattern recognizer, a nonlinear device, and a pattern substituter. Using classical optical elements and phase-only holographical elements, it is possible to construct optical systems for both recognition and substitution. Systems using one or two holographical elements are presented, and procedures for designing the elements are also discussed.