The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

Acoustooptic techniques have been used to perform computationally intensive signal processing operations and form subsystems of larger signal processing systems. Key aspects of acoustooptic devices and of the range of possible signal processing applications, including the advantages of acoustooptic implementation, are reviewed. Developments that improve acoustooptic device performance, increase system dynamic range such as by reduction of optical crosstalk from optical scatter and wavefront error, and implement data reduction operations that allow easier interfacing into a larger signal processing/computation system are described. >

Acoustooptic signal processing and computing

In a recent work, an operator algebra was developed for the description of axially symmetrical coherent optical systems. The present work extends the operator representation to incorporate cylindircal lenses and is used to analyze the transforming properties of an arbitrarily oriented cylindrical lens. The results provide the basis for synthesizing various systems for signal processing, such as convolution and correlation operations.

Cylindrical lens systems described by operator algebra.

The operator description of Fourier optics is extended and applied to holography. The existing lens models for ideal holographic processes appear as a self-evident intermediate result; generalization to include apertures, recording-material modulation transfer function, and extended source effects is straightforward. The extended source effect is generally shown to be equivalent to a modification of the actual holographic apertures. The final result is a compact expression for the description of the holographically reconstructed field distribution at an arbitrary plane. A useful, comprehensive list of operator relations is given in two appendixes.

Holography described by operator algebra

Optical data processing. Principles and application to EEG audiometry.

Generalized optical processors are examined from the point-of-view of developing a systematic method for determining which linear processing operations may be performed in a coherent optical system. In this paper a procedure is presented for examining a general n-plane processor and expressing the resulting system in terms of a conventional linear processing model. The generalized kernel of the resulting integral equation is used to describe currently well understood coherent linear processors as simple examples of a more general n-plane processor. A 2-plane processor is shown to correspond to the Fourier transform operation with a simple lens, and the 3-plane processor is associated with convolution or correlation. The kernel of a 4-plane system is shown to resemble the ambiguity function, and to represent an oblique to rectangular plane inverter, when an appropriate assumption is made about the complex amplitude-transmittance function of one optical plane. The more general n-plane kernels have integral representations for which simple physical realizations remain to be developed.

F.P. Carlson

Papers

Generalized linear processors for coherent optical computers