This thesis describes the design of free-space optical interconnections between two arrays within commercial constraints for use as an incoherent correlator in image recognition or compression applications. Critical reviews are given of computer generated holograms and of refractive microlenses. Photoresist microlenses were chosen due to their ease of fabrication, efficient operation under incoherent illumination and the compactness of the system which results. Novel long focal length (up to 4.7 mm) microlenses with diameters of 120 μm were realised by immersing the microlenses in fluids of appropriate refractive index. They had negligible astigmatic aberrations for off-axis angles of illumination. Two novel configurations are proposed for incoherent correlators based on the image multiplexer and shared microlens interconnect systems. The shared microlens total interconnect was used because it was shorter. Theoretical analysis of a shared microlens system, a shared pinhole system and a shadow casting system showed that the first gave the best combination of high efficiency with good resolution and low crosstalk in the correlation plane. Measurements of the angular responses of two diffusers for generating illumination gave a narrow but efficient response for the microlens diffuser and a wider spread for a bulk plastic diffuser which was then selected. An incoherent correlator was constructed successfully using two high contrast image transparencies giving correlation peaks as predicted and demonstrating translation invariance. The feasibility of using ferroelectric liquid crystal spatial light modulators was assessed. A theoretical computer simulation of the correlation process showed that the poor contrast ratio of the SLM (10:1) seriously degraded the output correlation contrast (2:1). Indeed in experiments using one SLM and a high contrast transparency it was impossible to discern any correlation peaks. We conclude that a higher contrast SLM, which may be in the form of an optically addressed SLM, is required for successful practical operation.