Optical correlator (4f / VanderLugt filter)
Realizes: cross-correlation / matched filtering (pattern detection in O(1) optical time)
A 4f lens system consists of two lenses separated by twice their focal length with a holographic or spatial-light-modulator (SLM) filter at the shared Fourier plane. The first lens computes the Fourier transform of the input image; the filter multiplies by the complex conjugate of the reference pattern's Fourier transform; the second lens inverse-Fourier-transforms the product, yielding the cross-correlation at the output plane. This implements a matched filter — the canonical operation for detecting a known pattern in a cluttered scene — in a single optical pass at the speed of light, regardless of image size. The system realizes the convolution theorem physically: FT(f⋆g) = F*·G. Used in optical character recognition, fingerprint identification, and radar pulse compression. Speed: picoseconds to nanoseconds (optical propagation through ~cm path). Capacity: full 2D cross-correlation of megapixel images in a single pass; filter change requires SLM reprogramming.