Abstract: Fractional Fourier transform properties inherent in lens systems and other light and particle-beam environments may be exploited to correct misfocus effects in photographs, digital files, video, and other types of images. Small corrections may utilize fractional Fourier transform approximations around the reflection operator. The fractional Fourier transform and approximations can be rendered by optical or numerical methods, alone or in combination, directly or though use of a conventional discrete Fourier transform in combination with multiplying phase “chirps.” The corrective fractional Fourier transform power may be determined automatically or by human operator.

Abstract: A system and method for real-time controlling of signal processors, synthesizers, musical instruments, MIDI processors, lighting, video, and special effects in performance, recording, and composition environments using images derived from tactile sensors, pressure sensor arrays, optical transducer arrays, chemical sensor arrays, body sensor arrays, and numerical computation. The invention provides for pressure sensor arrays and body sensor arrays as tactile control interfaces, for video cameras and light sensor arrays as optical transducers, for chemical sensor arrays, and for other numerical image generation from computer processing or numeric simulation. Tactile transducers may be put on instrument keys of conventional instruments, be attached to existing instruments, or be used to create entirely new instrument or controller configurations.