Partially coherent optical processor for enhancement of partial second order derivatives of an image: Analysis and implementation

We present an optical processor capable to perform partial second derivatives of an image working with partially coherent illumination. The proposed system utilizes a liquid crystal display, onto which images to be derived are displayed. The method is based on the capacity of these devices to generate simultaneously a contrast reverted replica of the image displayed on it. A positive replica of original image is obtained when the LCD is between crossed polarizers, while the negative one is obtained with the LCD is between parallel polarizers. Since the LCD is a diffraction element, both polarizer arrangements may be simultaneously implemented, for example, in a 4f optical processor using polarization filtering of the different diffraction orders. When three images (two replicas of original image displaced in opposite direction and the other one with contrast reverted and centered at the origin.) are imagined across a slightly defocused plane, one obtains an image with enhanced second derivatives in a given direction. No other incoherent (or partially coherent) optical system is presently known which can perform partial second-order derivatives of an image. Experimental results obtained are presented.