A monolithic or hybrid integrated optical information processor employing a plurality of controllable optical transfer functions at fractional Fourier planes between two optical imaging elements is described. The arrangement can be used to realize or closely approximate arbitrary non-positive-definite transfer functions of spatially-varying amplitude and phase. In various implementations, one or both of the optical imaging elements can comprise a lens or graded-index material. In some implementations, at least a portion of the arrangement is implemented in the form of a stack. Graded index material may lie between consecutive light modulating array elements. The controllable plurality of optical transfer functions are employed to create a controllable optical processor which can be used for image filtering and optical computations using complex-valued optical signal arithmetic. An image sensor may be included to transform the processed image into electrical output. Applications include optical computing systems and integrated optics.