Extended depth of field using a logarithmic asphere

Imaging systems are described which use a logarithmic asphere and image processing in order to increase the depth of field substantially beyond classical limits. A nonparaxial form of the diffraction theory integral for an impulse response is derived and evaluated in order to establish a precise expression for the transmission function of this asphere. This nonparaxial physical optics formulation provides results of fractional wavelength accuracy that enable one immediately to complete the design and fabrication of the optical system. Circularly symmetric aspherical lenses, either for single-lens cameras or blurring phase filters for use with commercial photographic lenses, have been fabricated using advanced grinding and finishing machines. Computer simulation studies are presented to show that a logarithmic asphere is capable of diffraction-limited performance over an extended depth of field. Experimental imaging results including digital processing by an inverse filter show a tenfold increase in the depth of field.