Optical Systems with Resolving Powers Exceeding the Classical Limit*

A new theorem on the ultimate limit of performance of optical systems is established: Not the bandwidth of the transferred spatial frequencies but only the number of degrees of freedom of the optical message transmitted by a given optical system is invariant. It is therefore possible (a) to extend the bandwidth by reducing the object area, (b) to extend the bandwidth in the x direction while proportionally reducing it in the y direction, so that the two-dimensional bandwidth is constant, and (c) to double the bandwidth when transmitting information about one state of polarization only.To achieve this, the optical systems are modified by inserting two suitable masks (generally gratings) into optically conjugate planes of object and image space. The transfer and spread function of the modified systems are calculated for the case of coherent illumination.