RECONSTRUCTION OF A WEAK PHASE-AMPLITUDE OBJECT .4. NEW SAMPLING THEOREMS FOR OBJECT RECONSTRUCTION EVEN FOR NON-ISOPLANATIC IMAGING .1. ONE DIMENSIONAL OBJECT RECONSTRUCTION

New inversion procedures are derived for one-dimensional object reconstruction which use sampling values of known distributions. Whittaker-Shannon sampling is derived as a special case. The theorems apply to optical imaging with aberrations which violate the isoplanacy condition. Also a reconstruction procedure is discussed where the sampling points can be chosen at will. The (non-trivial) extension to two dimensions will be discussed in a following paper.