The Trott nearfield calibration array (NFCA) is an experimentally proven concept for determining the farfield acoustic radiation of large underwater transducers from measurements in the nearfield. Existing successful NFCAs are large planar configurations of small reciprocal transducers whose responses are amplitude‐shaded to produce a nearly uniform plane wave directed normal to the NFCA throughout the volume to be occupied by the unknown transducer. Trott obtained effective shading coefficients by the use of semiempirical methods that are applicable to linear or planar arrays. In this paper a rigorous derivation of the NFCA reciprocity principle is presented for the first time. The results allow for both amplitude and phase shading and are applicable to NFCAs of any configuration. A numerical technique based on this principle is described which produces an optimum set of shading coefficients for any NFCA configuration with a prescribed plane wave direction, volume, and frequency domain. Numerical examples are presented and discussed. Included is the design of a cylindrical NFCA suitable for calibrating an enclosed cylindrical transducer without mechanical rotation.