This paper extends the analysis of optical imagery on the basis of Walsh functions to the determination of the diffraction-based optical transfer function (OTF) for on-axis systems. A semi-analytic and simplified expression for OTF is obtained which is directly amenable to subsequent operations which are often called for in optimization and tolerancing analyses. The computational speed for OTF evaluation is greatly increased where repetitive calculation of the OTF for different pupil plane parameters is required. Some computational results are presented and compared with the results obtained by other methods. © 1981 Taylor & Francis Group, LLC.