The thin lens equation for optical parametric image conversion

It is shown that the image upconverter can operate with point source pump-beams as well as the commonly used planar pump source. The major effect of the pump beam divergence is not to degrade the resolution but is to change the transverse and longitudinal magnification of the image. We demonstrate by a paraxial ray-tracing analysis that these changes in image dimensions and location obey relations quite similar to thin-lens formulae.