Roof angle error effect on modulation transfer function and spread function

Prisms including roof sections are frequent components in optical systems, usually serving to rectify images for direct viewing. Often the image forming rays pass the roof section in both directions. In such applications, the tolerances on the roof angle must be kept very tight to assure an acceptable resolving power. If, for example, the blurring due to this discrepancy is to be kept to a modest 0.1 mrad and the prism is made of crown glass, the tolerance on the roof angle will be ~15 microrad, i.e., ~3 sec of arc. This extremely tight tolerance illustrates the fact that the roof angle error can be an important factor in determining system performance. Here we develop the physical optics (OTF) and point spread functions associated with the roof angle error, assuming the rest of the optical system to be aberrationless.