A relay lens in air takes a narrow beam from a patch of a Lambertian source of…
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging
Optics and Photonics, Ch Radiometry and photometry
Problem
A relay lens in air takes a narrow beam from a patch of a Lambertian source of radiance L=500 W m−2 sr−1: the patch has area A=4.0 mm2, and the lens accepts a cone of half-angle u1=0.050 rad about the axis and forms an image of the patch at unit magnification, so that the converging cone at the image has the same half-angle. Behind the lens the edge of a badly placed mount clips that converging cone symmetrically down to a half-angle of u2=0.030 rad and absorbs what it stops, the vignetting of Chapter 2.
((a)) Find the etendue and the flux of the beam the lens accepts, before the mount.
((b)) Find the etendue and the flux of the beam that reaches the image. Is etendue conserved here? Say in one sentence why this does not contradict the conservation law of this chapter.
((c)) Find the radiance of the image patch, and compare it with L.
((d)) By what factor has the mount lowered the irradiance at the image? Could a second, lossless lens placed after the mount restore that irradiance while keeping the image the same size?