Diffraction corrections in the radiometry of extended sources.

The diffraction corrections associated with a circular aperture in the case of an extended source and a detector located in the fully illuminated region have been calculated in 1972 by Steel, De, and Bell. We have shown recently that the intensity distribution formula that they have used is not accurate in the central region of the diffraction pattern and greatly underestimates the diffraction corrections associated with a point source. In this paper, we take up the case of an extended source; we have followed Steel et al.'s method of calculation, but have used an intensity distribution which we have shown to be valid in the central region. We show that in the case of complex radiation, the variation of the diffraction correction with the source radius rho takes a very simple form: the diffraction correction remains approximately constant as rho increases, until the source and detector subtend equal angles at the center of the aperture; if rho is increased further, the diffraction correction decreses linearly with 1/rho over a certain range of rho. Experimental results are presented that confirm these theoretical predictions.