Radiance, which is the density of radiative power in phase space, has been the subject of a rich literature over the past 40 and more years. Emil Wolf, whom we, along with his many students and colleagues, honor herein, has been a principal contributor to the development of this subject. It is a tribute to the work of Emil Wolf and his school that the development of a wave theory of radiance, known as “generalized radiance,” continues today as exemplified by Ref. . Our own work has been complementary to this line of development in that we have attempted to bridge the gap between theory and practical radiometry. Radiometric measurements are important in many branches of science and technology. For example, in illumination engineering, the visibility of displays is quantified by radiometers. In astrophysics, radiometry in the far infrared has played a critical role in understanding the large space-time structure of the universe. Of course, in the short wavelength limit where diffraction effects can be neglected, geometrical optics suffices and one can dispense with the technical difficulties that the wave property of light introduces. But it is precisely in the regime where diffraction effects cannot be neglected that the properties of the measuring instrument have to be taken into account.Moreover, in the absence of a consistent formalism that does take the diffraction property of the instrument into account, it may be difficult to assess the significance of such effects. “Back-of-the-envelope” estimates of diffraction effects may not be reliable and the practical scientist carrying out radiometeric measurements is left with little guidance as to the magnitude of such effects. For example, an excellent text on radiometry famously states that diffraction effects are “beyond the scope” of the book. In recent papers we showed how the measurement of radiance can be understood in terms of the statistical properties of the electromagnetic field and the properties of the instrument. However, the utility of this approach was limited by the availability of accessible instrument functions that represent the measuring apparatus. In the process, we exhibited a remarkable analogy between the result of measuring radiance and the van Cittert-Zernike theorem. In this paper we first give an overview of a wave description of the measurement of radiance, referring details to previous publications. Then we compare the theory to experiments we performed with highly sophisticated radiometers, finding excellent agreement. The excellent agreement with the analytical model suggests that while our demonstration was confined to the measurement of radiance, it is likely that similar considerations apply to a wide class of optical measurements, where diffraction effects are significant.
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