#### Abstract

In practical radiometry, it can be helpful to consider the diffraction effects on radiation in the short-wavelength limit as well as effects on total power in the high-temperature limit. Following Focke and Blevin, one can exploit limiting behavior of diffraction effects to describe the salient features thereof in an expansion in powers of wavelength or inverse powers of temperature. The Fourier transform of the average photon number per mode for a thermal source, which may be called the “S-function,” is central to assessing the effects on total power because of arrival of radiation at a detector after transiting a variety of path lengths stemming from the Fresnel-Kirchhoff formulation of diffraction. Use of a higher-order boundary diffraction wave method and analysis of the Mellin transform of the S-function clarifies strategies helpful for treating a myriad of situations, including the following four: (1.) a radiometer viewing a source through a series of two non-limiting baffles; (2.) a radiometer viewing a source through one limiting aperture and one non-limiting baffle located in the aperture’s shadow region; (3.) a radiometer viewing a source through one limiting and one non-limiting baffle between the aperture and radiometer but located in an illuminated region; and (4.) a radiometer viewing an extended source viewed through a pinhole, when the pinhole itself views only a portion of the source because of a limiting aperture located between the pinhole and the source. These situations arise in several practical instances, including several satellite-based total-solar irradiance instruments, collimators with blackbody sources that are used to simulate remote objects, and calibration of blackbody sources used as radiation standards. Oftentimes, modest computation by computer is required to assess diffraction effects, whereas we have also developed compact formulas can serve as effectual approximations in many instances.

Diffraction Effects on Broadband Radiation in Multi-staged Systems

In practical radiometry, it can be helpful to consider the diffraction effects on radiation in the short-wavelength limit as well as effects on total power in the high-temperature limit. Following Focke and Blevin, one can exploit limiting behavior of diffraction effects to describe the salient features thereof in an expansion in powers of wavelength or inverse powers of temperature. The Fourier transform of the average photon number per mode for a thermal source, which may be called the “S-function,” is central to assessing the effects on total power because of arrival of radiation at a detector after transiting a variety of path lengths stemming from the Fresnel-Kirchhoff formulation of diffraction. Use of a higher-order boundary diffraction wave method and analysis of the Mellin transform of the S-function clarifies strategies helpful for treating a myriad of situations, including the following four: (1.) a radiometer viewing a source through a series of two non-limiting baffles; (2.) a radiometer viewing a source through one limiting aperture and one non-limiting baffle located in the aperture’s shadow region; (3.) a radiometer viewing a source through one limiting and one non-limiting baffle between the aperture and radiometer but located in an illuminated region; and (4.) a radiometer viewing an extended source viewed through a pinhole, when the pinhole itself views only a portion of the source because of a limiting aperture located between the pinhole and the source. These situations arise in several practical instances, including several satellite-based total-solar irradiance instruments, collimators with blackbody sources that are used to simulate remote objects, and calibration of blackbody sources used as radiation standards. Oftentimes, modest computation by computer is required to assess diffraction effects, whereas we have also developed compact formulas can serve as effectual approximations in many instances.