#### Abstract

Calculating diffraction corrections in radiometric measurements can be a time-consuming process. However, computer calculations are most difficult for small wavelengths and/or high source temperatures, and in these cases there is the greatest potential for deriving sufficiently accurate analytical formulas for the corrections, eliminating the need for numerical calculations. To capitalize maximally on this fact, we have developed methods that bridge the numerically “easy” region of long wavelengths with increasingly detailed analytical expressions for diffraction effects. In this presentation, three areas of innovation will be noted.

- Diffraction corrections for thermal and spectrally resolved radiation are presented for point and extended sources in the context of a three-element, source-aperture-detector system. Detailed numerical integrals are avoided altogether, as is detailed wavelength sampling, even though diffraction effects oscillate rapidly as a function of wavelength, through judicious use of Lagrange-Chebyshev interpolation techniques.
- Second-order diffraction corrections, which account for light diffracting twice between the source and detector in an optical setup, can be significant, for instance, when measuring the radiance temperature of blackbodies based on total-power measurements. We apply a higher-order boundary-diffraction wave formulation to include the most severe second-order corrections, in which non-limiting baffles diffract less than expected because the light reaching them is diminished by diffraction at a blackbody pinhole aperture.
- Because it is an invariant quantity, radiance can be favored instead of irradiance as a measurement that is used in a calibration strategy for treating sources or radiometers under test. (For radiometers, one considers the radiance responsivity.) Here, we consider which measurement issues involving diffraction become resolved, and which issues remain, when calibrating NIST’s Missile Defense Transfer Radiometer (MDXR) in radiance mode as compared to irradiance mode.

Streamlined Diffraction Corrections in Practical Radiometry

Calculating diffraction corrections in radiometric measurements can be a time-consuming process. However, computer calculations are most difficult for small wavelengths and/or high source temperatures, and in these cases there is the greatest potential for deriving sufficiently accurate analytical formulas for the corrections, eliminating the need for numerical calculations. To capitalize maximally on this fact, we have developed methods that bridge the numerically “easy” region of long wavelengths with increasingly detailed analytical expressions for diffraction effects. In this presentation, three areas of innovation will be noted.

- Diffraction corrections for thermal and spectrally resolved radiation are presented for point and extended sources in the context of a three-element, source-aperture-detector system. Detailed numerical integrals are avoided altogether, as is detailed wavelength sampling, even though diffraction effects oscillate rapidly as a function of wavelength, through judicious use of Lagrange-Chebyshev interpolation techniques.
- Second-order diffraction corrections, which account for light diffracting twice between the source and detector in an optical setup, can be significant, for instance, when measuring the radiance temperature of blackbodies based on total-power measurements. We apply a higher-order boundary-diffraction wave formulation to include the most severe second-order corrections, in which non-limiting baffles diffract less than expected because the light reaching them is diminished by diffraction at a blackbody pinhole aperture.
- Because it is an invariant quantity, radiance can be favored instead of irradiance as a measurement that is used in a calibration strategy for treating sources or radiometers under test. (For radiometers, one considers the radiance responsivity.) Here, we consider which measurement issues involving diffraction become resolved, and which issues remain, when calibrating NIST’s Missile Defense Transfer Radiometer (MDXR) in radiance mode as compared to irradiance mode.