Diffraction Corrections in Radiometry

It is important to account for the wave nature of light, which causes the throughput of optical systems to differ from what geometrical optics predicts. A practical method to account for the wave nature of light is Kirchhoff’s theory of diffraction, particularly its Fresnel/paraxial version. In this context, one may refer to deviations from the throughput expected based on geometrical optics as diffraction effects. As a rule, the longer the wavelength, the more severe are the diffraction effects. Hence, diffraction effects are especially pronounced in the important far-infrared region of the spectrum, and accounting for them can be an indispensable component of accurate measurements.

To illustrate the effects of the wave nature of light, and our abilities to simulate it, consider the optical layout illustrated schematically in Figure 1a. A point source illuminates an 11.6 mm diameter detector through two 6.1844 mm diameter apertures placed in series in front of the detector with two 650 mm spaces between optics. The point source is off-axis by 0.229 degrees.

Figure 1a

Figures 1b-1d illustrate the diffraction ring patterns that would appear in the detector plane for 2 µm radiation. Figure 1b illustrates the pattern for only the furthest aperture (A) being present, while Figure 1c illustrates the pattern for only the closer aperture (B) being present. One can routinely calculate these ring patterns by using Lommel’s treatment. Figure 1d illustrates the pattern that would occur with both apertures present. In the Figures, the large (yellow) circle indicates the detector perimeter, whereas the smaller green circles indicate the geometrical shadow boundaries of the apertures. In geometrical optics, one would have uniform illumination within the interiors of the green circles or their intersection. Because of diffraction, the illumination is not uniform, varying between being lighter and darker than what is expected geometrically, and some radiation also falls in geometrical shadow regions.

Figure 1b	Figure 1c	Figure 1d

The topic of diffraction correction in radiometry is reviewed in Chapter 9 of Optical Radiometry, and several of our contributions to the diffraction literature in the context of radiometry are listed below.

References

• Diffraction Effects in Radiometry,
  Shirley, E.L.,
  in Optical Radiometry, Experimental Methods in The Physical Sciences, Vol. 41, Chapter 9, pp. 409-451, ed. by A.C. Parr, R.U. Datla, and J.L. Gardner (Academic Press, 2005).
• Diffraction corrections in radiometry: spectral and total power and asymptotic properties,
  Shirley, E.L.,
  J. Opt. Soc. Am. A 21, 1895-906 (2004).
• Diffraction effects on broadband radiation: formulation for computing total irradiance,
  Shirley, E.L.,
  Appl. Opt. 43, 2609-2620 (2004).
• Intuitive diffraction model for multistaged optical systems,
  Shirley, E.L.,
  Appl. Opt. 43, 735-743 (2004).
• Fraunhofer diffraction effects on total power for a Planckian source,
  Shirley, E.L.,
  J. Res. Natl. Inst. Stand. Technol. 106, 775-779 (2001).
• Revised formulas for diffraction effects with point and extended sources,
  Shirley, E.L.,
  Appl. Opt. 37, 6581-6590 (1998).
• Optimally Toothed Apertures for Reduced Diffraction,
  Shirley, E.L. and Datla, R.U.,
  J. Res. Natl. Inst. Stand. Technol. 101, 745-753 (1996).