A simple formalism is found for the measurement of wave fields that satisfy the Helmholtz equation in free space. This formalism turns out to be analogous to the well-known theory of measurements for quantum-mechanical wave functions: A measurement corresponds to the squared magnitude of the inner product (in a suitable Hilbert space) of the wave field and a field that is associated with the detector. The measurement can also be expressed as an overlap in phase space of a special form of the Wigner function that is tailored for Helmholtz wave fields.
© 2000 Optical Society of America
(030.1670) Coherence and statistical optics : Coherent optical effects
(030.5630) Coherence and statistical optics : Radiometry
(040.0040) Detectors : Detectors
(260.0260) Physical optics : Physical optics
(350.7420) Other areas of optics : Waves
Miguel A. Alonso, "Measurement of Helmholtz wave fields," J. Opt. Soc. Am. A 17, 1256-1264 (2000)