Talbot (1836), Montgomery (1967), Lau (1948) and Wolf (1955) on periodicity in optics

Adolf W. Lohmann*, David Mendlovic, Gal Shabtay

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


If a wave is laterally periodic, then it is also longitudinally periodic. Nevertheless, lateral periodicity is not needed for longitudinal periodicity. Lateral quasi-periodicity is a more general case and sufficient for longitudinal periodicity. These results can be drawn from the Helmholtz equation, if the light is quasi-monochromatic and spatially coherent. For partially coherent light, similar results can be deduced from the Wolf equations. The triple correlation of a complex amplitude obeys a pair of wave equations, which are constructed exactly like the Wolf equations. Hence, the same laws on periodicity are valid. We present a historical and systematic view of all of those periodicity laws.

Original languageEnglish
Pages (from-to)1121-1124
Number of pages4
JournalPure and Applied Optics (Print edition) (United Kingdom)
Issue number5
StatePublished - Sep 1998


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