TY - JOUR

T1 - Talbot (1836), Montgomery (1967), Lau (1948) and Wolf (1955) on periodicity in optics

AU - Lohmann, Adolf W.

AU - Mendlovic, David

AU - Shabtay, Gal

PY - 1998/9

Y1 - 1998/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032164818&partnerID=8YFLogxK

U2 - 10.1088/0963-9659/7/5/018

DO - 10.1088/0963-9659/7/5/018

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AN - SCOPUS:0032164818

SN - 0963-9659

VL - 7

SP - 1121

EP - 1124

JO - Pure and Applied Optics (Print edition) (United Kingdom)

JF - Pure and Applied Optics (Print edition) (United Kingdom)

IS - 5

ER -