FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2159739412> ?p ?o ?g. }

• W2159739412 endingPage "265" @default.
• W2159739412 startingPage "246" @default.
• W2159739412 abstract "The results of part I of this investigation are generalized to stationary fields with a spectral range of arbitrary width. For this purpose it is found necessary to introduce in place of the mutual intensity function of Zernike a more general correlation function <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mover> <mml:mrow> <mml:mi mathvariant=normal>Γ</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> </mml:mover> <mml:mo>⁡</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=<</mml:mo> <mml:mover> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> </mml:mover> <mml:mo>⁡</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mover> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:mover> <mml:mo>⁡</mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>></mml:mo> </mml:math> , which expresses the correlation between disturbances at any two given points P 1 (x 1 ), P 2 (x 2 ) in the field, the disturbance at P 1 being considered at a time τ later than at P 2 . It is shown that Г ˆ is an observable quantity. Expressions for Г ˆ in terms of functions which specify the source and the transmission properties of the medium are derived. Further, it is shown that in vacuo the correlation function obeys rigorously the two wave equations <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mover> <mml:mrow> <mml:mi mathvariant=normal>Γ</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> </mml:mover> <mml:mo>⁡</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=<</mml:mo> <mml:mover> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> </mml:mover> <mml:mo>⁡</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mover> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:mover> <mml:mo>⁡</mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>></mml:mo> </mml:math> , where ∇ 2 3 is the Laplacian operator with respect to the co-ordinates ( x s , y s , z s ) of P s (x s ). Using this result, a formula is obtained which expresses rigorously the correlation between disturbances at P 1 and P 2 in terms of the values of the correlation and of its derivatives at all pairs of points on an arbitrary closed surface which surrounds P 1 and P 2 . A special case of this formula ( P 2 = P 1 , τ = 0) represents a rigorous formulation of the generalized Huygens principle, involving observable quantities only." @default.
• W2159739412 created "2016-06-24" @default.
• W2159739412 creator A5039182024 @default.
• W2159739412 date "1955-06-21" @default.
• W2159739412 modified "2023-10-14" @default.
• W2159739412 title "A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width" @default.
• W2159739412 cites W1995047442 @default.
• W2159739412 cites W2038560547 @default.
• W2159739412 cites W2091297744 @default.
• W2159739412 cites W2116225724 @default.
• W2159739412 cites W2301836001 @default.
• W2159739412 cites W2515984061 @default.
• W2159739412 cites W4231465487 @default.
• W2159739412 doi "https://doi.org/10.1098/rspa.1955.0127" @default.
• W2159739412 hasPublicationYear "1955" @default.
• W2159739412 type Work @default.
• W2159739412 sameAs 2159739412 @default.
• W2159739412 citedByCount "163" @default.
• W2159739412 countsByYear W21597394122012 @default.
• W2159739412 countsByYear W21597394122013 @default.
• W2159739412 countsByYear W21597394122015 @default.
• W2159739412 countsByYear W21597394122016 @default.
• W2159739412 countsByYear W21597394122017 @default.
• W2159739412 countsByYear W21597394122019 @default.
• W2159739412 countsByYear W21597394122020 @default.
• W2159739412 countsByYear W21597394122021 @default.
• W2159739412 countsByYear W21597394122022 @default.
• W2159739412 countsByYear W21597394122023 @default.
• W2159739412 crossrefType "journal-article" @default.
• W2159739412 hasAuthorship W2159739412A5039182024 @default.
• W2159739412 hasConcept C11413529 @default.
• W2159739412 hasConcept C192562407 @default.
• W2159739412 hasConcept C41008148 @default.
• W2159739412 hasConceptScore W2159739412C11413529 @default.
• W2159739412 hasConceptScore W2159739412C192562407 @default.
• W2159739412 hasConceptScore W2159739412C41008148 @default.
• W2159739412 hasIssue "1181" @default.
• W2159739412 hasLocation W21597394121 @default.
• W2159739412 hasOpenAccess W2159739412 @default.
• W2159739412 hasPrimaryLocation W21597394121 @default.
• W2159739412 hasRelatedWork W2018879842 @default.
• W2159739412 hasRelatedWork W2737498735 @default.
• W2159739412 hasRelatedWork W2744391499 @default.
• W2159739412 hasRelatedWork W2898370298 @default.
• W2159739412 hasRelatedWork W2899084033 @default.
• W2159739412 hasRelatedWork W3041790586 @default.
• W2159739412 hasRelatedWork W3120461830 @default.
• W2159739412 hasRelatedWork W3144504424 @default.
• W2159739412 hasRelatedWork W4230250635 @default.
• W2159739412 hasRelatedWork W4292492973 @default.
• W2159739412 hasVolume "230" @default.
• W2159739412 isParatext "false" @default.
• W2159739412 isRetracted "false" @default.
• W2159739412 magId "2159739412" @default.
• W2159739412 workType "article" @default.