Theory of Fresnel Images I Plane Periodic Objects in Monochromatic Light*

Winthrop, John; Worthington, C.R.

doi:10.1364/josa.55.000373

Cited by 432 publications

(181 citation statements)

References 11 publications

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“…El inicio del periodo moderno de las investigaciones sobre el efecto Talbot se coloca en los 1960s con el artículo de Winthrop y Worthington [4], en el cual se provee un análisis teórico detallado de la difracción de campo cercano (Fresnel) y se introduce el efecto Talbot fraccionario correspondiente a distancias fraccionarias p/q de la distancia Talbot y múltiplos de estas donde p y q son números coprimos. En este caso las imágenes de Talbot son una superposición de q imágenes idénticas de la rejilla.…”

Section: Materialesunclassified

Efecto Talbot Unidimensional y Bidimensional

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Flores

Rosu

et al. 2014

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En este trabajo se muestran los resultados de los experimentos realizados en el verano del 2014 en el IPICYT, para corroborar la existencia del efecto Talbot el cual consiste en la reaparición de una imagen nítida de un objeto periódico iluminado por una fuente de luz cada cierta distancia después del objeto. Esta distancia se le conoce como distancia de Talbot y da la escala espacial de este fenómeno. Se utilizaron rejillas unidimensionales periódicas, aperiódicas y bidimensionales con estructura hexagonal, todas fueron creadas previamente con el programa grafico Adobe Illustrator con las frecuencias espaciales que se calcularon que darían una distancia de Talbot que permite la observación del efecto en el laboratorio. Las rejillas se iluminaron con un láser de He-Ne de longitud de onda de 633 nm (rojo) y posteriormente se localizó a que distancia se volvía a formar la auto-imagen de la rejilla. Palabras claveAdobe Illustrator, Auto-imagen, Distancia Talbot, Efecto Talbot, Rejilla. AbstractIn this paper, we show some experimental results obtained by us in the summer of 2014 in IPICyT to prove the occurrence of the Talbot effect. This effect is due to the constructive interference which leads to the appearance of clear images at a certain distance behind a periodic object illuminated by a light source. The distance of appearance is known as the Talbot distance and provides the spatial scale of this self-imaging phenomenon. We used onedimensional periodic and quasi-periodic gratings as well as two-dimensional hexagonal ones which have been produced by using the Adobe Illustrator graphical program at calculated spatial frequencies that allowed the observation of the effect within the laboratory. The gratings have been illuminated with a He-Ne laser of wavelength 633 nm (red) for which we determined the distance at which a clear self-image of the gratings could be obtained. KeywordsAdobe Illustrator, Grating, Self-image, Talbot distance, Talbot effect. IntroducciónEl estudio del efecto Talbot es de gran interés debido a que de manera natural se forman réplicas de una imagen sin que sean asociadas a algún tipo de lente. En 1836 Henry Fox Talbot mientras inspeccionaba la difracción de luz blanca al atravesar una rejilla se sorprendió al observar que se formaban imágenes nítidas cada cierta distancia del orden de metros que consistían de bandas alternantes, de colores complementarios (por ejemplo rojo-verde) sin importar que la lente estuviera fuera de foco

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Section: Materialesunclassified

Efecto Talbot Unidimensional y Bidimensional

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“…In this section, we will review the fractional Talbot phenomena [3,20,25,43] and consider a relation between the Gauss sum and the Gauss optics explicitly. As in [3,25], we will consider the δ-comb grating plane z = 0,…”

Section: Talbot Phenomenamentioning

confidence: 99%

“…I am also grateful to Y.Ônishi for some discussions and encouragements and J. McKay for some discussions and telling me the reference [27]. Further I appreciate the referees for critical suggestions and references [2,16,31,43].…”

mentioning

confidence: 91%

“…In the previous article [25], we investigated a relation between the Gauss reciprocity and wave-particle complementary on an optical system, the fractional Talbot system [43] following the excellent work of Berry and Klein [3].…”

Section: Introductionmentioning

confidence: 99%

“…Though it is historical irony, K. F. Gauss studied well the Gauss sum and wrote it in [11] 1818 and summarized the Gauss optics in [12] 1840, in which he described the critical relation between Sp(2, R) = SL(2, R) and optical system, whereas H. F. Talbot discovered the original Talbot phenomena around 1836 [37], though the fractional Talbot phenomena was discovered by J. T. Winthrop and C. R. Worthington in [43]. Talbot also studied elliptic integrals as a mathematician [6, p.413] and wrote several articles in the creation of the theory of elliptic functions [44].…”

Section: Introductionmentioning

confidence: 99%

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