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圆孔的菲涅耳衍射 被引量:3

Fresnel diffraction by a circular aperture
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摘要 得到了圆孔菲涅耳衍射光强分布的表达式,此式由贝塞尔函数的数列(或Lommel函数)给出,因此很容易利用普及的数学软件算出结果.并且利用CCD照相机量度了衍射光强分布,与运算的结果作了比较,也与Burch在1985报导的结果作了比较. An analytic expression in terms of Bessel' s functions or Lommel' s functions of two variables, is obtained for the intensity distribution of the Fresnel diffraction by a circular aperture. The Fresnel pattern in any transverse plane at an axial distance from the aperture is then easily computable using commonly available software packages. Comparison with Burch's theoretical results(in 1985) is made and satisfactory agreement with experiment is found. The light intensity patterns are recorded by the use of CCD camera, which may be adapted as a student experiment in universities.
出处 《大学物理》 北大核心 2009年第10期31-34,共4页 College Physics
关键词 圆孔 菲涅耳衍射 贝塞尔函数 Lommel函数 CCD照相机 circular aperture Fresnel diffraction Bessel function Lommel function CCD camera
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  • 1Burch D S. Fresnel diffraction by a circular aperture [J]. Am J Phys 1985,53: 255.
  • 2Watson G N Theory of Bessel Functions [ M ]. 2^nd ed. Cambridge University Press, 1944:537-550.
  • 3Born M,Wolf E. Principles of Optics [ M ]. 7^th( expanded) ed. Cambridge University Press, 1999:484-492.
  • 4Walker J. The Analytic Theory of Light [ M ]. Cambridge University Press, 1904:See his Eq. (66) on p. 147 in particular.
  • 5See for example, Fowles G R. Introduction to Modern Optics [M], Holt, Rinehart, and Winston 1968: 110- 111 ;or Born M, Wolf E. Principles of Optics [ M ]. 7^th (expanded) ed. Cambridge University Press, 1999: 484-492.
  • 6See, for example, Gradshteyn I S, Ryzhik I M. Table of Integration, Series, and Products [ M ]. translation ed. by Jeffrey A. Academic Press 1965:8. 511(4) p. 973.
  • 7Walker J. The Analytic Theory of Light [ M ]. Cambridge University Press, 1904:147. Note that 2 2 in (63) is u^2 P0^2 simply a constant for p1>P0.

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