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  • Fresnel diffraction - Wikipedia
    According to the Rayleigh–Sommerfeld diffraction theory, the electric-field diffraction pattern at a point (x, y, z) is given by the following solution to the Helmholtz equation: where is the imaginary unit The analytical solution of this integral quickly becomes impractically complex for all but the simplest diffraction geometries
  • 6. 4: Rayleigh-Sommerfeld Diffraction Integral
    Another method to propagate a wave field is by using the Rayleigh-Sommerfeld integral A very good approximation of this integral states that each point in the plane z = 0 z = 0 emits spherical waves, and to find the field in a point (x, y, z) (x, y, z), we have to add the contributions from all these point sources together
  • 5. Scalar diffraction theory — Advanced Optical Imaging
    The goal of this chapter is to derive the Rayleigh-Sommerfeld (RS) diffraction integral The RS diffraction integral is the basis for exact diffraction calculations Applying approximations to this integral makes it possible to make more simple calculations the diffraction field at different distances from the diffraction object
  • 人类能看懂的衍射光学（含基尔霍夫衍射，瑞利--索末菲衍射，夫琅禾费衍射，角谱衍射，菲涅尔衍射积分，菲涅尔衍射的S-FFT算法,T-FFT算法 . . .
    基尔霍夫公式，瑞利–索末菲公式，以及角谱传播公式分别是亥姆霍兹方程的三个解（光是一种电磁波，故其传播特性可由经典电磁场理论的麦克斯韦方程推出，这里不具体展开，其实是笔者对于波动方程真的深恶痛绝）。 在标量衍射理论框架下，光传播的物理过程可以严格地由基尔霍夫公式和瑞利–索末菲公式以及衍射的角谱的传播公式表示。 如果知道空间中垂直于光传播方向的一个平面上的光波场，便能计算该平面前后的空间光波场分布尤其是在观察屏上的分布。 如果只是告诉大家基尔霍夫，瑞利–索末菲公式是亥姆霍兹方程的解而来可能难以理解其物理含义，但如果大家通过惠更斯–菲涅尔原理，以及场论中的格林定理电磁场的边值条件等一步步推导就能逐渐窥见那些大佬的逻辑所在。 这里就不展开来了，移步工程光学一书吧。
  • A Tutorial on the Classical Theories of Electromagnetic Scattering and . . .
    The Huygens-Fresnel-Kirchhoff scalar theory of diffraction is the subject of Sec 4, followed by the Rayleigh-Sommerfeld modification and enhancement of that theory in Sec 5
  • doi:10. 1016 j. optcom. 2007. 08. 053 - Cold Spring Harbor Laboratory
    In scalar diffraction theory, Kirchhoff formula, Rayleigh–Sommerfeld formula, and angular spectrum transmission formula are classic formulas that express diffraction correctly
  • 2. Rayleigh-Sommerfeld (RS) — Python diffraction and interference 1. 0. 0 . . .
    The Rayleigh-Sommefeld implementation allows an amplification of the field since, sometimes, light diverges Processing time increases approximately linearly with amplification number
  • Calculating Diffraction Patterns
    Note that the angular spectrum approach and the Rayleigh-Sommerfeld integral yield identical predictions of the diffracted field (p 61) A lens simply introduces a phase factor proportional to its thickness at a given position on its plane In the paraxial approximation (rays close to parallel with the optical axis) it can be written (p 101):
  • A Tutorial on the Classical Theories of Electromagnetic Scattering and . . .
    Starting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering These results are then extended to cover the case of vector electromagnetic fields





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