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chiraganand
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Hi, I have read about the rayleigh sommerfeld integral and its a surface integral. Why is it difficult to calculate the integral directly?
Oh wow I had moved on from this one, but thanks for replying! This is the the reference. so there are a lot of different ways to make it easier to calcualte but my main question was how would one go about solving it without any simplifications and at which step would one get stuckSsnow said:Can you give a reference for this question ?
Ssnow
The Rayleigh-Sommerfeld integral, also known as the Fresnel diffraction integral, is a mathematical formula used to calculate the diffraction pattern of a wave passing through an aperture or diffracting object. It was developed by British physicist Lord Rayleigh and German physicist Arnold Sommerfeld in the late 19th and early 20th centuries.
The Rayleigh-Sommerfeld integral is derived from the Huygens-Fresnel principle, which states that every point on a wavefront can be considered as a point source for a new wave. By integrating the contributions of all these point sources, the resulting formula describes the diffraction pattern of the wave.
The Rayleigh-Sommerfeld integral is an important tool in the field of optics, as it allows scientists and engineers to predict and analyze the diffraction patterns of light passing through various diffracting objects. This is crucial for understanding and designing optical systems, such as microscopes and telescopes.
Yes, the Rayleigh-Sommerfeld integral has some limitations. It assumes that the diffracting object is infinitely thin and that the diffracted waves propagate in a vacuum. It also does not take into account the effects of polarization or multiple scattering, which may be important in certain scenarios.
The Rayleigh-Sommerfeld integral is used in various practical applications, such as designing optical systems for imaging and lithography, analyzing the diffraction patterns of laser beams, and studying the behavior of waves in different media. It is also used in fields like acoustics, where it can be applied to predict the diffraction of sound waves.