Understanding Spectral Coherence w/ Radiation Sources

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SUMMARY

The discussion focuses on the relationship between spectral coherence and a radiation source's mean wavelength and bandwidth. Key calculations are provided, including the coherence length formula \( L_c = c \Delta t \) and the relationship \( \Delta t = \frac{1}{\Delta f} \). The derived equation \( L_c = \frac{\lambda^2}{\Delta \lambda} \) is crucial for estimating spectral coherence from a given radiation spectrum. The discussion references additional resources for further understanding of coherence in optics.

PREREQUISITES
  • Understanding of spectral coherence in optics
  • Familiarity with the speed of light (c) and its implications in calculations
  • Basic knowledge of wavelength (\(\lambda\)) and frequency (f) relationships
  • Proficiency in algebra for manipulating equations
NEXT STEPS
  • Study the derivation of coherence length in more detail
  • Explore the implications of bandwidth on spectral coherence
  • Learn about the role of factors like \(2\) and \(\pi\) in coherence calculations
  • Investigate practical applications of spectral coherence in optical systems
USEFUL FOR

Physicists, optical engineers, and students studying wave optics who seek to understand the principles of spectral coherence and its calculations.

pbeierle
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What is the relationship between spectral coherence with respect to a radiation source's mean wavelength and bandwidth? I have no idea how to estimate, given a particular radiation spectrum from a source, what it's spectral coherence is going to be.
What is the relationship between spectral coherence with respect to a radiation source's mean wavelength and bandwidth? I have no idea how to estimate, given a particular radiation spectrum from a source, what it's spectral coherence is going to be.
 
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A couple simple calculations should get you there: ## L_c=c \Delta t ##, and ## \Delta t=\frac{1}{\Delta f} ## (approximately). Since ## f=\frac{c}{\lambda} ##, ## |\Delta f|=\frac{c}{\lambda^2}\Delta \lambda ##. The result is ## L_c=\frac{\lambda^2}{\Delta \lambda} ##, so that ## \Delta \lambda=\frac{\lambda^2}{L_c} ## if I got all of the algebra right. ## \\ ## See also http://electron6.phys.utk.edu/optics421/modules/m5/Coherence.htm Factors of 2 and ##\pi ## are somewhat arbitrary here.
 

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