# A What is the relationship between spectral coherence with respect to a radiation source's mean wavelength and bandwidth?

#### pbeierle

Summary
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.

"What is the relationship between spectral coherence with respect to a radiation source's mean wavelength and bandwidth?"

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