- #1
Steve Drake
- 53
- 1
Hi,
Those of you familar with dynamic light scattering (DLS), will know that a common method used to obtain a particle size distribution is via a laplace inversion of the autocorrelation function.
What I want to know is why? What does Laplace space have to do with DLS (I've only learned basics Laplace transforms and Laplace inversions from simple elec eng...). My understanding is that the scattered light depends on how fast the particles are diffusing. And that the propagating light from the sample to the detector undergoes an optical Fourier transform.
I also know that you can take the Fourier transform of the ACF to obtain the power spectrum...
But where does laplace come into this? All papers I read just say that the spectrum can be described by the equation
[itex]g^{(1)}=\int G(\Gamma )e^{(-\text{$\Gamma $t})}[/itex]
Thanks
Those of you familar with dynamic light scattering (DLS), will know that a common method used to obtain a particle size distribution is via a laplace inversion of the autocorrelation function.
What I want to know is why? What does Laplace space have to do with DLS (I've only learned basics Laplace transforms and Laplace inversions from simple elec eng...). My understanding is that the scattered light depends on how fast the particles are diffusing. And that the propagating light from the sample to the detector undergoes an optical Fourier transform.
I also know that you can take the Fourier transform of the ACF to obtain the power spectrum...
But where does laplace come into this? All papers I read just say that the spectrum can be described by the equation
[itex]g^{(1)}=\int G(\Gamma )e^{(-\text{$\Gamma $t})}[/itex]
Thanks