Ignoring multiple scattering

Summary:

How to perform first order calculations?

Ignoring multiple scattering

Yon (guest) 24 Nov 2016 13:50

I would like to perform calculations without taking into account multiple scattering between dipoles (first order calculation). Is possible with DDSCAT ? Perhaps by fixing MXITER = 1 ? thanks per advance.

draine (guest) 24 Nov 2016 14:23

I'm not sure I understand why this calculation would be meaningful, but an easy way to do it is to set the refractive index to a value like m_small=1.0001+0.0001i — this will make the self-polarization field very small, so that each dipole essentially sees only the incident plane wave. Then run ddscat (it will probably converge in one or two iterations), and rescale the scattering intensities (e.g., S_11).
If the refractive index m is not too large, you would rescale by a factor |(m^2-1)/((m_small)^2-1)|^2 to scale up the power scattered by each dipole to the intended value.
However, as stated above, neglecting the interaction between dipoles is unphysical.

Yon (guest) 26 Nov 2016 21:17

Thanks for the nice proposition.
pcirrus has all understood. I'm trying to compare exact scattered intensities with the theroretical Rayleigh-Gans Debye approach (corresponding to pair-autocorrelation calculation). The idea is to understand the influence of the internal dipole-multiple scattering to the deviation from first-order theoretical approaches. If I can do that directly with your code, it is just easier for me.
This is possible with GMM code, it is the reason why I wondered if it is also possible with DDSCAT.
Many thanks.

Yon (guest) 13 Dec 2016 19:54

It's OK, I have performed calculations with m=1.01+i0.01 and I obtained a phase function that is in perfect agreement with another independent approach that suppose there is no multiple scattering. Thanks you very much for your advice.

Re: Ignoring multiple scattering

pcirrus 26 Nov 2016 05:19

Hi Yon, I am curious: are you trying to calculate Rayleigh-Gans-Debye scattering form factors
(this approximation is valid for |m-1| «1 and phase shift rho=2ka(m-1)«1)
It is discussed for example here
http://www.astro.spbu.ru/DOP/3-REVS/KHLEB1/node13.html
Rayleigh-Debye-Gans (RDG) is also called Born (or the first Born).

Last edited on 26 Nov 2016 21:34 by pcirrus Show more

Yon (guest) 26 Nov 2016 21:16

Hi pcirrus, it is exact (see my answer just above). Many thanks for the link.

pcirrus 26 Nov 2016 21:43

Aha! You should be able to calculate RGD using DDSCAT. To understand it you need to look at Discrete Dipole Approximation in terms of an integral equation and make an approximation E=E0. This reduces to RGD. In fact there was a version of the DDSCAT code in which we were calculating first approximation to the solution that way. Look also at paper by Shermila Brito Singham and Craig F. Bohren, Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method, Journal of the Optical Society of America A Vol. 5, Issue 11, pp. 1867-1872 (1988) and subsequent references to it. Let us now if you are successful of using DDSCAT in nthis approximation. Piotr Flatau.

good

pcirrus 13 Dec 2016 20:19

Thanks for reporting it. You may also want to play with your choice of the refractive index. The choice suggested by Bruce was deliberately small (m=1.0001+0.0001i) and his point was to be close to |m|=1 (but for numerical reasons slightly off). Your choice of the real part is OK, but complex part 0.01 is relatively large. On somewhat related topics - there is an amusing story about complex refractive index discussed by Craig Bohren on p. 438, Figure 14.1 in his book "Absorption of Scattering of Light by Small Particles". His point is that except black carbon particles with i*0.01 are rare. Piotr