Hello community, I am messing up my brain by a very particular question. I am using Deirmedjians Calculation from 1969 ("Electromagnetic Scattering on Spherical Polydispersions") to calculate phase functions. But in his and my calculations the phase functions of P1 are exceeded by P2 to P4 several times. I am asking myself what this means since I thought that the phase function shows the fraction of scattered light towards a certain angle. In my understanding this would mean that e.g. a stoke vector of (1 1 0 0) would be scattered to reach (a b 0 0) with b>a. This does not make any sense from my point of view. So what do I misunderstand here?
Dear Ariadne, thank you very much for your answer. I read the paper but I might have overlooked an explanation of why the total flux and can be lower than the linearity factor within the stokesvector. Also, I would like to add that this can been seen even by single scatterer not just by multi-scattering.
Concerning Stokes vector (I, Q, U, V) you are completely right I>=Q. But (P1, P2, P3, P4) and (I, Q, U, V) are not the same. To clarify it check eq. 65 and 75 of that work.
Dear Dmytro, thank you very much. Yes, I am talking about these formulas, indeed.
(65) states for example that I_1 = s_1*I_01 and I_2 = s_2*I_02. So if I_01=I_02 (linear Polarisation) but s_2 > s_1, the final vector turns to I_2 > I_1. This would mean that the final polarisation value of I_x-I_y is higher than the final overall intensity I_x+I_y after scattering. This is what I do not understand.
The same happens with the values for the phase function (compare in the attached picture the values at e. g. 50° or 60° for p1 and p2).
Dear Thorsten, concerning the present issue I should say the following. Looking at the eq 65 and 75 you can find out the relation between (I1, I2, U, V) vector and (P1, P2, P3, P4). Such relation can be shown in the matrix form as in eq. 64 (btw, there is a typo in eq. 64). Instead of nonzerro elements of that matrix you can use P1, P2, P3 and P4 values with corresponding coefficient (as in eq 76 before the matrix). So P1, P2, P3 and P4 defines scattering matrix. But that scattering matrix is not a Mueller Matrix! You see, (I1, I2, U, V) is not a Stokes vector (I, Q, U, V). Of course there is a relation between (I1, I2) and (I, Q) and it is described in eq. 58a, 58b. So using your definitions I_x and I_y I would say that I_x=I1, I_y=I2 in this case. So in that work author uses modified ses of Stokes parameters to make scattering matrix partially diagonalized.
Oh dear, I am so blind! Thank you very much, Dmytro. I am understanding it now. By the way, the error in (64) is the missing * after A1A1, right?
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