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Mueller matrix - rotation

  1. Jan 5, 2009 #1
    Hi,
    I have a basic question on Mueller matrix which I came across upon reading through the Handbook of Optic, chapter 22 polarimetry. It says that :-

    when a polarization element with Mueller matrix M is rotated about the beam of light by an angle \theta such that the angle of incident is unchanged, the resulting Mueller matrix M is :

    = M(\theta)
    = R(\theta) M R(-\theta)
    = [matrix elements of R(\theta)] [matrix elements of M] X [matrix elements of R(-theta)]

    My question is, what does the "X" mean here..
    From my reading, the cross product is used with vector. This time, it's a matrix.

    Sorry if this is too basic, I've just started brushing up my matrix since college.

    Appreciate any help.

    regards,
    --islahna
     
  2. jcsd
  3. Jan 6, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi islahna! Welcome to PF! :smile:
    I don't know what that X is doing there …

    in fact, I don't understand what that third line
    is supposed to mean at all. :confused:

    The first and second lines, effectively M' = RMR-1, are just the standard formula for the effect of rotation R on matrix M …

    it's ordinary matrix mulitplication. :smile:
     
  4. Jan 8, 2009 #3
    hi tiny-tim,
    thank you so much for the insight. I'll take it as ordinary matrix mulitplication for now.
    But I'm still curious, why they use that X sign, has got to be something ..mm.

    thanks,
    --islahna
     
  5. Jan 9, 2009 #4

    tiny-tim

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    Hi islahna! :smile:

    dunno :confused:

    i don't have a copy of that book …

    can you scan it? :smile:
     
  6. Jan 11, 2009 #5
    hi tiny-tim,

    I've contacted the author since and the following is the snippet from his response that I'd like to share.
    Hope it clarifies any doubts ..

    ------- start -------

    The x in Eq. 12 & 13 is just matrix multiplication and is there because the equation continued onto a second line. I understand how these little things can be so difficult to those starting who need the information the most.
    ------- end -----------

    thanks you.

    --islahna
     
  7. Jan 12, 2009 #6

    tiny-tim

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    Well done!! :biggrin:

    Duh :rolleyes: … an author trying to avoid one source of confusion by creating another one! :rolleyes:
     
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