The Stokes Parameter of M 1

Hello everybody,
although M1 is an "everyday object", this topic would fit into the board "Off the beaten path" as well, because the imaging/sketching technique is really far off the beaten path!
So... it started with the homepage of Richard Crisp, who mapped the Stokes Parameter of several objects by photography:
http://www.narrowbandimaging.com/col...aging_page.htm
I simply had to know, if it is possible to get any results visually. I made 5 sketches of M1 during the HTT (a german starparty; "Herzberger Teleskoptreffen) two weeks ago. The 1st sketch without Filter, only a 10mm - eyepiece (TV Delos) in my 24" dobsonian with 252x. Afterwards, I added a polarization filter and made 4 other sketches at different, but well known polarizer angles: 0°, 45°, 90° and 135°. For further information about the Stokes Parameter, please check out the wikipedia site... Finally, I had the same workflow as I described in "M27 in bicolor", but I had more possibilities, as you can see in the following images:
Attachment 2301
1. The image shows the distribution of the max. polarization angle in rad - but only the linear components of the light. Note the scale on the right.

Attachment 2302
2. This is the final Stokes Parameter Map as LRGB-composite. L = observation sketch without filter = S_0, red = S_1, green = S_2, blue = S_3


BTW: the sketches were made on transparency paper, that got quickly wavy as you can see around the nebula...
Since it was not possible to observe only the circular polarized light which are required for S_3, this Parameter can be calculated by
S_3 = sqrt{(S_0)² - (S_1)² - (S_2)²}.
Therefore, the first image contains linear components only. If circular components were not neglected, everything would cancel out...

Best regards + CS
Daniel

Quote:

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Originally Posted by Daniel_Sp

Hello everybody,

BTW: the sketches were made on transparency paper, that got quickly wavy as you can see around the nebula...
Since it was not possible to observe only the circular polarized light which are required for S_3, this Parameter can be calculated by
S_3 = sqrt{(S_0)² - (S_1)² - (S_2)²}.
Therefore, the first image contains linear components only. If circular components were not neglected, everything would cancel out...

Best regards + CS
Daniel

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Dear Daniel

I was also telling Uwe Glahn when I met him a few days ago that this is an incredible idea! A brilliant idea to even consider such an undertaking.

However, I have a comment about your method of determining S_3. I believe that the relation you mention is true only for purely polarized light. Partially polarized light, as we may expect to be the case for most of the light in the universe, instead has the sum of squares of Stokes parameters < 1. (I remember this vaguely as being analogous to the trace of the density matrix in a mixed state in QM.) I think therefore that the parameters are independent and the only way to measure S_3 would be to use a waveplate. I guess the waveplate can be made specifically for the OIII wavelength(s), since the crab nebula emits it strongly.

Clear Skies
Akarsh

Hi Akarsh,
thanks for your reply and your nice comments!
You are right, but the procedure as I showed here is not completely correct: I observed with a Newton and the secondary mirror is a major problem due its reflection properties of s- and p-wave. A correct calculation would take account of the Jones-Matrix of the complete layer system (glass substrate, Al refelction layer ans SiO2 coating). Finally, what I did is more or less a feasibility study...

best regards + CS
Daniel

Quote:

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Originally Posted by Daniel_Sp

Hi Akarsh,
thanks for your reply and your nice comments!
You are right, but the procedure as I showed here is not completely correct: I observed with a Newton and the secondary mirror is a major problem due its reflection properties of s- and p-wave. A correct calculation would take account of the Jones-Matrix of the complete layer system (glass substrate, Al refelction layer ans SiO2 coating). Finally, what I did is more or less a feasibility study...

best regards + CS
Daniel

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Oh, yes you are right. I never thought about the change in polarization from reflection and other aspects of the optics. I understand the purpose of your sketch now! Like I said, very interesting idea! And thanks for the very educative discussion.

Warm regards and CS
Akarsh

Hi,
the primary mirror should be no problem because of its rotational symmetry. Only the secondary leads to trouble - or hard calculation :)
best regards + CS
Daniel