Hello, I have a microscopic system as shown in attached figure. I want to measure the linear degree of polarization at 90 degrees. How can I measure it?
Acoording to our parametric solution the stokes parameters can be caclulated as:
S0=Ex^2+Ey^2;
S1=Ex^2-Ey^2;
S2=2ExEycos(delta)
S3=2ExEysin(delta)
The definition of the linear degree of polarization is :
LDOP=sqrt(S1^2+S2^2)/S0;
Now how can I measure the linear degree of polarization?
In my mind just i have to set modulator at 0 degree (Io) and at 90 degrees (I90) and then by following formula:
DOLP(degree of linear polarization)= I90-I0/I90+I0?
Please give me suggestions. Thanks
I am not sure what you mean by DOLP. How does this differ from linear degree of polarisation LDOP?
If you simply want normalised Stokes coefficient s1/s0, then your DOLP expression is fine.
However, your DOLP equation does not distinguish between circularly polarised light (LDOP = 0) and light linearly polarised at 45 degrees (LDOP = 1). Both of these give DOLP=0. Is this what you intend?
If what you need is LDOP, then:
Set the both the fast axis of the quarter wave plate and the polarizer axis to 0 degrees. Measure intensity I0.
Set both wave plate axis and polarizer axis to 90 degrees. Measure I90.
Set both wave plate axis and polarizer axis to 45 degrees. Measure I45.
Set both wave plate axis and polarizer axis to 135 degrees. Measure I135.
s0 = I0 + I90
s1 = I0 - I90
s2 = I45 - I135
LDOP = sqrt(s12 + s22) / s0
If you also need s3, then:
Set wave plate axis to 45 degrees and polarizer axis to 0 degrees. Measure IRC.
Set wave plate axis to 45 degrees and polarizer axis to 90 degrees. Measure ILC.
s3 = IRC - ILC
If your wave plate delay is not exactly 1/4 wavelength then refer to: http://gabrielse.physics.harvard.edu/gabrielse/papers/1977/MeasuringStokesParameters.pdf
HTH
I have already get Stokes from my system. we fit the curve over full circle rotation of sinusoidal wave. I have gotten the Stokes. Can I just by putting formula S1/S0, find the LDOP????
The reference is as attached in which all info of our system is there.
I don't understand what you are trying to calculate.
Your original post defines LDOP = sqrt(s12 + s22) / s0
Your definition of DLOP = (I90-I0)/(I90+I0) is equivalent to ( - s1 / s0 )
If you have all 4 Stoke parameters, it is trivial to calculate either expression, but they represent different physical quantities.
Note that equation 2 in your paper should read
S1 = ExEx* - EyEy*, and similarly for S0 (modulus squared terms)
S2 = ExEy*+ EyEx* (add terms - not subtract)
Note also that the Stokes parameter S0 describes the total intensity, including unpolarised light, but the paper also refers to S0 as "total degree of polarisation". Is this the same quantity?
Degree of polarisation is usually defined as DOP = sqrt(S12 + S22 + S32)/S0
S0 is the total polarization intensity, and I don't think so it is the same as the total degree of polarization. so you mean if I can put -S1/S0, I can calculate the DLOP??? I was also thinking that I just want to confirm that because I have all four Stokes parameters and I think by putting the -S1/S0 we can calculate the linear degree of polarization.
Kaleem
The definition of "linear degree of polarisation" in your original question
LDOP = sqrt(S12 + S22) / S0
is the fraction of power which is linearly polarised. It excludes circularly polarised and unpolarised components, and can take values between 0 and 1 when the signal is perfectly linearly polarized. The value is independent of the plane of polarisation, or of the orientation of the major axis for elliptical polarisations.
You introduced a different parameter:
DOLP = (I90-I0)/(I90+I0) = ( - S1 / S0 ) = - LDOP cos(2 theta)
where theta is the orientation of the polariser.
S1/S0 is the first Stokes parameter normalised by the total intensity. S1 is the excess of power transmitted through a linear polariser at 0 degrees over the power through a polariser at 90 degrees.
For linearly polarised light, DOLP varies from 1 for light polarised at 90 degrees, to 0 at 45 degrees, -1 at 0 degrees and 0 at 135 degrees. It is zero for circularly polarised light and takes intermediate values for elliptical polarisations.
If you want a parameter which varies between 0 and 1, you could instead use (DOLP+1)/2 which takes values 1 for linear 90, 0 for linear 0 degrees, and 0.5 for either linear 45 or circular.
Your original question defined LDOP in terms of Stokes parameters, then asked how to measure it. You did not mention that you already had a full set of Stokes parameters, so I initially assumed you needed a procedure to measure LDOP, using the apparatus in your diagram.
Can you explain what you mean by "Linear degree of polarisation at 90 degrees"? You have not specified exactly what you want the parameter to represent or how you expect to use it, so I cannot tell you which formula to use.
If DOLP varying between 1 and -1 is what you want, then use (-S1/S0).
Thanks a lot, dear Alan, my source is unpolarized and then there is a modulator I am not using the linear polarizer source. Yes, i have already had Stokes. So according to your answer, i can calculate from the already available Stokes ,LDOP=-S1/S0(yes I want my LDOP should vary between -1 and 1...... basically, I want to experimentally measure the LDOP as in the attached reference they have calculated for the detection of the electric and magnetic modes.
So Alen , now the formula for -S1/S0 is Ok???
Yes - if the perpendicular and parallel orientations are aligned with the -S1 and +S1 axes of your Stokes measurement, then -S1/S0 is the linear polarisation degree defined in equation (1) of Braulio García-Cámara's 2010 Optics Letter paper.
EDIT: ratio S1/S0 corrected.
Alan.
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