The POLAR Project

What is the Modulation Factor?

Short Reply: The modulation factor is the degree of modulation expected in the absence of background and for a 100% polarized beam.

The Modulation Factor and its context with POLAR

A flux of photons is said to be polarized when their polarization vectors are aligned. The azimuthal distribution of polarized X-ray photons is also called modulation curve and presents the form of a sinus curve with a period equal to pi as shown in the figure below. The modulation curve can be fitted with the following function:

C(xi) = A cos 2 ( xi - C ) + B,

where xi is the azimuthal scattering angle measured with respect to the detector X-axis, and A, B, and C are the fitting parameters (amplitude, offset and phase shift of the curve, respectively). The position of the minimum in the modulation curve corresponds to the angle of polarization of the incoming photons. A/B is the so-called modulation factor (mu) that serves to calculate the degree of linear polarization of the incoming photons:

Pi = mu/mu100 = A/B mu100 = 1/mu100 (Cmax- Cmin)/(Cmax+Cmin)

where Pi is the polarization degree, Cmin and Cmax are the minimum and the maximum of the curve as marked in the figure and mu100, i.e., the 100 percent polarization factor, is the response of the instrument to a fully polarized photon flux. This last value is a characteristic of the instrument and can be determined experimentally or via simulations.
detector image