where  \(\theta_0\) is the (fixed) angle of the first (reference) linear polarizer, \(\theta\) is the (variable) angle of the second linear polarizer, \(\theta\ -\theta_0\) is the relative angle between them, and  \(I_0\) is the maximum intensity of the light passing through both polarizers ( which occurs when \(\theta=\theta_0\)).  The offset C represents any 'dc' offset in the signal from the photo-detector (resulting in a nonzero signal in the absence of light), any additional light reaching the photo-detector that didn't pass through the polarizers, and if the polarizers are not perfect (ideal), the fraction of  light passing through but not polarized by both polarizers. 
Rewriting in terms of the measured output photodiode voltage \(V_{pd}\) , the relative polarizer angle  \(\phi=\theta-\theta_0\) , and assuming a linear response between the photo-detector output voltage and light intensity, we have