Both Eqs. (1) and (2) show, however, that the value of must be known in order to recover the desired Jones matrices from the measurement data , etc. This requires that the EOM must be carefully calibrated. In practice, it is also necessary to compensate the fiber-induced birefringence in the sample arm fiber. To do this, the Jones matrix at the sample surface is used as a reference matrix to calculate the birefringence in the sample. The double-pass phase retardance and fast-axis orientation of the sample can then be obtained from the matrix diagonalization of the following equation (6), Display Formula
(3)where , are two transmittances of the eigenvectors of the sample, and is a general unitary matrix, whose columns are the fast and slow eigenpolarizations of . is extracted from these eigenpolarizations. The degree of the phase retardance can be extracted through the phase difference of the resulting diagonal elements. We will now show that this surface calibration procedure in fact completely cancels the effects of varying of the value of , i.e., can be calculated without knowing the actual value of . To do this, we first note Eq. (2) can be matrix-factorized into the following form: Display Formulawhere Display Formula
(4)Here, we define three new Jones matrices: , , and . Note that is determined solely by the experimentally measured signals , etc. , are determined solely by the values of the Bessel functions at the value and is a constant Jones matrix. becomes the identity matrix and Eq. (4) reduces to Eq. (1) when . , are clearly invertible matrices. Substituting Eq. (4) into Eq. (3) Display Formula
(5)where corresponds to as measured at the sample surface. Equation (5) shows that the calibrated Jones matrix , which by Eq. (3) contains all the information needed to determine the sample phase retardance and relative optic-axis orientation, can be derived purely from the experimentally measured signals , etc. at the desired depth as well as at the surface. The value of is not specifically required and this makes it possible to avoid the EOM calibration process. Values of can also be used, which can simplify the provision of the EOM drive voltage.