Determination of the misalignment error of a compound zero-order waveplate using the spectroscopic phase shifting method

• We use phase shifting method to determine the misalignment error.
• A new way is provided to understand the alignment angle.
• This method is highly efficient for only four spectra are needed.

The spectroscopic phase shifting method was proposed to determine the misalignment error of a compound zero-order waveplate. The waveplate, which is composed of two separate multi-order quartz waveplates, was measured by a polarizer-waveplate-analyser setup with a spectrometer as the detector. The theoretical relationship between the misalignment error and the azimuth of the polarized light that emerged from the waveplate was studied by comparing two forms of the Jones matrix of the waveplate. Four spectra were obtained to determine the wavelength-dependent azimuth using a phase shifting algorithm when the waveplate was rotated to four detection angles. The misalignment error was ultimately solved from the wavelength-dependent azimuth by the Levenberg–Marquardt method. Experiments were conducted at six misalignment angles. The measured results of the misalignment angle agree well with their nominal values, indicating that the spectroscopic phase shifting method can be a reliable way to measure the misalignment error of a compound zero-order waveplate.