Strehl ratio analysis for the wavefront coding system

Strehl ratio is an important aspect in evaluating the performance of the optical imaging system. Even in wavefront coding imaging systems, Strehl ratio also plays an important role. It can be used to evaluate the sensitivity of phase masks to aberrations, and it can also be added as the penalty in the optimization of phase mask parameters to make sure that the noise gain of the intermediate image recovery is not too large. However the conventional Strehl ratio analyses are only suitable for the optical system with a small amount of aberration, while the wavefront coding imaging system is an optical system with a large aberration, the most of which are the characteristic aberrations introduced by the phase plate. In this paper, the approximate expressions of Strehl ratio are derived for the wavefront coding system with phase plates of free order and free type. These expressions show a good coincidence with the numerical ones. Based on these expressions, the impact of the phase mask's order can be analyzed. Besides, the sensitivity of Strehl ratio to all kinds of aberrations can also be analyzed for the wavefront coding system with phase plates. Phase plates of different types are shown to be sensitive to aberrations of different types, and the impact of the aberration order can also taken into account. At last, some advice is given for taking Strehl ratio as one of the performance aspects while choosing phase plates.