Wavefront motion optical transfer function and point spread function for dynamic wavefront error in multi-element segmented optical systems

Static, quasi-static, and dynamic effects in multi-element segmented optical systems induce wavefront error that degrades image quality. Dynamic effects of vibration are motion and deformation of the optical elements during an exposure interval. The optical transfer function (OTF) and point spread function (PSF) are functions of the dynamic wavefront and are essential for predicting optical performance. We have developed an algorithm to compute the statistical expected mean of the PSF and OTF from the covariance of the dynamic response of the optical system to disturbances. The algorithm is a natural extension of established structural–optical–control system performance analysis techniques. The statistical PSF and OTF provide additional performance information beyond the root mean square wavefront error that takes into account correlation among the wavefront errors. It is also shown that under certain assumptions, the statistical OTF reduces to the Hufnagel OTF, and under an additional assumption, it reduces to the Strehl ratio for a random wavefront.