Modal sensitivity and dynamic range tuning with the bi-orthogonal edge wavefront sensor

The bi-orthogonal edge wavefront sensor (WFS) is, to our knowledge, a new wavefront sensor based on the Foucault knife-edge test. In this paper, we show by calculating sensitivity with the spatial frequency of Fourier modes that the bi-orthogonal edge WFS has higher photon and read noise sensitivity than the pyramid, roof, 3-sided, and cone WFS for both low-order (gradient) and high-order (Hilbert) modes. We propose the use of other (nonlinear) transmittance functions in the transition region of the amplitude masks of the bi-orthogonal edge WFS and show that this can be used to either increase the sensitivity or the dynamic range of the low-order modes. We demonstrate a relative improvement in closed-loop Strehl of up to 8% in turbulent conditions by using a nonlinear sigmoid function compared to a linear transmittance curve.