Wave-front sensing from subdivision of the focal plane with a lenslet array

A wave-front sensing scheme based on placing a lenslet array at the focal plane of the telescope with each lenslet reimaging the aperture is analyzed. This wave-front sensing arrangement is the dual of the Shack-Hartmann sensor, with the wave front partitioned in the focal plane rather than in the aperture plane. This arrangement can be viewed as the generalization of the pyramid sensor and allows direct comparisons of this sensor with the Shack-Hartmann sensor. We show that, as with the Shack-Hartmann sensor, when subdividing in the focal plane, the quality of the wave-front estimate is a trade-off between the quality of the slope measurements over each region in the aperture and the resolution to which the slope measurements are obtained. Open-loop simulation results demonstrate that the performance of the lenslet array at the focal plane is equivalent to that of the Shack-Hartmann sensor when no modulation is applied to the lenslet array. However, when the array is modulated in a manner akin to that of the pyramid sensor, subdivision at the focal plane provides advantages when compared with the Shack-Hartmann sensor.