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Local Slope and Curvature Tests via Wave Front Modulations in the Shack–Hartmann Sensor

To provide slope and full curvature measurements with a single image for each subaperture in zonal wave front sensing, we propose to introduce a wave front modulation to each subaperture of the Shack–Hartmann sensor. This idea is preliminarily realized on a new sensor, which uses a four-hole mask array to modulate the test wave front incident on the lenslet array. Centroid estimation for the local slope measurements can be performed with reduced variance, thanks to the reduced size of the central lobe offered by the four-hole mask modulation. Meanwhile, the side lobes in the focal image give three intensity-normalized differential signals for the local curvature measurements. Each of the three signals shows approximately linear response to the corresponding second order term of the local wave front. In this way, the full curvature information for each subaperture can be directly determined without any complicated post processing algorithms required in other focal plane sensing techniques. Accuracy of the sensor in a single subaperture is examined by simulation.