Hadamard circular masks: high focal depth with high throughput

We present a class of binary masks that encode, in polar coordinates, the values of a Hadamard matrix of order N. For order N ≥ 2, the binary masks increase the Strehl ratio vs. focus error by the factor N, with the highest possible light throughput. Since a Strehl ratio with high tolerance to defocus does not guarantee a modulation transfer function (MTF) with low sensitivity to focus errors, then, we show that for N = 16 the binary mask reduces also the impact of focus error on the MTF. Equivalently, the discrete binary mask has Fisher information with low variations to defocus.