Abstract
In the Hartmann test, a wave aberration function is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as , where is the radius of a reference sphere. The function and the transversal aberrations calculated at the plane are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between and the transversal aberrations calculated at any arbitrary Hartmann-plane distance . We also show how to directly estimate the wavefront surface from the information of . The use of arbitrary values could improve the reliability of the measurements of , or , when finding difficulties in adequate ray identification at .
© 2016 Optical Society of America
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