Non-null testing of the aspheric surface using a quadriwave lateral shearing interferometer

A non-null aspheric surface testing system using a quadriwave lateral shearing interferometer (QWLSI) based on the randomly encoded hybrid grating is proposed. The system uses a non-null lens to partially compensate for the longitude aberration of the aspheric surface, which is more versatile than the null configuration. QWLSI is a common-path and self-reference system and requires no reference surface. Compared with the conventional Twyman–Green interferometer (TGI), QWLSI has higher dynamic range, better antivibration ability, and higher stability. For a non-null testing system based on the QWLSI and TGI, the compensation ranges of different aspheric surfaces and the allowable range of aspheric axial positions are analyzed under the condition that the interference fringe satisfies the Nyquist sampling theorem. The iterative reverse optimization retrace error-correction algorithm based on the exact system modeling and the localization algorithm of aspheric axial position are discussed. Simulation results show that the root mean square value of the aspheric surface reconstruction residual is less than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>200</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mi>λ</mml:mi> </mml:math> , which indicates that the system has extremely high theoretical testing accuracy. In the experiment, the QWLSI non-null system and the autocollimation null method with a ZYGO interferometer agree with the testing results of the same aspheric surface, which demonstrates the feasibility and accuracy of the QWLSI aspheric non-null testing method.