A methodology for measuring the parameters of large concave aspherical mirrors by means of a wavefront sensor

A methodology has been developed for measuring radius $R_v$ and eccentricity (conic parameter $k$) of large concave aspherical mirrors using a wavefront sensor. Analytical expressions that directly relate Zernike coefficients $a_4$ and $a_9$ to parameters $R_v$ and $k$ of the mirror are obtained. It is shown that the technique does not require accurate mirror alignment before measurements. A computer analysis showed that the developed scheme enables measurements with errors of $\delta R_v<0.1\%$ and $\delta k<0.01$ for mirrors with radii from $100$ to $2000$ mm and with errors of $\delta R_{v}<0.01\%$ and $\delta k<0.001$ for mirrors with radii of more than $5000$ mm.