## Abstract

We describe the interferometric testing of a slow (*f*/16 at the center of curvature) off-axis parabola, intended for use in an x-ray spectrometer, that uses a spherical wave front matched to the mean radius of the asphere. We find the figure error in the off-axis mirror by removing the theoretical difference between the off-axis segment and the spherical reference from the measured wave-front error. This center of curvature test is easy to perform because the spherical reference wave front has no axis and thus alignment is trivial. We confirm that the test results are the same as the double-pass null test for a parabola that uses a plane autocollimating mirror. We also determine that the off-axis section apparently warped as the result of being cut from the symmetric parent part.

© 1995 Optical Society of America

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### Equations (7)

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(1)
$${{{a}_{n}}^{\prime}}^{m}={{a}_{n}}^{m}\hspace{0.17em}\text{cos}(m\mathrm{\theta})+{{a}_{n}}^{-m}\hspace{0.17em}\text{sin}(m\mathrm{\theta}),$$
(2)
$${{{a}_{n}}^{\prime}}^{-m}={{a}_{n}}^{-m}\hspace{0.17em}\text{cos}(m\mathrm{\theta})-{{a}_{n}}^{m}\hspace{0.17em}\text{sin}(m\mathrm{\theta}),$$
(3)
$$x={x}^{\prime}+h,\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}y={y}^{\prime}.$$
(4)
$${x}^{\prime}={bx}^{\u2033},\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{y}^{\prime}={by}^{\u2033},$$
(5)
$$\mathrm{\Delta}z=(k/8{{R}_{v}}^{3}){[{({bx}^{\u2033}+h)}^{2}+{(b{y}^{\prime})}^{2}]}^{2}+[k(k+2)/16{{R}_{v}}^{5}]{[{({bx}^{\u2033}+h)}^{2}+{({by}^{\u2033})}^{2}]}^{3}.$$
(6)
$$\mathrm{\Delta}z={{a}_{4}}^{0}{{U}_{4}}^{0}+{{a}_{3}}^{1}{{U}_{3}}^{1}+{{a}_{2}}^{2}{{U}_{2}}^{2}+{{a}_{2}}^{0}{{U}_{2}}^{0}+{{a}_{1}}^{1}{{U}_{1}}^{1}+\hspace{0.17em}{{a}_{0}}^{0}{{U}_{0}}^{0}+\text{higher}\hspace{0.17em}\text{order}\hspace{0.17em}\text{terms},$$
(7)
$$\mathrm{\Delta}R=k(4{h}^{2}+{b}^{4})/4{R}_{v}.$$