The classical Welter type I grazing-incidence x-ray telescope consists of a
paraboloidal primary mirror and a confocal hyperboloidal secondary mirror.
This design exhibits stigmatic imaging on-axis hut suffers from coma, asti
gmatism, field curvature, and higher-order aberrations such as oblique sphe
rical aberration. Wolter-Schwarzschild designs have been developed that str
ictly satisfy the Abbe sine condition and thus exhibit no spherical aberrat
ion or coma. However, for wide-field applications such as the solar x-ray i
mager (SXI), there is little merit in a design with stigmatic imaging on-ax
is. Instead, one needs to optimize some area-weighted-average measure of re
solution over the desired operational field of view. This has traditionally
been accomplished by mere despacing of the focal plane of the classical We
lter type I telescope. Here we present and evaluate in detail a family of h
yperboloid-hyperboloid grazing-incidence x-ray telescope designs whose wide
-field performance is much improved over that of an optimally despaced Welt
er type I and even somewhat improved over that of an optimally despaced Wol
ter-Schwarzschild design. (C) 2001 Optical Society of America OCIS codes: 3
40.7440, 340.7470, 220.1000, 220.2740.