X-ray Imaging Systems
In order for any optical system to form an image, it must satisfy the
"Abbe sine condition", at least approximately. The Abbe sine
condition states that an optical system will form an image of an infinitely
distant object only if for each ray in the parallel beam emanating from
the source:
| h/sin(theta) = f |
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Figure 1
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where h is the (radial) distance of the ray from the optical axis, theta
is the angle of the final path of the ray relative to its initial path
(and thus the optical axis) and f is a constant for all rays. In other
words, an image will be formed if the principal surface, defined as the
locus of intersections of the initial and final paths of rays, is
spherical. An optical system satisfying the Abbe sine condition thus
acts as a simple spherical lens.
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| Figure 2 - A simple parabolic mirror |
A simple parabolic mirror (often used as the primary reflector in an optical
telescope), originally proposed in 1960 by Riccardo Giacconi and Bruno Rossi,
the founders of extrasolar X-ray astronomy, does not satisfy the Abbe sine
condition, since the principal surface is the paraboloid itself (see figure 2).
Paraxial rays (rays impinging on the mirror parallel to the optical axis) will
indeed focus to a point, but images of off-axis objects will be severely
blurred. (An optical reflecting telescope gets around this by use of a
secondary lens to correct this blurring.) The German physicist Hans Wolter
showed in 1952 that the reflection off a combination of two elements, a
paraboloid, followed by a confocal and coaxial paraboloid, will allow the Abbe
sine condition to be nearly satisfied. Wolter also showed demonstrated that
any odd number of coaxial conic sections will not form an image, but any even
number can.
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Figure 3 - Two element reflection image system
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Another system which forms real images consists of a set of two orthogonal
parabolas of translation, off which incident X-rays reflect successively,
as first proposed in 1948 by Kirkpatrick and Baez. A simplified
Kirkpatrick-Baez design in shown in figure 4a. In practical designs, the
surface area is increased by using many approximately parallel mirrors
(i.e., nesting) in each reflecting stage as in figure 4b. The
Kirkpatrick-Baez system offers inexpensive construction since the reflecting
surfaces can be optically flat glass plates, bent to the proper curvature by
mechanical stressing. On the other hand, the coalignment of many reflecting
surfaces to form an optimum image is a difficult process. Since this was the
first imaging telescope used for non-solar X-ray astronomy, the
Kirkpatrick-Baez system is worthy of mention if only for historical reasons.
The most commonly used X-ray mirrors are the cylindrically symmetric systems
first described by Wolter.
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Figure 4 - The Kirkpatrick-Baez X-ray Telescope Design
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Wolter described three different imaging configurations, the Types I, II,
and III, which are depicted in figure 5. The design most commonly used by
X-ray astronomers is the Type I since it has the simplest mechanical
configuration (figure 5a). In addition, the Type I design offers the
possibility of nesting several telescopes inside one another, thereby
increasing the useful reflecting area. This is an extremely important
attribute, as virtually all X-ray sources are weak, and maximizing the light
gathering power of a mirror system is critical. The primary advantage of the
Type II design (figure 5b) over the Type I is that, because the second
reflection is off the outside of a surface, longer focal lengths and thus
higher focal plane magnifications are attainable than in a Type I possessing a
comparable aperture and average grazing angle. However, since off-axis images
suffer much more severely from blurring in Type II configurations, the Wolter
Type II is useful only as a narrow-field imager or as the optic for a
dispersive spectrometer. The Wolter Type III has never been employed for X-ray
astronomy. |
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Figure 5 - The Wolter X-ray Telescope Designs
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Show me a movie about imaging X-rays
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