A single moving element can give zooming in a catadioptric design due to the double pass of light through the moving element.

1. Catadioptric optically compensated zooming with one moving element
David Shafer
David Shafer Optical Design
56 Drake Lane, Fairfield, Ct. 06430
ABSTRACT
The distinction between mechanically and optically compensated
zoom systems has an interesting counterpart in certain catadioptric
systems. The simplest such system is very simple indeed: a front
refractive air-spaced nearly afocal doublet near the front focus of a
spherical concave mirror. The front positive lens and the mirror
have a fixed separation and the following negative lens moves back in
forth in the space between, while also being traversed again by the
focused light from the mirror. By having the negative lens used in
double pass during its zooming motion a,quartic focus curve can be
obtained. The image falls near the center of the front positive
lens, where a detector can be placed. A sample design with a 2.5X
zoom ratio is described. The two front lenses are germanium and it
zooms from an f/2.0, 5.0 degree diameter field to an f/5.0, 2.0
degree diameter field with good image quality.
Keywords: Zoom, catadioptric, optically compensated, zoom mirrors
INTRODUCTION
In a conventional optically compensated zoom lens, two or more
separated lenses or lens groups are linked together and move
together. As far as the light rays are concerned, there are two
moving lenses or lens groups. But mechanically there is just one
motion. This concept has an interesting counterpart in certain
catadioptric systems.
NEW DESIGNS
Figure 1 shows the optical system which is the subject of this
paper. In its simplest version it consists of just two germanium
lenses and a spherical mirror. The front positive lens is fixed,
relative to the spherical mirror, and is a little further away from
the mirror than half the mirror radius. The negative lens slides
back and forth in the space between the front positive lens and the
mirror, and thereby causes the system focal length to vary.
Now if the negative lens were used just once, in single pass, by
the light rays then we would have a conventional zooming type of
system. If the negative lens were to pass through its unit
magnification conjugates, and also work on both sides of that
position, then the well-known quadratic focus shift would occur. The
resulting focus error would be quite large if any appreciable zoom
ratio was attempted.
Proc. of SPIE Vol. 2539, Zoom Lenses, ed. A Mann (Oct 1995) Copyright SPIE
235

2. Here, however, the negative lens is seen twice by the light
rays: once on the way to the mirror and once on the way back. As far
as the light rays are concerned, it looks as though there are two
moving negative lenses, even though there is actually only one. This
makes it possible to achieve a much better focus shift, with zoom.
It does not happen automatically, however. The lens and mirror
powers must be chosen just right in order to get the best effect,
which is a quartic focus shift. This is shown, for one
representative case, in Figure 2. The particular balance of the
curve will depend on what zoom range the system is optimized for.
Here I show a 2.5X zoom range.
There is an inferior counterpart to this system, shown in Figure
3, where all the powers are reversed. For the same system length and
2.5X zoom ratio, the moving component only moves half as much as in
the Figure 1 system. It has worse performance, probably due to its
considerably stronger components. Notice that the closest approach
of the two lenses in Figure 1 corresponds to the shortest system
focal length, while it corresponds to the longest focal length in the
Figure 3 design.
Both versions of the design have largely uncorrected field
curvature, coming from the mirror. Best performance comes from
adding a field lens or two down near the image. In the infrared,
color may be acceptable if the system aperture is not too large.
Aspherics added to the germanium lenses can improve performance.
Figure 4 shows a design for the visible region, for a CCD
detector chip, with some field lenses near the image. It has all
spherical surfaces. The end positions of the 2.5X zoom range, of the
middle element, are similar to the Figure 1 picture.
236

3. 2
z:0 n
B0 cl
2.5 X ZOOM RANGE
ALL SPHERICAL SURFACES
7 w
FIGURE 1
237

4. FOCUSSHIFT
238

5. u
ALTERNATE SOLUTION
FIGURE 3' 2.5 X ZOOM lQlXG&
239

6. I
240