Catadioptic Imaging is like refractive imaging (Dioptic Refraction) except in order to get steeper refractive gradients, you use prisms or mirrors for a steeper refractive angle, and achieve a shorter focal length. In modern technology this is typically done with mirrors. A Catadioptic telescope is a refractor and reflector telescope hybrid, as show below .
Figure
3
Figure
3 shows graphically how the Fresnel lens works. To bend and focus the rays
to form a single, concentrated beam of high intensity light, the catadioptic
prisms refract* and reflect; the dioptic prisms and center bull's
eye lens refract. With just a 1000 watt bulb, a first-order Fresnel lens
can generate a 680,000 candlepower beam visible up to 21 miles out to sea
if set high enough.
Hybrid/SCT/Catadioptic Telescope
Hybrid or Catadioptic scopes offer excellent high-power viewing without having the long tube associated with the other two types of scopes. This is accomplished by using a fairly complex arrangement of mirrors. The corrector plate is located at the front of the telescope and there is a large mirror located at the back of the telescope. There is a smaller mirror behind the front lens (corrector plate) which folds the light and reflects the light back into the eyepiece at the back of the telescope. The compact design makes this type of telescope one of the most popular for serious amateurs. There are two different types of catadioptic scopes: the Schmitt-Cassegrains and the Maksutov-Cassegrains. Both are considerably more expensive than similar size Newtonian telescopes.
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Even a perfectly made telescope will suffer from flaws in the focusing of the image caused by the shape of the mirrors. They are exaggerated when the telescope is not pointing directly at the object of interest. Telescopes without aberrations can be constructed using a system of lens and mirrors. Such telescopes are known as catadioptic and are designed in such a way that the aberrations of the lens counteract the aberrations of the mirror.
Refractor
Astronomical refractors are renowned for their image quality.
Views of the Moon and planets are crisp, and stars appear pinpoint sharp.
Refractors are ideal telescopes for terrestrial viewing too, when an image
erecting prism is used.
Refractors have a long, narrow tube containing a multi-element objective
lens. The lens focuses the incoming light and directs it out the
back of the telescope. Andy quality refractor has at least a two
element, or achromatic objective lens. Which consists of one convex
lens made of crown glass and on concave lens made of flint glass.
This reduces the chromatic aberration caused whenever white light passes
through glass. Apochromatic objective lenses have two to four lens
elements. At least one is made with fluorite glass, which provides
even better color correction.
Reflector
The Newtonian reflector (named after Sir Isaac Newton, the inventor)
is a popular and economical astronomical telescope. Its simple, high
performance design provides tremendous light grasp at the lowest cost per
unit of aperture of any telescope type.
A reflector focuses light with mirrors, instead of lenses. In
coming light is reflected off a concave primary mirror at the base of the
optical tube up to a smaller, flat elliptical secondary mirror near the
front end of the scope. The light is deflected out of the optical
tube into the eyepiece by this secondary mirror.
Catadioptic orSchmidt-Cassegrain
telescope
This type of telescope combines the best of both the previously discussed
designs. It's compact design and versatility has made it a popular
type with amateur astronomers.
The optical tube is short because the light path is folded. Light enters through a corrector plate at the front of the telescope and is reflected off the primary mirror to an adjustable, magnifying secondary mirror on the inside of the corrector lens. The light beam is then directed out the back of the tube to the eyepiece.
Now for something completely different:
Here is a catadioptic mirror/lenses system for a hemispherical field of view:
There are several ways to enhance the field of view of an imaging system.
Our approach is to incorporate reflecting surfaces (mirrors) into conventional
imaging systems that use lenses. This is what we refer to as catadioptric
imaging system. It is easy to see that the field of view of a catadioptric
system can be varied by changing the shape of the mirror it uses. However,
the entire imaging system must have a single effective viewpoint to permit
the generation of pure perspective images from a sensed image. At Columbia
University, a new camera with a hemispherical field of view has been developed.
Two such cameras can be placed back-to-back, without violating the single
viewpoint constraint, to arrive at a truly omnidirectional
sensor. Columbia's camera uses an optimized optical design that includes
a parabolic mirror and a telecentric lens. It turns out that, in order
to achieve high optical performance (resolution, for example), the mirror
and the imaging lens system must be matched and the device must be carefully
implemented. Several early prototypes of Columbia's omnidirectional camera
are shown below. Further information related to omnidirectional image sensing
can be found at http://www.cs.columbia.edu/CAVE/omnicam.
Software Generation of Perspective and Panoramic Video Interactive visualization
systems, such as Apple's QuickTime VR, allow a user to navigate around
a visual environment. This is done by simulating a virtual camera whose
parameters are controlled by the user. A limitation of existing systems
is that they are restricted to static environments, i.e. a single wide-angle
image of a scene. The static image is typically obtained by stitching together
several images of a static scene taken by rotating a camera about its center
of projection. Alternatively, a wide-angle capture device is used to acquire
the image. Our video-rate omnidirectional camera makes it possible to acquire
wide-angle images at video rate. This has motivated us to develop a software
system that can create perspective and panoramic video streams from an
omnidirectional one. This capability adds a new dimension to the concept
of remote visual exploration. Our software system, called omnivideo, can
generate (at 30 Hz) a large number of perspective and panoramic video streams
from a single omnidirectional video input, using no more than a PC. A remote
user can control the viewing parameters (viewing direction, magnification,
and size) of each perspective and panoramic stream using an interactive
device such as a mouse or a joystick. The output of the omnivideo system
(as seen on a PC screen) is shown below. Further details related to omnivideo
can be found at http://www.cs.columbia.edu/CAVE/omnicam/omnivideo.htm.
Our current work is geared towards the incorporation of a variety of image
enhancement techniques into the omnivideo system.
References:
"Omnidirectional Video Processing,"
Venkata N. Peri and Shree K. Nayar,
Proc. of IROS U.S.-Japan Graduate Student Forum on Robotics, Osaka,
November 1996.
This remote reality environment allows the user to naturally look around, within the hemispherical field of view of the omnidirectional, and see objects/action at the remote location.
If the omnidirectional video is recorded, say using a standard camcorder, the visualization can be remote in both space and time. Current the system provides 320x240 resolution color images of 30frame-per-second (fps) video with position updates from the head-tracker at between 15 and 30 fps. While the resolution is limited compared to today's high end graphics simulators, we believe this has much to offer for training and very significant advantages for very-short turn around "VR model acquisition" for in situ training and mission rehearsal. The system is quite inexpensive. The HMD/display system costs under $3000 for us to build from Common-Off-The-Shelf (COTS) components, with omnidirectional recording system costing about the same. The image insert shows the HMD component of system and an Omnidirectional camera on a vehicle mounting bracket.
For the general training the system has the advantage of having very realistic, albeit lower resolution, motion/action while not limiting the users viewing direction. The omnidirectional camera can be mounted on a vehicle or carried in a field-back to allow remote users to better experience the field conditions. Further its low cost combined with the ease with which one can easy acquire a new training "environment" would mean that it could be used at local facilities and maintained/customized with very little training. It can also be used for recording/review of training exercises.
For the pre-mission rehearsal, the system provides a very unique capability.
If a omnivideo were acquired either by a vehicle drive through an area
of interest and/or by a very-low altitude UAV fly-through, then an in-field
remote-reality system could provide in situ rehearsal where users could
review the site, in any direction. As the system could either use live
video transmissions from the remote camera, or if more practical, a recorded
tape, the "turn-around time" from acquiring the data to mission rehearsal
would minimal. With a monocular display the system and the next generation
of wearable computers, the system could be extended to allow a group of
mobile agent to independently view remote sites, e.g. with a robotic vehicle
carrying the camera into forward locations.
Commercial Off The Shelf Available Hardware
