Welcome to the page of Catadioptric Sensor Design. Catadioptric
sensors are imaging sensors built with combinations of mirrors
(catoptrics), and lenses (dioptrics). The main advantage of using
mirrors with cameras is that by using a curved mirror a wide field of
view can be obtained. Catadioptric sensors are sometimes also known as
omnidirectional sensors. For more details see my introduction -
Here is a list of some devices and some facts proved about
catadioptric sensors. Note that for patents, the year refers t0 the
year that the patent was filed. To keep things tractable, I have
chosen (for the moment) to omit catadioptric telescopes, microscopes,
heads-up displays etc.
THERE ARE MANY OMISSIONS ON THIS PAGE.
This subject is enormous, and I haven't had the time to enter every
sensor that I know of.
If you don't see something that should be here, please let me know.
Method of taking Likenesses by Means of a Concave Reflector and Plates so Prepared as that Luminous or other Rays with act Thereon.
U.S. Patent 1582
Rudolf Kingslake, The History of the Photographic Lens, Academic Press 1989.
Description: Kingslake (page 175) claims that this was the first
mirror system used for photography. A daguerroetype plate was used in
conjunction with a concave mirror (no lenses!). The shape of the
mirror is not specified in the text of the patent, but on the drawing
is written "concave cylinder".
Apparatus for Producing Topographic Views
Louis Henry Kleinschmidt
U.S. Patent 994,935
Description: Basically a camera coupled with a conical mirror, but the
camera is also designed to rotate
Josesph De Falco
U.S. Patent 1,157,154
Description: This device is kind of omnidirectional camera
obscura. The scene is reflected off of a spherical mirror, into a
building or box through a series of lenses, and onto a spherical
shell, which serves as a screen. In a second embodiment of the
invention, the spherical shell is mirrored, and is viewed with a
second auxiliary mirror.
Optical System for Viewing Tubes
Man Mohane Kirtane
U.S. Patent 1,653,575
Description: This device is another omnidirectional camera
obscura, but interestingly it contains no mirrors, but makes use of total
internal reflection by removing a conical region from a solid cylinder
of glass. Two of these "cylindrical prisms" are used in the invention
- the first to direct light from the scene onto a second, which
projects to a cylindrical screen.
Optical Device for Horizontal Panoramic and Zenithal View
U.S. Patent 1,616,279
Description: This device is meant to be used as a periscope which
projects an image onto a cylindrical screen. Two toric lenses are used
to capture and project the image. No mirrors are used, so presumably
the rays experience total internal reflection.
James C. Karnes
U.S. Patent 1,797,867
Description: Karnes' Omniscope appears to be a periscope equipped with
a parabolic mirror for panoramic viewing, with a hole in the parabola,
where the viewer would see themselves. This hole has been augmented
with a prism, so that this region may contain the image of something
useful, such as an unseen portion of the scene or a compass.
U.S. Patent 2,176,554
Description: Hardy's periscope contains a truncated conical mirror,
which projects the scene though a lens and onto a reflective tabletop.
Cycloramic Optical System
Waldemar A. Ayres
U.S. Patent 2,244,235
Description: Ayres proposes using a spherical mirror mounted on a
still or movie camera, suspended with transparent cylinder.
Apparatus and Method for taking and Projecting Pictures
James S. Conant
U.S. Patent 2,299,682
Description: Conant's patent describes several catadioptric sensors,
using spherical, parabolic and conical mirrors, and also some
projection/screen inventions. Conant proposes using a conical mirror
so that the camera does not appear in the image, and so that the film
is used more efficiently. (What Conant means by conical though is any
mirror that is a surface of revolution that does not have a horizontal
tangent at its lowest point.) This is the first occurrence that I know
of of a sensor being designed to maximize image quality.
Apparatus Employed in Computing Illuminations
U.S. Patent 2,371,495
Description: This is one of the most interesting of the old
patents. Benford is interested in radiometry - the goal is to build a
catadioptric sensor with a mirror shape designed to make it easy to
measure the amount of illumination from a light source. While he
doesn't give explicit equations he says that the curvature of the
mirror is such that the area of the image of a spherical source should
be proportional to a certain other projection of the source, which is
related to its illuminance. Here is the
page of drawings .
Wide-angle Optical System
William A. Young
U.S. Patent 2,430,595
Description: Young's invention is a two mirror system designed to
address the problem of the camera appearing in the middle of a mirror.
This is done by placing the camera behind a convex mirror, which faces
a second mirror. It is pointed out that an advantage of using two
mirrors is that it reduces aberrations.
Unitary Catadioptric Lens System
Donald Robert Buchele and William Martin Buechele
U.S. Patent 2,638,033
Description: This device is meant to be used as a periscope. It
consists of two hemispherical lenses of different radii, joined on
their flat sides. The smaller sphere is partially mirrored, in an
annular region. Light is meant to pass though the larger sphere,
reflect off of the mirrored portion of the smaller lens, and back out
the larger lens to form an image.
Robert P. Gutterman
U.S. Patent 2,737,864
Description: This camera is designed to inspect holes or pipes. There are two versions - one using a flat mirror and another using a conical mirror.
Pickup and Projection Mirror System for Panoramic Photography and Panoramic Picture Projection at Horizontal Plane Angles
U.S. Patent 3,240,113
Description: Stechemesser points that the problem of non-uniform
resolution that occurs when images are created using spherical,
parabolic or conical mirrors and reprojected onto a spherical or
cylindrical screen. The solution he proposes is to use as a mirror a
surface of revolution with a pointy bottom, i.e., the surface is
formed by rotating a curve about an axis and the curve is not normal
to the axis at the intersection point. An explicit curve is not
Extreme Wide Angle Television Photography
U.S. Patent 3,209,073
Description: Falbel proposes three distinct types of sensors to be
used for television. The first is a toroidal lens coupled with a flat
mirror, which, through internal reflection obtains a panoramic
view. The second is a retrofocus lens, and the third is a convexc
mirror of undescribed shape. Falbel also suggests that the electron
beam in the television tube be scanned spirally, and that the image
should be projected on a cylindrical screen.
Hyperbolic Ellipsoidal Real Time Display Panoramic Viewing Installation for Vehicles
Donald W. Rees
U.S. Patent 3,229,576
Description: This is the oldest reference I know of where single
viewpoint properties are made use of to "unwarp" an image. Rees
proposes a camera/hyperbolic mirror combination, with the center of
projection of the camera placed at the lower focus of the mirror. The
image is then projected onto an elliptical (360 degree) viewing screen
that presents the images to the operator.
Panoramic Optical System having an Annular Afocal Lens System
Albert R. Tokarzewski
U.S. Patent 3,283,653
Description: This invention is similar to the annular lens of Buechle
(1950), but much more elaborate. It is unusual in that the image is a
hybrid, formed in one portion from light that has been reflected, and
in another formed by light that has only refracted. In another
embodiment, prisms are used to invert the positions of these two
portions of the image.
Orthoscopic Panoramic and Straight-View Optical System
U.S. Patent 3,404,934
Description: This invention, like the invention of Tokarzewski (1963)
has a hybrid nature. Part of the image is formed by viewing a
spherical mirror, and another part is formed from light that travels
through a hole drilled in the mirror, which is replaced with a lens.
Full Circumferential Viewing System
Harry P. Brueggemann
U.S. Patent 3,203,328
Description: This patent describes two devices - one for capturing
images (as photographs) and another for displaying (projecting)
them. The images are captured using a two mirror system - a primary
mirror that is hyperbolic and a secondary mirror that is
spherical. The reason given for the second mirror's use is to reduce
aberrations. The device does make use of the hyperbola having a focus
(i.e. a single effective viewpoint), and uses this to "unwarp" the
image, i.e., present it to the viewer as the viewer would have seen it
from that viewpoint.
Panoramic View Objective using an Aspherical Lens
U.S. Patent 3,552,820
Description: This device is shaped like a bullet, with the nose
consisting of a lens that is mirrored in the lower region, i.e, an
annular region that reflects light that has entered the upper portion
of the lens. The lower body of the device contains conventional
Hyperbolic Mirror for TV Viewing
Donald W. Rees
U.S. Patent 3,505,465
Description: This invention is much like Rees' 1962 invention, except
that rather than projecting the image onto a 360 degree elliptical viewing
screen, a portion of it is viewed unwarped on a television screen via
an elliptic mirror.
Reflectors and Mounts for Panoramic Optical Systems
Joseph A. Pinzone, Gerald J. Troje and Edward L. Sciavone
U.S. Patent 3,846,809
Description: The invention consists of a spherical mirror joined to a
small conical mirror at its bottom and supported by a single central
post that is screwed into the center of the camera lens.
Optical System for 360 Degree Annular Image Transfer
Gottfried R. Rosendahl, Wiley V. Dykes
U.S. Patent 4,012,126
Description: This system consists of two hyperbolic mirrors (a camera
or projector is placed behind one of them) that share a focal
point. The purpose of this is to reduce aberrations (The patent
contains a fairly detailed discussion of the aberration issues.) The
vertical field of view is 30 degrees above and 60 degrees below the
Wide angle optical imaging system
La Russa; Joseph A. (451 Rutledge Drive, Yorktown Heights, NY 10598)
US Patent 4,045,116.
Discontinuous wide-angle optic
Erik Arne Bergqvist
U.S. Patent 3,984,178
Description: This sensor is very much like the Buechle patent
described above, but the wall are segmented. The application is as a
proximity fuse, where wide-angle sensing is important. It is argued
that the discontinuities caused by the segmented mirrors are not a
problem because the object being sensed is generally quite large.
Spiratone Bird's Eye
S.F. Spira (???)
The History of Photography: As Seen Through the Spira Collection by
S. F. Spira, Eaton S. Lothrop Jr., Jonathan B. Spira, Publisher:
Aperture; 1st edition (December 7, 2001), ISBN: 0893819530. Here is an
Description: I don't know anything about this device, other than the single reference found in the above book.
Method for Operating a Panoramic Optical System
Don G. King
US Patent 4,326,775
Panoramic Zoom Lens Assembly
Don G. King
US Patent 4,429,957.
Description: This design is a mirror (any surface of revolution) with a
movable lens system beneath it that can zoom in on it. The "annular"
image is to be transformed into a rectangular one with another of
King's inventions. I believe this is the first example of unwarping an
image into a flat rectangular form. From the patent:
The annular image is projected upon the target surface of a video
camera and is scanned in a horizontal scanning pattern. The image
reproduced in the video receiver is an exact duplicate of the annular
image including a central region of the raster surface of the video
receiving tube which is unused. In order to make efficient use of the
raster surface of the video picture tube, the annular image is
"spread" or transformed into a rectangular image in which the complete
panoramic view is portrayed on the receiver screen without image
inversion, as set forth in my co-pending U.S. patent application
Ser. No. 159,613, filed June 16, 1980, now U.S. Pat. No. 4,327,312
entitled "Circular Raster Sweep Generator".
Lens system for panoramic imagery
Gottfried R. Rosendahl
US Patent 4,395,093.
Description: Double hyperbolic system, carefully designed to make use
of the focal points of the parabola and with complex dioptrics to
Omnidirectional visual sensor having a plurality of mirrors with surfaces of revolution
Yasushi Yagi and Masahiko Yachida
Sources: U.S. Patent 6,130,783
Omnidirectional Imaging with Hyperboloidal Projection", K. Yamazawa et al., Proceedings of the 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems, Yokohama, Japan, Jul. 26-30, 1993, pp. 1029-1034.
Optics Assembly for Observing a Panoramic Scene
John E. Davis, Marion N. Todd, Mitchell Ruda, Tilman W. Stuhlinger and
Kenneth R. Castle
Sources: U.S. Patent 5,627,675
David Southwell, Anup Basu, Mark Fiala and Jerome Reyda
David Southwell, Anup Basu, Mark Fiala and Jerome Reyda, Panoramic Stereo.
Proc. IEEE International Conference on Pattern Recognition,
Vienna, Austria, August 1996.
A conical mirror pipeline inspection system
David Southwell, Basil Vandergriend and Anup Basu
David Southwell, Basil Vandergriend and Anup Basu,
A conical mirror pipeline inspection system.
Proc. IEEE International Conference on Robotics and Automation,
Minneapolis, USA, April 1996.
Method and system for panoramic viewing with curved surface mirrors
Alfred M. Bruckstein
Sources: U.S. Patent 5,920,376
Panoramic projection apparatus (Mirror Pyramid)
Vishvjit S. Nalwa
Sources: U.S. Patent 5,539,483
A True Omnidirectional Viewer", Technical Report, Bell Laboratories, February 1996.
Panoramic surveillance system (Equiangular Mirror w/Perspective Projection)
Javann Chahl and Mandyam Srinivasan
Sources: U.S. Patent 5,790,181
J. Chahl and M. Srinivasan. Reflective surfaces for panoramic imaging. Applied Optics, 36(31):8275--85, November 1997.
Panoramic fish-eye imaging system
Powell; Ian (Gloucester, CA)
US Patent 5,631,778.
Method and apparatus for implementing a panoptic camera system
Edward Driscoll Jr. (Portola Valley, CA), Willard Curtis Lomax
(Sunnyvale, CA), Howard Morrow (San Jose, CA)
US Patent 6,356,296.
Omnidirectional imaging apparatus (Parabolic Mirror w/Orthographic Projection)
Sources: U.S. Patent 6,118,474
Catadioptric omnidirectional camera. In IEEE Conf. Computer Vision and Pattern Recognition, pages 482--488, Puerto Rico, June 17-19, 1997.
Method and apparatus for omnidirectional imaging
Zheng Jason Geng (4950 Cloister Dr., Rockville, MD 20852)
US Patent 6,304,285.
Panoramic viewing system with offset virtual optical centers
Vishvjit Singh Nalwa (Middletown, NJ)
US Patent 6,219,090.
Resolution invariant surfaces (Equiangular Mirror w/Perspective Projection)
Tanya Conroy and John Moore
T. Conroy and J. Moore. Resolution invariant surfaces for panoramic vision systems. In IEEE ICCV'99, pages 392-- 397, 1999.
R. Andrew Hicks
Sources: U.S. Patent 6,412,961
Reflective Surfaces as Computational Sensors. Proc. of the Second Workshop on Perception for Mobile Agents, Fort Collins, Colorado, 1999, pages 82-86.
Description: This family of mirrors provide perspective wide-angle views. See the webpage
Equi-Angular Pixel Cameras
Mark Ollis, Herman Herman and Sanjiv Singh
U.S. Patent 6,594,448
Analysis and Design of Panoramic Stereo Vision Using Equi-Angular Pixel Cameras
M. Ollis, H. Herman, and S. Singh
tech. report CMU-RI-TR-99-04, Robotics Institute, Carnegie Mellon University, January, 1999.
Super wide-angle panoramic imaging apparatus (Folded Catadioptrics)
Sergey Trubko, Venkat Peri, Shree Nayar and James Korein
U.S. Patent 6,611,282
S. Nayar and V. Peri. Folded catadioptric cameras. In Conference on Computer Vision and Pattern Recognition, Fort Collins, Colorado, volume II, pages 217-223.
A New Catadioptric Sensor for Panoramic Vision of Mobile Robots
Ryad Benosman, E. Deforas, and J. Devars
R. Benosman, E. Deforas, and J. Devars, "A New Catadioptric Sensor for Panoramic Vision of Mobile Robots," Proc. IEEE Workshop Omnidirectional Vision, pp. 112-118, June 2000.
Rectifying Sideview mirror
R. Andrew Hicks and Ronald K. Perline
R. Andrew Hicks and Ronald K. Perline. Geometric Distributions for Catadioptric Sensor Design. Proc. of CVPR 2001, Kauai, Hawaii, December 2001, pages 584-589.
Multiview Mirror Pyramid Panoramic Cameras
Hong Hua and Narendra Ahuja
Hong Hua and Narendra Ahuja. A High-Resolution Panoramic Camera. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, Vol. I, pages 960-967, 2001.
Multiview Mirror Pyramid Panoramic Cameras
Mirrors that Rectify Vertical Lines
S. Gaechter and T. Pajdla
S. Gaechter, T. Pajdla, and B. Micusik. Mirror design for an omnidirectional camera with a space variant imager.
IEEE Workshop on Omnidirectional Vision Applied to Robotic Orientation and Nondestructive Testing, pages 99-105, August 2001.
Equiresolution Catadioptric Sensors
R. Andrew Hicks and Ronald Perline
R. Andrew Hicks and Ronald K. Perline. Equi-areal Catadioptric
Sensors, Proc. of Omnivis02, Copenhagen, Denmark, June 2, 2002, pages
Mirror Design of a Prescribed Accuracy Omni-directional Vision System
Fabio M. Marchese, Domenico. G. Sorrenti
Fabio M. Marchese, Domenico. G. Sorrenti. Mirror Design of a Prescribed
Accuracy Omni-directional Vision System. Proc. of Omnivis02, Copenhagen, Denmark, June 2, 2002, pages. 136-142.
Mirrors that Rectify Tilted Lines
Jose Gaspar, Claudia Decco, Jun Okamoto Jr., Jose Santos-Victor
Jose Gaspar, C. Decco, C., J. Okamoto, Jr,
Constant resolution omnidirectional cameras, Proc. of Omnivis02, Copenhagen, Denmark, June 2, 2002, pages 27-34.
Differential Methods in Catadioptric Sensor Design with Applications to Panoramic Imaging
R. Andrew Hicks
R. Andrew Hicks. Differential Methods in Catadioptric Sensor Design with Applications to Panoramic Imaging,
arXiv preprint cs.CV/0303024 . March 24, 2003.
Mirror for Wide-angle Imaging
Mandyam V. Srinivasan
Mandyam V. Srinivasan. A New Class of Mirrors for Wide-angle Imaging. In Proceedings of IEEE Workshop on Omnidirectional Vision and Camera Networks, Madison Wisconsin, USA, June 2003.
Framework for Designing Catadioptric Projection and Imaging Systems
R. Swaminathan and S. Nayar and M. Grossberg
In Proc. IEEE International Workshop on Projector-Camera Systems, 2003.
Forward Looking Rectifying Mirror
R. Andrew Hicks and Ronald K. Perline
The Fixed Surface Method for Catadioptric Sensor Design, Drexel University Department of Mathematics Technical Report 02-04-1. PDF
Description: This mirror allows the viewer a wide-angle rectified view
of a plane in front of the camera. Additionally, the paper derives
expressions for functionals whose minimums are mirror shapes that
minimize image error.
Mirror to prevent projection beam obstruction
R. Andrew Hicks
Sources: This website and
R. Swaminathan and S. Nayar and M. Grossberg. Framework for Designing Catadioptric Projection and Imaging Systems. In Proc. IEEE International Workshop on Projector-Camera Systems, 2003.
Description: This mirror is designed to be used in conjunction with a
projector mounted over a screen, so that the speaker cannot block the
beam. The original idea is due to Swaminathan et al. assuming that the
projector beam is columnated. In that case the solution is a rotationally symmetric rectifying mirror. This
device is the "perspective" case, i.e. the case when the beam has some