The Page of Catadioptric Sensor Design



Maintained by
R. Andrew Hicks
Department of Mathematics
Drexel University

Designs by Andy Hicks















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 -

What are catadioptric sensors ?

You may also be interested in looking at the Page of Omnidirectional Vision at the GRASP Laboratory.

An excellent related page is A Timeline of Panoramic Cameras.


The Designs

(Change log)

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.

1840

Method of taking Likenesses by Means of a Concave Reflector and Plates so Prepared as that Luminous or other Rays with act Thereon.
A.S. Wolcott
Sources:
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".

1909

Apparatus for Producing Topographic Views
Louis Henry Kleinschmidt
Sources:
U.S. Patent 994,935
Description: Basically a camera coupled with a conical mirror, but the camera is also designed to rotate

1915

Observation Apparatus
Josesph De Falco
Sources:
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.

1924

Optical System for Viewing Tubes
Man Mohane Kirtane
Sources:
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.

1925

Optical Device for Horizontal Panoramic and Zenithal View
Roberto Parodi
Sources:
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.

1927

Omniscope
James C. Karnes
Sources:
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.

1937

Periscope
William Hardy
Sources:
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.

1938

Cycloramic Optical System
Waldemar A. Ayres
Sources:
U.S. Patent 2,244,235
Description: Ayres proposes using a spherical mirror mounted on a still or movie camera, suspended with transparent cylinder.

1939

Apparatus and Method for taking and Projecting Pictures
James S. Conant
Sources:
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.

1943

Apparatus Employed in Computing Illuminations
Frank Benford
Sources:
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 .

1944

Wide-angle Optical System
William A. Young
Sources:
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.

1950

Unitary Catadioptric Lens System
Donald Robert Buchele and William Martin Buechele
Sources:
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.

1951

Borehole Camera
Robert P. Gutterman
Sources:
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.

1961

Pickup and Projection Mirror System for Panoramic Photography and Panoramic Picture Projection at Horizontal Plane Angles
Ernst Stechemesser
Sources:
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 mentioned.

Extreme Wide Angle Television Photography
Gerald Falbel
Sources:
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.

1962

Hyperbolic Ellipsoidal Real Time Display Panoramic Viewing Installation for Vehicles
Donald W. Rees
Sources:
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.

1963

Panoramic Optical System having an Annular Afocal Lens System
Albert R. Tokarzewski
Sources:
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
Heinz Brachvogel
Sources:
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
Sources:
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.

1966

Panoramic View Objective using an Aspherical Lens
Heinz Brachvogel
Sources:
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 lenses.

1970

Hyperbolic Mirror for TV Viewing
Donald W. Rees
Sources:
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.

1973

Reflectors and Mounts for Panoramic Optical Systems
Joseph A. Pinzone, Gerald J. Troje and Edward L. Sciavone
Sources:
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.

1974

Optical System for 360 Degree Annular Image Transfer
Gottfried R. Rosendahl, Wiley V. Dykes
Sources:
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 horizon.

1975

Wide angle optical imaging system
La Russa; Joseph A. (451 Rutledge Drive, Yorktown Heights, NY 10598)
Sources:
US Patent 4,045,116.
Description:

Discontinuous wide-angle optic
Erik Arne Bergqvist
Sources:
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.

1976

Spiratone Bird's Eye
S.F. Spira (???)
Sources:
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 image.
Description: I don't know anything about this device, other than the single reference found in the above book.

1980

Method for Operating a Panoramic Optical System
Don G. King
Sources:
US Patent 4,326,775
Description:

1981

Panoramic Zoom Lens Assembly
Don G. King
Sources:
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
Sources:
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 handle aberrations.

1982

Panoramic Lens
Cox; Arthur (Des Plains, IL)
Sources:
US Patent 4,484,801.
Description:

1984

Panoramic unity vision system
Cody B. Kreisher
Sources:
US Patent 4,561,733 .
Description:

1985

Panoramic Annular Lens
Pal Greguss
Sources:
US Patent 4,566,763.
Description:

1986

Reflective Optical Element
Glen A. Rines and John D. Kuppenheimer, Jr.
Sources:
U.S. Patent 4,662,726
Description:

1987

An All-Sky Reflector
Jeffrey Charles
Sources:
U.S. Patent D312,263
J. Charles and C. Schur and R. Reeves, How to build and use an all sky camera, Astronomy Magazine, April 1987.
An All-Sky Reflector
Description:

1990

Real-Time Omnidirectional Image Sensor (COPIS) for Vision-Guided Navigations (Conical Mirror)
Yasushi Yagi, Shinjiro Kawato and Saburo Tsuji
Sources:
Catadioptric omnidirectional camera. In IEEE Conf. Computer Vision and Pattern Recognition, pages 482--488, Puerto Rico, June 17-19, 1997.
Description:

Robotic Vision System
Shree K. Nayar
Sources:
U.S. Patent 4,893,183
Description:

1993

Panoramic lens
Powell; Ian (Gloucester, CA)
Sources:
US Patent 5,473,474.
Description:

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.
Description:

1995

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
Description:

1996

Panoramic Stereo
David Southwell, Anup Basu, Mark Fiala and Jerome Reyda
Sources:
David Southwell, Anup Basu, Mark Fiala and Jerome Reyda, Panoramic Stereo. Proc. IEEE International Conference on Pattern Recognition, Vienna, Austria, August 1996.
Description:

A conical mirror pipeline inspection system
David Southwell, Basil Vandergriend and Anup Basu
Sources:
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.
Description:

Method and system for panoramic viewing with curved surface mirrors
Alfred M. Bruckstein
Sources:
U.S. Patent 5,920,376
Description:

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.
Description:

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.
Description:

Panoramic fish-eye imaging system
Powell; Ian (Gloucester, CA)
Sources:
US Patent 5,631,778.
Description:

1997

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)
Sources:
US Patent 6,356,296.
Description:

Omnidirectional imaging apparatus (Parabolic Mirror w/Orthographic Projection)
Shree Nayar
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.
Description:

1998

Method and apparatus for omnidirectional imaging
Zheng Jason Geng (4950 Cloister Dr., Rockville, MD 20852)
Sources:
US Patent 6,304,285.
Description:

A Theory of Catadioptric Image Formation
Simon Baker and Shree Nayar
Sources:
Simon Baker and Shree Nayar , A Theory of Catadioptric Image Formation, Proceedings of ICCV, pages 35-42, 1998.
A Tutorial on Catadioptric Image Formation
Description:

1999

Panoramic viewing system with offset virtual optical centers
Vishvjit Singh Nalwa (Middletown, NJ)
Sources:
US Patent 6,219,090.
Description:

Resolution invariant surfaces (Equiangular Mirror w/Perspective Projection)
Tanya Conroy and John Moore
Sources:
T. Conroy and J. Moore. Resolution invariant surfaces for panoramic vision systems. In IEEE ICCV'99, pages 392-- 397, 1999.
Description:

Rectifying Mirror
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. HTML   PDF
Description: This family of mirrors provide perspective wide-angle views. See the webpage

Equi-Angular Pixel Cameras
Mark Ollis, Herman Herman and Sanjiv Singh
Sources:
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.
Description:

Super wide-angle panoramic imaging apparatus (Folded Catadioptrics)
Sergey Trubko, Venkat Peri, Shree Nayar and James Korein
Sources:
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.
Description:

A New Catadioptric Sensor for Panoramic Vision of Mobile Robots
Ryad Benosman, E. Deforas, and J. Devars
Sources:
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.
Description:

2001

Rectifying Sideview mirror
R. Andrew Hicks and Ronald K. Perline
Sources:
R. Andrew Hicks and Ronald K. Perline. Geometric Distributions for Catadioptric Sensor Design. Proc. of CVPR 2001, Kauai, Hawaii, December 2001, pages 584-589.
Description:

Multiview Mirror Pyramid Panoramic Cameras
Hong Hua and Narendra Ahuja
Sources:
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
Description:

Mirrors that Rectify Vertical Lines
S. Gaechter and T. Pajdla
Sources:
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.
Description:

2002

Equiresolution Catadioptric Sensors
R. Andrew Hicks and Ronald Perline
Sources:
R. Andrew Hicks and Ronald K. Perline. Equi-areal Catadioptric Sensors, Proc. of Omnivis02, Copenhagen, Denmark, June 2, 2002, pages 13-18. Description:

Camera apparatus
Masami Takahashi (Zushi, JP)
Sources:
US Patent 6,575,643.
Description:

Mirror Design of a Prescribed Accuracy Omni-directional Vision System
Fabio M. Marchese, Domenico. G. Sorrenti
Sources:
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.
Description:

Mirrors that Rectify Tilted Lines
Jose Gaspar, Claudia Decco, Jun Okamoto Jr., Jose Santos-Victor
Sources:
Jose Gaspar, C. Decco, C., J. Okamoto, Jr, Constant resolution omnidirectional cameras, Proc. of Omnivis02, Copenhagen, Denmark, June 2, 2002, pages 27-34.
Description:

Panoramic imaging lens
Doi; Tadashi (Toyama, JP)
Sources:
US Patent 6,646,818.
Description:

2003

Differential Methods in Catadioptric Sensor Design with Applications to Panoramic Imaging
R. Andrew Hicks
Sources:
R. Andrew Hicks. Differential Methods in Catadioptric Sensor Design with Applications to Panoramic Imaging, arXiv preprint cs.CV/0303024 . March 24, 2003.
Description:

Mirror for Wide-angle Imaging
Mandyam V. Srinivasan
Sources:
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.
Description:

Framework for Designing Catadioptric Projection and Imaging Systems
R. Swaminathan and S. Nayar and M. Grossberg
Sources:
In Proc. IEEE International Workshop on Projector-Camera Systems, 2003.
Description:

2004

Forward Looking Rectifying Mirror
R. Andrew Hicks and Ronald K. Perline
Sources:
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 spread.

Last modified Tue Apr 6 17:01:00 EDT 2004


Sources:
US Patent .
Description: