Rectifying mirror

• US 6,412,961 B1
• Filed: 03/09/2001
• Issued: 07/02/2002
• Est. Priority Date: 05/30/2000
• Status: Expired due to Fees

• Current Assignee: Robert Andrew Hicks
• Original Assignee: Robert Andrew Hicks
• Inventors: Hicks, Robert Andrew
• Primary Examiner(s): SIKDER, MOHAMMAD YUNUS
• Application Number:
  US09/802,711
• Time in Patent Office: 480 Days
• Field of Search: 859/846, 859/847, 859/848, 859/849, 859/850, 859/853, 859/838, 362/61, 362/80, 362/297, 362/299, 362/304, 362/328, 362/343, 362/346, 362/347
• US Class Current: 359/846
• CPC Class Codes: G02B 13/06 Panoramic objectives; So-called "sky lenses" including panoramic objectives having reflecting surfaces
• CPC Class Codes: G02B 27/0025 for optical correction, e.g. distorsion, aberration
• CPC Class Codes: G02B 5/10 with curved faces
• CPC Class Codes: H04N 23/58 Means for changing the camera field of view without moving the camera body, e.g. nutating or panning of optics or image sensors

Abstract

A mirror for use in a catadioptric system, is provided which is a substantially circular mirror having a rotationally symmetric cross section by a set of points substantially close to a curve satisfied by a differential equation as follows: $\frac{2F^{\prime }\left(x\right)}{1-{F^{\prime }\left(x\right)}^2}=\frac{d\left(x\right)-x}{F\left(x\right)}$

where x is the radius of the mirror and F(x) is the cross-sectional shape. Alternatively, a mirror for use in a catadioptric system, is provided which is a substantially circular mirror having a rotationally symmetric cross section determined by a differential equation as follows: $\frac{\frac{x}{f}+\frac{2F^{\prime }\left(t\right)}{1-{F^{\prime }\left(t\right)}^2}}{1-\frac{x}{f}\frac{2F^{\prime }\left(t\right)}{1-{F^{\prime }\left(t\right)}^2}}=\frac{d\left(x\right)-t}{F\left(t\right)}$

where x=f(t)/(F(t)−f−h), f is the focal length, h is the height above an object plane, and F(t) is the cross-sectional shape.

Claims

1. A mirror for use in a catadioptric system, comprising a substantially circular mirror having a rotationally symmetric cross section by a set of points substantially close to a curve satisfied by a differential equation as follows:

$\frac{2<br><br>F^{\mathrm{\prime <br><br>}}<br><br>\left(x\right)}{1-{F^{\mathrm{\prime <br><br>}}<br><br>\left(x\right)}^2}=\frac{d<br><br>\left(x\right)-x}{F<br><br>\left(x\right)}$

where x is the horizontal coordinate of the mirror and where the largest value of x is the radius of the mirror and F(x) is the cross-sectional shape.