Optical: systems and elements – Lens – Including a nonspherical surface
Reexamination Certificate
2003-03-19
2004-03-30
Schwartz, Jordan M. (Department: 2873)
Optical: systems and elements
Lens
Including a nonspherical surface
C359S619000, C359S625000
Reexamination Certificate
active
06714361
ABSTRACT:
RELATED U.S. APPLICATIONS
Not applicable.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not applicable.
REFERENCE TO MICROFICHE APPENDIX
Not applicable.
FIELD OF THE INVENTION
The invention here presented deals with an optical system enabling such an imaging of an object, the result of which is a generally distorted, deformed image of an object.
BACKGROUND OF THE INVENTION
Lenses, or more precisely optical systems currently used in photographic cameras are characteristic by providing perfect image of the taken object with minimum distortion. When photographing an object located within finite distance from a camera lens the co-ordinates of (x,y) of any point are related to the co-ordinates (x′, y′) of the image of this point by relations
x′=m
x
x, y′=m
y
y,
where m
x
and m
y
represent magnification in the direction of the co-ordinates and their value is constant for the given distance of the object from the camera lens. The relation is always m
x
=m
y
=m except for anamorphotic lenses. The relation between an object and its image is thus described as linear transformation. For infinite object distance the size of the image, created by the photographic lens is, defined by the relation
y′=f.tgw−
central projection,
where f is the lens focal length and w is the angle of the lens field of view. For extremely wide-angle lenses of “fish eye” type (2w>180°) the size of image created by such a lens is defined by one of these relations:
y′=f.w−
equidistant projection
y′=
2
f
sin(
w/
2)−ortographic projection
y′=
2
f tg
(
w/
2)−stereographic projection.
As can be seen from these relations, current photographic lenses only allow such a projection of an object, which is described by one of the above relations. The above, optical systems, or more precisely photographic lenses have a drawback, in that they are not capable of giving a generally distorted image of an object.
BRIEF SUMMARY OF THE INVENTION
The above drawbacks are removed by the optical system for distorted image of an object according to the invention, particularly intended for photographic cameras. It is based on the principle a distorting optical system consisting of one or more lenses where at least one of the lenses has at least one asymmetrical aspherical optical surface and/or of one or more diffractive elements, where at least one diffractive element has a surface with asymmetric diffractive structure and/or at least two lenses with mutual general space orientation. The following relations apply to the orthogonal co-ordinates (x, y, z) of any point of the object whose image is to be distorted, and the orthogonal co-ordinates (x′, y′, z′) of the image of this point with the required distortion:
x
′
=
∑
i
=
1
i
=
N
a
i
f
i
(
x
,
y
,
z
)
,
y
′
=
∑
i
=
1
i
=
N
b
i
g
i
(
x
,
y
,
z
)
,
z
′
=
∑
i
=
1
i
=
N
c
i
h
i
(
x
,
y
,
z
)
where N≧1 is an integer number, a
i
, b
i
, c
i
are weight constants of distortion in the appropriate direction and f
i
(x,y,z), g
i
(x,y,z), h
i
(x,y,z) are functions for ensuring achievement of the chosen required distortion of image.
One of the possible variants is, that the distorting optical system may be located between the first and the second optical systems.
In another version the first optical system is placed before the distorting optical system in the direction from the object the image of which is to be shot.
In another version the second optical system is placed after the distorting optical system in the direction from the object the image of which is to be shot.
The first and/or the second optical system may consist of a centered system of lenses or by a common photographic lens.
In another possible version at least one of the optical elements forming the distorting optical system may be designed as rotary.
Any object located in the space in front of the distorting optical system, or any image of an object located in the space in front or behind the distorting optical system, created by another optical system, may be the object the image of which is to be distorted.
An optical system setup this way has the advantage that it enables such an image of an object, the result of which is a generally distorted, deformed image of the object. The distortion size and character may be changed anyhow according to the user's intention by changes of weight constants and functions.
REFERENCES:
patent: 6052230 (2000-04-01), Clark
Mik{haeck over (s)} Antonín
Ondra{haeck over (s)}ík Ivan
Harrison & Egbert
Schwartz Jordan M.
Thompson Tim
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