U.S. patent number RE30,804 [Application Number 05/935,958] was granted by the patent office on 1981-11-24 for optical air lens system.
Invention is credited to John B. Goodell, Harley B. Lindemann.
United States Patent |
RE30,804 |
Lindemann , et al. |
November 24, 1981 |
Optical air lens system
Abstract
In an optical system the use of .Iadd.one or .Iaddend.a
plurality of air lenses set in an optical medium of higher
refractive index than air at a predetermined distance from an
object such that various optical aberrations are minimized or
eliminated by using aplanatic optical surfaces. Refraction occurs
only for a ray going from the higher to the lower refractive index
medium. Rays entering the higher refractive index medium from the
lower are never refracted since the optical surface is always
chosen to have its center .[.or.]. .Iadd.of .Iaddend.radius
coincident with the object or image being optically operated on by
the lens. The system can be used to magnify the image of an object,
the object being most any two-dimensional representation such as a
negative or a positive print. The object might alternatively be a
light source or an external object whose rays are imaged onto an
embedded light sensor so that the functions of the source or sensor
respectively can be enhanced by the optical system.
Inventors: |
Lindemann; Harley B.
(Baltimore, MD), Goodell; John B. (Baltimore, MD) |
Family
ID: |
25467971 |
Appl.
No.: |
05/935,958 |
Filed: |
August 23, 1978 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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427257 |
Dec 21, 1973 |
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Reissue of: |
559011 |
Mar 17, 1975 |
03976364 |
Aug 24, 1976 |
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Current U.S.
Class: |
359/667;
351/43 |
Current CPC
Class: |
G02B
1/06 (20130101) |
Current International
Class: |
G02B
1/00 (20060101); G02B 1/06 (20060101); G02B
025/00 (); G02B 001/06 () |
Field of
Search: |
;350/179,212,175ML,175E
;351/43 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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1112278 |
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Nov 1955 |
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FR |
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3164 of |
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1912 |
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GB |
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Other References
Jenkins, F., and H. F. White, Fundamentals of Optics, pp. 146-147,
Third Ed., 1957, McGraw-Hill..
|
Primary Examiner: Clark; Conrad J.
Attorney, Agent or Firm: Finnegan, Henderson, Farabow,
Garrett & Dunner
Parent Case Text
BACKGROUND OF THE INVENTION
This application is a continuation-in-part of application Ser. No.
427,257, filed Dec. 21, 1973 and now abandoned.
Claims
What is claimed is:
1. An optical lens system operative on a light ray comprising:
a first optical medium having a first refractive index,
a second optical medium having a second refractive index of a
higher value than said first refractive index,
a plurality of pockets formed in said second optical medium
containing said first optical medium, said plurality of pockets
having a single coincident optical axis and each defining first and
second optical surfaces at the interfaces between said first and
second optical mediums,
an object located substantially at an aplanatic point of at least
one of said optical surfaces within or contiguous to said second
.[.opical.]. .Iadd.optical .Iaddend.medium,
selected surfaces from among said first and second optical surfaces
through which said light ray when emanating in a direction from
said object toward said plurality of pockets is refracted when
passing from high to low refractive index mediums being so
constructed and arranged relative to said object to refract said
ray aplanatically thereby substantially eliminating spherical
aberration and coma, and
all said optical surfaces other than said selected surfaces are so
constructed and arranged to pass said light ray substantially
without refraction.
2. The optical lens system of claim 1 wherein said selected optical
surfaces are the first optical surfaces of each of said plurality
of pockets.
3. The optical lens system of claim 1 wherein all of said first and
second optical surfaces are concave with respect to said
object.
4. The optical lens system of claim 1, further including at least
one final optical surface of low .[.powder.]. .Iadd.power
.Iaddend.for causing final collimation of said light ray relative
to the longitudinal axis of said optical lens system.
5. The optical lens system of claim 1, wherein all said optical
surfaces other than said selected optical surfaces are so
constructed and arranged to have their respective centers of
curvature substantially coincident with the image formed by the
next preceding optical surface.
6. The optical lens system of claim 1 wherein said second optical
medium is a light-transmissive, isotropic, monolithic solid, said
object being embedded in or contiguous to said second optical
medium and all said optical surfaces of said plurality of pockets
being so constructed and arranged to form a magnified image of said
object while reducing optical aberrations.
7. The optical lens system of claim 6 wherein said first optical
medium is a gas.
8. The optical lens system of claim 1, wherein said object is an
optical sensor and wherein said optical surfaces defined by said
plurality of pockets are so arranged and constructed to optimize
light gathering at said optical sensor.
9. The optical lens system of claim 1 wherein said second optical
medium is a light transmissive, isotropic solid, said object is a
light emitting source and said optical surfaces defined by said
plurality of pockets are so arranged to collimate said light ray
emanating from said optical system relative to the optical axis of
said optical system.
10. An optical lens system operative on a light ray comprising:
a first optical medium having a first refractive index,
a second optical medium having a second refractive index,
a plurality of pockets which contain said first optical medium,
a third optical medium having a third refractive index configured
to define said pockets and being contiguous to said first and
second optical mediums,
said third refractive index being higher in .[.valve.]. .Iadd.value
.Iaddend.than said second refractive index and said second
refractive index being higher in value than said first refractive
index,
a plurality of optical surfaces having coincident optical axes and
being defined by the interface between said first and third optical
mediums and said second and third optical mediums,
an object located substantially at an aplanatic point of at least
one surface within or contiguous to said first optical medium,
selected optical surfaces from among said plurality of optical
surfaces through which said light ray emanating in a direction from
said object toward said plurality of pockets is refracted when
passing from high to low refractive index mediums being so arranged
and constructed relative to said object to refract said ray
aplanatically thereby substantially eliminating aberration and
coma, and
all said optical surfaces other than said selected optical surfaces
are so constructed and arranged to pass said light ray
substantially without refraction.
11. The optical lens system of claim 10 wherein all said optical
surfaces other than said selected optical surfaces are so
constructed and arranged that their respective centers of curvature
are located coincident with the image formed by the next preceding
optical surface.
12. The optical lens system of claim 10 wherein said selected
optical surfaces are sequentially alternate optical surfaces from
among said plurality of optical surfaces.
13. The optical air lens system of claim 10 wherein said .[.fist.].
.Iadd.first .Iaddend.optical medium is a gas, said second optical
medium is a liquid and said third optical medium is a solid.
14. The optical air lens system of claim 13 further including
structural support means for holding and positioning in fixed
relationship said plurality of pockets relative to said object.
15. The optical air lens system of claim 14 wherein said object is
removably positioned by said structural means for easy
interchangeability of objects.
16. The optical air lens system of claim 14 further including a
drinking straw rigidly attached to said structural support
means.
17. The optical lens system of claim 10 wherein said plurality of
pockets are individually detachably held by said structural wall
means so that said pockets are interchangeable.
18. The optical lens system of claim 10 wherein said object is an
optical sensor and said plurality of optical surfaces are so
arranged and constructed to optimize light gathering at said
optical sensor.
19. The optical lens system of claim 10 wherein said object is a
light emitting source and said plurality of optical surfaces are so
arranged and configured to collimate a uniform output beam of light
rays emanating from said light emitting source relative to the
optical axis of said optical lens system.
20. An optical lens system operative on a light ray for viewing an
object within or contiguous to a liquid medium from a medium of
lower refractive index such as air, comprising:
a plurality of light transmissive air lenses formed from a thin
walled optical material,
structural wall support means for holding and positioning in fixed
relationship said plurality of air lenses so that the optical axes
of all of said air lenses are parallel and coincident,
each said air lens having a first and second optical surface
defined by the interface between said air and said liquid formed by
said thin walled optical material,
said thin walled optical material having walls of a thickness to
have negligible refracting effect on the ray,
an object positioned in an object plane relative to said plurality
of air lenses such that the center of curvature of one surface of
at least one of said air lenses lies in said object plane,
selected optical surfaces from among said first and second optical
surfaces through which said light ray emanating in a direction from
said object toward said plurality of air lenses is refracted when
passing from high to low refractive index medium being so
constructed and arranged relative to said object to refract said
ray aplanatically thereby substantially eliminating spherical
aberrations and coma, and
all said optical surfaces other than said selected surfaces are so
constructed and arranged to pass said light ray substantially
without refraction.
21. The optical lens system of claim 20 wherein all said optical
surfaces of said air lenses other than said selected optical
surfaces are constructed and arranged such that the center of
curvature of each is substantially coincident with the image formed
by the next preceding optical surface whereby said light ray passes
without refraction.
22. The optical lens system of claim 20 wherein said object lies at
the bottom of said liquid medium and the buoyancy of said
structural wall support means is such that in a given depth of said
liquid medium, said structural support means will stabilize at a
predetermined distance above said object.
23. The optical lens system of claim 20 wherein said structural
wall support means further supports said object at a predetermined
distance from said plurality of air lenses.
24. The optical lens system of claim 23 wherein said object is
removably positioned in said object plane for easy
interchangeability of objects.
25. The optical lens system of claim 23 further including a
drinking straw rigidly attached to said structural support
means.
26. The optical lens system of claim 20 wherein said plurality of
air lenses are individually detachably held by said structural wall
means so that said lenses are interchangeable.
27. The optical lens system of claim 20 wherein said object is an
optical sensor and said plurality of said air lenses are so
arranged and constructed to optimize light gathering at said
optical sensor.
28. The optical lens system of claim 20 wherein said object is a
light emitting source and said plurality of air lenses are so
arranged and configured to collimate a uniform output beam of light
rays emanating from said light emitting source relative to the
optical axis of said optical lens system.
29. An optical lens system operative on a light ray comprising:
a first optical medium having a first refractive index,
a second optical medium having a second refractive index of a
higher value than said first refractive index,
a single pocket formed in said second optical medium containing
said first optical medium, said pocket having first and second
optical surfaces at the interfaces between said first and second
optical mediums,
an object located substantially at an aplanatic point of at least
one of said optical surfaces within or contiguous to said second
optical medium,
a surface selected from said first and second optical surfaces
through which said light ray when emanating in a direction from
said object toward said .[.at least one.]. pocket is refracted when
passing from high to low refractive index mediums so constructed
and arranged relative to said object to refract said ray
aplanatically thereby substantially eliminating spherical
aberration and coma, and
said optical surface other than said selected surface is so
constructed and arranged to .[.pass said light ray substantially
without refraction.]. .Iadd.refract said light ray so as to
substantially minimize spherical aberration and coma while tending
to complete collimation of said ray.Iaddend..
30. The optical lens system of claim 29 wherein said first and
second surfaces are concave with respect to said object.
31. The optical lens system of claim 29, further including at least
one final optical surface of low power for final collimation of
said light ray relative to the longitudinal axis of said optical
lens system. .[.32. The optical lens system of claim 29, wherein
said surface other than said selected surface is so constructed and
arranged to have its center of curvature substantially coincident
with the image formed by the selected
optical surface..]. 33. The optical lens system of claim 29 wherein
said second optical medium is a light-transmissive, isotropic,
monolithic solid, said object being embedded in or contiguous to
said second optical
medium. 34. The optical lens system of claim 29 wherein said first
optical
medium is a gas. 35. The optical lens system of claim 29, wherein
said object is an optical sensor and wherein said optical surfaces
defined by said pocket are so arranged and constructed to optimize
light gathering at
said optical sensor. 36. The optical lens system of claim 29,
wherein said second optical medium is a light transmissive,
isotropic solid, said object is a light emitting source and said
optical surfaces defined by said pocket are so arranged to
collimate said light ray emanating from said optical system
relative to the optical axis of said optical system. .Iadd. 37. An
optical lens system operative on a light ray comprising:
a first optical medium having a first refractive index,
a second optical medium having a second refractive index,
a pocket which contains said first optical medium,
a third optical medium having a third refractive index configured
to define said pocket and being contiguous to said first and second
optical mediums,
said third refractive index being higher in value than said second
refractive index and said second refractive index being higher than
said first refractive index,
first, second, third and fourth optical surfaces having coincident
optical axes, said first and fourth surfaces being defined by the
interfaces between said second and third optical mediums and said
second and third surfaces being defined by the interfaces between
said first and third optical mediums,
an object located substantially at an aplanatic point of said
second surface within or contiguous to said second optical
medium,
said first surface being so constructed and arranged to pass said
light ray substantially without refraction,
said second surface being so arranged and constructed relative to
said object to refract said light ray aplanatically thereby
substantially eliminating aberration and coma, and
said third and fourth surfaces being so constructed and arranged to
refract said light ray so as to substantially minimize spherical
aberration and coma while tending to complete collimation of said
ray. .Iaddend..Iadd. 38. The optical air lens system of claim 10,
further including at least one final optical surface of low power
for causing final collimation of said light ray relative to the
longitudinal axis of said optical lens system. .Iaddend.
Description
This invention relates to an optical system and more particularly
to one using air lenses formed either as pockets in a solid
monolithic optical medium or from thick or thin walled shells
adapted to be immersed in a liquid optical medium.
The use of air lenses in submarine applications such as for
swimmers or underwater photography has long been common to
compensate for distortions introduced by the differences in
refraction of light in water and air due to the difference in
optical densities of the two mediums. The lenses of the human eye,
being immersed in a watery solution which has an index of
refraction quite similar to that of water, cannot focus light
transmitted through a water medium, and undistorted vision is
impossible without some optical correction. The use of air lenses
formed from thin walled transparent material compensates for such
distortion under water but has no substantial diffracting effect
when used in air, thus permitting a swimmer to wear such lenses in
and out of the water. In underwater photography air lenses have
been interposed between the camera optics and the water medium to
effect such corrections as are necessary for proper focus.
Because the refractive index of air is less than that of water, the
refraction of a ray of light passing from water to air to water is
exactly the opposite of the refraction of a water lens in air. A
water or glass lens in air would have to be convex to focus the
light at some certain point. But in water or in some other optical
medium of high refractive index, an air lens would necessarily have
to be concave to achieve the same result.
Optical systems of this type relate closely to immersion optics
used in some high power microscopes. Such systems achieve nearly
aberration- and distortion-free magnification based largely on the
utilization of the aplanatic points of a system. The significance
of an aplanatic point of a system is that a ray emanating from such
a point within an optical medium having a refractive index higher
than its surroundings appears to come exactly from another point
(the aplanatic conjugate). The light rays are not in general
collimated when they leave the high index medium but they have no
spherical aberration. This is an important property of aplanatic
points since spherical aberration is a common form of aberration
which consequently is most important to correct. For on-axis
imaging, it is indeed the only aberration. For near off-axis
points, the sine condition is satisfied and coma is also
eliminated.
A well-known aplanatic lens which will increase the convergence of
a cone of rays without introducing spherical aberration must meet
several general conditions. A first optical surface or "aplanatic
surface" is arranged in relation to the object according to the
following relationship:
where l is the distance between the vertex of the surface and the
object; r is the radius of curvature of the surface; n.sub.1 and
n.sub.2 are the refractive indices of the first and second optical
mediums (n.sub.2 >n.sub.1). A second surface is made concentric
with the image formed by the first surface. The rays are then not
refracted by the second surface but are refracted by the first
surface without introducing spherical aberration.
In the present invention an improved optical system is achieved
utilizing air lenses in an optical medium of high refractive index
by applying the aplanatic principle to the arrangement of lenses
and object.
SUMMARY OF THE INVENTION
In accordance with the invention, an optical system is provided
composed of a first optical medium of a relatively high refractive
index having a plurality of pockets therein of an optical medium of
a relatively low refractive index. An object either embedded within
the first optical medium or directly contiguous to it is positioned
at a fixed predetermined distance from the pluratity of pockets,
which for instance if filled with air would comprise air lenses.
The plurality of pockets having properly configured interfaces with
said first optical medium are so constructed to give substantially
spherical aberration- and coma-free magnification of the object.
Each pocket has at least two optical surfaces defined by the
interfaces between optical mediums. A ray exiting a high refractive
index medium is either refracted according to the aplanatic
principle or passes through the optical surface unrefracted. But a
ray exiting a low refractive index medium into a high refractive
index medium is never refracted. The radii of curvature and the
vertices for each of the surfaces are chosen to meet these
conditions. When more than two optical mediums are used, the same
principles are applied. In alternative arrangements the object can
be a light source or a light sensor or other proper optical object,
the optical system being so designed to improve the functional
operation of either device.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1, 2 and 3 respectively show schematically an eye viewing an
object unaided by optics, aided by a normal condensing lens in air
and aided by an air lens in a solid optical medium, the object
being embedded in the solid.
FIG. 4A shows a series of air lenses in a solid homogeneous optical
medium utilizing the principles of the present invention.
FIG. 4B shows a system of air lenses made from variable thickness,
light-transmissive material immersable in a liquid and utilizing
the principles of the present invention.
FIG. 5 shows a modified embodiment of a series of air lenses made
from thin-wall, light transmissive material immersible in a liquid
and utilizing the principles of the present invention.
FIG. 6A shows an embodiment of the present invention in partial
cross-section.
FIG. 6B shows a detail cross-section of the object structure of the
embodiment of FIG. 6A.
FIG. 7 shows the detailed relationship of the elements of FIG. 6A
in cross-section.
FIG. 8 shows another embodiment of the present invention in which
individual lens elements are detachable.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
As used in this specification it is to be understood that the terms
light and optical broadly include and refer to electromagnetic
radiation in the wavelength range including infrared, visible, and
ultraviolet.
Referring now to FIGS. 1, 2 and 3 an object 8 is positioned in each
Figure a specific distance from a viewer represented by eye 10. In
FIG. 1 the unaided eye 10 views object 8 which subtends an angle
.beta. at eye 10, encompassing the total length of object 8.
In FIG. 2 a simple positive lens 12 is interposed between eye 10
and object 8. By converging action of the lens 12 an image 14 of
the object 8 is formed and magnified in a ratio proportional to
.alpha./.beta. Magnification is determined by the linear size of
the image 14 and its distance from eye 10.
In FIG. 3 a block 16 of a solid, homogeneous, isotropic optical
medium, such as glass, plastic, etc., which is transmissive to
light is shown in cross-section. The block 16 has a refractive
index n.sub.2. Embedded in block 16 is object 8. The block 16 is
located such that object 8, for ease of comparison, is the same
distance from eye 10 as in FIGS. 1 and 2. It is to be noted that
essentially the same magnifying action will occur when object 8,
which for instance could be a photographic print or a negative is
contiguous to block 16, such as being affixed as a thin film flat
against the bottom 18 of block 16.
A pocket 20 is formed in the block 16 during fabrication which
contains air, a less dense optical medium, having a refractive
index n.sub.1. The refractive index of the block 16, n.sub.2, is
higher than n.sub.1, thereby providing an optical system with just
the reverse refractive characteristics from that shown in FIG. 2
where an optically dense lens 12 is immersed in air.
The pocket 20 acts as an air lens in the embodiment shown in FIG. 3
having concave optical surfaces 22 and 24. The object 8 is shown at
a distance d from the optical mid-plane of air lens 20, the
particular distance and curvature of surfaces 22 and 24 being
determined by good design considerations to give an image with as
little distortion as possible.
The magnified image 14 is formed as a result of light refraction at
the interface between the top surface of block 16 and the air and
also the refraction at the interfaces of the air lens 20 in the
block 16. The magnified image 14 is subtended at eye 10 by the
angle .alpha., and a measure of the magnification is the ratio of
angles .alpha./.beta..
In FIG. 4A a block 28 of a solid isotropic and homogeneous optical
medium is shown in cross-section having a plurality of air pockets
30, 32 and 34, formed therein. The air pockets are essentially lens
elements each having optical surfaces formed in a spherically
concave shape with respect to the object 36. It will be appreciated
that various combinations of concave and convex surfaces could be
used which would be optically equivalent to the system shown.
In this optical system, the aplanatic principle is successively
applied to each air lens 30, 32, and 34 by the proper choice of
curvature for the air lens interfaces (optical surfaces) with the
surfaces of the block 28. The sequentially alternate optical
surfaces, going from high to low refractive index mediums in the
direction of ray 38, refract the ray aplanatically. This is
accomplished by designing the vertices of each such surface to be
at an aplanatic point in accordance with equation (1). The other
sequentially alternate optical surfaces, going from low to high
refractive index mediums, do not refract ray 38 at all. This is
accomplished by designing these surfaces to have centers of
curvature coincident with the location of the images formed by the
preceding surface. Spherical aberration and coma are thereby
essentially eliminated. The refractive index for the optical medium
comprising the block 28 is indicated by n.sub.2, while the
refractive index for the air contained in the air lenses is
n.sub.1, where n.sub.1 .perspectiveto.1.0.
Assuming for purposes of explanation that object 36 is a light
source, a typical light ray 38 from object 36 will be traced
through the block 28 and air lenses 30, 32 and 34 until it emanates
from the optical system. The object 36 is positioned at the
aplanatic point nearest the vertex of surface 40 whose curvature is
defined by a radius R.sub.1. Because the object is at an aplanatic
point refraction is free from spherical aberration and coma.
Ray 38 proceeds through the air lens 30 as though it emanated from
the aplanatic point 44 farthest from the vertex of surface 40. The
second surface 42 of the air lens 30 having a radius of curvature
R.sub.2 is designed such that the light source appears to be at its
center of curvature 44; therefore no refraction occurs and the ray
proceeds undeviated.
The first surface 48 of the air lens 32 is designed so that the
image of the object 36 located at point 44, which is at the center
of curvature of surface 42, lies at the aplanatic point nearest the
vertex of the surface 48. The radius of curvature for surface 48 is
R.sub.3. Again, because of aplanatic refraction the ray appears to
come from the aplanatic point farthest from the vertex of surface
48. Surface 50 having radius R.sub.4 is designed so that rays
appear to come from point .[.56.]. .Iadd.53.Iaddend., the center of
curvature of surface 50. Therefore the path of ray 38 is undeviated
upon leaving this surface.
The first surface 52 of air lens 34 is designed so that the
apparent source of ray 38 lies at point 55 on the optical axis 46,
the center of curvature of surface 50 and at the aplanatic point
nearest the vertex of surface 52. The radius of curvature for
surface 52 is R.sub.5. Aplanatic refraction of ray 38 occurs at
surface 52 causing the ray 38 to appear to come from the aplanatic
point 55 farthest from the vertex of surface 52.
At surface 56 of air lens 34, having a radius R.sub.6, the ray 38
is slightly but not aplanatically refracted to assist in
collimating it with respect to axis 46. The top surface 57 with a
radius R.sub.7 acts to complete the collimation of the ray 38. Thus
these last two surfaces cause only slight refraction of the ray and
therefore complete final collimation with negligible introduction
of aberration.
More than the three air lenses shown could be used in alternate
configuration so that the light emanating from block 28 is so
nearly collimated that optical surfaces such as surfaces 56 and 57
need have very weak power. Thus although not aplanatic, they could
complete the collimation while introducing almost completely
negligible spherical aberration and coma. It is to be noted that
the rays from the object point must originate or appear to
originate inside the optical medium of high refractive index
n.sub.2. In the optical system of FIG. 4A this condition for
aplanacity was satisfied by choosing a curvature of surface 40 so
that aplanatic refraction occurred there.
Where object 36 is a light source embedded in the high refractive
index medium, block 28, the rays emanating therefrom, start from
the high refractive index medium, thereby satisfying the condition
for immersion optics as discussed above. Of course, conversely,
rays arriving in the high refractive index medium can be brought to
a focus at object 36, which can alternatively be a light detector.
In the case where object 36 is a detector, the gain in brightness
over a system, whose image surface is in air, varies as the square
of the refractive index of the medium. Therefore, the light gain of
the optical system of FIG. 4A is greatly enhanced because of the
high optical density of the medium and because of freedom from
spherical aberration. The configuration of FIG. 4A can collect and
gather light effectively at a detector, or conversely collimate
efficiently the light from a radiant source such as a
light-emitting diode into a beam of constant cross-section.
The block 28 also lends itself to a structure of overall stability,
for once properly aligned, each optical surface and the light
source, detector or object to be magnified, being embedded in block
28, would be rigidly held in proper inter-relationship. The block
28, indeed, may be a monolithic structure of a material such as an
acrylic, polyester, polycarbonate, glass, or other similar type
optical material.
The optical air lens system described herein utilizes only a single
optical material in addition to air. This introduces chromatic
aberration when using white light and thus necessitates special
design considerations. Chromatic aberration in conventional systems
is generally reduced or eliminated by using optical materials
having different dispersion (the variation of refractive index with
wavelength) characteristics. The use of this technique is obviously
not possible in the design of an optical system which utilizes a
single optical material.
In order to realize an achromatic condition in such a system, the
design approach here is to arrange the powers and spacings so that,
in addition to correction of other aberrations, the total power
variation relative to be a refractive index change is small or
zero. Thus, denoting the total optical power by .phi., ##EQU1##
The principle is illustrated in a well-known doublet eyepiece as
follows. The total power is:
where n is the refractive index, which is identical for both
doublet components, K.sub.1 and K.sub.2 are geometrical constants,
and s is the doublet separation. The derivative of .phi. is:
##EQU2## and this must equal zero. Multiplying the derivative
through by n-1 produces:
Since (n-1)K.sub.1 and (n-1)K.sub.2 are powers, respectively, of
the two components, .phi..sub.1 and .phi..sub.2, ##EQU3## where
.function..sub.1 and .function..sub.2 are the focal lengths of
components 1 and 2. Therefore the doublet shows no variation with
wavelength and is achromatic when the doublet separation equals the
mean of the focal lengths.
The optical air lens system of a single optical material is not so
simple, especially as the object rays originate in the high index
medium. However, the principle is the same and will produce
achromaticity if in the design of the air lens system the same
general considerations are taken.
The values for the optical parameters of an exemplary design for
the embodiment of FIG. 4A wherein the first optical medium 28 is a
solid, acrylic plastic and the second optical medium in pockets 30,
32 and 34 is a gas such as air are given in the table below. An
aplanatic air lens system employing the principles described in the
instant case including object image relationships stated in
equation 1 is exemplified in the following design.
The monolithic material which is acrylic plastic has a refractive
index n.sub.2 =1.491, and an Abbe constant V=61.6. The refractive
index n.sub.1 of the air in pockets 30, 32 and 34 is unity. The
object is at location 36 of FIG. 4A. The vertex of the first
spherical surface, 40 is 0.417673 units above object 36, all
vertices lying on the optical axis, 46. The radius of curvature
R.sub.1 of surface 40 is -0.25 units (concave toward the object
36); therefore, according to equation 1, the object is at an
aplanatic point of refracting surface 40. Upon refraction, it will
appear to come from a point 0.62275 units below surface 40, the
magnification being 1.491. The vertex of surface 42 is 0.06 units
above that of surface 40. The radius of surface 42 is 0.68275
units; therefore the image formed by surface 40 is at the center of
curvature of surface 42 and no refraction occurs as the rays
re-enter the high refractive index medium.
The rays proceed to surface 48 of air lens 38 where they are
aplanatically refracted upon leaving the high refractive index
medium, the radius of curvature of surface 48 is -0.707941 units
(concave toward the object 36). The vertex of surface 48 lies on
optical axis 46, 0.5 units above the vertex of surface 42.
Surface 50 has its center of curvature at the image formed by
surface 48 and no refraction occurs upon re-entering the high
refractive index medium. The first surface 52 of air lens 34
produces the final aplanatic refraction in the same fashion as
before described for surfaces 40 and 48.
The final surfaces, namely the second surface, 56 of cavity 34, and
the top surface 57 of the block 28 do not refract ray 38
aplanatically according to equation 1, but ray 38 is so nearly
parallel to optical axis 46 that these surfaces need exert only
weak refractive power to render ray 38 parallel. The required
dioptics are so few, in fact, that a configuration wherein the top
surface of block 28 is plano would produce high optical quality.
Allowing the top surface 57 of block 28 to have a non-zero
curvature as shown in FIG. 4A permits a design providing near
perfect optical quality.
The following table summarizes the optical parameters for the above
design. All negative radii indicate concave downward curvature and
all centers and vertices are on the optical axis 46. The curvatures
and spacings are referenced starting from the bottom of block 28.
Dimensions are in arbitrary units. The refractive index and Abbe
constant of the first optical material are n.sub.1 =1.491 and
V=61.6 and since the second optical medium is air, n.sub.2
=1.0.
______________________________________ Separation from Surface
Radius (R) Previous Vertex (d)
______________________________________ 417673 (Separation 40 -.25
(R1) from object 36) 42 -.682750 (R2) .06 48 -.707941 (R3) .5 50
-1.823480 (R4) .06 52 -1.390682 (R5) .5 56 10.990797 (R6) .06 57
-2.094874 (R7) 125 ______________________________________
The following table confirms the near perfect optical performance
of the design. The table shows the longitudinal spherical
aberration of parallel rays incident at the top of block 28,
parallel to axis 46, and brought to a point focus at the location
of object 36 on optical axis 46. This reverse ray trace is, of
course, a classical optical test of image quality. Unaberrated rays
will come to a focus 0.417673 units below the vertex of surface 40
as stated in the table below.
The column denoted L.S.A. (longitudinal spherical aberration)
indicates the height above the ideal point at which rays intersect
the optical axis 46. The first column indicates the distance from
optical axis 46 at which parallel rays, parallel to axis 46 enter
block 28. The optician designates this quantity the ray height.
______________________________________ Ray Height L.S.A. Tangential
Coma ______________________________________ .1 .00020 .2 .00075 .3
.00165 .4 .00287 .5 .00439 .003 (Maximum)
______________________________________
The significance of the table is emphasized by the air lens system
speed of approximately .function./1. This illustrates its efficient
light-gathering power, or again its unusual ability to collimate a
small light source.
One should be aware that the object's position can be adjusted
within limits. The object 36 is shown in FIG. 4A located at the
bottom of block 28, either within the block 28 itself or contiguous
to the bottom surface 35. Object 36 should be substantially located
at the nearest aplanatic point to the surface 40, but indeed small
changes in the location of the object 36 may introduce only slight
aberration. For instance placing the object in a depression in the
bottom surface or even next adjacent the block 28 but still
approximately at the aplanatic point may not introduce significant
aberration for a given application. Also the object 36 can be
placed in a spherical air cavity in the bottom surface 35 centered
on optical axis 46 without introducing any additional aberration,
provided the object is still substantially at the aplanatic point
of surface 40 and at the center of curvature of the cavity.
Now referring to FIG. 4B, a further embodiment of the present
invention is shown which utilizes three optical mediums and in
which air lenses 140 and 142 are constructed of variable wall
thickness shells made of a translucent optical material such as
plastic or glass and immersed in a liquid 144 such as water. An
object 146 is shown on the optical axis 148 of the optical air lens
system.
The optical system including lenses 140 and 142 and object 146 are
held in relative position one to the other by structure not shown
here such as that disclosed with the embodiment shown in FIG. 5.
This particular embodiment refracts light according to the
aplanatic principle at alternate surfaces as the light passes from
a high to a low refractive index medium. Alternate optical
surfaces, as the light goes from low to high refractive index
medium, however, are so constructed to have their center of
curvature coincident with the image or object therefore causing no
refraction of light. It will be recognized that this embodiment
consequently does not require the assumption of the negligible
refraction at certain surfaces as is required by the embodiment of
FIG. 5.
Typically the pockets 150 and 152 of air lenses 140 and 142
respectively, contain air having a refractive index n.sub.1. The
walls of lenses 140 and 142 can be constructed of an optical
material such as glass or plastic having a refractive index
n.sub.3. The liquid 144 is typically water having a refractive
index n.sub.2. In such a configuration, the refractive indices of
the various materials are related as follows n.sub.1 <n.sub.2
<n.sub.3.
Assuming object 146 to be a light source, a ray 154 can be traced
through the system of FIG. 4B. Ray 154 emanates from object 146
which is coincident with the center of curvature of the first
optical surface 156 which has a radius R.sub.1. No refraction
therefore occurs at surface 156.
The second optical surface 158 having a radius of curvature R.sub.2
is so constructed to cause the object point 146 to be an aplanatic
point according to equation 1. The liquid in the system does not
alter the aplanatic refraction process since only air and the solid
shell material of lens 142 define the interface and affect the
direction of ray 154. At the surface 158, ray 154 passes from a
high to a low refractive index medium.
Ray 154 proceeds undeviated through the next or third optical
surface 160 which has a radius of curvature R.sub.3. There is no
refraction at the third surface 160 since the center of curvature
coincides with the point 161 located on optical axis 148. The image
point 161 is the point from which ray 154 appears to come after
refraction at the second optical surface 158. The upper surface of
lens 142, i.e. the fourth optical surface 162 which has a radius of
curvature R.sub.4 does refract the ray 154 aplanatically. Here the
interfacing optical media producing aplanatic refraction are the
liquid having a refractive index n.sub.2 and the solid shell
material of lens 142 having refractive index of n.sub.3. The ray
154 now twice aplanatically refracted proceeds through the liquid
medium 144 as though it were emanating from image point 163 on
optical axis 148.
The ray 154 proceeds unrefracted through the fifth optical surface
164 which has a radius of curvature R.sub.5 since the center of
curvature of this surface coincides with the image point 163. But
the ray 154 is again aplanatically refracted at the sixth optical
surface 166 which has a radius of curvature R.sub.6. This
refraction occurs because the image point 163 is at an aplanatic
point with reference to surface 166 as required by equation 1.
The ray 154 now proceeds through the air pocket 150 being nearly
parallel with the optical axis 148 of the system. Therefore a
non-aplanatic refraction at surface 168 which has a radius or
curvature R.sub.7 tends to complete the collimation of the ray
without introducing significant image degradation. The final
optical surface 170 with a radius of curvature R.sub.8 further
completes the collimation process. The last two optical surfaces
are curved to minimize the residual aberrations introduced at this
refraction. Of course, the final interface is that of the liquid
air boundary 172 where ray 154 emerges from the system. This
boundary is necessarily optically flat, having no effect on ray 154
assuming the system has successfully collimated the ray and it
exits normal to surface 172.
The values for the optical parameters of an exemplary design for
the embodiment of FIG. 9, are given in the table below. It is
assumed that the liquid medium is water, the optical shell material
is BK-7 optical glass and the pockets 150 and 152 are air pockets.
The respective refractive indices are: water--1.330; BSC-2
(BK-7)--1.51700 and air--1.0. All measurements are made on optical
axis 148 where all centers of curvature lie. The first spacing d is
the distance from the object point 146 to the vertex of the first
surface 156 and the subsequent spacings indicate the distances
between the respective vertices of the optical surfaces. The final
spacing is the distance from the optical surface 170 to the surface
172. The radii are numbered starting from the first surface 156 and
the dimensions are in arbitrary units.
______________________________________ Separation from Surface
Radius (R) Previous Vertex (d)
______________________________________ 1 (156) -.25 (R.sub.1) .25 2
(158) -.18684 (R.sub.2) .06 3 (160) -.53027 (R.sub.3) .06 4 (162)
-.34916 (R.sub.4) .125 5 (164) -1.24404 (R.sub.5) .49663 6 (166)
-.82513 (R.sub.6) .125 7 (168) +100 (R.sub.7) .25 8 (170) -.45583
(R.sub.N) .125 9 (172) .varies. .5
______________________________________
As can be seen from the above design parameters, all optical
refracting interfaces, except those final low powered surfaces for
collimation and the top surface of the system, are designed to
either aplanatically refract ray 154 or not to refract it at all.
For those surfaces which aplanatically refract, namely optical
surfaces 158, 162 and 166, the relationship between object or image
and surface curvature are determined by equation 1.
A special modification of this optical lens system having a
thin-walled shell structure is shown in FIG. 5. This system can be
considered to be comprised of only two optical materials (gas and
liquid) thereby assuming the shell structure itself to have
negligible optical effect. Or it can be considered to be a system
including three optical materials (gas, liquid and solid), but with
the optical surfaces of the shell being shaped and configured to
minimize its effect on the optical characteristics of the system.
When characterized as a system comprised of three optical
materials, it will be recognized to be a modification of the
embodiment of FIG. 4B, discussed above.
In FIG. 5 a thin-walled structure 58 of a light-transmitting
material is shown immersed in a liquid having a refractive index
n.sub.2. The walls of structure 58 have a constant thickness and
for purposes of this analysis will be assumed to be made of an
optical material having a refractive index n.sub.3 >n.sub.2. For
instance the walls could be of an optical glass with n.sub.3
.perspectiveto.1.5 and the liquid could be water with n.sub.2
.perspectiveto.1.33.
A first air lens 59 is shown defined by curved, light-transmissive
walls 60 and 62 which form, relative to object 61, first and second
refraction interfaces, respectively, between the liquid medium and
the air within the cavity 64 of the air lens 59. Since air has a
refractive index of unity, n.sub.1 <n.sub.2 <n.sub.3.
A second air lens 66 is defined by curved, light-transmissive walls
68 and 70 which form, relative to object 61, first and second
refraction interfaces, respectively, between the liquid medium and
the air within cavity 72 of air lens 66. The first and second air
lens 59 and 66 are held rigidly relative one to the other by
structure 58 so that the optical axis 74 of the system is also the
axis of symmetry of the lens system.
For magnification of object 61 the structure 58 is positioned so
that object 61 coincides with the center of curvature of the curved
wall 60 as determined by radius R.sub.1. Structure 58 can be
positioned manually, or it can be so fabricated so that its
buoyancy causes it to stabilize at some given depth in a liquid
medium. Alternatively, the structure 58 could include a stand, not
shown in FIG. 5, which would position the air lens system the
proper distance above object 61 by finding support on the floor 76
of the liquid container.
Light ray 78 is representative of the path of light through the air
lens system of FIG. 5. As is readily apparent, the principle of
aplanacity can be used in this structure to effectively eliminate
or limit spherical aberration and coma. Tracing ray 78 through the
first wall 60 there is no refraction. Each side of the wall 60
offers an optical surface between mediums of different refractive
indices. But the object 61 is located at the center of curvature
for each surface and so no refraction of ray 78 occurs at
either.
The ray 78 passes from a lower refractive index medium (n.sub.1) to
a higher refractive index medium (n.sub.3) as it enters the wall
62. Consequently there should be no refraction to be consistent
with the aplanatic principles previously discussed. Rather than no
refraction, a small refraction occurs at the first surface of wall
62. However, ray 78 is aplanatically refracted at the upper surface
of wall 62 as the ray exits the higher refractive index medium
(n.sub.3) and enters the lower refractive index medium, (n.sub.2).
To accomplish a slight refraction at the bottom surface of wall 62
and an aplanatic refraction at the top surface of wall 62 may
require the two surfaces to have somewhat different radii. The ray
78 then proceeding through the liquid medium appears to come from a
point 80 on the optical axis 74.
The wall 68 is designed to have a center of curvature at point 80
and a radius of curvature R.sub.2. Consequently, the ray 78 passes
through wall 68 with no refraction into the cavity 72 of lens 66.
The ray 78 when it emerges from the second surface of wall 70 of
air lens 66 is refracted as before discussed in reference to wall
62.
The optical system of FIG. 5 operates on light in a manner
analogous to that of the system in FIG. 4B. Three optical mediums
with indices n.sub.1, n.sub.2, and n.sub.3 are integrated into the
system, but the principle of refracting only when the object or
image is at an aplanatic point relative to the optical surface is
substantially followed in the system of FIG. 5. Refraction also
occurs only from high to low refractive index mediums, except for
negligible refraction at the air to wall interface within each lens
59 and 66.
In FIG. 6A a particular application for the air lens systems of
either FIGS. 4B or 5, incorporated in a drinking straw, is shown in
cross-section wherein additionally the object structure 82 is
fixedly positioned a given distance D.sub.1 and D.sub.1 +D.sub.2
relative to the lens system comprised of air lenses 84 and 86
respectively. In the embodiment of FIG. 6A the air lens system has
been permanently attached to a drinking staw 88 (representative of
one application to novelty-type devices) which can be submerged in
a liquid having a refractive index n.sub.2.
The air lenses 84 and 86 have air cavities 90 and 92, respectively,
having a refractive index n.sub.1 where n.sub.1 <n.sub.2. Each
is confined by curved, light-transmissive walls with an index
n.sub.3 higher than n.sub.1 and n.sub.2 which also establish the
optical surfaces of the air lenses 84 and 86. Lens 84 can be made
having a smaller radius than that of lens 86, as for instance was
done in FIG. 5, thereby maximizing magnification of system. The
lens 84 includes curved walls 94 and 96, and lens 86 includes
curved walls 98 and 100.
The structure is given stability by struts 101 and 103 and by straw
88, which can all be of plastic for instance. The object structure
82 can also be made removable or replaceable as shown in FIG. 6B,
for example, wherein element 83 containing the object 85 is
threadably attached to the bottom 87 of the straw assembly.
The optical principles previously described can be applied likewise
to the device of FIG. 6A. This is shown in detail in FIG. 7.
Generally, it will be readily seen that by proper optical design,
the aplanatic principle can be repeatedly applied to any number of
air lenses such as 84 and 86 to obtain magnification with little or
no spherical aberration. Of course the optical system having
variable wall thickness of FIG. 4B could also be used in the
structure of FIG. 7.
In FIG. 8 another variation using a plurality of air lenses 102,
104 and 106, which can be removably attached one to another, is
shown. This embodiment can use the basic concepts of either FIGS.
4B or 5, each lens is self-contained and fabricated of a thin
walled, light-transmissive material having curved wall portions,
enclosing an air cavity. Air lens 106, for example, has side wall
segments 108 forming a cylinder spanned by curved wall portions 110
and 112 which provide the optical surfaces for the lens. Such a
lens could be immersed in a liquid medium individually or attached
in combination with other air lenses.
Small magnetic segments 114 of a suitable magnetic material are
affixed to the outer perimeter of the cylindrical wall portions
108, 109 and 111 of the lenses 106, 104 and 102 respectively. The
segments 114 can be spaced equally around the circumference of each
lens in a manner such that corresponding segments of different lens
elements can easily be aligned. Sufficient segments 114 are used to
hold the lenses in a detachable alignment one with another, and in
the limiting case the segments 114 can form a continuous magnetic
ring around the entire circumferance of the wall portions. It is to
be understood that other methods of attaching the lenses in a
stacked relationship can be used, such as with bolts or pins
inserted through appropriate brackets or alternate interior and
exterior threaded portions on the wall segments.
Each lens element 102, 104 and 106 is additionally designed with
holes 118 in the wall portions 111, 109 and 108 respectively, or
with fluted edges 120 to allow passage of fluid into the spaces
between the attached lenses.
An object disc 122 containing some object 124, such as a
photographic print, is shown having side wall segments 126 which
form a cylinder spanned by light-transmissive top wall 128 and
bottom wall 130. The object disc 122 is scaled to the size of the
individual lens elements 102, 104 and 106 and also has magnetic
segments 114 mounted in sidewall segments 126 so that the disc can
be attached to one or more of the air lens elements. Thus a total
optical air lens system comprised of an object disc 122 and a
plurality of lenses such as 102, 104 and 106 can be put together
into a rigid structure which also can be easily disassembled by
applying sufficient force to overcome the magnetic holding
force.
It should be clear that the plurality of air lens elements and the
object disc 122 of FIG. 8 can be designed with proper curvature of
optical surfaces and adjustment of distances between elements by
using various surfaced optical elements, including prisms,
magnifying and demagnifying lenses, such that the optical
principles describes above can be applied to this embodiment.
* * * * *