U.S. patent number 3,708,221 [Application Number 05/025,179] was granted by the patent office on 1973-01-02 for aspheric lens and method of manufacture.
This patent grant is currently assigned to Anchor Hocking Corporation. Invention is credited to Howard A. Schaefer.
United States Patent |
3,708,221 |
Schaefer |
January 2, 1973 |
ASPHERIC LENS AND METHOD OF MANUFACTURE
Abstract
An aspheric lens is made with an aspheric curvature on its
frontal surface wherein the curvature is defined in the X-Y
coordinate system by a particular relationship in accordance with
the index of refraction, heighth, focal distance and radius of back
surface parameters.
Inventors: |
Schaefer; Howard A. (Lancaster,
OH) |
Assignee: |
Anchor Hocking Corporation
(Lancaster, OH)
|
Family
ID: |
21824503 |
Appl.
No.: |
05/025,179 |
Filed: |
April 2, 1970 |
Current U.S.
Class: |
359/718; 359/728;
362/335; 359/742 |
Current CPC
Class: |
F21S
41/255 (20180101); F21V 5/045 (20130101); F21S
41/275 (20180101); G02B 3/04 (20130101) |
Current International
Class: |
F21V
5/00 (20060101); G02B 3/04 (20060101); G02B
3/02 (20060101); F21V 5/04 (20060101); G02b
003/04 (); G02b 003/08 () |
Field of
Search: |
;350/178,189,190-192,211
;240/106.1 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Schonberg; David
Assistant Examiner: Sacher; Paul A.
Claims
What is claimed is:
1. An aspheric lens having a frontal surface and a back surface,
said frontal surface having an aspheric curvature which produces
paths of light parallel to its optical axis from the rays of light
passing therethrough with the emitted light being concentrated and
having minimal chromatic aberration, said curvature being defined
in the X-Y coordinate system by B.sub.1 being equal to {X.sub.1
[COT(A.sub.6)] + Y.sub.1 -J.sub.1 + D.sub.1
[TAN(A.sub.4)]}/[TAN(A.sub.4) + COT(A.sub.6)] and C.sub.1 being
equal to J.sub.1 + (B.sub.1 -D.sub.1)[ TAN(A.sub.4)] wherein
N.sub.1 is the index of refraction, H.sub.1 is the heighth, X.sub.1
is the X value of the previous calculated point and Y.sub.1 is Y
value of the previous calculated point, F.sub.1 is the focal
distance from the focal point to said back surface, R.sub.1 is the
radius of the back surface, G.sub.1 = 4(2 R.sub.1 F.sub.1 +
F.sub.1.sup.2), A.sub.1 = ATN(H.sub.1 /F.sub.1), E.sub.1 =
2(R.sub.1 +F.sub.1)[COS(A.sub.1)], E.sub.2 = E.sub.1.sup.2 -
G.sub.1, M.sub.5 = (E.sub.1 - .sqroot.E.sub.2) (0.5), J.sub.1 =
M.sub.5 [SIN(A.sub.1)], D.sub.1 = (J.sub.1 -H.sub.1)[TAN(A.sub.1)],
A.sub.2 = ASN (J.sub.1 /r.sub.1), A.sub.7 = A.sub.1 + A.sub.2,
A.sub.3 = ASN[SIN(A.sub.7)/N.sub.1 ], A.sub.4 = A.sub.3 - A.sub.2,
A.sub.5 = ATN{SIN(A.sub.4)/[N.sub.1 - COS(A.sub.4)]}, A.sub.6 =
A.sub.4 + A.sub.5, B.sub.1 = X value of point being calculated; and
C.sub.1 = Y value of point being calculated.
2. An aspheric lens as set forth in claim 1 wherein said back
surface is convex being the segment of a sphere.
3. An aspheric lens as set forth in claim 2 wherein said frontal
surface includes a peripheral substantially planar rim around said
aspheric curvature, and said peripheral rim having parallel
flutes.
4. An aspheric lens as set forth in claim 1 wherein said frontal
surface includes a peripheral substantially planar rim around said
aspheric curvature, and said peripheral rim having parallel
flutes.
5. An aspheric lens as set forth in claim 1 wherein said back
surface is planar.
6. An aspheric lens as set forth in claim 5 wherein a portion of
said back surface has parallel flutes to create an auxiliary spread
light pattern.
7. An aspheric lens as set forth in claim 6 wherein said flutes are
disposed in a circular area having its center on said optical axis
of said lens.
8. An aspheric lens as set forth in claim 6 wherein said back
surface includes a circular area having its center on said optical
axis of said lens, said circular area being free of flutes, a
peripheral ring shaped area being around said central area, and
said flutes being in said ring shaped area.
9. An aspheric lens as set forth in claim 6 wherein said back
surface includes a central area centered on said optical axis of
said lens, and said flutes being in parallel portions adjacent to
and on two sides of said central area.
10. An aspheric lens as set forth in claim 6 wherein each flute is
defined in cross-section by a radius r.sub.1 = h.sub.1
/SIN(A.sub.4) and a chord heighth h.sub.2 = [ r.sub.1 -
0.5.sqroot.4(r.sub.1).sup.2 - (2h.sub.1).sup.2 ], wherein N.sub.1
is the index of refraction, h.sub.1 is the half heighth of the
flute, a is the degrees spread, a.sub.1 = a.pi./360, a.sub.2 =
ASN[SIN(a.sub.1)/N.sub.1 ], a.sub.3 = ATN[SIN(a.sub.2)/ N.sub.1 -
COS(a.sub.2)] , and a.sub.4 = a.sub.2 + a.sub.3.
11. An aspheric lens as set forth in claim 1 in combination
therewith, a housing having an open end, a point source of light in
said housing, said lens closing said open end of said housing, and
said housing being connected in the headlight system of a vehicle.
Description
BACKGROUND OF INVENTION
Aspheric lenses have been utilized in the prior art as a means of
minimizing chromatic aberration. Such lenses, for example, are
utilized in the photographic field as exemplified by U. S. Pat.
Nos. 2,637,242 and 2,685,821. A further use of such a lens has been
in flashlights as exemplified in U. S. Pat. No. 2,282,167. A
further early use of such lenses is exemplified by U. S. Pat. No.
1,389,291 which discloses an aplanatic lens incorporated in a
vehicle headlight system. This use in a vehicle headlight system
has been recently revived wherein the aspheric lens is used as a
supplementary source of concentrated light in addition to the high
beam and low beam headlights.
The prior art has heretofore constructed such aspheric lenses
wherein the back surface is convex in that it is in the form of a
spherical segment of constant radius. A difficulty exists with the
prior art aspheric lenses in the accurate forming of the aspheric
curvature. Where attempts have been made to attain a high degree of
accuracy and control over the specific aspheric curvature, the
prior art has been forced to increase the time and labor
requirements which in turn increases the costs of constructing such
aspheric lenses. Because of lack of ready controls the prior art
techniques have not been adaptable to mass producing such high
quality products.
SUMMARY OF INVENTION
An object of this invention is to provide an aspheric lens with an
aspheric curvature having a high degree of accuracy while reducing
the time and labor requirements therefore.
A further object of this invention is to provide such an aspheric
lens wherein the aspheric curvature may be determined by computer
techniques to enable mass production thereof.
A still further object of this invention is to provide an aspheric
lens which incorporates flutes for creating auxiliary spread
light.
In accordance with this invention an aspheric lens is made with an
aspheric curvature on its frontal surface wherein the curvature is
defined in the X-Y coordinate system by a particular relationship
in accordance with the index of refraction, heighth, focal distance
and radius of back surface parameters.
The above indicated formulation can be simplified by eliminating
the radius as a variable parameter when the lens is formed with a
planar back surface. In further embodiments of this invention
auxiliary spread light may be obtained by incorporating parallel
flutes in portions of the planar back surface.
In another form of this invention the back surface is made convex
as the segment of a sphere while a substantially planar rim
surrounds aspheric curvature on the frontal surface. The spread
light flutes are then provided in this planar peripheral rim.
THE DRAWINGS
FIG. 1 is a front elevation view of an aspheric lens formed in
accordance with this invention;
FIG. 2 is a side elevation view of the convexo-aspheric lens of
FIG. 1 schematically incorporated in a vehicle headlight
system;
FIG. 3 is a schematic showing of the various parameters utilized in
determining the specific aspheric curvature;
FIG. 4 is a front elevation view of a modified form of aspheric
lens;
FIG. 5 is a side elevation view showing the ray trace with the
plano-aspheric lens of FIG. 4;
FIG. 6 is a front elevation view of a further modified form of
aspheric lens;
FIG. 7 is a rear elevation view of the fluted plano-aspheric lens
illustrated in FIG. 6;
FIG. 8 is a ray trace of the aspheric lens shown in FIGS. 6-7;
FIG. 9 is a front elevation view of a still further embodiment of
this invention;
FIG. 10 is a rear elevation view of the fluted plano-aspheric lens
shown in FIG. 9;
FIG. 11 is a ray trace of the aspheric lens shown in FIGS.
9-10;
FIG. 12 is a front elevation view of yet another embodiment of this
invention;
FIG. 13 is a rear elevation view of the fluted plano-aspheric lens
shown in FIG. 12;
FIG. 14 is a ray trace of the aspheric lens shown in FIGS.
12-13;
FIG. 15 is a rear elevation view of still yet another embodiment of
this invention;
FIG. 16 is a front elevation view of the fluted convexo-aspheric
lens shown in FIG. 15;
FIG. 17 is a ray trace of the aspheric lens shown in FIGS.
15-16;
FIG. 18 is a schematic illustration of the parameters used for
calculating the flute spread for the various fluted aspheric
lenses;
FIG. 19 is a rear elevation view of a further modified form of
aspheric lens;
FIG. 20 is a cross-sectional view taken through FIG. 19 along the
line 20--20;
FIG. 21 is a rear elevation view of still yet another embodiment of
this invention; and
FIG. 22 is a cross-sectional view taken through FIG. 21 along the
line 22--22.
DETAILED DESCRIPTION
FIGS. 1-2 show a convexo-aspheric lens 10 formed in accordance with
this invention and particularly adapted for use in the headlight
system of a vehicle. As indicated therein the lens 10 includes an
aspheric frontal surface 12 and a convex back surface 14 which is
in the segment of a sphere. A peripheral rim 16 adapts the lens 10
to be mounted in a vehicle headlight system which may include for
example a housing 18 having any suitable point source of light
which may be simulated by utilizing light source f.sub.2 and an
elliptical reflector 20 to refocus the light rays 22 to infinity
with minimum chromatic aberration. As schematically illustrated in
FIG. 2 lens 10 closes the open end of the housing 18. Housing 18
also includes an aperture plate 24 having its aperture at the focal
point f.sub.1 with lens 10 being symetrically arranged on the
optical axis 26 of the headlight system. The paths of light passing
through lens 10 are parallel to the optical axis 26 to an unusually
high degree of accuracy thereby producing a highly concentrated
light beam which is particularly effective for lighting a roadway.
The housing 18 and its various components are connected in the
headlight system as an auxiliary light or as a replacement for
either the conventional high or low beams. Any suitable glass
composition such as a borosilicate glass may be utilized with this
invention while still attaining the high degree of accuracy. It is
to be understood, of course, that although the lens 10 is described
with particular reference to use in a vehicle other uses are also
possible within the scope of this invention where there is a
requirement for a concentrated light beam having minimal chromatic
aberration and wherein the paths in the light beam are parallel to
the optical axis.
In accordance with this invention frontal surface 12 is formed with
an aspheric curvature which may be accurately reproduced and
controlled through a series of mathematical calculations which
particularly lend themselves to the use of computer techniques
thereby vastly reducing the time and labor requirements. The
formulas used for determining the aspheric curvature are
particularly noteworthy in that the many parameters can be varied
while still producing a highly accurate relatively low cost mass
produced lens with very good light control properties. The
parameters which can be varied in accordance with this invention
are the radius of back curve, the focal distance to the face of the
back curve, the refractive index of the glass, the diameter of the
lens and the thickness of the lens.
FIG. 3 schematically illustrates the various parameters which must
be considered in forming the lens 10 and which are taken into
account in accurately producing and reproducing the aspheric
curvature on the frontal surface 12. As is readily apparent in FIG.
3 the aspheric curvature is a smooth curve with constantly changing
radius. As indicated in FIG. 3 the focal point FP lies upon the
optical axis 26. This axis is also designated as the X--X axis of
the X-Y coordinate system. Where the optical axis intersects the
face of the back curve of the convex back surface and tangent
thereto is the Y--Y axis of the X-Y coordinate system. The heighth
of the ray of light is indicated as H.sub.1 and corresponds to the
Y distance at which the ray of light intersects the Y axis. The
various points on the aspheric frontal surface 12 each have a
corresponding X and Y value in accordance with the X-Y coordinate
system. As later used in the formulas for defining this curvature
these X and Y values are indicated as X.sub.1 and Y.sub.1 which
represents the variable X and Y coordinates. The maximum thickness
of the lens is illustrated in FIG. 3 as T.sub.1 while F.sub.1
represents the focal distance of the focal point FP to the back
surface of the lens. K.sub.1 designates the limit of active
surface. It is not necessary to continue the aspheric curvature
beyond K.sub.1 and thus the remaining portion 16 of the frontal
surface may be used for mounting the lens 10 in any suitable
housing. The lower computer limit of the X value of K.sub.1 is
indicated as L.sub.1 while the upper limit is designated as
L.sub.2. The radius of the convex back surface is designated as
R.sub.1.
The various points on the aspheric curvature are defined in the X-Y
coordinate system by the variable B.sub.1 being equal to {X.sub.1
[COT(A.sub.6)]+Y.sub.1 -J.sub.1 + D.sub.1
[TAN(A.sub.4)]}/[TAN(A.sub.4) + COT(A.sub.6)] and the corresponding
C.sub.1 being equal to J.sub.1 + (B.sub.1 -D.sub.1)[TAN(A.sub.4)].
These formulas represent a shorthand method of computing the
aspheric curvature and the designations therein are derived from
the following mathematical calculations wherein N.sub.1 is the
index of refraction and other parameters have their designations in
FIG. 3; B.sub.1 is the X value of the point being calculated and
C.sub.1 is its corresponding Y valve; and wherein X.sub.1 is the X
value of the previous calculated point, while Y.sub.1 is the Y
value of the previous calculated point and wherein: G.sub.1 = 4(2
R.sub.1 F.sub.1 + F.sub.1.sup.2); A.sub.1 = ATN(H.sub.1 /F.sub.1);
E.sub.1 = 2(R.sub.1 +F.sub.1) .sup.. [COS(A.sub.1)]; E.sub.2 =
E.sub.1.sup.2 - G.sub.1 ; M.sub.5 = (E.sub.1 - .sqroot.E.sub.2)
.sup.. (0.5); J.sub.1 = M.sub.5 [SIN(A.sub.1)]; D.sub.1 = (J.sub.1
-H.sub.1) .sup.. [ TAN(A.sub.1)]; A.sub.2 = ASN (J.sub.1 /R.sub.1);
A.sub.7 = A.sub.1 + A.sub.2 ; A.sub.3 = ASN[SIN(A.sub.7)/N.sub.1 ];
A.sub.4 = A.sub.3 - A.sub.2 ; A.sub.5 = ATN{SIN(A.sub.4)/[N.sub.1 -
COS(A.sub.4)]}; and A.sub.6 = A.sub.4 + A.sub.5.
In the practical application of these formulas, rough limits
L.sub.4 and L.sub.5 are set up for computer usage which in turn
sets up rough limits that confine the point K.sub.1 as far as X
values are concerned. This locates the limits that the X value of
K.sub.1 must fall within, in relation to the X-Y axis intersection
located tangent to the back spherical radius. Then the computer is
made to refine the calculated curve by use of the fine limits
L.sub.1 and L.sub.2 which tie down the X value of point K.sub.1 to
any degree of precision desired.
It is understood that for any particular computer run, other
variable parameters such as R.sub.1, F.sub.1, N.sub.1, T.sub.1 are
given numerical values. This process of calculation of aspheric
curves allows one to choose an N.sub.1 (Index of Refraction) of a
commercially available glass for the design of aspheric lens with a
high degree of accuracy that can be mass produced from conventional
glasses.
By utilizing conventional computer techniques and selecting an X
dimension with sufficient significant numbers it is, therefore,
possible to quickly obtain an unusually high degree of accuracy of
for example 10.sup.-.sup.8 with respect to the emitted rays of
light being parallel to the optical axis. It is even possible
through computer techniques with the inventive manner of forming
the aspheric curvature to obtain a degree of accuracy as fine as
10.sup.-.sup.15.
The aspheric lens illustrated in FIGS. 1-2 is somewhat similar to
the conventional aspheric lens in the utilization of a convexo back
surface but differs from the conventional lens of course in the
specific curvature and the manner of quickly and accurately
determining the curvature. FIGS. 4-5, however, represent a more
radical departure from the conventional aspheric lens. As
illustrated in FIGS. 4-5 the back surface is made planar. This not
only gives more flexibility in thickness requirements (since the
back surface is flat rather than convex) but also simplifies the
formulas for computing the aspheric curvature. In this respect the
radius R.sub.1 is no longer a factor. With the radius thus
eliminated as a variable the ultimate formulas for defining X and Y
are reduced to B.sub.1 = {(Y.sub.1 -H.sub.1)[ TAN(A.sub.4)] +
X.sub.1 }/{[TAN(A.sub.2)][TAN(A.sub.4)] + 1} and C.sub.1 = B.sub.1
[TAN(A.sub.2)] + H.sub.1 ; wherein A.sub.1 = ATN(H.sub.1 /F.sub.1);
A.sub.2 = ASN[SIN(A.sub.1)/N.sub.1 ]; A.sub.3 = ATN{
SIN(A.sub.2)/[N.sub.1 - COS(A.sub.2)]}; A.sub.4 = ASN{N.sub.1
.sup.. [SIN(A.sub.3)]}; B.sub.1 = X value of point being
calculated; C.sub.1 = Y value of point being calculated; X.sub.1 =
X value of previous calculated point; and Y.sub.1 = Y value of
previous calculated point. It is to be understood that the formulas
indicated above are actually the same as the formulas previously
described with respect to the convexo-aspheric lens but appear more
simplified with the radius R.sub.1 being removed as a
parameter.
FIG. 5 illustrates the ray trace obtained with the plano-aspheric
lens 28 of FIG. 4 wherein the frontal surface includes the aspheric
curvature 12 and the back surface is planar as indicated at 30. As
in the case of the convexo-aspheric lens 10 the paths of light
limited therefrom are parallel to the optical axis 26 to the same
unusually high degree of accuracy. It is further noted that with
the ray trace of FIG. 5 as well as the various other ray traces of
FIGS. 8, 11, 14 and 17 the aspheric lens is shown in cross-section
along a section line taken through the center of the lens.
The aspheric lenses 10 and 28 illustrated in FIGS. 1 and 4 are
highly effective in producing a concentrated light beam wherein all
of the rays of light are parallel to the optical axis with minimal
chromatic aberration. For certain uses, however, as for example
automobile headlights it is desirable to provide an additional
spread light which is less concentrated than the main concentrated
parallel beam but sufficiently lights up the surroundings to
increase the scope of vision of the driver rather than limiting it
to the main concentrated beam of light produced by the aspheric
curvature. Accordingly, this invention provides means for creating
this spread light. In general this means comprises flutes
incorporated in the lens to create the auxiliary light. As later
described the flutes are parallel with each flute being rounded or
smooth and having for example a cross-section which is a spherical
segment.
FIGS. 6-8 show one modification which incorporates flutes 32
recessed in the planar surface 34 of the plano-aspheric lens 36.
FIG. 8 illustrates the ray trace resulting from this arrangement.
As indicated therein the concentrated light beam is produced from
the rays of light 38 passing through the planar portion 34 of the
lens 36 while a divergent less concentrated light beam is produced
from the paths of light 40 passing through the flutes 32. In the
embodiment illustrated in FIGS. 6-8 the flutes are disposed in a
central area 42 of the planar surface 34 wherein the center of area
42 lies on the optical axis 26. Although the flutes are illustrated
as being recessed the flutes may be substantially co-planar with
surface 34 or may extend outwardly from surface 34. Further,
although each flute is illustrated as being a mirror image of its
adjacent flutes all of the flutes may be convex or all of the
flutes may be concave.
FIGS. 9-11 show another modification of this invention wherein the
plano-aspheric lens 44 includes parallel flutes 46 arranged in a
ring shaped area at the periphery of planar surface 48. As shown in
FIG. 10 the planar surface 48 includes a circular area 50 which is
free of flutes and which lies on the optical axis 26.
FIGS. 12-14 show still another form of this invention wherein the
flutes 52 are incorporated in spaced parallel portions at the
periphery of the plano-aspheric lens 54. In the form illustrated in
this embodiment the central area 56 of the substantially planar
surface 58 is slightly concave.
FIGS. 15-17 show still another form of this invention wherein the
flutes 60 are incorporated in a convexo-aspheric lens 62. Lens 62
includes a convex back surface 64 with the aspheric curvature 12 on
its frontal surface. The flutes 60 are disposed in a ring shaped
substantially planar surface 66 around aspheric curvature 12. FIG.
17 illustrates the ray trace produced with lens 62 wherein the
concentrated parallel light beam is obtained from the rays 68
passing through the aspheric curvature 12, while the spread light
which is initially convergent is produced from the rays 70 passing
through flutes 60.
It is ordinarily undesirable to have flutes of the exit side of a
headlight lens since these irregularities may become dirty,
damaged, or wet which would lead to distortion. Since, however, the
flutes 60 are smooth curvatures the likelihood of distortion is
minimized. Moreover, the spherical cross-section of each flute
assures a uniform spread of light.
FIG. 18 illustrates the manner of computing the flute spread. Since
the intensity of the light beam is not as critical with the spread
light, it is assumed that each flute is symetrically arranged with
respect to the optical axis 26 having its focal point FP lying on
the X--X axis of an X-Y coordinate system. The Y-Y axis is disposed
tangential to the flute outer surface at the intersection of the
optical axis and the back surface thereof. The half heighth of a
flute is designated as h.sub.1 while the heighth of cord or maximum
distance the flute extends into the lens is designated as h.sub.2.
Each flute has a cross section which is the segment of a sphere
having a radius indicated as r.sub.1. The angle in degrees of
spread is designated in FIG. 18 as "a." The flute spread may then
be calculated as r.sub.1 = h.sub.1 /SIN(A.sub.4) and h.sub.2 =
{r.sub.1 - 0.5 .sqroot. [ 4(r.sub.1).sup.2 - (2h.sub.1).sup.2 ]}
wherein a.sub.1 = a.pi. /360; a.sub.2 = ASN[SIN(a.sub.1)/N.sub.1 ];
a.sub.3 = ATN{SIN( a.sub.2)/[N.sub.1 - COS(a.sub.2)]}; a.sub.4 =
a.sub.2 + a.sub.3 ; and N.sub.1 = the index of refraction. With the
above defined relationship the flutes are formed to provide any
specified amount and angular spread of the spread light. The
parameters that may be varied include the indicies of refraction,
thickness of lens, diameter of lens, focal distance from FP to the
back surface of lens, amount of spread light desired, angular
spread desired and width of flutes.
FIGS. 19-20 show a further modified form of this invention wherein
a plano-aspheric lens 72 is provided similar to the lens 44 shown
in FIGS. 9-11. The lens 72, however, includes provision to create a
convergent spread light at the upper portion of the lens so that
the spread light will not shine into the eyes of the oncoming
driver. Thus the planar surface 74 includes two types of flutes.
One type of flute is the parallel spherical segmental flute 76
which creates a divergent spread light. At the uppermost portion of
the planar back surface, however, fresnel type parallel flutes 78
are provided. Unlike conventional fresnel lenses, the flutes 78
form in cross-section, portions of a continuous aspheric curvature,
rather than the conventional spherical curvature or prism type
lens. This aspheric curvature would be formed in accordance with
the manner of computing the aspheric curvature described in
connection with FIG. 3.
FIGS. 21-22 show still another form of aspheric lens. As indicated
therein a fresnel type surface is formed on the rear, rather than
the frontal surface of the lens 80. The frontal surface 82 is made
planar. The fresnel surface 84, unlike conventional fresnel
surface, is formed wherein the individual segments comprise
portions of an aspheric curvature as previously discussed. By
forming the fresnel surface 84 at the rear, the light entering the
lens 80 is made parallel to the optical axis within the lens and
remains parallel when emerging therefrom since the frontal surface
82 is planar. This embodiment is particularly advantageous since it
renders the emerging path of light independent of its environment
beyond the frontal surface 82. Lens 80 is thus equally adapted for
use underwater, in air or any other environment, regardless of the
index of refraction of the environment.
* * * * *