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`Page 1 of 6
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`SAMSUNG EXHIBIT 1037
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`Page 1 of 6
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`SAMSUNG EXHIBIT 1037
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`Sept. 24, 1940.
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`R'. E. BITN ER
`CATADIOPTEICAL LENS
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`Filed OCt. 28, 1939
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`2,215,900
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`2 Sheets—Sheet 2
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`'——"-—365———————————
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` ‘- —- 3.12
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`INVENTOR
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`Page 2 of 6
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`Page 2 of 6
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`Patented Sept. 24, 1940 .
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`2,215,900
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`UNITED 'srArEs
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`IV‘P‘ATENT OFFICE
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`2,215,9oo-
`caramomrcAL LENS '
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`Ralph .E- Bitner, New York, N. Y ,
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`. Application October as, 1939,. Serial'No. $01,815
`(01. 240—413)
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`BClaims.
`-Since the source is sur-'
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`parent synthetic resin;
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`This invention relates to lens units that both
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`rounded by the lens it is possible to utilize all
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`reflect and refract and more particularly relates to ,
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`luminous flux radiated, and project it all in a
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`lenses cast from a single-block of transparent ma-
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`single parallel beam. By designing the reflect-‘
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`terial, the surfaces of which are aspherical,
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`ing surfaces of the lens unit to receive the in--
`The use of aspherical surfaces for'lens units was
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`- cident beams at a greater angle than the critical
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`first proposed many years ago by some of the first
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`angle, total reflection is obtained without the
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`investigators in . optical
`science.~ It has been
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`use of silvering-or any other metallic reflector.
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`shown that these surfaces, called “Cartesian” sur-. ,
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`Throughout this specification» therelative posi-
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`faces, are free from spherical aberration and rep-
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`tion of lines and surfaces will be indicated by
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`the precise geometrical form which an
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`specifying the angle between the line and a nor-
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`optical surface should have in order to transmit
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`1mal to the surface.
`invention is to pro-
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`radiant energy, either. by refraction or by reflec-
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`One'of the objects of the
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`tion, according to the known laws of these phe-
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`-vide a lens unit cast from a. single block of trans-
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`nomena, accurately from one focus to the other.
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`parent material which willefocus practically all
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`For amodern scientific treatment of, this subject,
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`the available light rays into a single parauel beam. -
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`see Southall’s “Mirrors, Prisms, and Lenses,” page
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`Another object of the invention is to provide a
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`singe lens unit which reflects the marginal and
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`In spite of their obt'ious advantages, very few
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`intermediate rays by means of total internal re-
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`lenses with these surfaces have. been manufac—
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`flection, thereby eliminating the necessity of me-
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`tured because of the difficulties in grinding and
`tallic reflectors.
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`polishing. , Recently, however, with the advent'of
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`Another object of the invention is to provide a
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`mouldable synthetic resins of good optical quali—
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`lens of easily mouldable material having refract-
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`ties, it is possible toproduce at a reduced cost,
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`ing and reflecting surfaces :free from spherical
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`aspherical lenses of high quality. Such a lens is
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`aberration.
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`described in the 11:55. Patent No. 2,086,286, issued
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`Another object of the invention is to provide a
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`to N. M. Stanley, although the exact surface con- ,
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`v flashlight lens unit which will gather in and focus.
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`figuration in this case is not specified.
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`all the available light rays from a commercial
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`U. 8. Patent No. 1,507,212 issued to L. Silber?
`flashlight lamp. ‘
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`stein, illustrates the application of an aspherlcal
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`Another object of the invention is to provide an
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`surface to part of a lens system and gives'mathe-
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`efficient lens which has a small overall diameter '
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`matlcal equations for calculating such surfaces.
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`in comparison to the size of the source, generally
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`The present invention employs . a single block
`having a ratio of less than three.
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`of transparent material with a'cavity at one side
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`Still another object of the inventionis to pro-
`at
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`thereof. symmetrical. about, the optical axis,‘ in
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`vide aliens which’may be'moulded of synthetic
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`which the source of light is positioned. The walls
`resin or other suitable: material in a; simple two:
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`of this cavity are formed 'wlth surfaces of revolu-
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`piece mmildby-automatic machinery.
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`tion which refract the rays of light from the
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`other objects and structural details of the in-
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`source and: direct .them through the lens in three
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`vention will be apparent. from the following de-‘
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`One of these, the Central 'or
`I well defined pencils,
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`scription when read in connection with the ace
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`paraxial pencil, is again refracted by an exit 'sur-'
`companying drawings, wherein;
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`face and is thereby ‘rendered‘parallel. The other
`Fig.1. is a sectional viewtaken 011:3, meridian '
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`pencils are flr’stinternally reflected and then re-
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`plane of. the lens .uni‘t, showing the‘rassociated .
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`fracted at the exit shrf'ace into two other par--
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`curves u‘s‘edfiin forming the surfaces;
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`' allel beams, all three resultant beams being par-I
`(Fig.:2:is a half sectional view showing: that
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`45'
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`allei to the optical",ar‘:is. All surfaces uSedl‘are
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`part of'theclens block. nearest the-source.
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`surfaces of revolution taken around the optical
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`Fig. 3 is alsectional view of the refraCting an.»
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`axis; and all 'are‘ known generally as "Cartesian”. 3
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`trance surface, adjoining that shown in Fig, ‘2;
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`surfaCes.
`'The‘ lens block is so designed as 'to be
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`with dimensions showing its focal length and axial
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`moulded in a-Sin’ipl'e‘two'piece m‘ouldof any suite ,
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`50
`inclin‘ationfiv'
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`able transparent material but preferably of trans— -
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`Page 3 of 6
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`Page 3 of 6
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`2,215,900
`Fig. 4 is a sectional View of another refracting
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`entrance surface adjoining that shown in Fig. 3
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`and similar to it except; for focal
`length and
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`axial displacement.
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`Fig. 5 is a sectional view of one of the reflecting
`surfaces showing the characteristics of the pa-
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`rabola from which it is taken.
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`Fig. 6 is a_ sectional view of the second reflect-
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`ing surface, similar to Fig. 5 except for axial .dis-
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`placement and focal length.
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`Fig. 7 is a sectional View of the two exit sur-
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`faces, ‘both shown as a part of the ellipsoid from
`which they were derived.
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`Referring now to Fig. 1, the lens block 20 is in-
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`dicated with an optical axis Zl—Zl and a source
`of light f1 on'said axis. This source may be any
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`convenient lamp or light image but the present
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`design is intended to'be used With a small flash-
`light bulb. The lens unit is a solid block bounded
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`by eight faces, all surfaces of revolution about
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`the optical axis Zl—Zl. These surfaces are as
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`follows:
`(1) A paraxial entrance surface A con-
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`sisting of an aspherical quartic surface of revolu-
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`tion which receives the light rays from the source
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`f1 and refracts them to a virtual focus of f2.
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`(2) A refracting entrance surface B consisting
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`of a convex hyperboloid formed by the revolution .
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`of a section of a hyperbola. about the axis and
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`refracting the, rays from f1 into a beam of par-
`allel rays.
`(3) A refracting entrance surface C
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`similar to B except for focal length and axial
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`inclination.
`(4) A reflecting surface D consist—
`ing of a paraboloid formed by the revolution of a
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`section of a parabola about the optical axis and
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`reflecting the parallel rays from surface C toward
`a focal point is on the optical axis.
`(5) A part
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`of the surface of a cone E which connects two
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`optical surfaces but has no optical function of
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`its own.
`(6) a reflecting surface F similar to D
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`but receiving parallel rays from surfaceB and
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`reflecting them by a diflerent path toward the
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`point is.
`('7) A refracting c'oncave exit surface G
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`consisting of an ellipsoid formed by the revolu-
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`tion of a section of an ellipse about the optical
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`axis and retracting the light rays received from
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`surfaces D and F'into a beam of parallel rays.
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`(8) A refracting par-axial exit surface H formed
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`by the revolution of a section of an ellipse about
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`the optical axis and retracting the light rays
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`coming in the direction from the virtual focus
`f2 into a beam of parallel rays.
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`Each of these eight surfaces will now be con-
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`sidered in detail and methods and means for their
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`computation disclosed.
`Fig. 2 is designed to
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`show some of the mbre important characteris-
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`tics of paraxial surface A. The optical axis is
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`represented by the line 2l—2I as in Fig. 1.’ The
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`source fl is placed .275 unit~from the axial sur-
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`face point‘ 22 and the virtual focal point f2 from
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`which the refracted rays appear to originate, is
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`just twice this distance or .55 unit. The resultant
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`curvature of face A is far from a spherical sur-
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`' face and may change its curvature from convex
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`. at the axis to concave near the rim. The equa-
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`tion of this curve, as generally expressed in
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`terms of the coordinates of any point 'on the
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`curve, is a complicated fourth degree equation or
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`quartic and is very difficult to compute. Silber-
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`.stein in Patent 1,507,212 gives an approximate
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`method 'of solution by expansion into a series.
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`I prefer, however, to calculate such curves by
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`using a parametric form with the length of op-
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`tical path as the parameter.
`In accordance with
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`the fundamental concepts of image formation,
`this equation is G=a+pb where a is the length of
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`the" incident ray. b the length of the refracted
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`ray. u the refractive index and G a constant
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`quantity. When a virtual image is formed. as
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`is the case in Fig. 2, the length b is considered.
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`negative, hence the equation becomes G=a—ab.
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`From the geometrical construction as shown in
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`Fig. 2 it is obvious that the following relations are
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`true: .
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`a2=b2+cz——2bc cos a.
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`. X=b cos a.
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`X9+Y2=b2
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`By suitable rearrangement we get:
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`c“—_a2+b2
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`2c
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`YfiJH—fl
`where X and Y are the coordinates of any point
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`on the required curve and the parametric quan-
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`tity
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`a-—G
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`p.
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`X=
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`b:
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`This series of equations may be used for com-
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`puting the points on the refracting surface and
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`25
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`a much simpler and shorter method results.
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`has one disadvantage over the older method in
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`that neither the value of X or Y» is knowu at
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`the start of the computation. This feature is of
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`no consequence, however, When a curve is to be
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`computed with a large number of points.
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`The lens block herein'disclosed was designed
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`for a. lens material haying an index of refraction
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`equal to 1.52.
`It is obvious that other similar
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`lenses may be designed within the scope of this
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`invention which have different indices of refrac-
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`tion.
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`Fig. 3 shows the construction of a convex re-
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`fracting surface B which adjoins the surface
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`shown in Fig. 2. This part of the lens receives
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`light rays emanating from the source In on the
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`optical axis and refracts them into a parallel-
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`beam. The curve is a hyperbole. with its apex
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`.3 unit from the source and an eccentricity of
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`1.52. The portion used in the lens block is desig-
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`nated by the line 23—2! and the angular tilt
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`of 56° given the-axis is to assure easy withdrawal
`of the die during the moulding operation.
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`Fig. 4 shows the construction of the hyper-
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`boloid similar to the one in Fig. 3 except for focal
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`length and axial tilt. As may be seen from Fig. 1,
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`this refracting surface C adjoins the surface B.
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`Its axis is 78" from the optical axis of the lens
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`block with the apex being .35 unit from the source
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`of light f1. The line between the points 24—25
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`denotes the segment used in the block. The ec-
`centricity of this curve is also 1.52.
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`Figs. 5 and 6 show the characteristics of a pair
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`of parabolas' which are used to form surfaces of
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`revolution about the main optical axis. The use
`of paraboloids as focussing means is quite old in
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`the flashlight art but' previ'as structures have
`placed the light source at ‘ne focus of the parab-
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`oloid to obtain a reflecteu parallel beam directly.
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`The present design uses the paraboloid in a re-
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`versed manner since the parallel light rays are
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`received by the mirror and reflected toward the
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`focal point fa. The dire’tion of light with re-
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`spect to the paraboloid is, therefore, opposite to
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`that in general usage.
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`The primary reason for employing the parab-
`oloids in this manner is to save space.
`If the
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`older design were employed, the resultant diam-
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`eter of the lens block would be greatly increased.
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`Another advantage of using paraboloids for point r
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`10
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`15
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`20
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`30
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`40
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`46.
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`50
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`55.
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`70
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`Page 4 of 6
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`

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`3
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`2,915,900
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`marginal lens mirror. combinations composed of
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`focussing is that the resultant light beam is more
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`a hyperboloid retracting entrance surface, a pa-'
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`concentrated as it leaves the lens and therefore
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`raboloid total internal reflection mirror and a
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`permits the formation of a smaller and more in- _
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`concave ellipsoid retracting exit surface, theaxes
`tense spot of light.
`.
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`of said .hyperboloid and said parabolold disposed
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`It will be'obvious from the drawings (Figs. 1, 3,
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`at equal angular inclinations to the optical axis
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`and 6)
`that the hyperboloid B and the parabr
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`of the block; the second of said marginal lens
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`oloid F'coop‘erate-to direct the same pencils of
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`mirror combinations composed of a hyperboloid
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`light from the source f1 to a point I: on‘ the axis.
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`retracting entrance surface, a parabolold total
`10
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`These points are spaced 4*units apart. The hy-
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`internal reflection mirror and a concave ellipsoid
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`perboloid B is formed with its axis 56° from the
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`retracting exit surface, the axes of said hyper-
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`optical axis, hence the axis of the. parabolold F
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`boloid and said paraboloid disposed at equal an-
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`is similarly disposed. The dimensions as indi-
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`gular inclinations to the optical axis of theblock;
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`cated in Figs. 3. 4, 5, and 6 are in units of any
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`the first mentioned hyperboloid having a focal
`16
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`system of measurement, the radius'of the circle
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`length which is substantially less than the focal
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`forming the exit edge of-the block being taken as
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`one.
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`length of the second mentioned hyperboloid; said
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`second concave ellipsoid exit surface being a con-
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`The retracting hyperboloid C and the reflecting
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`tinuation of the first mentioned concave ellipsoid
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`parabolold D, as shown in Figs. 1, 4, and 5, also
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`exit surface and all of said surface components
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`cooperate to direct another group of light rays
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`being surfaces of revolution about the optical axis.
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`from the source f1 toward'the point it. Both of
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`20‘
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`2. A lens block for focusslng light from a con-
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`these sections have the same axial inclination.
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`centrated source into a parallel beam having in
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`. 78°, this value being a result of an effort to keep
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`combination;- one paraxial lens component and
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`the reflecting angle in the paraboloid well within
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`,two *margihal
`lens mirror combinations;
`said
`25
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`the limit for total internal reflection and at the
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`paraxial lens comprising a quartic entrance sur-
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`same time gather in as much light from the source
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`face and a convex ellipsoid exit surface, both of‘
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`as possible. The limiting angle for total reflec-
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`said surfaces having their axes coincident with
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`tion in a medium with a refractive index of 1.52' is
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`41° 8’ 20".
`»
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`the optical axis of the lens block; one of said
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`marginal lens mirror combinations composed of
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`Fig. 7 illustrates the formation of exit surfaces
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`a hyper-boloid refraction entrance surface, aparab-
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`G and H, both ellipsoids and both retracting. .
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`oloid total internal reflection mirror, and a con-
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`Every retracting ellipsoid must have its'ecceni-
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`cave ellipsoid retracting Exit surface, the axes of
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`tricity equal to the reCiprocal of the refractive
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`said hyperbolold andsaid parabolold disposed'at
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`index of the medium, hence one figure may be
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`equal angular inclinations to the optical axis of
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`used for both surfaces although in the actual
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`the block; the second of said marginal lens niir-
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`lens block, surface G is derived from an ellipse
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`ror combinations composed of a hyperboloid re-
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`3.5 times as large as the ellipse used to form the
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`tracting entrance surface, a parabolold total in-
`surface H.
`,.
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`ternal reflection mirror and a concave ellipsoid
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`The extent of surface G is indicated by angular
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`retracting exit surface. the axes of said hyper-
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`boundaries, 11° 40’ and 5°,4with point In taken as
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`boloid and said paraboloid disposed at equal an-"‘
`40
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`a center. The distance L is 3.5 units. As may
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`gular inclinations to the optical axis of the block;
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`' be seen fromFig. 1,
`the rays of light are re- '
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`the first mentioned angular inclinations being
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`flected from surfaces D and F, directed toward
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`substantially less than the second mentioned in-
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`the point is. The concave ellipsoid G renders
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`clinations; and all of said surface components
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`these rays parallel to the optical axis. The el-
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`being surfaces of revolution about the optical
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`lipse which forms this surfacehas a major axis.
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`axis.
`'
`'
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`(26—21) of 4.222 units and a minor axis of 3.18
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`3. A lens block for focussing light from a con-
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`units. The distance between fool is 2.7777 units.
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`centrated source into a parallel beam having in
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`Surface H is a convex ellipsoid which retracts
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`combination; one paraxial lens component and
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`the rays of light that have been refracted by
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`two, marginal
`lens mirror combinations;
`said
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`surface A. While in the lens block, these rays
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`paraxial lens comprising a qu‘artic entrance sur-
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`are divergent with f2 as a. virtual'focus. The ‘
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`face and a convex ellipsoid exit surface. both of
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`surface H renders them parallel to the optical
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`said surfaces having their axes coincident with
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`axis. The focal distance K of this lens compo-
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`the- optical axis of the lens black; one of said
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`nent, measured from fa to the axial boundary 1",
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`marginal lens mirror combinations .composed of
`55
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`is 1 unit and therefore all characteristic values
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`a hyperboloid retracting entrance surface, a pa—
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`. of the generating ellipse will have to be reduced
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`rabolold total internal reflection mirror, and a
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`in the ratio 3.5 to 1 as compared to the values
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`concave ellipsoid retracting exit surface, the axes
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`given in the above paragraph.
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`of said hyperboloid and said parabolold disposed
`While I have described 'what AI consider to be
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`at equal angular inclinations to the optical axis
`a highly desirable embodiment of my invention, '
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`of theblock; the second of said marginal lens
`it is obvious that many changes in form could
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`mirror combinations composed of a hyperboloid
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`be made without departing from the spirit of my
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`retracting entrance Surface, a parabolold total in-
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`invention, and I,,therefore, do not limit myself
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`ternal reflection mirror, and a concave ellipsoid
`05
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`to the exact form herein shown and described nor
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`retracting exit surface, the axes of said hyper-
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`to anything less than the whole of my invention
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`boloid and said parabolold disposed at equal an-
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`as hereinbefore 'set forth, and hereinafter claimed.
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`, gular inclinations to the optical axis of the block;
`I claim:
`,
`i
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`the first mentioned angular inclinations being
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`-1. A lens bloci: for-focusSing light from a con- "
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`substantially less than the second mentioned in-
`70
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`centrated source into 'a parallel beam having in
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`clinations; said second concave ellipsoid exit sur-
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`combination; one paraxial ‘lens component and
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`face being a continuation of the first mentioned
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`two marginal. lens mirror combinations;
`said
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`concave ellipsoid exit surface and all of said sur-
`
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`
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`paraxial lens comprising a quartic entrance sur-
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`face components being surfaces of
`revolution
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`face and a convex ellipsoid exit surface. both of
`' about the optical axis.
`-
`.
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`7t
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`said Surfaces having. their axes coincident with
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`4. A lens block for focussing light from a con-
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`the optical axis of the lens block; one of said
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`10
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`15
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`25
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`30
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`35
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`50
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`so
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`'65
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`70
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`Page 5 of 6
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`Page 5 of 6
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`

`

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`.
`4
`2,215,900
`said hyperboloid and said paraboloid in anyone
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`
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`cefitrated source into a parallel beam having in
`
`
`
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`
`
`of said combinations disposed at equal angular
`combination; one paraxial lens component and
`
`
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`
`
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`
`
`
`
`
`
`
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`
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`a plurality of marginal lens mirror combinations;
`
`
`
`
`
`
`inclinations to the optical axis of the block; the
`axial angular inclinations of said combinations
`said paraxial lens comprising a quartic entrance
`
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`
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`
`
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`r being substantially different. one from the other
`, surface and a convex ellipsoid exit surface, both
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`and all of said surface components being surfaces
`
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`of said surfaces having their axe's coincident with
`the optical axis of the lens block; said plurality
`of revolution about the optical axis.
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`
`6. A lens block for focussing light from a con-
`of lens mirror combinations each, composed of a
`
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`
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`
`
`
`
`
`
`
`centrated source into a parallel beam having in
`
`
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`
`
`
`
`
`
`
`
`hyperboloid refracting entrance surface, a parab-
`oloid total internal reflection mirror and a con—
`1
`combination; one paraxial lens component and
`
`
`
`
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`
`
`
`
`
`
`
`
`cave ellipsoid refracting exit surface, the axes of
`a plurality of marginal lens mirror combinations;
`
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`
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`
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`
`
`
`
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`
`
`
`
`said paraxial lens comprising a quartic entrance
`
`
`
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`
`
`
`said hyperboloid and said paraboloid in any one
`of said combinations disposed at equal angular
`and a convex ellipsoid exit, surface; both of said
`
`
`
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`
`
`
`
`
`
`
`
`
`
`inelinations to the axis of the block; and all of
`surfaces having their axes coincident with the
`
`
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`
`
`
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`
`
`
`said surface components being surfaces of revo-
`optical axis of the lens, block; said plurality of
`
`
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`
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`
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`
`
`
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`lens mirror combinations each composed of a 4
`lution about the optical axis.
`
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`
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`
`
`5. A lens block for focussing light from a cone
`
`
`
`
`
`
`
`
`
`
`
`
`hyperboloid retracting entrance surface, a parab-
`oloid total internal reflection mirror and a con-
`centrated source into a parallel beam having in
`
`
`
`
`
`
`
`
`
`
`
`
`
`combination; one paraxial lens component and‘
`cave ellipsoid rei'racting exit surface, the axes of
`
`
`
`
`
`
`
`
`
`
`
`
`
`a plurality of marginal lens mirror combinations;
`said hyperboloid and said paraboloid in any one
`
`
`
`
`
`
`
`
`
`
`
`
`
`of 'said combinations disposed at equal angular
`said paraxial lens comprising a quartic entrance
`
`
`
`
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`inclinations to the optical axis of the block; said
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`surface and a convex ellipsoid exit surface, both
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`of said surfaces having their axes coincident with
`concave ellipsoid exit surfaces being continua-
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`the optical axis of the lens block; said plurality
`tions of a'single ellipsoid and all of said surface
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`components being surfaces of revolution about
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`of lens mirror combinations eachcomposed of a
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`hyperboloid refracting entrance surface, a parab-
`the optical axis.
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`RALPH E. BITNER.
`oloid total internal reflection mirror and a con-
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`cave ellipsoid refracting exit surface, the axes of *
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`10
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`15
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`20
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`25
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`Page 6 of 6
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`Page 6 of 6
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