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`Sept. 24, 1940.
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`R. E. BITNER
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`CATADIOPTRICAL LENS
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`1939
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`2,215,900
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`2 Sheets—Sheet 1
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`Filed Oct. 28,
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`NXNNASSKANSANSSSSSS
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`KANNANNNNNN
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`CAAKLSSSASS
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`\NNN.SNANxNNo°NANieLetAN=NNNiNN>NNz
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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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`2,215,900
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`2 Sheets~Sheet 2
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`R. E. BITNER
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`CATADIOPTRICAL LENS
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`Filed Oct. 28, 1939
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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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`UNITED STATES PATENT OFFICE |
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`2,215,900 ce _
`CATADIOPTRICAL LENS -
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`Ralph E. Bitner, New York, N. Ye.
`Application October 28, 1939, SerialNo. 301,815
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`(Cl. 240—41.3)
`6 Claims.
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`. Since the. source is sur-—
`This invention relates to lens units that both
`parent: synthetic resin.
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`reflect and .refractand more particularlyrelates to - rounded. by the lens it is possible to utilize all
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`lenses cast from a single-block of transparent ma~
`luminous flux radiated,.and project it all in a
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`terial, the surfaces of which are aspherical.
`single parallel beam. By designing the reflect-'
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`The use of aspherical surfaces for:lens units was
`ing surfaces of the lens unit to receive the in-. 5 ©
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`first proposed many years ago by some of the first - cident beams at a.greater angle than thecritical
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`investigators in optical science. It has been
`angle,total reflection is obtained -without the
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`shown that these surfaces, called “Cartesian” sur-.. use of silvering-or any other metallic reflector.
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`faces, are free from spherical aberration and rep-
`Throughout this. specificationtherelative posi-
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`the precise geometrical form which an
`10 resent
`tion of ‘lines and surfaces will be indicated by 10
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`optical surface should have in order to transmit
`specifying the angle between the line and a nor-
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`radiant energy, either by refraction. or by reflec- mal to the surface...
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`tion, according to the known laws of these phe-
`| One’of the objects. of the invention is. to pro-.
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`nomena,accurately from one focus to the other.
`-vide a lens unit cast from a single block of trans-
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`15 For a,modern scientific treatment ofthis subject,
`parent. material which will: focus practically all js
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`see Southall’s “Mirrors, Prisms, and Lenses,” page
`the available light rays into a single parallel beam. -
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`518.
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`Another object of the invention is to provide a
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`In spite of their obvious advantages, very few singelens unit which reflects the marginal and
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`lenses with these surfaces have. been manufac-
`intermediate rays by means of total internal re-
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`20 tured because of the difficulties in grinding and.
`flection, thereby eliminating. the necessity of me- gp ,
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`polishing. Recently, however, with the adventof
`tallic reflectors.
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`mouldable synthetic resins of good optical quali-
`Another object. of theinvention is to provide a
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`ties, it is possible to-produce at a reduced cost,
`lens of easily mouldable material having refract-
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`‘aspherical lenses of high quality. Such a lens ig
`ing and reflecting surfaces free from spherical
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`25
`coe,
`g5 described in the U..S. Patent No. 2,086,286, issued
`aberration.
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`to N. M. Stanley, although the exact surface con- ,
`Another object: of the invention is to provide a
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`figuration in this case is not specified.
`. flashlight lens unit, which will gatherin. and focus.”
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`U. S. Patent No. 1,507,212 issued to L. Silber-
`all the. available light rays from a commercial
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`stein, illustrates the application of an aspherical
`flashlight lamp. -
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`surface to part of a lens system and givesmathe-
`Another object of the invention is to provide an 39
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`matical equations for calculating such surfaces.
`efficient. lens which has @ small overall diameter
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`‘The present invention employs.a single block
`in comparison to the size of the source, generally
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`of transparent material with acavity at one side
`having a ratio of less than three.
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`thereof, symmetrical. about. the optical axis, in
`Still another object of the invention-is to pro-.
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`which the source oflight is positioned.
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`vide a-lens which: may: be’ moulded of synthetic 36
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`of this cavity are formed with surfaces of revolu-
`resin. or other suitable. material in a simple two.
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`_ tion whichrefract the rays of. light from the
`piece mouldbyautomatic machinery. ae
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`* source and. direct them through theJens in three
`Other objects and structural details of the in-
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`well defined pencils.. Oneofthese, the central or
`vention will be apparentfrom the following de-
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`40 paraxial pencil, is again refracted by anexit sur-'
`scription when read in connection with the ac- 40
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`face and.is thereby renderedparallel. The other’
`companying drawings, wherein,.
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`pencils are firstinternally reflected and then re-
`Fig. 1. is-a. sectional view. taken on-a meridian.
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`fracted at the exit surface into two otherpar-.
`plane: of. the lens unit, showing the’-associated |
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`“allel beams, all three resultant beams being par-'
`curves usedin forming the surfaces,..
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`45allel to the optical axis.
`‘All surfaces used: are
`“Fig: 2-is a half séctional view showingthat 45°
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`surfacesof revolution taken around the optical
`part of-the-lens block nearest the-source. °. |
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`axis.and all are knowngenerally as “Cartesian?.
`Fig. 3 is:a-sectional view: of, the refracting en--
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`surfaces.
`‘Thelens block is so designedas to be
`trance ‘surfaceadjoining. that shown in’ Fig. 2:
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`moulded in a:simpletwopiece mouldof any suit-: with dimensions showingits focal length and axial.
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`50 able transparent material but preferably of trans--
`inclination,
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`Page 3 of 6
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`Page 3 of 6
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`a?—b?4-c?—2be cos a
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`XI+y2—p2
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`By suitable rearrangement we get:
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`2
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`xe £+B
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`Cc
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`y= era
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`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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`2
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`2,215,900
`Fig. 4 is a sectional view of another refracting
`the incident ray, b the length of the refracted
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`entrance surface adjoining that shown in Pig. 3
`ray, » the refractive index and G a constant
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`and similar to it except for focal
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`quantity. When a virtual image is formed, as
`axial displacement.
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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—xb.
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`Fig. 5 is a sectional view of one of the reflecting
`From the geometrical construction as shown in
`surfaces showing the characteristics of the pa-
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`Fig. 2 it is obvious that the following relations are
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`rabola from which it is taken.
`true: .
`Fig. 6 is a sectional view of the second reflect-
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`ing surface, similar to Fig. 5 except for axial dis-
`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 withanoptical axis 2I—2i and a source
`of light f: 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-
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`light bulb. The lens unit is a solid block bounded
`by eight faces, all surfaces of revolution about
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`the optical axis 2i—2l. These surfaces are as
`follows:
`(1) A paraxial entrance surface A con-
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`sisting of an aspherical quartic surface of revolu-
`This series of equations may be used for com-
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`‘tion which receives the light rays from the source
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`puting the points on the refracting surface and
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`fi and refracts them to a virtual focus of fe.
`It
`a@-much simpler and shorter method results.
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`(2) A refracting entrance surface B consisting
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`has one disadvantage over the older method in
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`of a co.ivex hyperboloid formed by the revolution .
`‘that neither the value of X or Y-is known at
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`of a section of a hyperbola. about the axis and
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`the start of the computation. This feature is of
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`refracting the rays from fi inte a beam of par-
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`no consequence, however, when a curve is to be
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`allel rays..
`(3) A refracting entrance surface C
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`computed with a large number of points.
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`Similar to B. except for focal length and axial
`The lens block herein disclosed was designed
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`inclination..(4) A reflecting surface D consist-
`for alens material having an index of refraction
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`ing of a paraboloid formed by the revolution of a
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`equal to 1.52.
`It is obvious that other similar
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`section of a parabola about the optical axis and
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`lenses may be designed within the scope of this
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`reflecting the parallel rays from surface C toward
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`invention which have different indices of refrac~
`a focal point fs on the optical axis.
`(5) A part
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`tion.
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`of the surface of a cone E which connects two
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`Fig. 3 shows the construction of a convex re-
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`optical surfaces but has no optical function of
`fracting surface B which adjoins the surface
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`its own.
`(6) a reflecting surface Fsimilar to D
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`shown in Fig. 2. This part of the lens receives
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`but receiving parallel rays from surface B and
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`light rays emanating from the source f1 on the
`reflecting them by a different path toward the
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`optical axis and refracts them into a parallel
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`point fs.
`(7) A refracting concave exit surface G
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`beam. The curve is a hyperbola with its apex
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`consisting of an ellipsoid formed by the revolu-
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`3 unit. from the source and an eccentricity of
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`tion of a section of an ellipse about the optical
`‘The portion used in thelens block is desig-
`1.52.
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`axis. and retracting. the light rays received from
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`nated by the line. 23—24 and the angular tilt
`surfaces D and F into a beam of parallel rays.
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`of 56° given the.axis is to.assure easy withdrawal
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`(8) A refracting paraxial exit surface H forméd
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`of the die during the moulding operation.
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`by the revolution of a section of an ellipse about
`Fig. 4 shows the construction of the hyper-
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`the optical axis and refracting the light rays
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`boloid similar to the one in Fig. 3 except for focal
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`coming in the direction from the virtual focus
`‘length and axial tilt. As may be seen from Mg.1,
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`f2 into a beam of parallel rays.
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`this refracting surface C adjoins the surface B.
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`Each of these eight surfaces. will now be con-
`Its axis is 78° from the optical axis of the lens
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`sidered in detail and methods and meansfortheir
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`block with the apex being .35 unit from the source
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`computation disclosed.
`Fig. 2 is designed to
`of light fi. The line between the points 24—2&
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`show some of the more important characteris-
`denotes the segment used in the block. The ec-
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`tics of paraxial surface A. The optical axis is
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`centricity of this curve is also 1.52.
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`represented by the line 2i—2{ as in Fig. 1. The
`Figs. 5 and 6 show the characteristics of a pair
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`source fi is placed .275 unit-from the axial sur-
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`of parabolas which are used to form surfaces of
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`face point 22 and the virtual focal point fe from
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`revolution about the main optical axis. The use
`which the refracted rays appear to originate, is
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`of paraboloids as focussing means is quite old in
`just twice this distance or .55 unit. The resultant
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`the flashlight art but' previ- us structures have
`curvature of face. A is far from a spherical sur-
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`placed the light source at ’ae focus of the parab-
`' face and may change its curvature from convex
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`oloid to obtain a reflectec. parallel beam directly.
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`_ at the axis to concave near the rim. The equa-
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`The present design uses the paraboloid in a re-
`tion of this curve, as generally expressed in
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`versed manner since the parallel light rays are
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`terms of the coordinates of any point on the
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`received by the mirror xnd reflected toward the
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`curve, is a complicated fourth degree equation or
`focal point fs. The dire-tion of light with re-
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`quartic and is very difficult to compute. Silber-
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`spect to the paraboloid is, therefore, opposite to
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`stein in Patent 1,507,212 gives an approximate
`that in general usage.
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`method ‘of solution by expansion into a series.
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`The primary reason for employing the parab-
`I prefer, however, to calculate such curves by
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`oloids in this manner is to. save space.
`If the
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`using a parametric form with the length of op-
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`older design were employed, the resultant diam-
`tical path as the parameter.
`In accordance with
`eter of the lens block would be greatly increased.
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`the fundamental concepts of image formation,
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`Another advantage of using paraboloids for point «©
`this equation is G=a-+-ub where a is the lenzth of
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`Page 4 of 6
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`Page 4 of 6
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`

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`3
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`2,216,900
`marginal Jens mirror‘combinations composed of
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`focussing is that the resultantlight beam is more
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`a hyperboloid refracting entrance surface, & pa-
`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 refracting exit surface, the axes
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`tense spot of light.
`:
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`of said hyperboloid and said paraboloid 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 parab-
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`of the block; the second of said marginal lens
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`oloid F cooperate to direct the same pencils of
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`mirror combinations composed of a hyperboloid
`light from the source fi to a point fa onthe axis.
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`refracting entrance surface, a paraboloid total
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`These points are spaced 4 units apart. The hy-
`10
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`internal reflection mirror and a concave ellipsoid
`perboloid B is formed with its axis 56° from the
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`refracting exit surface, the axes of said hyper-
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`optical axis, hence the axis of the. paraboloid F
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`poloid and said paraboloid disposed at equal an-
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`is similarly disposed. The dimensions as indi-
`gular inclinations to the optical axis of the. block;
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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
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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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`length of the second mentioned hyperhboloid; said
`:
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`second concaveellipsoid exit surface being a con-
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`The refracting hyperboloid C and thereflecting
`tinuation of the first mentioned concave ellipsoid
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`paraboloid D, as shown in Figs. 1, 4, and 5, also
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`exit surface and all ofsaid 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.
`from the source fi toward the point 7s. Both of
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`20
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`3. A lens block for focussing light from a con~-
`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 -marginal
`lens mirror combinations;
`said
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`the limit for total internalrefiection and at the
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`25
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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
`face and a convex ellipsoid exit surface, both of
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`as possible. The limiting angle for total reflec-
`said surfaces having their axes coincident with
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`tion in 2 medium with a refractive index of 1.52is
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`the optical axis of the lens block; one of said
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`41° 8’ 20°’.
`:
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`marginal lens mirror combinations composed of
`Fig. 7 filustrates the formation of exit surfaces
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`a hyperboloid refraction entrance surface, a parab-
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`G and H, both ellipsoids and both refracting. .
`oloid total internal reflection mirror, and a con-
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`Every refracting ellipsoid must have its eccen+
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`cave ellipsoid refracting éxit surface, the axes of
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`tricity equal to the reciprocal of the refractive
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`said hyperboloid and said paraboloid disposed at
`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 mir-
`Jens 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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`fracting entrance surface, a paraboloid 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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`refracting exit surface, the axes of said hyper-
`boundaries, 11° 40’ and 5°, with point fs taken as
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`boloid and said paraboloid disposed at equal an-"
`a center. The distance L is 3.5 units. As may
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`40
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`gular inclinations to the optical axis of the block;.
`- be seen from Fig. 1,
`the rays of light are re- ,
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`the first, mentioned angular inclinations being
`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 fs.. The concave ellipsoid G renders
`clinations; and all of said surface components
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`these rays parallel to the optical axis. The el-
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`peing surfaces of revolution about the optical
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`lHipse which forms this surface has a major axis.
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`‘axis.
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`(26—27) 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-
`units. The distance between foci is 2.1777 units.
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`centrated source into a parallel beam having in
`Surface H is a convex ellipsoid which refracts
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`combination; one paraxial lens ‘component and
`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 quartic entrance sur-
`‘are divergent with fz 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-
`the: optical axis of the lens block; one of said
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`nent, measured from fi to the axial boundary 27,
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`marginal lens mirror combinations composed of
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`is 1 unit and therefore all characteristic values
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`65
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`a hyperboloid refracting entrance surface, a Da-
`_ of the generating ellipse will have to be reduced
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`raboleid 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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`concaveellipsoid refracting exit surface, the axes
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`given in the above paragraph.
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`of said hyperboloid and said paraboloid disposed
`While I have described what I consider to be
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`at equal angular inclinations to the optical. axis
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`a highly desirable embodiment of my invention, ©
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`of the. block; the second of said marginal lens
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`it is obvious that many changes in form could
`mirror combinations composed of a hyperboloid
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`be made without departing from the spirit of my
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`refracting entrance surface, 2 paraboloid total in-
`invention, and I, therefore, do not limit myself
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`ternal reflection mirror, and a concave ellipsoid
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`to the exact form herein shown and described nor
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`65
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`refracting exit surface, the axes of said hyper-
`to anything less than the whole of my invention
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`poloid and said paraboloid disposed at equal an-
`as hereinbefore set forth, and hereinafter claimed.
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`_ gularinclinations to the optical axisof. the block;
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`Ielaim:
`|
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`the first mentioned angular inclinations being
`4. A lens block for focussing light from a con-~
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`substantially less than the second mentiéned in-
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`70
`centrated source into-a parallel beam having in
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`Clinations; said second concave ellipsoid exit sur-
`combination; one paraxial Jens 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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`paraxial lens comprising a quartic entrance sur-
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`face components being surfaces of
`revolution
`face and a convex ellipsoid exit surface, both of
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`- about the optical axis.
`said. surfaces having. their axes coincident with
`4. A Jens block for focussing light from a con-
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`7
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`the optical axis of the lens block; one of said
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`15
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`65
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`70
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`a2tr
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`Page 5 of 6
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`Page 5 of 6
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`

`

`
`4
`2,215,900
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`said hyperboloid and said paraboloid in any. one
`cefitrated source into a parallel beam having in
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`of said combinations disposed at equal angular
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`combination; one paraxial lens component and
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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
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`said paraxial lens comprising a quartic entrance
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`‘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 axes coincident with
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`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-
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`of Jens mirror combinations each. composed of a
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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
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`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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`said paraxial lens comprising 2 quartic entrance
`said hyperboloid andsaid paraboloid in any one
`of.said combinations disposed at equal angular
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`and a convexellipsoid exit surface; both of said
`intlinations to the axis of the block; and all of
`surfaces having their axes coincident with the
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`said surface components being surfaces of revo-
`optical axis of the lensblock; said plurality of
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`lens mirror combinations each composed of a -
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`lution about the optical axis.
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`5, A lens block for focussing light from a con-
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`hyperboloid refracting entrance surface, a parab-
`oloid total internal reflection mirror and a con-
`centrated source into a parallel beam having in
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`combination; one paraxial lens component and
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`cave ellipsoid refracting exit surface, the axes of
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`a plurality of marginal lens mirror combinations;
`said hyperboloid and said paraboloid in any one
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`of said combinations disposed at equal angular
`said paraxial lens comprising a quartic entrance
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`
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`inclinations to the optical axis of the block; said
`surface and a convex ellipsoid exit surface, both
`of said surfaces having their axes coincident with
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`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
`of lens mirror combinations each composed of a
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`hyperboloid refracting entrance surface, a parab-
`the optical axis.
`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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