AN OPTICAL SYSTEM FOR PROJECTION

Abstract: An optical system for projection with a projector apparatus intended to project an image on a screen made with negative curvature includes a single, generally concavo-convex lens, both surfaces of which are aspherically corrected, and the front surface of which is oriented towards the plane of the object. The lens is provided with a diaphragm arranged behind the lens at a distance therefrom at least amounting to that of the diaphragm aperture. The display screen preferably has the form of a hyperboloid with splayed-out edges. The optical system is made with a numerical aperture of 0.09 and is intended to afford an enlargement of 6 to 10 times for objects of the format 190 x 250 mm. The optical system is suitably adapted for an overhead projector and has a Gauss focal length of 230 mm. The lens can be made from methyl methacrylate.

Description: TITLE OF INVENTION AN OPTICAL SYSTEM FOR PROJECTION TECHNICAL FIELD The invention relates to an optical system for a pro- jection apparatus, which is preferably intended for pro¬ jecting an image on a display screen with generally nega¬ tive curvature. BACKGROUND ART In the construction of projection objectives with relatively short Gauss focal length, e.g. for portable overhead projectors, the conventional method has been to make the objective with a small aperture, in order to ob¬ tain with few lenses, a generally acceptable image quality. An optical system is thus afforded which can be produced at relatively low costs and which _has relatively small di¬ mensions and low weight, so that the condition of portabi¬ lity is satisfied, but with the disadvantage that such an optical system at best only allows acceptable projection of very highly luminous objects such as transparencies or the like. An attempt to make an objective allowing acceptable image quality and light strength, even when projecting objects of relatively small luminosity, is disclosed in the Swedish patent No. 7407134-1. Such an objective in- ludes a modified triplet supplemented by a large positive lens a long way in front of the triplet. This kind of objective has indeed a large aperture, and affords accept¬ able image quality, but as indicated, it requires four large lens elements and the Gauss focal length needs to be about 600 mm, in order that the projector operator can manipulate the image of the object. Due to the necessary size and weight of the objective, as well as the large number of lenses necessary for it, this previously known objective is neither economically acceptable nor co - patible with the portability requirement. The conviction of those skilled in the art has been that a proper projection objective must include a plura¬ lity of lens elements, even if some lens surface has been given an aspheric correction. The technique of aspherical¬ ly correcting a lens surface for reducing certain image reproduction errors or abera ions is known, but is com¬ mercially limited, since the cost of producing such lenses is relatively high. It has therefore appeared as being more economically favourable in the construction of a projector objective to increase the number of lens elements therein, if it is desired to improve the resulting image quality, instead of aspherically correcting any of the lens surfaces in the objective since, as mentioned, such persons were convinced that the objective necessarily must include a plurality of lens elements in order to avoid the most serious aberrations. PURPOSE OF INVENTION One purpose of the invention is to propose an ob¬ jective structure for projectors, said structure having a short Gauss focal length, great numerical aperture, high image quality, low weight and a small number of lens ele- ' ments, so that an overhead projector, for example, equipped with such an optical system will actually be light in weight, meet the portability condition, and with acceptable visual quality be capable of depicting objects which are less luminous, such as epidiascope pictures, i.e. non- transparent pictures illuminated by an ordinary light source from above. Extremely surprisingly, it has now been found possible to achieve said purpose by means of an objective of the kind apparent from the appended patent claims. Especially surprisingly is the fact that the objective only needs to contain a single lens element of generally concavo-convex O PI or plano-convex type, the convex surface of which is direct¬ ed towards the plane of the object. 3oth the surfaces of the lens will be aspherically corrected, preferably so that in annular areas concentric with the lens axis there will be a positive deviation in the vicinity of said axis, nega¬ tive deviation in an intermediate annular area and positive deviation in an outmost annular area, the deviation being related to the sphere best fitting the respective lens surface. The correction has continuous first and second order derivatives which are = 0 in the axial point. The aspherical correction of both lens surfaces can be simulta¬ neously calculated by means of methods already known in principle. The lens is also provided with a diaphragm arranged behind said lens at a distance therefrom at least corresponding to the aperture of the diaphragm. The optical system is preferably adapted for projecting the image on a display screen made with a generally negative curvature, which may -have hyperboloidal form with splaye -out edges. 3y means of apparatus thus executed there is achieved that the quality of the projected image, in contradiction to the prejudices of those skilled in the art, will be fully acceptable, thus accomplishing with said apparatus the purposes described above. The lens will suitably be made with a relatively short Gauss focal length of 230 mm, for example, whereby the longitudinal color error is reduced as well as projector apparatus equipped with this optical system being given relatively small dimensions, so that the portability requirement is achieved. If the lens is manufactured from a plastics such as methyl metha- crylate with a D-refractive index of 1.49166 and υ = 57.37, with a diameter of 100 mm and a thickness of 18 mm, the lens will have a weight of about 150 g. The optical system affords a magnification of about 6-10 times at a projection distance of between 1.7 and 2.7 m, and the field curvature problem is thereby reduced by the display screen being executed with a relatively severe negative ~~ > - curvature, and preferably given the form of a hyperboloid with splayed-out edges. This gives, inter alia, the ad¬ vantage that the slope of the screen in the peripheral portions is kept relatively small. By the stated placing of the diaphragm, there is achieved that the variation on the object side of the field angle will be comparatively small. In the preferred embodiment, in which the diaphragm aperture is 45 mm, the diaphragm should lie about 50 mm behind the lens, although at most about 120 mm behind the lens. By selecting about 70 mm to- be the distance., there is afforded space between the lens and the diaphragm for a supplementary objective therebetween. The supplementary objective can be provided with a holder for film material carrying scaled-down in- formation, e.g. a microfiche or 24 x 36 mm transparencies, oτ the like, the supplementary objective suitably being adapted for providing, in combination with the objective, substantially the same picture size of the nominal object as for said information. A deflecting mirror, normally required when the objective is to be utilized in an over¬ head projector, can suitably be placed at the diaphragm. The inventive objective suitably has a Gauss focal length < 400 mm. The invention will now be described in detail in the form of an example, while referring to the accompany¬ ing drawing. BRIEF DESCRIPTION OF DRAWING Fig. 1 is a section through an apparatus in accord- ance with the invention, certain edge rays being indicat¬ ed. Fig. 2 is a section through the optical system with diaphragm. Fig. 3 illustrates the transmission through the optical system. Fig. 4 illustrates a suitable filter for adjusting the transmission to visual sensitivity (indicated in Fig. 5). Figs. 5a-5c illustrate the aber¬ rations of the optical system for certain wavelengts at C PI •s- some field points. Fig. 6a-6c illustrate the meridonal and sagittal aberration of the optical system for a wavelength at some other field points. Fig. 7a-7f illustrate the modulation of the optical system at different field points. 5 PREFERRED EMBODIMENT An optical system in accordance with the invention includes a single, generally concavo-convex lens 1.provided with a diaphragm .2, the optical system formed by lens and diaphragm being intended to project an image on a display 0 screen 3 with generally negative curvature (see Fig. 1). For the particular purpose of utilizing the invent¬ ive apparatus in an overhead projector, the apparatus is formed with the following prerequisites and data. Object: 190 x 250 mm 5 Gaussian focal length of lens 230 mm Lens material: methyl methacrylate . with D-refractive index 1.49166 and v = 57:37 Lens diameter: 100 mm 0 Front surface of lens; best suited sphere with a radius of 103.804 mm, the aspherical correction being carried out in accordance with the following table. Lens front surface Semi-aperture Deviation from Deviation rrom Slope ox surrace 5 best suited tangent piane shpere (mm) (mm) (mm) degrees 0.00000 0.00000 0.00000 0.00000 1.00000 .00026 .00485 .55504 0 2.00000 .00095 .01933 1.10239 3.00000 .00193 .04330 1.64211 4.00000 .00307 .07662 2 .17428 5.00000 .00424 .11919 2.69393 6.00000 .00530 .17087 3.21630 S 7.00000 .00613 .23154 5.72633 8.00000 .00658 .30108 4.22920 9.00000 .00653 .37940 4.72500 10.00000 .00584 .46-656 5.21386 11.00000 .00442 .56189 5.70160 12.00000 .00251 .66607 6.19401 13.00000 -.00043 .77899 6.69117 14.00000 -.00372 .90074 7.19515 OMPI Semi-aperture Deviation from Deviation from Slope of surface best suited tangent plane sphere (mm) (mm) (mm) degrees 15.00000 -.00749 1.05144 7.70000 16.00000 -.01167 1.17119 8.21181 17.00000 -.01618 1.32010 3.72865 18.00000 -.02095 1.47829 9.2S051 19.00000 -.02591 1.64588 9.77752 20.00000 -.03098 1.82298 10.30970 21.00000 -.03607 2.00974 10.84872 22.00000 -.04106 2.20633 11.39620 23.00000 -.04582 2.41294 11.95216 24.00000 -.05020 2.62976 12.51659 25.00000 -.05408 2.85700 13.08948 26.00000 -.05730 3.09486 13.67081 27.00000 -.05975 3.34354 14.26055 28.00000 -.06126 3.60326 14.85867 29.00000 -.06171 3.87423 15.46513 30.00000 -.06095 4.15667 16.07987 31.00000 -.05890 4.45076 16.69456 32.00000 -.05566 4.75647 17.30107 33.00000 -.05141 5.07371 17.89966 34.00000 -.04633 5.40241 18.49062 55.00000 -.04057 5.74251 19.07424 36.00000 -.03430 . • 6.09395 19.65081 37.00000 -.02769 6.45666 20.22066 38.00000 -.02090 6.85061 20.78410 • 39.00000 -.01410 7.21574 21.34143 40.00000 -.00743 7.61203 21.89515 41.00000 -.00114 8.01938 22.42867 42.00000 .00426 8.43739 22.95793 43.00000 .00816 8.86562 23.42181 44.00000 .00998 9.30363 23.88119 45.00000 .00913 9.75097 24.31693 46.00000 .00501 10.20725 24.72993 47.00000 -.00295 10.67200 25.12105 48.00000 -.01534 11.14487 25.49118 49.00000 -.03274 11.62544 25.84121 50.00000 -.05571 12.11336 26.17204 The back surface of the lens : best suited sphere with a radius of 1651 . 582 mm , the aspherical correction being carried out with the following data : OMPI Lens back surface Semi-aperture Deviation rrom Deviation from Slope of surface best suited tangent plane sphere ^ (mm) (mm) (mm. degrees 0.00000 0.00000 0.00000 0.00000 1.00000 .00017 .00047 .05250 2.00000 .00058 .00179 .09750 3.00000 .00110 .00383 .13500 4.00000 .00161 .00646 .16500 5.00000 .00198 .00954 .13749 6.00000 .00206 .01296 .20249 7.00000 .00173 .01657 .20999 8.00000 .00087 .02025 .20999 9.00000 -.00067 .02386 .20248 10.00000 -.00300 .02727 .18748 11.00000 -.00623 .03040 .17254 12.00000 -.01026 .03334 .16521 13.00000 -.01495 .03621 .16549 14.00000 -.02018 .03916 .17338 15.00000 -.02581 .04231 .18888 16.00000 -.03171 .04580 .21200 17.00000 -.03774 .04975 .24273 18.00000 -.04378 .05431 .28107 19.00000 -.04963 .05961 .32703 20.00000 -.05533 .06577 .38060 21.00000 -.06058 .07293 .44093 22.00000 -.06533 .08120 .50717 23.00000 -.06949 .09067 .57933 24.00000 -.07293 - .10146 .65739 25.00000 -.07557 .11365 .74137 26.00000 -.07729 .12737 .85125 27.00000 -.07801 .14271 .92705 23.00000 -.07760 .15977 1.02875 29.00000 -.07597 .17865 1.13635 30.00000 -.07302 .19947 1.24986 31.00000 -.06868 .22227 1.36065 32.00000 -.06312 .24691 1.46009 33.00000 -.05653 .27319 1.54318 34.00000 -.04910 .50090 1.62494 35.00000 -.04104 .32986 1.69035 36.00000 -.03254 .55986 1.74442 37.00000 -.02380 .39070 1.78716 38.00000 -.01502 .42219 1.31357 39.00000 -.00640 .45414 1.83364 40.00000 .00188 .48653 1.84733 41.00000 .00953 .51352 1.33409 42.00000 .01606 .55013 1.78805 43.00000 .02090 .58076 1.70926 44.00000 .02347 .60968 1.59771 45.00000 .02319 .63635 1.45539 46.00000 .01951 .66023 1.27650 ώemi-aperture Deviat ion from Deviat ion rrom Sl ope or surrace best suited tangent p l ane sphere 47 . 00000 .01183 68072 ■ 1.06642 48 . 00000 -.00039 69727 .32374 49 . 00000 -.01775 70929 .54825 50 . 00000 -.04081 71621 .23997 Diaphragm: semi-aperture 22.41 mm (corresponding to initial iris) , the distance between the back surface of the lens and diaphragm being substantially 73 mm. Lens thickness: 18 mm. The optical system thus constructed affords a magni¬ fication of about 6 x with the object distance of 1645 mm and a magnification of about 10 x for the object distance of 2700 mm. For a magnification of 6 x (see Fig. 1) the display screen can be carried out' with a best suited sphere having a radius of -1200 mm, relative to which the surface of the screen has the following data: Screen surface emi-ape rture Deviat ion from Deviat ion r rom Slope o f surface best su ited tangent p lane sphere (mm) (mm) (mm) degrees 0.00000 0.00000 0.00000 0.00000 25.00000 -.26050 -.52074 -2.38512 50.00000 -1.03977 -2.08189 -4.75707 75.00000 -2.33415 -4.68020 -7.10306 100.00000 -4.13636 -8.31029 -9.41102 125.00000 -6.43651 -12.96468 -11.66984 150.00000 -9.22190 -18.63381 -15.869S8 175.00000 -12.47705 -25.30604 -16.00158 200.00000 -16.18360 -32.96764 -13.05843 225.00000 -20.32030 -41.60276 -20.05398 250.00000 -24.86280 -51.19333 -21.92315 275.00000 -29.78353 -61.71888 -25.72183 300.00000 -35.05139 -73.15637 -25.42659 325.00000 -40.63143 -35.47991 -27.03453 550.00000 -46.48435 -98.66030 -23.54302 375.00000 -52.56601 -112.66467 -29.94942 400.00000 -58.82668 -127.45580 -31.25087 425.00000 -65.21023 -142.99146 -52.44403 450.00000 -71.65341 -159.22360 -53.52480 475.00000 • -78.08423 -176.09734 -34.48805 500.00000 -84.42118 4 -193.54992 -55.32725 525.00000 -90.57152 -211.50938 -56.03416 550.00000 -96.42968 -229.39317 -36.59830 575.00000 -101.87535 -248.60656 -37.00638 600.00000 -106.77140 -267.54084 -37.24155 625.00000 -110.96154 -286.57140 -37.23238 650.00000 -114.26767 -505.55553 -37.10150 675.00000 -116.48696 -324.33012 -36.66376 700.00000 -117.38862 -342.70907 -35.92373 725.00000 -116.71021 -360.48051 -34.32255 750.00000 -114.15365 -377.40381 -53.28282 775.00000 -109.33062 -393.20637 -51.20549 800.00000 -102.00744 -407.S8008 -23.45240 82S.00000 -91.59915 -420.17771 -24.85972 350.00000 -77.66278 -430.60887 -20.21604 875.00000 -59.65938 -438.43577 -14.28647 900.00000 -36.89445 -443.16881 -6.86307 Tolerances The tolerance for a parallel displacement of both the axes of symmetry of the lens is 0.157 mm. The tolerance for a relative tilt of these axes is 0.5°. Maximum permitted axial deviation from the desired surface is -.597 E-01 and 0.737 E-02 for the back lens surface and -0.507 E-03 and 0.371 E-01 for the front sur¬ face. The maximum permitted deviation in the derivatives of the surfaces converted to degrees for the back lens surface is -0.007168 and 0.001154° and for the front surface -0.000091 and 0.004412°. It has been found that the lens is relatively insen- sitive to deformation of the type brought about by press¬ ing on the centre of the lens. Both surfaces of the lens element are suitably coated with an 'anti-reflex coating of the single layer type. Single layer deposits of the type MGF2 with a thickness of 103.26 nono eter and a refractive index of 1.38000 can be utilized. Fig. 3 illustrates the resulting transmission of the optical system as a function of the wavelength. An optical system executed according to the explicit embodiment example has the following distorsion: Field point Distorsion Relative di±±erential radial enlargement rro object to image 0/0 0 1 0/116 -16.7 0.69 0/157 -18.0 0.96 Distorsion and relative differential enlargement have been defined in a direction normal to the optical axis. The field points relate to abscissae and ordinates in image points normalized to image width 200 mm. The color enlargement error is less than in the modified triplet according to the Swedish patent specific- ation 7407134-1 , and the vignettement is ' about 65. in the corner. Fig. 1 is an axial section through an apparatus in accordance with the invention, edge rays for _a the middle of the side edge, b_ middle of the upper-lower edge, and c corner of the object 4 (190 x 250 mm) being shown. Fig. 2 is the objective portion to a larger scale of an in¬ ventive apparatus, the marginal rays for the corners of the object £ and the middle of the upper edge b_ of the object being indicated. Fig. 3 illustrates (in a •■ transmission T/wave length u ' graph) the transmission factor JL of the optical system when the object is illuminated by a lamp at the temperature of 5200° Kelvin (halogen lamp) as appreciated by the human eye. The spectrum sensitivity of the human eye k is also illustrated in Fig. 5. In Fig. 5 there is furthermore illustrated the transmission factor m for the optical system when it has been corrected by a short-pass filter of the type illustrated in Fig. 4, (therein T shows transmission an υ wavelength in nm) , whereby the result¬ ing transmission factor ' m of the optical system will be substantially symmetrical to curve . Figs. 5a-5c, 6a-6c and 7a-7f illustrate the properties of _ the system at different field points, which relate to abscissae and ordinates in image points normalized to image width 200 (mm) . In Fig. 5 the following symbols are used: 7 which refers to meredional aberration, at .5700 wavelength i which refers to meredional aberration at ' wavelength ■000 Δ which refers to meredional aberration at wavelength 6500 -. which refers to meredional aberration at wavelength ,5500 x which refers to -meredional aberration at wawelength 6100 which refers to sagittal aberration at wavelength 5700 OMPI In Fig. 6 the following symbols are used: 7 which refers to meredional aberration wavelength .5700 o which refers to sagittal aberration at wavelength .5700 In Fig. 7 the following symbols are used: 7 MTF at orientation angle 0.0 o MTF at orientation angle 90.0 Δ real part of OTF at orientation angle 90.0. In Fig. 5a-5c and Fig. 6a-6c the abscissa indicates relative aperture and the ordinate indicates the aberrat¬ ion in mm. In Fig. 7a-7f the abscissa indicates lines per mm and the ordinate indicates the modulation. In Figs. 5-7 the graphs have been normalized to the 250 x 190 mm object. The calculated MTF graphs in the peripheral parts of the image are primarily a mirroring of the color enlarge¬ ment error in a radial direction (90°) . A considerably better result would be obtained monochromatically. It will be seen that the MTF almost entirely coincides with the real portion of the OTF, and the conclusion can thus be drawn that the phase does not affect the information con¬ tent of the -image to any notable degree. Ξ OMPI

Claims: CLAIMS 1. An optical system for a projector apparatus which is preferably adapted for projecting an image on a display screen with a generally negative curvature, characterized in that the system includes a lens with a generally con¬ vex surface oriented towards the object plane and with a substantially planar, preferably generally concave surface, both surfaces of the lens being aspherically corrected, and in that the lens is provided with a diaphragm arranged behind the lens at a distance therefrom corresponding at least to the aperture of said diaphragm. 2. An optical system as claimed in claim 1, cha¬ racterized in that the aspherical correction is carried out so that in annular areas concentric with the lens axis the * lens surfaces have positive deviation in the vicinity of said axis, then negative deviation, and outmost posi¬ tive deviation, said deviations being related to the best suited sphere for the respective lens surface. 5. An optical system as claimed in claim 2, characterized in that the best suited sphere for the back and front surfaces of the lens have a radius of the order of magnitude +110 mm and +1650 mm, respectively, in that the lens has an aperture preferably attaining about 1O0 mm, the diaphragm having. an aperture of about 45 mm and being arranged about 70 mm in front of the front lens surface said system being suited to projecting an object with a format of the order of magnitude of 190 x 250 mm with an enlargement of about 6 to 3 times. 4. An optical system as claimed in claim 3, characterized in that the best suited sphere for the back and front surfaces of the lens has radii of 108.804 mm and 1651.582 mm, respectively. 5. An optical system as claimed in claim 3 or 4, characterized in that the distance between the front surface of the lens and the diaphragm is substantially 73 mm, and that the distance between the front and back OMPI surfaces of the lens is preferably 18 mm. 6. An optical system as claimed in any one of the preceding claims, characterized in that the lens consists of methyl methacrylate with a D-refractive index of 1.49166 and - = S7.37. 7. An optical system as claimed in claim 1, characterized in that the screen has the form of a hyper- boloid with ≤played-out edges. 8. An optical system as claimed in any one of claims "4-7, characterized in that the surfaces of the lens have the following numerical data: Lens front surface Semi-aperture Deviation from Deviation rrom Slope or surrace best suited tangent plane shpere (mm) (mm) (mm) degrees 0.00000 0.00000 0.00000 0.00000 1.00000 - .00026 .00485 .55504 2.00000 .00095 .01955 1.10259 ' 5.00000 .00195 .04550 1.64211 4.00000 .00507 .07662 2.17428 5.00000 .00424 . .11919 2.69898 6.00000 .00550 .17087 5.21650 7.00000 .00615 .25154 5.72655 8.00000 .00658 .50108 4.22920 -9.00000 .00655 .57940 4.72500 10.00000 .00584 .46656 5.21586 11.00000 .00442 .56189 5.70160 12.00000 .00251 .66607 6.19401 15.00000 -.00045 .77899 6.69117 14.00000 -.00572 .90074 7.19515 15.00000 -.00749 1.05144 7.70000 16.00000 -.01167 1.17119 8.21181 17.00000 -.01618 1.52010 8.72365 13.00000 -.02095 1.47829 9.25051 19.00000 -.02591 1.64538 9.77752 20.00000 -.05098 1.32298 10.50970 21.00000 -.05607 2.00974 10.84372 22.00000 -.04106 2.20655 11.59620 25 * 00000 -.04582 2.41294 11.95216 ' 24.00000 -.05020 2.62976 12.51659 25.00000 -.05408 2.85700 15.08948 26.00000 -.05750 5.09486 15.67081 27.00000 -.05975 5.54554 14.26055 ^^ 3.E- CMP! Semi-aperture Deviat ion from Deviat ion from Sl ope o f surfac e best su it ed tangent pl ane snhere (mm) (mm) (mm) degrees 28.00000 -.06126 3.60326 14.85367 29.00000 -.06171 3.87423 15.46515 30.00000 -.06095 4.15667 16.07987 31.00000 -.05890 4.45076 16.69456 32.00000 -.05566 4.75647 17.50107 35.00000 -.05141 5.07371 17.89966 54.00000 -.04635 5.40241 18.49062 35.00000 -.04057 5.74251 19.07424 36.00000 -.05450 6.09395 19.65081 37.00000 -.02769 6.45666 20.22066 38.00000 -.02090 6.83061 20.78410 39.00000 -.01410 7.21574 21.54148 40.00000 -.00743 7.61203 21.89315 41.00000 -.00114 8.01938 22.42367 42.00000 .00426 8.43759 22.93793 43.00000 .00816 8.36562 23.42181 44.00000 .00998 9.50565 23.88119 45.00000 .00915 9.75097 24.51693 46.00000 .00501 10.20725 24.72993 47.00000 -.00295 10.6720.0 25.12105 48.00000 -.01554 11.14487 25.49118 - 49.00000 -.05274 11.62544 25.84121 50.00000 -.05571 12.11556 26.17204 Lens back surface Semi-aperture Deviation irom Deviation from Slope of surface best suited tangent plane sphere - _# (mm) (mm) (mm) degrees 0.00000 0.00000 0.00000 0.00000 1.00000 .00017 .00047 .05250 2.00000 .00058 .00179 .09750 3.00000 .00110 .00585 .15500 4.00000 .00161 .00646 .16500 5.00000 .00198 .00954 .18749 6.00000 .00206 .01296 .20249 7.00000 .00175 .01657 .20999 8.00000 .00087 .02025 .20999 9.00000 -.00067 .02586 .20243 10.00000 -.00500 .02727 .18748 11.00000 -.00625 .05040 .17254 12.00000 -.01026 .05554 .16521 15.00000 -.01495 .05621 .16549 14.00000 -.02018 .05916 .17358 15.00000 -.02581 .04251 .1S888 CMPI Semi-aperture Deviation from Deviation from Slope of su:riacc best suited tangent plane sphere 16.00000 -.05171 .04580 .21200 17.00000 -.05774 .04975 .24275 18.00000 -.04578 .05451 .23107 19.00000 -.04968 .05961 .52705 20.00000 -.05555 .06577 .58060 21.00000 -.06058 .07295 .44095 22.00000 -.06555 .08120 .50717 25.00000 -.06949 .09067 .57955 24.00000 -.07295 .10146 .65759 25.00000 -.07557 .11565 .74157 26.00000 -.07729 .12757 .85125 27.00000 -.07801 .14271 .92705 28.00000 -.07760 .15977 1.02375 29.00000 -.07597 .17865 1.15655 50.00000 -.07502 .19947 1.24986 51.00000 -.06868 .22227 1.56065 52.00000 -.06512 .24691 1.46009 55.00000 -.05655 .27519 1.54818 54.00000 -.04910 .50090 1.62494 55.00000 -.04104 .52986 1.69055 56.00000 -.05254 .55986 1.74442 57.00000 -.02580 .59070 1.78716 58.00000 -.01502 .42219 1.81857- 59.00000 -.00640 .45414 1.85864 40.00000 .00188 .48655 1.84758 41.00000 .00955 . " 51852 1.85409 42.00000 .01606 .55018 1.78805 45.00000 .02090 .58076 1.70926 44.00000 .02547 .60968 1.59771 45.00000 .02519 .65655 1.45559 * # 46.00000 .01951 .66025 1.27650 47.00000 .01185 .63072 1.06642 48.00000 -.00059 .69727 .82574 49.00000 -.01775 .70929 .54825 50.00000 -.04081 .71621 .25997 • -ξ " _ _l_- O PI 9. An optical system as claimed in claim 8, characterized in that for the enlargement of 6 x, the best suited sphere for the screen has the radius -1200 mm and that the numerical data for the surface of the screen are as follows: Screen surface Semi-aperture Deviation from Deviation from Slope of sur±ace " best suited tangent plane sphere (mm) (mm) (mm) degrees 0.00000 0.00000 0.00000 0.00000 25.00000 -.26050 -.52074 -2.38512 50.00000 -1.05977 -2.08189 -4.75707 75.00000 -2.55415 -4.68020 -7.10306 100.00000 -4.15656 -8.5-029 -9.41102 125.00000 -6.45651 -12.96468 -11.66984 150.00000 -9.22190 -18.65581 -15.86958 175.00000 -12.47705 -25.50604 -16.00158 200.00000 -16.13360 -52.96764 -IS.05843 225.00000 -20.32050 -41.60276 -20.05598 250.00000 -24.86280 -51.19555 -21.92515 275.00000 -29.78555 -61.71883 -25.72185 500.00000 -55.05159 -75.15657 -25.42659 525.00000 -40.65145 -85.47991 -27.05455 350.00000 -46.48455 -98.66050 -23.54502 575.00000 -52.56601 -112.66467 -29.94942 400.00000 -58.82668 -127.45530 -51.25087 425.00000 -65.21028 -142.99146 -52.44405 450.00000 -71.65541 -159.22560 -55.52480 4.75.00000 -78.08425 -176.09754 -54.48305 5D0.00000 -84.42118 -193.54992 -55.52725 525.00000 -90.57152 -211.50938 -56.05416 550.00000 -96.42968 -229.89317 -56.59850 575.00000 -101.87555 -248.60656 -57.00658 600.00000 -106.77140 -267.54084 -57.24155 625.00000 -110.96154 -286.57140 -57.28238 650.00000 -114.26767 -305.55553 -57.10150 675.00000 -116.43696 -524.35012 -56.66576 700.00000 -117.5S862 -342.70907 -35.92373 725.00000 -116.71021 -560.48051 -54.82255 750.00000 -114.15565 -377.40581 -55.28282 775.00000 -109.58062 -595.20657 -51.20549 80Tj.00000 -102.00744 -407.53008 -28.45240 825.00000 -91.59915 -420.17771 -24.S5972 850.00000 -77.66278 -430.60887 -20.21604 375.00000 -59.63938 -458.43577 -14.23647 900.00000 -36.89445 -443.16831 -6.86507 ;?.__. CMPI

Inventors: ASTEROE U
Applicants: ASTEROE U, OPTIK INNOVATION AB OIAB
Application year: 1981
Main classification: G02B27
IPC codes: G02B3, G02B13, G02B27