text: the surface of an aspheric lens can be described in general with the aid of the following formula : z = cy 2 1 + 1 - ( 1 + k ) · c 2 ⁢ y 2 + dy 4 + ey 6 + fy 8 + gy 10 , z specifies the sagitta ( in mm ) with reference to the plane perpendicular to the axis , that is to say the direction of the deviation from the plane perpendicular to the optical axis , that is say in the direction of the optical axis . c specifies the so - called apex curvature . the apex curvature vanishes for a plane - parallel plate . it serves to describe the curvature of a convex or concave lens surface . y specifies the distance from the optical axis ( in mm ). y is a radial coordinate k specifies the so - called cone constant , which plays no role here since k and c vanish . d , e , f , g represent the so - called aspheric coefficients , which are the coefficients of a polynomial expansion of the function for describing the surface of the asphere . the aspheric coefficients are specified in each case for the following exemplary embodiments . fig2 shows the diagrammatic design of the projection lens in accordance with the first exemplary embodiment . this is a projection lens having a focal length of 60 mm and a relative aperture of 1 : 1 . 7 . in the illustration in accordance with fig2 , the screen or the enlarged image is located on the left , and the object or the film on the right . the projection lens in accordance with the first exemplary embodiment comprises the following elements in the sequence from the enlarged image to the object , that is to say from the left to right : a second positive lens in the form of a meniscus lens 16 , a third negative lens in the form of a biconcave lens 18 , a fourth negative lens in the form of a biconcave lens 20 , a fifth positive lens in the form of a meniscus lens 22 , and a sixth positive lens in the form of a biconvex lens 24 . the optical axis is denoted by 26 . the precise data for the individual surfaces of the optical elements are to be found in the following table , together with the respectively associated reference numerals . v e = n e - 1 n f ′ - n c ′ , where n f , is the refractive index for 480 nm , and n c , is the refractive index for 643 . 8 nm . as a rule , only one plate side , preferably the outer plate side 28 , is aspherized , and not the inner plate side 30 . if the film to be imaged passes into the illuminating device from where it is projected onto the screen , it heats up under the intensive illumination . it warps when heated , to be precise the centre of the film is warped in the direction of the illuminating device , and the edges of the film are warped in the direction of the screen . the corners of the individual images are thereby moved forward as a rule by approximately 100 – 200 μm in the direction of the screen by comparison with the centre , typically by approximately 140 μm . in some projectors , the film is deliberately guided in a specified cambered shape for the purpose of better reproducibility of the camber . this is taken into account when designing the projection lens . the projection lens is optimized for imaging the cambered film . the resolution and the image - forming properties of the projection lens are explained in more detail below in accordance with the first exemplary embodiment and with the aid of a few figures . fig3 shows the resolution of the projection lens in accordance with the first exemplary embodiment . the resolution was calculated for a colour weighting which corresponds to the mean sensitivity of the human eye . three examples were calculated : the upper two curves belong to the example with a spatial frequency of 20 pairs of lines per mm ( lp / mm ), the middle two curves belong to 40 lp / mm , and the lower two curves to 80 lp / mm . the continuous line shows in each case the resolution of radially running pairs of lines , and the dashed line the resolution of tangentially running pairs of lines . the x - axis indicates the relative deviation from the centre of the image to be enlarged . the modulation transfer function is illustrated on the y - axis for a relative aperture of 1 : 1 . 7 . the imaging was carried out virtually to infinity . the resolution of the projection lens in accordance with the first exemplary embodiment corresponds to the resolution of very good projection lenses . fig4 shows the resolution of the projection lens in accordance with the first exemplary embodiment for a partially closed diaphragm ( stop number 2 . 4 ). otherwise , fig4 corresponds to fig3 . fig5 shows the relative intensity of illumination of the edges of the enlarged image compared with the centre for the projection lens in accordance with the first exemplary embodiment . the x - axis corresponds to the x - axis in accordance with fig3 . the continuous line was calculated for a stop number of 1 . 7 , the dashed line for 2 . 0 , and the dotted line for 2 . 4 . fig6 shows the distortion for the projection lens in accordance with the first exemplary embodiment , in % of deviation from the ideal image format . a minimum cushion - shaped distortion which is not , however , perceptible to a viewer in the cinema , is in evidence . fig7 shows the diagrammatic design of the projection lens in accordance with the second exemplary embodiment . this is a projection lens having a focal length of 82 . 5 mm and a relative aperture of 1 : 1 . 7 . in the illustration in accordance with fig7 , once again the screen or the enlarged image is located on the left , and the object or the film on the right . the projection lens in accordance with the second exemplary embodiment comprises the same optical elements as the projection lens in accordance with the first exemplary embodiment : a second positive lens in the form of a meniscus lens 62 , a third negative lens in the form of a biconcave lens 64 , a fourth negative lens in the form of a biconcave lens 66 , a fifth positive lens in the form of a meniscus lens 68 , and a sixth positive lens in the form of a biconvex lens 70 . the optical axis is denoted by 26 . the precise data for the individual surfaces of the optical elements are to be found in the following table , together with the respectively associated reference numerals . fig8 shows the resolution of the projection lens in accordance with the second exemplary embodiment , for stop number 1 . 7 ; fig9 shows the resolution of the projection lens in accordance with the second exemplary embodiment , for stop number 2 . 4 ; fig1 shows the relative intensity of illumination ( vignetting ) in the image field compared with the centre of the projection lens in accordance with the second exemplary embodiment ; and fig1 shows the distortion for the projection lens in accordance with the second exemplary embodiment . they correspond to fig3 to 6 for the first exemplary embodiment . a slight improvement in the image - forming properties , as was possible to expect given an enlargement of the focal length from 60 mm to 82 . 5 mm , can be seen .