referring to fig1 there is shown a camera 100 including a zoom lens 120 . the camera 100 includes a camera housing 110 in which photographic film 130 is supported in a suitable location so that an image is produced by the zoom lens 120 on the film . camera 100 includes other known structures or means for advancing the film and a shutter for enabling an exposure of the film to capture an image of a scene to be photographed . the preferred embodiment of the zoom lens according to the invention is shown in fig2 and is illustrated by an example set forth in table 1 . in the drawing , the surfaces r of the zoom lens 120 are numbered by subscripts from the front or object side of the lens to the rear or image side of the lens . the thickness of the lens elements and the spacings between lens elements , including the zooming space a , are located from front to rear ( i . e ., object to image ). in the table , surfaces and thicknesses are listed on the same line as the surface preceding the thickness or spacing as the case may be . all indexes of refraction n e are for the green mercury e line of the spectrum at a wavelength λ e of 5461 å . v is the abbe number of the lens elements . this embodiment contains two optical units , specified as u 1 and u 2 in the drawing . lens components u 1a and u 1b make up the first optical unit u 1 , and lens components u 2a and u 2b make up the second optical unit u 2 . lens component u 1a of the preferred embodiment is a weak lens component . by &# 34 ; weak &# 34 ; it is meant that the power of a lens component u 1a or the lens element e 1 is smaller than the power of the zoom lens in the wide angle mode so that the absolute value of the ratio of power , k 1a , of the lens component u 1a to the power , k w , of the zoom lens system in the wide angle mode is about 0 . 6 or less or ## equ3 ## in this embodiment , the power of the front - most lens component u 1a is negative and this lens component is a single meniscus lens element e 1 that has its concave surface oriented towards the object space . it is preferred that the frontmost lens element has one , and more preferably , two aspheric surfaces . accordingly , in this embodiment both surfaces of lens element e 1 are aspheric . the second lens component u 1b , of the first optical unit u 1 , is positive . it is contemplated that it may contain one or more lens elements . in this embodiment , it is a single positive lens element e 2 which is biconvex . it is preferred that the ratio of the focal length f 1b of the second lens component u 1b to the focal length f 1a of the first lens component u 1a be about equal to or less than 0 . 4 . that is ## equ4 ## where k 1a is the power of the first optical component u 1a and k 1b is the power of the second optical component u 1b . it is even more preferable that this ratio it be less than 0 . 35 . in this embodiment ## equ5 ## it should be noted that the stronger the front lens element , the more sensitive the optical system would be to the decenter of this lens element . that is , if the lens component u 1a ( or the lens element e 1 ) does not satisfy the above power ratio inequalities the zoom lens 120 is more likely to become sensitive to tilt or decenter . additional conditions for minimizing aspheric decenter sensitivity will be discussed further down in the specification . the index of refraction n 1 of the first lens element e 1 can be equal to or greater than 1 . 65 . the index of refraction n 2 of the second lens element e 2 can be equal to or greater than 1 . 52 . despite the fact that the indices of the first two lens elements are larger than 1 . 65 and 1 . 52 , we do not have a petzval problem or large astigmatism . the aperture stop as is positioned behind the second lens component u 1b . the second optical unit u 2 is negative in power . its movement provides most of the change in focal length of the lens during zooming . in this embodiment the optical unit u 2 consists of a first positive lens component u 2a corresponding to lens element e 3 and a second negative lens component u 2b corresponding to lens element e 4 . furthermore , in this embodiment , each of these lens components is a singlet . the negative power of the front lens element e 1 helps create an inverted telephoto effect of the front positive group . this effect creates more space between two zooming groups ( or optical units ) u 1 and u 2 and helps to expand a zooming range to 3 × or more . the overall zoom lens system of the preferred embodiment tends toward a telephoto - type system which facilitates net compactness , and in fact , at the long focal length mode , it is truly a telephoto lens with a 0 . 95 telephoto ratio . furthermore , when ew is defined as the nodal point separation when the zoom lens operates at the wide angle position and when et is defined as the nodal point separation when the zoom lens operates at the telephoto position , the preferred value for the ratio ew / et is about equal to or less than 1 . 7 . this value for ew / et helps to maintain the large zoom ratio such as 3 ×, for example . if this ratio is allowed to become significantly larger than 1 . 7 , the airspace a becomes too small to achieve the large zoom range and , in addition , the location of the aperture stop as and the location of the third lens component u 2a interfere with each other . note that the zoom lens of the preferred embodiment is corrected across a zoom range of 3 × with an effective aperture that varies from approximately f / 6 . 3 to f / 9 . 3 . this range of relative apertures for a 3 × four element zoom lens suitable as an objective or taking lens for a 35 mm camera is quite remarkable . table 1 provides specific parameters for the preferred embodiment illustrated in fig1 . the accompanying notes 1 - 3 provide further parameters as well as mtf values for the zoom lens of the preferred embodiment . table 1__________________________________________________________________________ index clear axial and vsurf aper . beam radius thickness number__________________________________________________________________________1 9 . 52 8 . 33 asphere 1 . 660 1 . 844 23 . 82 8 . 80 * 8 . 75 asphere 1 . 7363 9 . 37 9 . 37 66 . 4470 5 . 892 1 . 552 63 . 54 9 . 98 9 . 97 - 10 . 5410 1 . 327 8 . 90 8 . 90 diaphragm a5 14 . 79 8 . 25 asphere 3 . 517 1 . 590 30 . 96 15 . 61 7 . 55 asphere 2 . 4127 15 . 50 5 . 91 - 8 . 99500 1 . 254 1 . 804 39 . 68 21 . 22 * 5 . 85 - 99 . 5818__________________________________________________________________________ * do not exceed best n . p . n . p . x . p . x . p . ef bf ff focus a loc . diam . loc . diam . __________________________________________________________________________28 . 97 7 . 99 43 . 43 -. 09 10 . 567 6 . 74 4 . 28 - 8 . 74 2 . 4747 . 47 25 . 63 62 . 83 -. 50 5 . 048 6 . 74 6 . 07 - 6 . 75 4 . 1477 . 49 54 . 27 94 . 30 +. 11 1 . 700 6 . 74 8 . 50 5 . 16 6 . 52__________________________________________________________________________ lens stop rel . rel . coverageef length diam . aper . illum . ( half angle ) __________________________________________________________________________28 . 97 28 . 365 4 . 48 6 . 80 . 24 36 . 6 ° 47 . 47 22 . 846 6 . 35 7 . 90 . 47 24 . 3 ° 77 . 49 19 . 498 8 . 90 9 . 30 . 68 15 . 6 ° __________________________________________________________________________notes : 1 . aspheric equation : ## str1 ## surf . 1 c = - 0 . 0509762 d = - 0 . 2141500e - 03 e = 0 . 1045400e - 04 k = 0 . 0000000 f = - 0 . 3043000e - 06 g = 0 . 4268700e - 08surf . 2 c = - 0 . 0274527 d = - 0 . 4458200e - 04 e = 0 . 1198700e - 04 k = 0 . 0000000 f = - 0 . 3061900e - 06 g = 0 . 5166000e - 08surf . 5 c = - 0 . 0136101 d = 0 . 1921700e - 04 e = 0 . 3149300e - 06 k = 0 . 0000000 f = 0 . 7225300e - 08 g = - 0 . 1619300e - 09surf . 6 d = - 0 . 0580744 d = 0 . 0000000e + 00 e = 0 . 0000000e + 00 k = 3 . 0955000 f = 0 . 0000000e + 00 g = 0 . 0000000e + 00__________________________________________________________________________2 . surfaces ef bf ff__________________________________________________________________________ 1 - 4 20 . 74 23 . 04 13 . 06 5 - 8 - 19 . 78 - 19 . 65 - 25 . 30__________________________________________________________________________3 . mtf data at best focus using wavelengths 546 . 1 , 486 . 1 , and656 . 3 with respective weights . 5 , . 15 , . 35 : per cent field ( sagittal / tangential ) ef l / mm axis 40 % 60 % 75 % 90 % awa__________________________________________________________________________28 . 9720 77 71 / 51 74 / 59 80 / 70 30 / 28 65 . 228 . 975 96 96 / 93 96 / 93 97 / 94 91 / 85 94 . 447 . 4720 76 71 / 57 72 / 51 76 / 70 66 / 32 65 . 347 . 475 96 96 / 93 96 / 92 96 / 95 95 / 88 94 . 577 . 4920 70 64 / 63 62 / 65 59 / 58 51 / 28 61 . 677 . 495 95 94 / 94 93 / 94 93 / 93 90 / 87 93 . 3__________________________________________________________________________ this embodiment has another very important property -- it can be manufactured with relative ease due to a designed decrease of the aspheric decenter sensitivity . since the sensitivity to aspheric decentering is reduced to a tolerable level , the centering of the lens components u 1b and u 2b ( corresponding to lens elements e 2 and e 4 , respectively ) can be achieved by normal manufacturing assembly without micro - manipulating the lens components or lens elements in their mount . decenter sensitivity needs to be reduced because decentering a sensitive lens element with an aspheric surface introduces an image plane tilt ( as well as other aberrations )-- which is obviously very undesirable . the preferred embodiment described above incorporates four aspheric surfaces on two lens elements to achieve the large focal length range and maintain the required high quality . these aspheres exhibit special characteristics that make them unique to the manufacturing process . they have greatly decreased decenter sensitivity . the first element e 1 is a negative meniscus biasphere with the surfaces bent away from the image plane . it is found that sensitivity of the first surface , which is an aspheric surface ( of the first lens element e 1 ) to aberrations such as spherical aberration , astigmatism and coma is reduced when where d is the fourth order aspheric coefficient and h is the size of the image diagonal covered by the lens . in this embodiment , alternatively , or in addition , in order to reduce aspheric decenter sensitivity of any surface in an aspheric lens element , such as the front lens element e 1 , the designer &# 39 ; s goal should be to reduce the amount of asphericity difference δ from best fit sphere to the most minimal value without compromising the image quality . in addition , reducing δ enhances the manufacturability of the surface , i . e . the surface becomes easier to test and less material has to be removed from the best fit sphere . if this is not done , decentering of a sensitive aspheric element is likely to create a large amount of image plane tilt . as shown in fig3 we define the radius ( rs ) of the best fit sphere by constructing a perpendicular to the slope of the aspheric surface asp at the clear aperture , the numerical value for rs is computed by measuring the distance to the point where that perpendicular intersects the optical axis oa . the distance from that point of intersection to the vertex of the aspheric surface is rv . the difference of rs and rv is a measurement of asphericity . the asphericity difference is defined as : where λ is the wavelength of the light used to measure the difference ( usually 0 . 00066 mm ), can be used to measure the amount of aspheric departure from a best fit sphere in wavelengths of light . ( care must be taken not to allow inflection points to be present at smaller apertures than the clear apertures .) the larger is δ , the more it effects aberrations . as δ becomes smaller , the less sensitive is the surface to aspheric decentering . hence , the lens component or lens element becomes less sensitive to aspheric decentering , especially image surface tilt . it is preferred that δ for surface 1 be & lt ; 50 waves ; δ for surface 2 be & lt ; 250 waves ; and δ for front surface of element 3 be & lt ; 100 waves . with this definition , the amount of waves of departure for the first lens element e 1 , surfaces 1 and 2 are less than 20 waves and 128 waves , respectively . and at the first surface of the third lens component δ is less than 41 waves . obviously , if the aspheric surfaces were reduced to spherical surfaces , the differences would be zero , but the benefit of aspheric profile for correcting lens aberrations will be lost as well . however , given the large asphericity of surface 2 of the first lens element e 1 , the sensitivity to decenters of this surface is about equal to the sensitivity of surface 1 of this element . more importantly , when these surfaces are modeled for aspheric decentering sensitivity , they are found to be within normal manufacturing capabilities . this invention has been described in detail with particular reference to a preferred embodiment thereof , but it will be understood that variations and modifications can be effected within the spirit and scope of the invention as described hereinabove and as defined in the appended claims . for example , the single front lens elements forming lens component u 1b could be divided into two or more very weak lens elements . although such minor changes are within the scope of the invention , they would detract from its simplicity . thus , a two lens element first unit is preferred . similarly , it may be possible to reduce the second lens unit to a single negative lens component or lens element by eliminating the positive lens element . however , this change would make it harder to achieve an expanded zoom ratio such as 3 ×. nevertheless , such changes are within the scope of the invention .