the present invention relates to the field of broadband imaging optics . more specifically , the present invention relates to optical systems that have good transmission and are well corrected for a spectrum ranging approximately from 315 nm in the ultraviolet through 1100 nm in the infrared . in the summary of the invention above , the descriptions below and in the claims , the phrase “ well - corrected ” in relation to the optical system of the present invention is understood in the art to mean that the collective effect of aberrations in the optical system are reduced to the point where the optical system is able to satisfactorily perform its particular imaging function . for example , in a photographic objective optical system according to the present invention , the modulation transfer function ( mtf ) is an excellent and widely accepted means by which to judge the state of optical correction . in particular , a photographic objective with a focal length greater than about 45 mm and an aperture between f / 2 . 8 and f / 5 . 6 intended for a format size of about 24 mm × 36 mm is considered to be well - corrected if the mtf values at 10 cycles / mm and 40 cycles / mm have the following characteristics : 1 ) the mtf at 10 cycles / mm is approximately 90 % or greater on - axis and is approximately 60 % or greater at image heights less than or equal to 20 mm off - axis ; and 2 ) the mtf at 40 cycles / mm is approximately 50 % or greater on - axis and is approximately 30 % or greater at image heights less than or equal to 20 mm off - axis . for wide angle and zoom photographic objectives the criteria for “ well - corrected ” are relaxed somewhat , especially in the outer parts of the image field . thus , a photographic objective with a focal length less than about 38 mm and an aperture between f / 2 . 8 and f / 5 . 6 intended for a format size of about 24 mm × 36 mm is considered to be well - corrected if the mtf values at 10 cycles / mm and 40 cycles / mm have the following characteristics : 1 ) the mtf at 10 cycles / mm is approximately 80 % or greater on - axis and is approximately 30 % or greater at image heights less than or equal to 20 mm off - axis ; and 2 ) the mtf at 40 cycles / mm is approximately 40 % or greater on - axis and is approximately 10 % or greater at image heights less than or equal to 20 mm off - axis . fig9 illustrates the visible waveband mtf performance of several commercial zeiss contax photographic lenses intended for the 24 mm × 36 mm format , including a 25 mm f / 2 . 8 wide - angle lens , a 60 mm f / 2 . 8 macro lens , a 300 mm f / 2 . 8 telephoto lens and a 100 mm - 300 mm f / 4 - f / 5 . 6 zoom lens set to 300 mm . these lenses can be considered to be well - corrected for their intended use as photographic lenses , and thus serve as examples to verify that the statements made above regarding optical correction for the 24 mm × 36 mm format are reasonable . the zeiss mtf vs . image height data is provided for spatial frequencies of 10 cycles / mm , 20 cycles / mm and 40 cycles / mm , which are the same frequencies used to analyze examples 1 - 6 in fig1 d , 2 d , 3 d , 4 d , 5 d , 6 d , and 6 e . the zeiss contax mtf data was downloaded from their website at the following web address : http :// www . zeiss . com / c12567a8003b58b9 / contents - frame / 8401a54783ed1154c12570f90049667d photographic objectives intended for formats larger than 24 mm × 36 mm are still best judged by mtf , but the exact criteria for “ well - corrected ” are adjusted appropriately because the image area is significantly larger . a common large format size for extremely high quality digital photography is 72 mm × 96 mm , which is the format size used by many digital scanning cameras such as betterlight . the image circle needed to cover this format is at least 125 mm , and preferably at least 150 mm in order to allow camera movements . large format digital scanning cameras are typically used for precision copying of flat artwork . lenses intended for use with 72 mm × 96 mm large format scanning cameras with a focal length greater than about 150 mm and an aperture between f / 5 . 6 and f / 11 are considered to be well - corrected if the mtf values at 7 . 5 cycles / mm and 30 cycles / mm have the following characteristics : 1 ) the mtf at 7 . 5 cycles / mm is approximately 85 % or greater on - axis and is approximately 40 % or greater at image heights less than or equal to 75 mm off - axis ; and 2 ) the mtf at 30 cycles / mm is approximately 50 % or greater on - axis and is approximately 10 % or greater at image heights less than or equal to 75 mm off - axis . photographic lenses properly designed for the uv - vis - ir waveband of 315 nm - 1100 nm should be well - corrected according to the above criteria when the mit is calculated over this whole waveband . in addition , such lenses should also be well corrected for the uv ( 315 nm - 400 nm ), vis ( 400 nm - 700 nm ) and ir ( 700 nm - 1100 nm ) sub - wavebands when the mtf is calculated at a common focal plane . the reason for this is that in some applications the whole 315 nm - 1100 nm waveband will be imaged at the same time , but in many applications the waveband will be split by the use of filters so that only discrete portions will be imaged . in one important scenario , the lens will be focused via a viewfinder in the visible spectrum , and then uv , vis , and ir pass band filters will be placed in the optical path to photograph an object in the uv , vis , and ir sub - wavebands . clearly in this scenario it is important that there be little or no focus shift in the three different sub - wavebands . in the case of telescope objectives mt is less useful and it is more appropriate to use peak - to - valley wavefront error ( ptvwfe ) as a criterion of optical correction . in particular , the on - axis ptvwfe of a well - corrected uv - vis - ir telescope objective scaled to a focal length of 1000 mm and / or an entrance pupil diameter of about 100 mm should be less than ¼ wavelength throughout a major portion of the visible spectrum from 435 nm to 656 nm ; it should be less than ⅛ wavelength at approximately 550 nm ; it should be less than ½ wavelength in the extreme portions of the visible spectrum from 400 nm to 435 nm and from 656 nm to 700 nm ; and it should be less than ½ wavelength outside the visible spectrum from 315 nm to 400 nm and from 700 nm to 1100 nm . all evaluations of ptvwfe must be done a common focal plane , i . e ., without any focus shift as the wavelength is varied . example 1 , which is a 60 mm focal length macro - focusing photographic objective for 35 mm format , is illustrated in fig1 a , which shows cross - sectional layouts at magnifications of 0 and − 0 . 5 ×. elements 101 , 103 , 104 , 105 , and 109 are made from caf2 ; elements 102 , 108 , 110 and 111 are made from fused silica ( sio2 ); and element 106 is made from ohara s - lal18 . element 107 is the aperture stop and 112 is the image plane . this design has a very high internal transmission throughout the 315 nm - 1100 nm waveband because there is just a single thin element ( 106 ) that is not caf2 or fused silica . the addition of a negative - powered s - lal18 element 106 enables the apochromatic color correction to be far superior in the near infrared to apochromats made solely from caf2 and sio2 . example 1 is composed from just three different optical materials , however despite this simplicity it has the combination of both good optical correction and good transparency over the entire 315 nm - 1100 nm waveband . variation of coma during focusing is eliminated by fixing a weakly powered two - element rear group 115 at a constant distance from the image plane while moving a high - powered front group 114 . negative - powered elements 101 and 111 , and the weak meniscus element 102 , located near the front and rear of the lens act to flatten the field . this is of critical importance in a lens using so much low index material such as caf2 . elements 108 and 109 are cemented together to form a doublet 113 in order to avoid tight tolerances and to minimize the number of air - glass interfaces that must be ar coated . this latter point is important because ar coatings for the very broad 315 nm - 1100 nm waveband pose special challenges . the focal length of example 1 is 60 mm , the aperture is f / 4 , the image format is 24 mm × 36 mm ( 43 . 26 mm diagonal ), the diagonal field of view ( fov ) is 39 . 6 degrees , and the total transmission of the on - axis ray bundle at 315 nm is 82 . 8 %. chromatic focus shift vs . wavelength at a 0 . 7 pupil zone is illustrated in fig1 b , and transmission vs . wavelength is illustrated in fig1 c . the fact that there are three crossings in fig1 b indicates that this design is a true apochromat . fig1 d illustrates the mtf of example 1 wide open at f / 4 for an object located at infinity . the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 1100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 1100 nm , respectively . fig1 d clearly demonstrates that example 1 is well corrected over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . example 2 , which is a 35 mm focal length wide - angle photographic objective for 35 mm format , is illustrated in fig2 a , which shows cross - sectional layouts at magnifications of 0 and − 0 . 25 ×. elements 206 , 211 and 212 are made from caf2 ; elements 202 and 204 are made from ohara s - fpl51 ; elements 203 , 205 , 207 and 213 are made from ohara s - fsl5 ; element 201 is made from ohara s - bal42 ; and element 210 is made from ohara s - lal14 . element 209 is the aperture stop and 214 is the image plane . in this design , s - fpl51 has been used as a substitute for caf2 in the larger elements 202 and 204 in order to reduce costs . however , this reduces the transmission at 315 nm . s - lal14 and s - bal42 are used as matching flints . separating the design into two independently moving groups 216 and 217 eliminates variation of lateral chromatic aberration and astigmatism during focusing . element 208 is a 5 mm thick filter with plane parallel surfaces made of s - bsl7 . it is anticipated that in ordinary use a lens corrected over the 315 nm to 1100 nm waveband will be used with a filter . a typical scenario involves the following steps : first the lens is focused in the visible waveband with a visible pass band filter in place ; next a visible band photograph is taken with the visible pass band filter in place ; next a series of photographs are taken in the uv and ir portions of the spectrum after removing the visible pass band filter and attaching appropriate uv or ir pass band filters . a widely accepted practice for attaching a filter to a lens is to screw it onto a threaded outer portion of the lens barrel . however , in the cases of wide - angle lenses in which the chief ray height is large at the front element and large aperture lenses in which the marginal ray height is large at the front element the required diameter of the filter becomes very large . in such cases it may be advantageous to adopt a different filter attachment approach in which the filter is screwed onto a mounting flange located near the back of the lens , or is inserted into a slot opening in the lens barrel , or is swung into place by rotating an internal filter wheel . the latter approach of using an internal filter wheel is particularly desirable because it allows for a very rapid changing of filters and it keeps the filters clean . example 2 is well suited to this approach because the filter is located near the aperture stop and its diameter is thus very small relative to what it would have to be if it were located in front of the lens . for ordinary lenses in which the filter is located in front it is not necessary to include the filter in the optical design because the filter has no effect on the aberrations for a distant object . for ordinary close focusing magnification ratios ranging down to 1 : 1 the effect of the filter is very small and can be neglected . however , if the filter is located between the front vertex of the lens and the image plane it must be included in the optical prescription because then it will have a noticeable effect on the optical aberrations . although example 2 is a reversed telephoto type design with a natural separation of positive and negative power , this was not sufficient to flatten the field . the addition of meniscus element 213 with a strong concave surface facing the image plane was found to be very effective in correcting residual field curvature . elements 210 and 211 are cemented together to form a doublet 215 in order to avoid tight tolerances and to minimize the number of ar coated surfaces . the focal length of example 2 is 35 mm , the aperture is f / 4 , the image format is 24 mm × 36 mm ( 43 . 26 mm diagonal ), the diagonal field of view ( fov ) is 63 . 4 degrees , and the total transmission of the on - axis ray bundle at 315 nm is 32 . 2 %. chromatic focus shift vs . wavelength at a 0 . 5 pupil zone is illustrated in fig2 b , and transmission vs . wavelength is illustrated in fig2 c . the fact that there are three crossings in fig2 b indicates that this design is a true apochromat . fig2 d illustrates the mtf of example 2 wide open at f / 4 for an object located at infinity . the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 1100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 1100 nm , respectively . fig2 d clearly demonstrates that example 2 is well corrected over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . the level of correction is in fact unusually high for a wide - angle photographic objective . example 3 , which is a 24 mm focal length wide - angle photographic objective for 35 mm format , is illustrated in fig3 a , which shows cross - sectional layouts at magnifications of 0 and − 0 . 15 ×. elements 301 , 305 and 314 are made from fused silica ( sio2 ); elements 303 , 304 , 306 , 308 , 312 and 313 are made from caf2 ; element 302 is made from ohara s - fpl51y ; element 309 is made from ohara s - fpl51 ; element 307 is made from ohara s - bal42 ; and element 311 is made from ohara s - lal18 . element 310 is the aperture stop and 315 is the image plane . example 3 bears a resemblance to example 2 , but in example 3 there is more extensive use of caf2 , sio2 and s - fpl51y . as a result , example 3 has a significantly higher transmission at 315 nm than example 2 . apochromatic performance has been achieved by pairing caf2 and s - fpl51y with s - lal18 and s - bal42 . separating the design into two independently moving groups 317 and 318 eliminates variation of lateral chromatic aberration and astigmatism during focusing . similar to example 2 , the separation of positive and negative power inherent in the reversed telephoto design form was found insufficient to flatten the field , and residual field curvature is eliminated with meniscus element 314 with a strong concave surface facing the image plane . elements 311 and 312 are cemented together to form a doublet 316 in order to avoid tight tolerances and minimize the number of ar coated surfaces . the focal length of example 3 is 24 mm , the aperture is f / 4 , the image format is 24 mm × 36 mm ( 43 . 26 mm diagonal ), the diagonal field of view ( fov ) is 84 . 1 degrees , and the total transmission of the on - axis ray bundle at 315 nm is 63 . 2 %. chromatic focus shift vs . wavelength at a 0 . 67 pupil zone is illustrated in fig3 b , and transmission vs . wavelength is illustrated in fig3 c . the fact that there are three crossings in fig3 b indicates that this design is a true apochromat . fig3 d illustrates the mtf of example 3 wide open at f / 4 for an object located at infinity . the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 1100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 1100 nm , respectively . fig3 d demonstrates that example 3 is well corrected over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . example 4 , which is a 105 mm focal length macro - focusing photographic objective for 35 mm format , is illustrated in fig4 a , which shows cross - sectional layouts at magnifications of 0 and − 0 . 5 ×. elements 401 , 410 and 411 are made from ohara s - fsl5 ; elements 402 and 406 are made from ohara pbl6y ; elements 403 and 409 are made from ohara s - fpl51y ; element 404 is made from ohara s - fpl53 ; and elements 405 and 408 are made from ohara s - bal42 . element 407 is the aperture stop and 412 is the image plane . it is notable that none of the elements are made from caf2 or fused silica , but despite this the design has superachromatic color correction with very low tertiary spectrum , and also has very respectable transmission down to 315 nm . in example 4 , s - fpl53 and s - fpl51y effectively substitute for caf2 and s - bal42 acts as a matching flint . weak elements made from pbl6y are the key to achieving superachromatic color correction . variation of coma during focusing is eliminated by fixing a weakly powered two - element rear group 415 at a constant distance from the image plane while moving a high - powered front group 414 . negative - powered elements 401 and 411 , and the weak meniscus element 402 , located near the front and rear of the lens act to flatten the field . this is of critical importance in a lens made from materials having a low refractive index . elements 408 and 409 are cemented together to form a doublet 413 , and elements 403 , 404 , and 405 are cemented together to form a triplet in order to avoid tight tolerances and minimize the number of surfaces requiring an ar coating . the focal length of example 4 is 105 mm , the aperture is f / 4 , the image format is 24 mm × 36 mm ( 43 . 26 mm diagonal ), the diagonal field of view ( fov ) is 23 . 3 degrees , and the total transmission of the on - axis ray bundle at 315 nm is 24 . 4 %. chromatic focus shift vs . wavelength at a 0 . 7 pupil zone is illustrated in fig4 b , and transmission vs . wavelength is illustrated in fig4 c . the fact that there are four crossings in fig4 b indicates that this design is a true superachromat . fig4 d illustrates the mtf of example 4 wide open at f / 4 for an object located at infinity . the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 1100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 1100 nm , respectively . fig4 d clearly demonstrates that example 4 is well corrected over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . example 5 , which is a 300 mm focal length telephoto photographic objective for 35 mm format , is illustrated in fig5 a , which shows a cross - sectional layout . like example 4 , example 5 does not use either caf2 or fused silica , but nonetheless achieves extremely high optical correction and acceptable optical transmission throughout the 315 nm - 1100 nm waveband . elements 502 and 505 are made from ohara s - fpl53 ; elements 501 and 507 are made from ohara s - fpl51y ; element 503 is made from ohara s - bal42 ; element 510 is made from ohara s - bal35 ; and elements 506 and 508 are made from ohara pbl6y . element 509 is the aperture stop and 511 is the image plane . s - fpl53 and s - fpl51y were found to be good substitutes for caf2 , although the transmission does drop in the short uv range as a result . s - bal42 and s - bal35 were found to be very good matching flints for s - fpl51y and s - fpl53 . the use of a weak positive pbl6y element in the positive front group and a weak negative pbl6y element in the negative rear group was found to be very effective in improving the color correction from apochromatic to superachromatic . the normal separation of optical powers that occurs in telephoto objectives served to flatten the field without the addition of any additional unusual elements . elements 502 and 503 are cemented together to form a doublet 512 ; and elements 504 , 505 and 506 are cemented together to form a triplet in order to avoid tight tolerances and minimize the number of surfaces requiring ar coatings . the focal length of example 5 is 300 mm , the aperture is f / 4 . 55 , the image format is 24 mm × 36 mm ( 43 . 26 mm diagonal ), the diagonal field of view ( fov ) is 8 . 2 degrees , and the total transmission of the on - axis ray bundle at 315 nm is 8 . 2 %. chromatic focus shift vs . wavelength at a 0 . 7 pupil zone is illustrated in fig5 b , and transmission vs . wavelength is illustrated in fig5 c . the fact that there are four crossings in fig5 b indicates that this design is a true superachromat . fig5 d illustrates the mtf of example 5 wide open at f / 4 . 55 for an object located at infinity . the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 1100 nm , respectively . fig5 d clearly demonstrates that example 5 is well corrected over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . example 6 , which is a 100 mm - 300 mm focal length zoom photographic objective for 35 mm format , is illustrated in fig6 a , which shows cross - sectional layouts for focal length positions of 100 mm and 300 mm . elements 602 , 604 , 607 , 609 , 611 , 614 , 617 and 619 are made from caf2 ; elements 610 and 620 are made from sio2 ; elements 606 and 612 are made from ohara s - bal42 ; element 601 is made from ohara s - lal12 ; element 615 is made from ohara s - lal14 ; elements 608 and 616 are made from ohara s - lal18 ; and elements 603 , 605 and 618 are made from ohara pbl6y . element 613 is the aperture stop and 621 is the image plane . despite the fact that fully 10 of its 19 elements are made from either caf2 or fused silica , the overall transmission of example 6 at 315 nm is just barely acceptable at 7 . 6 %. the reason for this is that the various zooming groups must be independently color corrected , and thus some modifying glass types such as lanthanum crowns and light flints are necessary . this example serves to illustrate the difficulty of designing a complex zoom system suitable for the 315 nm - 1100 nm waveband . caf2 is extensively used as the material for positive elements in positive - powered groups and for negative elements in negative - powered groups . s - bal42 , s - lal12 , s - lal14 and s - lal18 are used as matching flints ; and weak pbl6y elements are used to achieve superachromatic performance . the large separation of optical powers combined with the negative - powered group 629 near the image plane ensures excellent correction for field curvature . all elements are combined in cemented groups of 2 ( 622 , 624 , 625 , 626 , 627 and 629 ), 3 ( 628 ), or 4 ( 623 ) elements . this allows the system to achieve excellent wideband correction while minimizing the number of air - glass interfaces and keeping the tolerances as loose as possible . the focal length of example 6 is continuously variable from 100 mm to 300 mm , the aperture is constant throughout the zoom range at f / 5 . 6 , the image format is 24 mm × 36 mm ( 43 . 26 mm diagonal ), the diagonal field of view ( fov ) ranges from 24 . 4 to 8 . 2 degrees , and the total transmission of the on - axis ray bundle at 315 nm is 7 . 6 %. chromatic focus shift vs . wavelength at a 0 . 7 pupil zone for both 100 mm and 300 mm focal lengths are illustrated in fig6 b , and transmission vs . wavelength is illustrated in fig6 c . the fact that there are four crossings for both curves in fig6 b indicates that this design is a true superachromat throughout the zoom range . fig6 d illustrates the mtf of example 6 wide open at f / 5 . 6 for an object located at infinity when the lens is adjusted to its shortest focal length of 100 mm . the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 1100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 1100 nm , respectively . fig6 d demonstrates that example 6 is well corrected at the 100 mm focal length over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . fig6 e illustrates the mtf of example 6 wide open at f / 5 . 6 for an object located at infinity when the lens is adjusted to its longest focal length of 300 mm . the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 1100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 100 nm , respectively . fig6 e demonstrates that example 6 is well corrected at the 300 mm focal length over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . example 7 , which is a 1000 mm focal length telescope objective , is illustrated in fig7 a , which shows a cross - sectional layout . element 701 is made from s - fpl53 , element 702 is made from ohara s - bal42 , element 703 is made from caf2 and element 704 is made from ohara pbl6y . this design has moderate internal transmission at 315 nm because the elements are fairly thick and because several glasses having moderate uv transmission loss were required to achieve superachromatic color correction . in particular , the positive - powered element 704 made from pbl6y is used for fine adjustment of the uv portion of the color curve to improve the color correction from apochromatic to superachromatic . elements 702 and 703 are cemented together to form a doublet 705 in order to improve tolerances and minimize the number of surfaces that must be ar coated . the focal length of example 7 is 1000 mm , the aperture is f / 10 , the diagonal field of view ( fov ) is 0 . 5 degrees , and the total transmission of the on - axis ray bundle at 315 nm is 28 . 6 %. chromatic focus shift vs . wavelength at a 0 . 7 pupil zone is illustrated in fig7 b , and transmission vs . wavelength is illustrated in fig7 c . the fact that there are four crossings in fig7 b indicates that this design is a true superachromat . fig7 d illustrates the on - axis peak - to - valley wavefront error vs . wavelength for example 7 , and it clearly indicates that example 7 is well - corrected . example 8 , which is a 180 mm focal length photographic objective for 72 mm × 96 mm digital scanning format , is illustrated in fig8 a , which shows a cross - sectional layout . elements 801 , 803 , 805 , and 807 are made from caf2 ; and elements 802 and 806 are made from ohara s - bal42 . element 804 is the aperture stop . this design has a very high internal transmission throughout the 315 nm - 1100 nm waveband because four of the six elements are caf2 and the two s - bal42 elements have very good transparency . the negative powered s - bal42 elements 802 and 806 serve as matching flints for the positive powered caf2 elements , and results in example 8 is composed from just two different optical materials , which has been found to be the minimum needed to ensure both good optical correction and good transparency over the entire 315 nm - 1100 nm waveband . elements 801 and 802 , and elements 806 and 807 , are cemented together to form doublets 808 and 809 in order to avoid tight tolerances and to minimize the number of air - glass interfaces that must be ar coated . this latter point is important because ar coatings for the very broad 315 nm - 1100 nm waveband pose special challenges . in order to ensure symmetry and to reduce manufacturing costs , doublets 808 and 809 are identical , and elements 803 and 805 have the same convex radius . example 8 is optimized for best performance at a magnification of − 0 . 2 ×. however due to the symmetry of the design it can be used for high quality imagery over a very broad magnification range , including but not limited to 0 to − 1 ×. the focal length of example 8 is 180 mm , the aperture is f / 9 , the intended image format is 72 mm × 96 mm , the image circle diameter at f / 9 is 125 mm , the image circle diameter at f / 11 is 150 mm , and the total transmission of the on - axis ray bundle at 315 nm is 65 %. chromatic focus shift vs . wavelength at a 0 . 7 pupil zone is illustrated in fig8 b , and transmission vs . wavelength is illustrated in fig8 c . the fact that there are three crossings in fig8 b indicates that this design is a true apochromat . fig8 d illustrates the mtf of example 8 stopped down to f / 11 for an object magnification of − 0 . 2 ×. the four different plots are calculated for the full uv - vis - ir waveband of 315 nm - 1100 nm , the uv sub - waveband of 315 nm - 400 nm , the vis sub - waveband of 400 nm - 700 nm , and the ir sub - waveband of 700 nm - 1100 nm , respectively . fig1 d clearly demonstrates that example 8 is well corrected over each of the uv , vis , and ir sub - wavebands as well as for the full uv - vis - ir waveband . tables 1a , 2a , 3a , 4a , 5a , 6a , 7 and 8a below provide optical prescription data for examples 1 , 2 , 3 , 4 , 5 , 6 , 7 and 8 , respectively . the data provided includes surface number , radius of curvature , thickness , glass type , and the diameter of the clear aperture . obj refers to the object surface , ima refers to the image surface , and sto refers to the aperture stop surface . a listing of refractive index at various wavelengths for all of the glass types used in the examples is provided in table 9 . a listing of transmission at various wavelengths for all of the glass types used in the examples is provided in table 10 . tables 1b , 2b , 3b , 4b , 5b and 8b provide focusing data for examples 1 , 2 , 3 , 4 , 5 , and 8 , respectively . in these tables obmg refers to object magnification , and obim refers to the total distance from the object plane to the image plane . table 6b provides zooming data for example 6 .