the illustrative embodiments to be described below are standardized to a length of about 100 millimeters of the basic optical system and mostly for a nominal magnification of unity . in this way the performance of the various examples can be conveniently compared . embodiments with other magnifications , field of views , numerical apertures , and with additional relays are presented in order to show that the general concept of the invention is effective over a wide range of applications . the embodiments use conventional , non - grin ( graded refractive index ) lens elements , and thus each lens has a uniform refractive index . in fig1 through 11 the object and image planes are indicated by an ‘ o ’ and ‘ im ’, respectively and the pupil planes by a ‘ p ’. the optical system features of object plane , pupil plane , lens surfaces and final image plane are numbered sequentially . table i through xi present the constructional parameters of the preferred embodiments illustrated in corresponding fig2 - 11 and the prior art embodiment illustrated in fig1 . all dimensions are in millimeters . the first column indicates the surface number shown in the figures , the second column indicates the radii , and the third column indicates the axial separations . the refractive indices and dispersion are presented in the usual manner , with respect to the e , f ′, and c ′ spectral lines . the aspheric data are presented in the standard manner . the surface and plane numbers refer to those in the figures . table i refers to the system shown in fig1 table ii to the system of fig2 and so on for the other tables and figures . [ 0027 ] fig1 is an optical schematic of an endoscope which is constructed in accordance with the classical concept of separation of the various functions . group i is an objective which contains the entrance pupil plane while group ii represents a field lens which is located at the focal plane of the objective . group iii represents a transfer lens which transfers the image formed by the objective unto a next focal plane . all groups are located at pupil planes or focal planes . it is apparent from the drawing as well as from the data of table xii that the distribution of optical power is very uneven . the value of the sum of the absolute values of the curvatures , which is a measure of difficulty of fabrication , is listed in table xii for this version which is uncorrected for chromatic aberrations . a version corrected for chromatic aberration would have more than double the value for the sum of the curvatures . the pertinent performance data are listed in table xii and the constructional parameters are listed in table i . [ 0028 ] fig2 is an optical schematic of an endoscope of extreme simplicity . only three plastic elements on non - meniscus shape and devoid of steep curves are needed to provide diffraction limited performance for the monochromatic aberrations . many applications do not require a line - of - sight deviating prism and in such cases a pencil - shaped tip , which is often an advantageous configuration , can be readily provided . the pertinent performance data are listed in table xii and the constructional parameters are listed in table ii . [ 0029 ] fig3 is an optical schematic of an endoscope which is also extremely simple in construction but is nevertheless highly corrected for all aberrations , including chromatic aberrations . although no negative element has been added to correct chromatic aberration , the chromatic aberration is more than a factor four smaller than in the classical layout ( c . f . fig1 ) and is within the diffraction limit . this example clearly shows the advantage which a redistribution of power , with the attendant shift of pupil ( p int ) location , brings . this somewhat extreme case is achieved at the cost of larger optical components . [ 0030 ] fig4 is an optical schematic of an endoscope which consists of only two components . the second and third groups are cemented to a rod - shaped element , so that there are only four glass / air surfaces . despite its simplicity , all aberrations are at the diffraction limit . this example shows that rod - shaped elements can be profitably employed in the present invention . it also shows that rod - shaped elements may alter the location of the intermediate pupil plane ( p int ) and focal plane of the objective , which have now moved beyond the third and second groups , respectively . a shorter rod - shaped element can put the intermediate focal and pupil planes ( p int ) at the second ( ii ) or third ( iii ) element if so desired . the exemplary embodiments do not require meniscus - shaped optical elements . this does not , of course , preclude their use , as is shown in this example . the gain in using meniscus shapes , however , is modest . [ 0031 ] fig5 is an optical schematic of an endoscope which is entirely constructed of glass elements , none of which are of the meniscus shape . all curvatures are shallow and of a spherical shape only . the first group provides without any strain the needed space for a line - of - sight deviation prism between the entrance pupil and the first group , even in the case of a large field of view of seventy degrees . it is important to note that , despite the fact that the first group is not color corrected in any way , the chromatic aberrations of the whole system are fully corrected by means of a single negative element only . all three groups are far removed from the intermediate image plane and the pupil plane , showing the full integration of the three groups . the pertinent performance data are listed in table xii and the constructional parameters are listed in table v . [ 0032 ] fig6 is an optical schematic of an endoscope which is partly constructed of glass and partly of plastic . again no steep curves nor meniscus elements are needed to achieve the relatively high n . a . of 0 . 025 . the distortion is well corrected . the object distance has been set at infinite distance to show that the basic design is not affected by a change in magnification as is generally the case with endoscopes . the pertinent performance data are listed in table xii and the constructional parameters are listed in table vi . [ 0033 ] fig7 is an endoscope to which one more groups of optical power have been added , resulting in a modestly improved monochromatic performance . the added element is positioned close to the image plane of the objective where it is most effective . its relative weak , in this case positive , power shows that most of the burden of the optical functions as well as the aberration correction is carried by the groups which are displaced from the image planes and pupil planes . this example shows that an additional element near an image plane or a pupil plane is not excluded . the pertinent performance data are listed in table xii and the constructional parameters are listed in table vii . [ 0034 ] fig8 is a highly corrected endoscope of all plastic elements with a relatively high n . a . of 0 . 025 . only one of the elements , the second element , favors a position which is close to an image or pupil plane but is again of low optical power . the pertinent performance data are listed in table xii and the constructional parameters are listed in table viii . [ 0035 ] fig9 is an endoscope of similar design as the one shown in fig8 . the magnification has been increased to 2x , showing that the design remains very similar to the 1x and 0 . 0x designs , as is generally the case with endoscopes . again a meniscus element has been employed to show that despite the fact that the present invention can be very well executed with non - meniscus elements , their employment is by no means excluded . in this case the fourth group , the meniscus element is of negative power , again showing that the fourth element is a non - essential addition to the three group concept of the invention . the pertinent performance data are listed in table xii and the constructional parameters are listed in table ix . [ 0036 ] fig1 is an endoscope to which a second relay has been added . it has a very large field of view of eighty degrees and a relatively high n . a . of 0 . 025 . despite these large values a deviation prism can be readily accommodated in between the objective and the entrance pupil . the total system is still very well corrected and needs only a single color correcting element of low power in order to provide full correction of the chromatic aberrations . as the first three groups are fully correctable by themselves , the addition of classical relays to those first three groups is not excluded . the pertinent performance data are listed in table xii and the constructional parameters are listed in table x . note that the second relay is different from the first relay . the number of curved optical surfaces in the second relay is different than the number of curved optical surfaces in the first relay . [ 0037 ] fig1 shows an endoscope with three image relays and is still very well corrected . again the chromatic aberrations are fully corrected with a single element of negative optical power . in this case the optical power of the color correcting element approaches a value comparable to those of the other components . all elements are of glass and no aspheric surfaces are employed . the pertinent performance data are listed in table xii and the constructional parameters are listed in table xi . note that the second relay is different from the first relay . the number of curved optical surfaces in the second relay is different than the number of curved optical surfaces in the first relay . it is thus evident from these embodiments that the integration of the three groups of which a conventional endoscope exists , the objective , a field lens , and a relay lens , greatly reduces the overall power requirement . the reduction in the overall power requirement naturally reduces the amount of aberrations to be corrected which results in a considerable simplification of the optical system . an additional , and in many cases a very valuable , feature is that the optimal location of the entrance pupil is outside the system . table i surf rd th index v - value cc 0 6 . 51 object plane 1 −. 51 entrance pupil plane 2 2 . 60 1 . 40 1 . 4938 57 . 0 − 52 . 0 3 − 1 . 60 3 . 00 air − 7 . 5 4 4 . 00 3 . 00 1 . 4938 57 . 0 − 12 . 0 5 − 3 . 80 33 . 00 air 6 18 . 00 2 . 00 1 . 4938 57 . 0 7 − 24 . 76 51 . 64 air 8 image plane [ 0039 ] table ii surf rd th index v - value cc 0 6 . 00 object plane 1 . 60 entrance pupil plane 2 infinity 1 . 2 1 . 4938 57 . 0 3 − 1 . 10 7 . 4 air −. 40 4 infinity 1 . 5 1 . 7762 49 . 3 5 − 6 . 30 36 . 80 air 6 infinity 1 . 50 1 . 4938 57 . 3 7 − 11 . 81 44 . 85 air − 3 . 00 8 image plane [ 0040 ] table iii surf rd th index v - value cc 0 6 . 00 object plane 1 6 . 00 entrance pupil plane 2 infinity 3 . 00 1 . 4938 57 . 0 3 − 4 . 7 51 . 30 air −. 65 4 25 . 70 7 . 00 1 . 4938 57 . 0 5 − 11 . 70 18 . 00 air − 2 . 90 6 7 . 00 2 . 00 1 . 4938 57 . 0 7 − 13 . 48 6 . 72 air − 560 . 00 8 image plane [ 0041 ] table iv surf rd th index v - value cc 0 6 . 00 object plane 1 2 . 00 entrance pupil plane 2 − 5 . 00 1 . 80 1 . 4938 57 . 0 3 − 2 . 10 1 . 70 air −. 56 4 5 . 83 2 . 00 1 . 6203 63 . 1 5 infinity 48 . 00 1 . 8126 25 . 2 6 infinity 2 . 00 1 . 4938 57 . 0 7 − 7 . 01 36 . 50 air − 1 . 30 8 image plane [ 0042 ] table v surf rd th index v - value cc 0 6 . 00 object plane 1 . 20 entrance pupil plane 2 infinity 3 . 00 1 . 7162 53 . 2 3 infinity 1 . 50 1 . 7762 49 . 3 4 − 4 . 0 . 20 air 5 13 . 50 1 . 50 1 . 7762 49 . 3 6 − 13 . 50 9 . 50 air 7 infinity 1 . 50 1 . 7762 49 . 3 8 − 10 . 9 30 . 80 air 9 infinity 1 . 20 1 . 8097 30 . 2 10 8 . 80 2 . 00 1 . 5914 61 . 0 11 − 8 . 47 42 . 55 air 12 image plane [ 0043 ] table vi surf rd th index v - value cc 0 infinity object plane 1 3 . 2 entrance pupil plane 2 4 . 90 2 . 5 1 . 4938 57 . 0 − 1 . 50 3 − 2 . 90 18 . 60 air − 2 . 50 4 infinity 2 . 00 1 . 4938 57 . 0 5 − 8 . 80 24 . 00 air −. 70 6 − 7 . 00 1 . 20 1 . 5901 29 . 6 1 . 40 7 infinity 2 . 00 1 . 6543 58 . 3 8 − 6 . 55 40 . 51 air 9 image plane [ 0044 ] table vii surf rd th index v - value cc 0 6 . 00 object plane 1 1 . 90 entrance pupil plane 2 infinity 2 . 50 1 . 4938 57 . 0 3 − 2 . 00 2 . 70 air −. 66 4 infinity 2 . 00 1 . 4938 57 . 0 5 − 16 . 80 25 . 00 air 32 . 00 6 infinity 2 . 00 1 . 4938 57 . 0 7 − 9 . 60 31 . 20 air − 1 . 20 8 infinity 2 . 00 1 . 4938 57 . 0 9 − 17 . 85 24 . 68 air − 28 . 00 10 image plane [ 0045 ] table viii surf rd th index v - value cc 0 6 . 00 object plane 1 3 . 20 entrance pupil plane 2 infinity 2 . 50 1 . 4938 57 . 0 3 − 2 . 50 3 . 00 air −. 64 4 infinity 2 . 00 1 . 4938 57 . 0 5 − 26 . 00 24 . 70 air 57 . 00 6 infinity 2 . 00 1 . 4938 57 . 0 7 − 9 . 20 25 . 00 air − 1 . 00 8 − 4 . 30 1 . 20 1 . 5901 29 . 6 −. 30 9 infinity 2 . 00 1 . 4938 57 . 0 10 − 3 . 61 28 . 35 air −. 70 11 image plane [ 0046 ] table ix surf rd th index v - value cc 0 3 . 00 object plane 1 2 . 40 entrance pupil plane 2 12 . 40 3 . 00 1 . 4938 57 . 0 3 − 2 . 32 9 . 70 air −. 80 4 − 7 . 60 2 . 00 1 . 4938 57 . 0 5 − 8 . 10 15 . 90 air 2 . 80 6 infinity 2 . 00 1 . 4938 57 . 0 7 − 10 . 00 28 . 50 air − 1 . 20 8 − 24 . 00 1 . 20 1 . 5901 29 . 6 70 . 00 9 5 . 00 2 . 50 1 . 4938 57 . 0 10 − 6 . 36 29 . 82 air 11 image plane [ 0047 ] table x surf rd th index v - value ad ae 0 8 . 00 object plane 1 . 10 entrance pupil plane 2 infinity 3 . 80 1 . 8126 25 . 2 3 infinity 1 . 80 1 . 7762 49 . 3 4 − 4 . 30 . 20 air 5 11 . 40 1 . 50 1 . 7762 49 . 3 6 − 17 . 00 10 . 00 air 7 infinity 2 . 00 1 . 7762 49 . 3 8 − 18 . 90 40 . 30 air 9 13 . 00 2 . 00 1 . 8550 23 . 6 10 8 . 50 2 . 50 1 . 4985 81 . 2 11 − 19 . 30 39 . 80 air 12 infinity 2 . 00 1 . 7762 49 . 3 13 − 8 . 34 20 . 00 air 14 infinity 2 . 00 1 . 7044 29 . 8 15 − 8 . 83 14 . 04 air 9 . 0e − 4 112 . 0e − 5 16 image plane [ 0048 ] table xi sur f rd th index v - value 0 12 . 00 object plane 1 . 10 entrance pupil plane 2 infinity 4 . 50 1 . 8126 25 . 2 3 infinity 2 . 00 1 . 7762 49 . 3 4 − 4 . 30 . 20 air 5 38 . 00 1 . 50 1 . 7762 49 . 3 6 − 14 . 00 15 . 00 air 7 infinity 1 . 60 1 . 7762 49 . 3 8 − 14 . 00 27 . 00 air 9 50 . 00 1 . 20 1 . 8550 23 . 6 10 4 . 50 3 . 00 1 . 4985 81 . 2 11 − 4 . 70 28 . 80 air 12 infinity 2 . 00 1 . 7762 49 . 3 13 − 11 . 00 26 . 70 air 14 infinity 2 . 00 1 . 7662 49 . 3 15 − 9 . 90 27 . 30 air 16 − 14 . 70 2 . 00 1 . 7662 49 . 3 17 − 8 . 00 40 . 70 air 18 infinity 2 . 00 1 . 7662 49 . 3 19 − 20 . 33 50 . 40 air 20 image plane [ 0049 ] table xii 1 2 3 4 5 6 7 8 9 10 11 12 fig . n . a . fov m epd el . relay sc dist ptz wavfr axclr 1 0 . 020 60 1 . 0 − 0 . 5 3 1 1 . 62 − 2 0 . 54 0 . 79 0 . 90 2 0 . 020 60 1 . 0 0 . 6 3 1 1 . 15 − 2 0 . 40 0 . 32 0 . 80 3 0 . 020 60 1 . 0 6 3 1 0 . 55 − 1 0 . 18 0 . 10 0 . 21 4 0 . 020 60 1 . 0 2 3 1 0 . 99 + 2 0 . 20 0 . 27 0 . 31 5 0 . 015 70 1 . 0 0 . 2 5 1 0 . 84 − 16 0 . 25 0 . 31 0 . 12 6 0 . 025 60 0 . 0 3 . 2 4 1 0 . 96 − 3 0 . 23 0 . 46 0 . 14 7 0 . 020 70 1 . 0 1 . 9 4 1 0 . 72 − 6 0 . 24 0 . 27 0 . 63 8 0 . 025 60 1 . 0 3 . 2 5 1 1 . 06 − 1 0 . 19 0 . 21 0 . 31 9 0 . 025 60 2 . 0 2 . 4 5 1 1 . 47 + 0 0 . 23 0 . 15 0 . 03 10 0 . 025 80 − 0 . 5 0 . 1 7 2 1 . 03 − 2 0 . 33 0 . 31 0 . 35 11 0 . 017 60 0 . 5 0 . 1 9 3 1 . 51 − 11 0 . 36 0 . 48 0 . 04