Catadioptric virtual-zoom optical system

Claim 2

A zoom optical system comprising a main light gathering objective mirror and a virtual object zoom relay system optically coupled to said main light gathering objective mirror.

Claim 3

A zoom optical system as recited in claim 1, wherein said main light gathering objective mirror is a mirror forming part of a Newtonian telescope.

Claim 4

A zoom optical system as recited in claim 1, wherein said virtual object zoom relay system comprises a first movable zoom element group comprising a plurality of first lens elements, a second movable zoom element group comprising a plurality of second lens elements, and at least one stationary lens element interposed between said first and second movable zoom element groups.

Claim 5

A zoom optical system as recited in claim 3, wherein said first movable zoom element group is positioned ahead of the position where the real image would be formed by the light gathering system.

Claim 6

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = 2000.00 -- PARABOLIC S.sub.1 = 785.622 APERTURE -- -- FLAT -- STOP S.sub.2 = VARIABLE I 1.4339 95.14 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 115.75 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -453.68 T.sub.2 = 11.43 R.sub.5 = -119.83 -- III 1.4339 95.14 R.sub.5 = -119.83 T.sub.3 = 6.35 R.sub.6 = 340.45 S.sub.4 = 508.00 IV 1.7550 27.57 R.sub.7 = 354.70 T.sub.4 = 6.35 R.sub.8 = 141.00 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 1589.80 T.sub.5 = 10.16 R.sub.10 = -191.67 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.05 T.sub.6 = 17.78 R.sub.12 = -167.55 -- VII 1.7550 27.57 R.sub.12 = -167.55 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 S.sub.3 S.sub.5 ______________________________________ 900 8.834 62.615 8.630 1200 23.435 48.014 24.046 1500 31.172 40.277 36.525 1800 35.757 35.692 47.291 2100 38.671 32.778 56.902 2400 40.613 30.836 65.677 2700 41.950 29.499 73.818 3000 42.889 28.560 81.458 3300 43.559 27.890 88.692 3600 44.039 27.410 95.588 3900 44.382 27.067 102.197 4100 44.598 26.851 105.600 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 1 -S 6 represent the thicknesses of the lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length range, F n-4 .5n, by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 7

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = 2000.00 -- PARABOLIC S.sub.1 = 785.622 APERTURE -- -- FLAT -- STOP S.sub.2 = VARIABLE I 1.4339 95.14 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 115.75 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -453.68 T.sub.2 = 11.43 R.sub.5 = -119.83 -- III 1.4339 95.14 R.sub.5 = -119.83 T.sub.3 = 6.35 R.sub.6 = 340.45 S.sub.4 = 508.00 IV 1.7550 27.57 R.sub.7 = 354.70 T.sub.4 = 6.35 R.sub.8 = 141.00 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 1589.80 T.sub.5 = 10.16 R.sub.10 = -191.67 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.05 T.sub.6 = 17.78 R.sub.12 = -167.55 -- VII 1.7550 27.57 R.sub.12 = -167.55 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 S.sub.3 S.sub.5 ______________________________________ 900 8.834 62.615 8.630 1200 23.435 48.014 24.046 1500 31.172 40.277 36.525 1800 35.757 35.692 47.291 2100 38.671 32.778 56.902 2400 40.613 30.836 65.677 2700 41.950 29.499 73.818 3000 42.889 28.560 81.458 3300 43.559 27.890 88.692 3600 44.039 27.410 95.588 3900 44.382 27.067 102.197 4100 44.598 26.851 105.600 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 1 -S 6 represent the thicknesses of the lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length range, F n-4 .5n, by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 8

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -2000.00 -- PARABOLIC S.sub.1 = 785.622 APERTURE -- -- FLAT -- STOP S.sub.2 = VARIABLE I 1.4865 84.46 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 124.02 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -1884.17 T.sub.2 = 11.43 R.sub.5 = -118.27 -- III 1.4865 84.46 R.sub.5 = -118.27 T.sub.3 = 6.35 R.sub.6 = 279.93 S.sub.4 = 508.00 IV 1.8049 25.42 R.sub.7 = 331.82 T.sub.4 = 6.35 R.sub.8 = 140.44 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 728.47 T.sub.5 = 10.16 R.sub.10 = -212.23 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.60 T.sub.6 = 17.78 R.sub.12 = -180.44 -- VII 1.7550 27.57 R.sub.12 = 180.44 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 S.sub.3 S.sub.5 ______________________________________ 900 8.840 68.078 8.786 1200 22.889 54.029 23.916 1500 30.320 46.599 36.199 1800 34.718 42.200 46.799 2100 37.513 39.405 56.257 2400 39.376 37.542 64.886 2700 40.660 36.258 72.883 3000 41.565 35.354 80.381 3300 42.211 34.707 87.473 3600 42.676 34.242 94.227 3900 43.010 33.908 100.693 4100 43.219 33.700 104.040 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 1 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 9

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -2000.00 -- PARABOLIC S.sub.1 = 785.622 APERTURE -- -- FLAT -- STOP S.sub.2 = VARIABLE I 1.4865 84.46 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 124.02 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -1884.17 T.sub.2 = 11.43 R.sub.5 = -118.27 -- III 1.4865 84.46 R.sub.5 = -118.27 T.sub.3 = 6.35 R.sub.6 = 279.93 S.sub.4 = 508.00 IV 1.8049 25.42 R.sub.7 = 331.82 T.sub.4 = 6.35 R.sub.8 = 140.44 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 728.47 T.sub.5 = 10.16 R.sub.10 = -212.23 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.60 T.sub.6 = 17.78 R.sub.12 = -180.44 -- VII 1.7550 27.57 R.sub.12 = 180.44 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 S.sub.3 S.sub.5 ______________________________________ 900 8.840 68.078 8.786 1200 22.889 54.029 23.916 1500 30.320 46.599 36.199 1800 34.718 42.200 46.799 2100 37.513 39.405 56.257 2400 39.376 37.542 64.886 2700 40.660 36.258 72.883 3000 41.565 35.354 80.381 3300 42.211 34.707 87.473 3600 42.676 34.242 94.227 3900 43.010 33.908 100.693 4100 43.219 33.700 104.040 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 1 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 10

A zoom optical system having design parameters, normalized for a 300-900 mm focal length range, F 300-900 , and a zoom range of approximately 3:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -1041.40 -- PARABOLIC S.sub.1 = 335.00 APERTURE -- -- FLAT -- STOP S.sub.2 = VARIABLE I 1.6203 60.32 R.sub.2 = -1122.04 T.sub.1 = 5.08 R.sub.3 = 111.11 S.sub.3 = VARIABLE II 1.7550 27.57 R.sub.4 = -198.69 T.sub.2 = 7.62 R.sub.5 = -82.29 -- III 1.6203 60.32 R.sub.5 = -82.29 T.sub.3 = 5.08 R.sub.6 = -166.79 S.sub.4 = 203.20 IV 1.7550 27.57 R.sub.7 = 416.23 T.sub.4 = 5.08 R.sub.8 = 93.46 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 380.00 T.sub.5 = 10.16 R.sub.10 = -146.62 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 60.17 T.sub.6 = 17.78 R.sub.12 = -82.29 -- VII 1.7550 27.57 R.sub.12 = -82.29 T.sub.7 = 5.08 R.sub.13 = 380.00 __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 S.sub.3 S.sub.5 ______________________________________ 300 7.534 57.620 7.468 350 20.531 44.623 13.033 400 29.824 35.330 18.022 450 36.664 28.490 22.561 500 41.820 23.334 26.736 550 45.783 19.370 30.608 600 48.882 16.272 34.226 650 51.338 13.815 37.627 700 53.310 11.844 40.842 750 54.908 10.246 43.894 800 56.215 8.939 46.803 850 57.291 7.863 49.586 900 58.154 7.000 52.492 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 1 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length range, F n-3n , by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 300 .

Claim 11

A zoom optical system having design parameters, normalized for a 300-900 mm focal length range, F 300-900 , and a zoom range of approximately 3:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -1041.40 -- PARABOLIC S.sub.1 = 335.00 APERTURE -- -- FLAT -- STOP S.sub.2 = VARIABLE I 1.6203 60.32 R.sub.2 = -1122.04 T.sub.1 = 5.08 R.sub.3 = 111.11 S.sub.3 = VARIABLE II 1.7550 27.57 R.sub.4 = -198.69 T.sub.2 = 7.62 R.sub.5 = -82.29 -- III 1.6203 60.32 R.sub.5 = -82.29 T.sub.3 = 5.08 R.sub.6 = -166.79 S.sub.4 = 203.20 IV 1.7550 27.57 R.sub.7 = 416.23 T.sub.4 = 5.08 R.sub.8 = 93.46 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 380.00 T.sub.5 = 10.16 R.sub.10 = -146.62 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 60.17 T.sub.6 = 17.78 R.sub.12 = -82.29 -- VII 1.7550 27.57 R.sub.12 = -82.29 T.sub.7 = 5.08 R.sub.13 = 380.00 __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 S.sub.3 S.sub.5 ______________________________________ 300 7.534 57.620 7.468 350 20.531 44.623 13.033 400 29.824 35.330 18.022 450 36.664 28.490 22.561 500 41.820 23.334 26.736 550 45.783 19.370 30.608 600 48.882 16.272 34.226 650 51.338 13.815 37.627 700 53.310 11.844 40.842 750 54.908 10.246 43.894 800 56.215 8.939 46.803 850 57.291 7.863 49.586 900 58.154 7.000 52.492 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 1 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length range, F n-3n , by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 300 .

Claim 12

A zoom virtual image relay system for use with an objective system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ I 1.4339 95.14 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 115.75 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -453.68 T.sub.2 = 11.43 R.sub.5 = -119.83 -- III 1.4339 95.14 R.sub.5 = -119.83 T.sub.3 = 6.35 R.sub.6 = 340.45 S.sub.4 = 508.00 IV 1.7550 27.57 R.sub.7 = 354.70 T.sub.4 = 6.35 R.sub.8 = 141.00 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 1589.80 T.sub.5 = 10.16 R.sub.10 = -191.67 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.05 T.sub.6 = 17.78 R.sub.12 = -167.55 -- VII 1.7550 27.57 R.sub.12 = -167.55 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 3 and S 5 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.3 S.sub.5 ______________________________________ 900 62.615 8.630 1200 48.014 24.046 1500 40.277 36.525 1800 35.692 47.291 2100 32.778 56.902 2400 30.836 65.677 2700 29.499 73.818 3000 28.560 81.458 3300 27.890 88.692 3600 27.410 95.588 3900 27.067 102.197 4100 26.851 105.600 ______________________________________ wherein the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 3 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the objective to the image plane, with all dimensions being expressed in millimeters, wherein elements I, II and III are positioned in the light path ahead of the position where the real image would be formed by the objective, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 13

A zoom virtual image relay system for use with an objective system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ I 1.4339 95.14 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 115.75 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -453.68 T.sub.2 = 11.43 R.sub.5 = -119.83 -- III 1.4339 95.14 R.sub.5 = -119.83 T.sub.3 = 6.35 R.sub.6 = 340.45 S.sub.4 = 508.00 IV 1.7550 27.57 R.sub.7 = 354.70 T.sub.4 = 6.35 R.sub.8 = 141.00 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 1589.80 T.sub.5 = 10.16 R.sub.10 = -191.67 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.05 T.sub.6 = 17.78 R.sub.12 = -167.55 -- VII 1.7550 27.57 R.sub.12 = -167.55 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 3 and S 5 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.3 S.sub.5 ______________________________________ 900 62.615 8.630 1200 48.014 24.046 1500 40.277 36.525 1800 35.692 47.291 2100 32.778 56.902 2400 30.836 65.677 2700 29.499 73.818 3000 28.560 81.458 3300 27.890 88.692 3600 27.410 95.588 3900 27.067 102.197 4100 26.851 105.600 ______________________________________ wherein the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 3 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the objective to the image plane, with all dimensions being expressed in millimeters, wherein elements I, II and III are positioned in the light path ahead of the position where the real image would be formed by the objective, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 14

A zoom virtual image optical relay system for use with an objective system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 for the entire system represented in the following table: ______________________________________ FOCAL LENGTH S.sub.3 S.sub.5 ______________________________________ 9000 68.078 8.786 1200 54.029 23.916 1500 46.599 36.199 1800 42.200 46.799 2100 39.405 56.257 2400 37.542 64.886 2700 36.258 72.883 3000 35.354 80.381 3300 34.707 87.473 3600 34.242 94.227 3900 33.908 100.693 4100 33.700 104.040 ______________________________________ wherein S 3 and S 5 are defined for various focal lengths by the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ I 1.4865 84.46 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 124.02 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -1884.17 T.sub.2 = 11.43 R.sub.5 = -118.27 -- III 1.4865 84.46 R.sub.5 = -118.27 T.sub.3 = 6.35 R.sub.6 = 279.93 S.sub.4 = 508.00 IV 1.8049 25.42 R.sub.7 = 331.82 T.sub.4 = 6.35 R.sub.8 = 140.44 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 728.47 T.sub.5 = 10.16 R.sub.10 = -212.23 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.60 T.sub.6 = 17.78 R.sub.12 = -180.44 -- VII 1.7550 27.57 R.sub.12 = 180.44 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 3 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the objective to the image plane, with all dimensions being expressed in millimeters, wherein elements I, II and III are positioned in the light path ahead of the position where the real image would be formed by the objective, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 15

A zoom virtual image optical relay system for use with an objective system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 for the entire system represented in the following table: ______________________________________ FOCAL LENGTH S.sub.3 S.sub.5 ______________________________________ 9000 68.078 8.786 1200 54.029 23.916 1500 46.599 36.199 1800 42.200 46.799 2100 39.405 56.257 2400 37.542 64.886 2700 36.258 72.883 3000 35.354 80.381 3300 34.707 87.473 3600 34.242 94.227 3900 33.908 100.693 4100 33.700 104.040 ______________________________________ wherein S 3 and S 5 are defined for various focal lengths by the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ I 1.4865 84.46 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 124.02 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -1884.17 T.sub.2 = 11.43 R.sub.5 = -118.27 -- III 1.4865 84.46 R.sub.5 = -118.27 T.sub.3 = 6.35 R.sub.6 = 279.93 S.sub.4 = 508.00 IV 1.8049 25.42 R.sub.7 = 331.82 T.sub.4 = 6.35 R.sub.8 = 140.44 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 728.47 T.sub.5 = 10.16 R.sub.10 = -212.23 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.60 T.sub.6 = 17.78 R.sub.12 = -180.44 -- VII 1.7550 27.57 R.sub.12 = 180.44 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 3 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the objective to the image plane, with all dimensions being expressed in millimeters, wherein elements I, II and III are positioned in the light path ahead of the position where the real image would be formed by the objective, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 16

A zoom virtual image optical relay system for use with an objective system having design parameters, normalized for a 300-900 mm focal length range, F 300-900 , and a zoom range of approximately 4.5:1 for the entire system represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ I 1.6203 60.32 R.sub.2 = -1122.04 T.sub.1 = 5.08 R.sub.3 = 111.11 S.sub.3 = VARIABLE II 1.7550 27.57 R.sub.4 = -198.69 T.sub.2 = 7.62 R.sub.5 = -82.29 -- III 1.6203 60.32 R.sub.5 = -82.29 T.sub.3 = 5.08 R.sub.6 = -166.79 S.sub.4 = 203.20 IV 1.7550 27.57 R.sub.7 = 416.23 T.sub.4 = 5.08 R.sub.8 = 93.46 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 380.00 T.sub.5 = 10.16 R.sub.10 = -146.62 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 60.17 T.sub.6 = 17.78 R.sub.12 = -82.29 -- VII 1.7550 27.57 R.sub.12 = -82.29 T.sub.7 = 5.08 R.sub.13 = 380.00 __________________________________________________________________________ wherein S 3 and S 5 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.3 S.sub.5 ______________________________________ 300 57.620 7.468 350 44.623 13.033 400 35.330 18.022 450 28.490 22.561 500 23.334 26.736 550 19.370 30.608 600 16.272 34.226 650 13.815 37.627 700 11.844 40.842 750 10.246 43.894 800 8.939 46.803 850 7.863 49.586 900 7.000 52.492 ______________________________________ wherein the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 3 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the objective to the image plane, with all dimensions being expressed in millimeters, wherein elements I, II and III are positioned in the light path ahead of the position where the real image would be formed by the objective, and wherein the design parameters may be renormalized to any other focal length, F n-3n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 300 .

Claim 17

A zoom virtual image optical relay system for use with an objective system having design parameters, normalized for a 300-900 mm focal length range, F 300-900 , and a zoom range of approximately 4.5:1 for the entire system represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ I 1.6203 60.32 R.sub.2 = -1122.04 T.sub.1 = 5.08 R.sub.3 = 111.11 S.sub.3 = VARIABLE II 1.7550 27.57 R.sub.4 = -198.69 T.sub.2 = 7.62 R.sub.5 = -82.29 -- III 1.6203 60.32 R.sub.5 = -82.29 T.sub.3 = 5.08 R.sub.6 = -166.79 S.sub.4 = 203.20 IV 1.7550 27.57 R.sub.7 = 416.23 T.sub.4 = 5.08 R.sub.8 = 93.46 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 380.00 T.sub.5 = 10.16 R.sub.10 = -146.62 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 60.17 T.sub.6 = 17.78 R.sub.12 = -82.29 -- VII 1.7550 27.57 R.sub.12 = -82.29 T.sub.7 = 5.08 R.sub.13 = 380.00 __________________________________________________________________________ wherein S 3 and S 5 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.3 S.sub.5 ______________________________________ 300 57.620 7.468 350 44.623 13.033 400 35.330 18.022 450 28.490 22.561 500 23.334 26.736 550 19.370 30.608 600 16.272 34.226 650 13.815 37.627 700 11.844 40.842 750 10.246 43.894 800 8.939 46.803 850 7.863 49.586 900 7.000 52.492 ______________________________________ wherein the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 3 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the objective to the image plane, with all dimensions being expressed in millimeters, wherein elements I, II and III are positioned in the light path ahead of the position where the real image would be formed by the objective, and wherein the design parameters may be renormalized to any other focal length, F n-3n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 300 .

Claim 18

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -2000.00 -- PARABOLIC S.sub.2 = VARIABLE I 1.4339 95.14 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 115.75 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -453.68 T.sub.2 = 11.43 R.sub.5 = -119.83 -- III 1.4339 95.14 R.sub.5 = -119.83 T.sub.3 = 6.35 R.sub.6 = 340.45 S.sub.4 = 508.00 IV 1.7550 27.57 R.sub.7 = 354.70 T.sub.4 = 6.35 R.sub.8 = 141.00 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 1589.80 T.sub.5 = 10.16 R.sub.10 = -191.67 S.sub.6 = 0.500 VI 1.6203 60.32 R.sub.11 = 85.05 T.sub.6 = 17.78 R.sub.12 = -167.55 -- VII 1.7550 27.57 R.sub.12 = -167.55 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 - 785.622 S.sub.3 S.sub.5 ______________________________________ 900 8.834 62.615 8.630 1200 23.435 48.014 24.046 1500 31.172 40.277 36.525 1800 35.757 35.692 47.291 2100 38.671 32.778 56.902 2400 40.613 30.836 65.677 2700 41.950 29.499 73.818 3000 42.889 28.560 81.458 3300 43.559 27.890 88.692 3600 44.039 27.410 95.588 3900 44.382 27.067 102.197 4100 44.598 26.851 105.600 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 2 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 19

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -2000.00 -- PARABOLIC S.sub.2 = VARIABLE I 1.4339 95.14 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 115.75 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -453.68 T.sub.2 = 11.43 R.sub.5 = -119.83 -- III 1.4339 95.14 R.sub.5 = -119.83 T.sub.3 = 6.35 R.sub.6 = 340.45 S.sub.4 = 508.00 IV 1.7550 27.57 R.sub.7 = 354.70 T.sub.4 = 6.35 R.sub.8 = 141.00 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 1589.80 T.sub.5 = 10.16 R.sub.10 = -191.67 S.sub.6 = 0.500 VI 1.6203 60.32 R.sub.11 = 85.05 T.sub.6 = 17.78 R.sub.12 = -167.55 -- VII 1.7550 27.57 R.sub.12 = -167.55 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 - 785.622 S.sub.3 S.sub.5 ______________________________________ 900 8.834 62.615 8.630 1200 23.435 48.014 24.046 1500 31.172 40.277 36.525 1800 35.757 35.692 47.291 2100 38.671 32.778 56.902 2400 40.613 30.836 65.677 2700 41.950 29.499 73.818 3000 42.889 28.560 81.458 3300 43.559 27.890 88.692 3600 44.039 27.410 95.588 3900 44.382 27.067 102.197 4100 44.598 26.851 105.600 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 2 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 20

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -2000.00 -- PARABOLIC S.sub.2 = VARIABLE I 1.4865 84.46 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 124.02 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -1884.17 T.sub.2 = 11.43 R.sub.5 = -118.27 -- III 1.4865 84.46 R.sub.5 = -118.27 T.sub.3 = 6.35 R.sub.6 = 279.93 S.sub.4 = 508.00 IV 1.8049 25.42 R.sub.7 = 331.82 T.sub.4 = 6.35 R.sub.8 = 140.44 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 728.47 T.sub.5 = 10.16 R.sub.10 = 212.23 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.60 T.sub.6 = 17.78 R.sub.12 = -180.44 -- VII 1.7550 27.57 R.sub.12 = 180.44 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 - 785.622 S.sub.3 S.sub.5 ______________________________________ 900 8.840 68.078 8.786 1200 22.889 54.029 23.916 1500 30.320 46.599 36.199 1800 34.718 42.200 46.799 2100 37.513 39.405 56.257 2400 39.376 37.542 64.886 2700 40.660 36.258 72.883 3000 41.565 35.354 80.381 3300 42.211 34.707 87.473 3600 42.676 34.242 94.227 3900 43.010 33.908 100.693 4100 43.219 33.700 104.040 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 2 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 21

A zoom optical system having design parameters, normalized for a 900-4100 mm focal length range, F 900-4100 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -2000.00 -- PARABOLIC S.sub.2 = VARIABLE I 1.4865 84.46 R.sub.2 = FLAT T.sub.1 = 6.35 R.sub.3 = 124.02 S.sub.3 = VARIABLE II 1.6540 39.62 R.sub.4 = -1884.17 T.sub.2 = 11.43 R.sub.5 = -118.27 -- III 1.4865 84.46 R.sub.5 = -118.27 T.sub.3 = 6.35 R.sub.6 = 279.93 S.sub.4 = 508.00 IV 1.8049 25.42 R.sub.7 = 331.82 T.sub.4 = 6.35 R.sub.8 = 140.44 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 728.47 T.sub.5 = 10.16 R.sub.10 = 212.23 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 85.60 T.sub.6 = 17.78 R.sub.12 = -180.44 -- VII 1.7550 27.57 R.sub.12 = 180.44 T.sub.7 = 6.35 R.sub.13 = FLAT __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 - 785.622 S.sub.3 S.sub.5 ______________________________________ 900 8.840 68.078 8.786 1200 22.889 54.029 23.916 1500 30.320 46.599 36.199 1800 34.718 42.200 46.799 2100 37.513 39.405 56.257 2400 39.376 37.542 64.886 2700 40.660 36.258 72.883 3000 41.565 35.354 80.381 3300 42.211 34.707 87.473 3600 42.676 34.242 94.227 3900 43.010 33.908 100.693 4100 43.219 33.700 104.040 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number, R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 2 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-4 .5n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 900 .

Claim 22

A zoom optical system having design parameters, normalized for a 300-900 mm focal length range, F 300-900 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -1041.40 -- PARABOLIC S.sub.2 = VARIABLE I 1.6203 60.32 R.sub.2 = -1122.04 T.sub.1 = 5.08 R.sub.3 = 111.11 S.sub.3 = VARIABLE II 1.7550 27.57 R.sub.4 = -198.69 T.sub.2 = 7.62 R.sub.5 = -82.29 -- III 1.6203 60.32 R.sub.5 = -82.29 T.sub.3 = 5.08 R.sub.6 = 166.79 S.sub.4 = 203.20 IV 1.7550 27.57 R.sub.7 = 416.23 T.sub.4 = 5.08 R.sub.8 = 93.46 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 380.00 T.sub.5 = 10.16 R.sub.10 = -146.62 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 60.17 T.sub.6 = 17.78 R.sub.12 = -82.29 -- VII 1.7550 27.57 R.sub.12 = -82.29 T.sub.7 = 5.08 R.sub.13 = 380.00 __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 - 335.00 S.sub.3 S.sub.5 ______________________________________ 300 7.534 57.620 7.468 350 20.531 44.623 13.033 400 29.824 35.330 18.022 450 36.664 28.490 22.561 500 41.820 23.334 26.736 550 45.783 19.370 30.608 600 48.882 16.272 34.226 650 51.338 13.815 37.627 700 53.310 11.844 40.842 750 54.908 10.246 43.894 800 56.215 8.939 46.803 850 57.291 7.863 49.586 900 58.154 7.000 52.492 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 2 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-3n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 300 .

Claim 23

A zoom optical system having design parameters, normalized for a 300-900 mm focal length range, F 300-900 , and a zoom range of approximately 4.5:1 represented in the following table: __________________________________________________________________________ ELEMENT η.sub.D ν.sub.D RADIUS THICKNESS SEPARATION __________________________________________________________________________ M.sub.1 -- -- R.sub.1 = -1041.40 -- PARABOLIC S.sub.2 = VARIABLE I 1.6203 60.32 R.sub.2 = -1122.04 T.sub.1 = 5.08 R.sub.3 = 111.11 S.sub.3 = VARIABLE II 1.7550 27.57 R.sub.4 = -198.69 T.sub.2 = 7.62 R.sub.5 = -82.29 -- III 1.6203 60.32 R.sub.5 = -82.29 T.sub.3 = 5.08 R.sub.6 = 166.79 S.sub.4 = 203.20 IV 1.7550 27.57 R.sub.7 = 416.23 T.sub.4 = 5.08 R.sub.8 = 93.46 S.sub.5 = VARIABLE V 1.6203 60.32 R.sub.9 = 380.00 T.sub.5 = 10.16 R.sub.10 = -146.62 S.sub.6 = 0.508 VI 1.6203 60.32 R.sub.11 = 60.17 T.sub.6 = 17.78 R.sub.12 = -82.29 -- VII 1.7550 27.57 R.sub.12 = -82.29 T.sub.7 = 5.08 R.sub.13 = 380.00 __________________________________________________________________________ wherein S 2 , S 3 , S 5 and S 6 are defined for various focal lengths by the following table: ______________________________________ FOCAL LENGTH S.sub.2 - 335.00 S.sub.3 S.sub.5 ______________________________________ 300 7.534 57.620 7.468 350 20.531 44.623 13.033 400 29.824 35.330 18.022 450 36.664 28.490 22.561 500 41.820 23.334 26.736 550 45.783 19.370 30.608 600 48.882 16.272 34.226 650 51.338 13.815 37.627 700 53.310 11.844 40.842 750 54.908 10.246 43.894 800 56.215 8.939 46.803 850 57.291 7.863 49.586 900 58.154 7.000 52.492 ______________________________________ wherein M 1 identifies an objective light gathering mirror, the Roman numerals I-VII identify the respective lens elements from the mirror to the image plane, η D is the refractive index; ν D is the dispersion number R 1 -R 13 represent the radii of successive surfaces from the mirror to the image plane, and T 1 -T 7 and S 2 -S 6 represent the thicknesses of lens elements and air spaces, respectively, from the mirror to the image plane, with all dimensions being expressed in millimeters, and wherein the design parameters may be renormalized to any other focal length, F n-3n by multiplying each of the surface radii, thicknesses and air spaces by the ratio of F n /F 300 .

Claim 24

A zoom optical system comprising: an objective mirror having a predetermined focal length and adapted to form a real image at a predetermined focal plane; a virtual zoom relay optically coupled to said objective mirror, said relay including a first group of first refractive lens elements positioned ahead of said predetermined focal plane, said first groups including at least one axially movable lens element, said relay further including a second group of second refractive lens elements spaced from said first group by a distance substantially greater than the distance between adjacent lens elements of said first group, said second group including at least one axially movable lens element, said first and second lens elements cooperating to form a real image at a second predetermined focal plane behind the last of said second elements but at no other point.

Claim 25

A zoom optical system comprising: an objective mirror having a predetermined focal length and adapted to form a real image at a predetermined focal plane; a virtual zoom relay optically coupled to said objective mirror, said relay including a first group of first refractive lens elements positioned ahead of said predetermined focal plane, said first groups including at least one axially movable lens element, said relay further including a second group of second refractive lens elements spaced from said first group by a distance substantially greater than the distance between adjacent lens elements of said first group, said second group including at least one axially movable lens element, said first and second lens elements cooperating to form a real image at a second predetermined focal plane behind the last of said second elements but at no other point.

Claim 26

A zoom optical system as recited in claim 14 further including a flat folding mirror interposed between said first group and said second group.