Catadioptric optical system

Abstract

A catadioptric optical system in sequence of ray tracing comprises a first mirrors group of Ritchey-Chrétien type hyperbolic mirrors with positive diopter including a concave primary mirror having a central through hole and a convex secondary mirror, a second corrector lens group with negative diopter positioned at the image-side of the first mirrors group including a first meniscus lens element having positive refractive power and a convex object-side surface, a second lens element having negative refractive power and biconcave surfaces, a third meniscus lens element having negative refractive power and a concave object-side surface, and a fourth lens element having positive refractive power and biconvex surfaces. The infinite conjugate beams of incident light within field of view pass through the catadioptric optical system to become a corrected beam having a small CRA angle.

Claims

1. A catadioptric optical system, comprising in sequence of ray tracing: a first mirrors group of Ritchey-Chrétien type hyperbolic mirrors with positive diopter including a concave primary mirror having a central through hole and a convex secondary mirror; and a second corrector lens group with negative diopter positioned at an image side of the first mirrors group and from the image side of the first mirrors group in order including a first meniscus lens element having positive refractive power and a convex object-side surface, a second lens element with negative refractive power having a concave object-side surface and a concave image-side surface, a third meniscus lens element having negative refractive power and a concave object-side surface, and a fourth lens element with positive refractive power having a convex object-side surface and a convex image-side surface; wherein a diopter of the whole catadioptric optical system is DW, a diopter of the second corrector lens group is DL, and the following condition is satisfied: $\frac{\mathrm{DL}}{\mathrm{DW}}=\left(P_4{\mathrm{EFL}}^4+P_3{\mathrm{EFL}}^3+P_2{\mathrm{EFL}}^2+P_1\mathrm{EFL}+P_0\right)*\left(1\pm 10\%\right);$ wherein
P.sub.0=−4.95*10.sup.−1;
P.sub.1=−1.81*10.sup.−3;
P.sub.2=5.59*10.sup.−7;
P.sub.3=−7.76*10.sup.−11;
P.sub.4=4.4*10.sup.−15; and EFL is an effective focal length of the catadioptric optical system.

2. The catadioptric optical system of claim 1, wherein the first lens element is constituted of a singular lens element and has an image-side surface being concave.

3. The catadioptric optical system of claim 1, wherein the third lens element is constituted of a singular lens element and has an image-side surface being convex.

4. The catadioptric optical system of claim 1, wherein a diopter of the first lens element is DL1, a diopter of the second lens element is DL2, a diopter of the third lens element is DL3, a diopter of the fourth lens element is DL4, and the following conditions are satisfied: $\frac{\mathrm{DL}1}{\mathrm{DL}}=\left(K_4{\mathrm{EFL}}^4+K_3{\mathrm{EFL}}^3+K_2{\mathrm{EFL}}^2+K_1\mathrm{EFL}+K_0\right)*\left(1\pm 10\%\right);$ wherein $K_0=-3.32;$ $K_1=1.23*{10}^{-3};$ $K_2=-3.86*{10}^{-7};$ $K_3=5.68*{10}^{-11};$ $K_4=-3.56*{10}^{-15};$ $\frac{\mathrm{DL}2}{\mathrm{DL}}=\left(L_4{\mathrm{EFL}}^4+L_3{\mathrm{EFL}}^3+L_2{\mathrm{EFL}}^2+L_1\mathrm{EFL}+L_0\right)*\left(1\pm 10\%\right);$ wherein $L_0=9.82;$ $L_1=-4.91*{10}^{-4};$ $L_2=-2.48*{10}^{-7};$ $L_3=7.24*{10}^{-11};$ $L_4=-3.11*{10}^{-15};$ $\frac{\mathrm{DL}3}{\mathrm{DL}}=\left(M_4{\mathrm{EFL}}^4+M_3{\mathrm{EFL}}^3+M_2{\mathrm{EFL}}^2+M_1\mathrm{EFL}+M_0\right)*\left(1\pm 10\%\right);$ wherein $M_0=2.74;$ $M_1=1.32*{10}^{-3};$ $M_2=-8.02*{10}^{-7};$ $M_3=1.53*{10}^{-10};$ $M_4=-9.43*{10}^{-15};$ $\frac{\mathrm{DL}4}{\mathrm{DL}}=\left(N_4{\mathrm{EFL}}^4+N_3{\mathrm{EFL}}^3+N_2{\mathrm{EFL}}^2+N_1\mathrm{EFL}+N_0\right)*\left(1\pm 10\%\right);$ wherein
N.sub.0=−5.99;
N.sub.1=−1.52*10.sup.−3;
N.sub.2=1*10.sup.−6;
N.sub.3=−1.95*10.sup.−10;
N.sub.4=1.11*10.sup.−14; and EFL is an effective focal length of the catadioptric optical system.

5. The catadioptric optical system of claim 4, wherein a composite diopter of the first lens element and the second lens element is DL12, a composite diopter of the second lens element and the third lens element is DL23, and a composite diopter of the third lens element and the fourth lens element is DL34, and the following conditions are satisfied: $\frac{\mathrm{DL}12}{\mathrm{DL}}=\left(R_4{\mathrm{EFL}}^4+R_3{\mathrm{EFL}}^3+R_2{\mathrm{EFL}}^2+R_1\mathrm{EFL}+R_0\right)*\left(1\pm 10\%\right);$ wherein $R_0=6.05;$ $R_1=-2.7*{10}^{-4};$ $R_2=-1.43*{10}^{-7};$ $R_3=4.21*{10}^{-11};$ $R_4=-1.66*{10}^{-15};$ $\frac{\mathrm{DL}23}{\mathrm{DL}}=\left(S_4{\mathrm{EFL}}^4+S_3{\mathrm{EFL}}^3+S_2{\mathrm{EFL}}^2+S_1\mathrm{EFL}+S_0\right)*\left(1\pm 10\%\right);$ wherein $S_0=11.7;$ $S_1=2.38*{10}^{-3};$ $S_2=-1.74*{10}^{-6};$ $S_3=3.46*{10}^{-10};$ $S_4=-1.98*{10}^{-14};$ $\frac{\mathrm{DL}34}{\mathrm{DL}}=\left(T_4{\mathrm{EFL}}^4+T_3{\mathrm{EFL}}^3+T_2{\mathrm{EFL}}^2+T_1\mathrm{EFL}+T_0\right)*\left(1\pm 10\%\right);$ wherein
T.sub.0=−4.23;
T.sub.1=1.66*10.sup.−4;
T.sub.2=1.16*10.sup.−7;
T.sub.3=−3.25*10.sup.−11;
T.sub.4=1.2*10.sup.−15; and EFL is an effective focal length of the catadioptric optical system.

6. The catadioptric optical system of claim 1, wherein the first lens element, the second lens element, the third lens element and the fourth lens element are made of the same optical material.

7. The catadioptric optical system of claim 6, wherein the first lens element, the second lens element, the third lens element and the fourth lens element are made of glass material, a refractive index of the glass material is nd, an Abbe number of the glass material is νd, and the following conditions are satisfied:
1.44<nd<1.47; and
64.41<νd<71.19.

8. The catadioptric optical system of claim 6, further comprising a third reflective surfaces group and a fourth image sensing group, wherein the third reflective surfaces group is positioned at an image side of the second corrector lens group and includes a first reflective surface and a second reflective surface, a contained angle is between the first reflective surface and the second reflective surface, an apex of the contained angle is positioned at an optical axis of the catadioptric optical system and faces toward the second corrector lens group, the fourth image sensing group includes a first image sensing device and a second image sensing device respectively placed at an image side of the first reflective surface and an image side of the second reflective surface.

9. The catadioptric optical system of claim 8, wherein a distance on the optical axis between the convex object-side surface of the first lens element facing toward the convex secondary mirror and the convex image-side surface of the fourth lens element facing toward the third reflective surfaces group is TLL1L4, and the following condition is satisfied:
TLL1L4=(U.sub.4EFL.sup.4+U.sub.3EFL.sup.3+U.sub.2EFL.sup.2+U.sub.1EFL+U.sub.0)*(1±10%); wherein
U.sub.0=−2.85*10.sup.2;
U.sub.1=3.87*10.sup.−1;
U.sub.2=−1.37*10.sup.−4;
U.sub.3=2.23*10.sup.−8;
U.sub.4=−1.28*10.sup.−12; and EFL is an effective focal length of the catadioptric optical system.

10. The catadioptric optical system of claim 1, wherein a chief ray angle of a corrected beam of the incident light corrected through the catadioptric optical system is CRA, and the following condition is satisfied:
CRA<3.5 degrees.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a schematic view of a catadioptric optical system according to an embodiment of the present invention.

(2) FIG. 1B schematically shows ray tracing of incident light within the catadioptric optical system of FIG. 1A.

(3) FIG. 2 is a relation diagram of chief ray angles vs. field of views of corrected beams from the catadioptric optical system of FIG. 1A.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(4) The present catadioptric optical system is a catadioptric telescope comprising Ritchey-Chrétien type primary and secondary hyperbolic mirrors, four elements corrector lens group and a reflective surfaces group. The infinite conjugate beams of incident light falling on the primary mirror, converging to the secondary mirror are reflected, then passing and being corrected through the corrector lens group to become corrected beams having small chief ray angles. The corrected beams having small chief ray angles are reflected by the reflective surfaces group and then focused unto image sensing devices, correspondingly.

(5) The present catadioptric optical system will be described in detail according to the following embodiment accompanying with the appended drawings.

(6) FIG. 1A shows a schematic view of a catadioptric optical system according to an embodiment of the present invention, and FIG. 1B schematically shows ray tracing of incident light within the catadioptric optical system of FIG. 1A. In the embodiment, the catadioptric optical system comprises in sequence of ray tracing a first mirrors group 10 with positive diopter and constituted by Ritchey-Chrétien type hyperbolic mirrors including a concave primary mirror 110 having a central through hole 112 and a convex secondary mirror 120, both of a concave reflective mirror surface 111 of the primary mirror 110 and a convex reflective mirror surface 121 of the secondary mirror 120 being aspheric; and a second corrector lens group 20 with negative diopter positioned at an image side of the first mirrors group 10 and from the image side of the first mirrors group 10 in order including a first meniscus lens element 210 with positive refractive power having a convex object-side surface 211 and a concave image-side surface 212, both of the convex object-side surface 211 and the concave image-side surface 212 being spherical, and the first lens element 210 made of glass material; a second lens element 220 with negative refractive power having a concave object-side surface 221 and a concave image-side surface 222, both of the concave object-side surface 221 and the concave image-side surface 222 being spherical and the second lens element made of glass material, a third meniscus lens element with negative refractive power having a concave object-side surface 231 and a convex image-side surface 232, both of the concave object-side surface 231 and the convex image-side surface 232 being spherical and the third lens element made of glass material; and a fourth lens element 240 with positive refractive power having a convex object-side surface 241 and a convex image-side surface 242, both of the convex object-side surface 241 and the convex image-side surface 242 being spherical and the fourth lens element 240 made of glass material.

(7) A third reflective surfaces group 30 is positioned at an image side of the second corrector lens group 20 and includes a first reflective surface 310 and a second reflective surface 320, a contained angle is between the first reflective surface 310 and the second reflective surface 320, an apex 300 of the contained angle is positioned at an optical axis OO′ of the catadioptric optical system and faces toward the second corrector lens group 20.

(8) A fourth image sensing group includes a first image sensing device 40 and a second image sensing device 42 respectively placed at corresponding image surfaces of the present catadioptric optical system, which are located at an image side of the first reflective surface 310 and an image side of the second reflective surface 320. In various implements of the present invention, the first image sensing device 40 can be a linear image sensing device and the second image sensing device 42 can be an area-array image sensing device.

(9) The optical data of five implements of the present catadioptric optical system of FIG. 1A are described in Table I through Table V.

(10) TABLE-US-00001 TABLE I EFL(mm) = 2244 Refractive Abbe Effective Curvature radius Conic Thickness index number focal length Surface (mm) constant (mm) (nd) (νd) (EFL) 111 Spherical −1088.749 −1.220708721 −375.99 −544.37 conic surface 121 Spherical −476.837 −5.500907062 418.30 −238.42 conic surface 211 Spherical 158.455 17.19 1.46 67.8 454.88 surface 212 Spherical 645.910 43.27 surface 221 Spherical −96.672 6.25 1.46 67.8 −108.59 surface 222 Spherical 103.816 9.10 surface 231 Spherical −113.502 10.71 1.46 67.8 −283.02 surface 232 Spherical −961.309 3.05 surface 241 Spherical 203.721 22.39 1.46 67.8 142.19 surface 242 Spherical −91.987 20.00 surface 310 First infinite — — reflective surface 320 Second infinite — reflective surface

(11) TABLE-US-00002 TABLE II EFL(mm) = 3366 Refractive Abbe Effective Curvature radius Conic Thickness index number focal length Surface (mm) constant (mm) (nd) (νd) (mm) 111 Spherical −1633.106 −1.213719458 −564.00 −816.55 conic surface 121 Spherical −715.280 −5.437490816 628.50 −357.64 conic surface 211 Spherical 238.352 19.86 1.46 67.8 681.93 surface 212 Spherical 990.329 65.09 surface 221 Spherical −147.858 6.02 1.46 67.8 −163.62 surface 222 Spherical 152.887 13.62 surface 231 Spherical −134.836 14.93 1.46 67.8 −464.38 surface 232 Spherical −383.284 4.17 surface 241 Spherical 406.209 25.67 1.46 67.8 219.76 surface 242 Spherical −130.601 45.00 surface 310 First Infinite — — reflective surface 320 Second Infinite — reflective surface

(12) TABLE-US-00003 TABLE III EFL(mm) = 4488 Refractive Abbe Effective Radius curvature Conic Thickness index number focal length Surface (mm) constant (mm) (nd) (νd) (mm) 111 Spherical −2177.343 −1.204980904 −752.06 −1088.67 conic surface 121 Spherical −953.934 −5.363546473 840.16 −476.97 conic surface 211 Spherical 318.001 19.88 1.46 67.8 908.29 surface 212 Spherical 1337.390 87.04 surface 221 Spherical −201.209 6.65 1.46 67.8 −217.45 surface 222 Spherical 197.980 18.20 surface 231 Spherical −156.538 19.20 1.46 67.8 −680.98 surface 232 Spherical −327.413 5.74 surface 241 Spherical 730.741 28.93 1.46 67.8 300.29 surface 242 Spherical −166.657 45.00 surface 310 First Infinite — — reflective surface 320 Second Infinite — reflective surface

(13) TABLE-US-00004 TABLE IV EFL(mm) = 5610 Refractive Abbe Effective Curvature radius Conic Thickness index number focal length Surface (mm) constant (mm) (nd) (νd) (mm) 111 Spherical −2721.783 −1.174198069 −940.08 −1360.89 conic surface 121 Spherical −1192.018 −5.039033272 1062.85 −596.01 conic surface 211 Spherical 424.777 20.35 1.46 67.8 1115.25 surface 212 Spherical 2524.751 110.08 surface 221 Spherical −291.321 19.26 1.46 67.8 −257.93 surface 222 Spherical 201.745 24.91 surface 231 Spherical −177.081 20.00 1.46 67.8 −887.18 surface 232 Spherical −325.784 11.87 surface 241 Spherical 660.495 33.26 1.46 67.8 362.55 surface 242 Spherical −217.383 45.00 surface 310 First Infinite — — reflective surface 320 Second Infinite — reflective surface

(14) TABLE-US-00005 TABLE V EFL(mm) = 6732 Refractive Abbe Effective Curvature radius Conic Thickness index number focal length Surface (mm) constant (mm) (nd) (νd) (mm) 111 Spherical −3266.086 −1.16201498 −1128.18 −1633.04 conic surface 121 Spherical −1430.321 −4.915618217 1289.51 −715.16 conic surface 211 Spherical 552.964 21.41 1.46 67.8 1325.23 surface 212 Spherical 6348.860 133.46 surface 221 Spherical −337.652 15.44 1.46 67.8 −304.48 surface 222 Spherical 239.664 30.92 surface 231 Spherical −191.216 20.00 1.46 67.8 −1260.53 surface 232 Spherical −295.756 23.92 surface 241 Spherical 1060.753 36.88 1.46 67.8 447.82 surface 242 Spherical −250.495 45.00 surface 310 First Infinite — — reflective surface 320 Second Infinite — reflective surface

(15) In the implements of Table I through Table V, with the implement of Table I as an example for explanation: the numberings of “Surface” column correspond element numerals shown in the drawings, “Thickness” column represents an on-axis air (vacuum) gap between adjacent lens surfaces or a lens element thickness, for instance −375.99 mm means an air (vacuum) gap on the optical axis OO′ between the concave reflective mirror surface 111 and the convex reflective mirror surface 121, 418.30 mm means an air (vacuum) gap on the optical axis between the convex reflective surface 121 and the object-side surface 211 of the first lens element 210, 17.19 mm means a thickness of the first lens element 210, and so on. Besides, in the implement of Table I, a distance between the first reflective surface 310 and the corresponding image surface of the present catadioptric optical system is 41.05 mm, a distance between the second reflective surface 320 and the corresponding image surface of the present catadioptric optical system is also 41.05 mm; in the implement of Table II, a distance between the first reflective surface 310 and the corresponding image surface of the present catadioptric optical system is 67.04 mm, a distance between the second reflective surface 320 and the corresponding image surface of the present catadioptric optical system is also 67.04 mm; in the implement of Table III, a distance between the first reflective surface 310 and the corresponding image surface of the present catadioptric optical system is 116.51 mm, a distance between the second reflective surface 320 and the corresponding image surface of the present catadioptric optical system is also 116.51 mm; in the implement of Table IV, a distance between the first reflective surface 310 and the corresponding image surface of the present catadioptric optical system is 136.48 mm, a distance between the second reflective surface 320 and the corresponding image surface of the present catadioptric optical system is also 136.48 mm; in the implement of Table V, a distance between the first reflective surface 310 and the corresponding image surface of the present catadioptric optical system is 161.97 mm, a distance between the second reflective surface 320 and the corresponding image surface of the present catadioptric optical system is also 161.97 mm.

(16) In the embodiment, a diopter of the catadioptric optical system is DW, a diopter of the second corrector lens group is DL, and the following condition is satisfied:

(17) $\frac{DL}{DW}=\left(P_4{\mathrm{EFL}}^4+P_3{\mathrm{EFL}}^3+P_2{\mathrm{EFL}}^2+P_1\mathrm{EFL}+P_0\right)*\left(1\pm 10\%\right);$
wherein,
P.sub.0=−4.95*10.sup.−1,
P.sub.1=−1.81*10.sup.−3,
P.sub.2=5.59*10.sup.−7,
P.sub.3=−7.76*10.sup.−11,
P.sub.4=4.4*10.sup.−15,
EFL is an effective focal length of the catadioptric optical system, and (±10%) means a tolerance allowance range of the present catadioptric optical system under an actual measure.

(18) In the embodiment, a diopter of the first lens element is DL1, a diopter of the second lens element is DL2, a diopter of the third lens element is DL3, a diopter of the fourth lens element is DL4, and the following conditions are satisfied:

(19) 0$\frac{\mathrm{DL}1}{\mathrm{DL}}=\left(K_4{\mathrm{EFL}}^4+K_3{\mathrm{EFL}}^3+K_2{\mathrm{EFL}}^2+K_1\mathrm{EFL}+K_0\right)*\left(1\pm 10\%\right);$
wherein,

(20) $K_0=-3.32,K_1=1.23*{10}^{-3},K_2=-3.86*{10}^{-7},K_3=5.68*{10}^{-11},K_4=-3.56*{10}^{-15},\frac{\mathrm{DL}2}{\mathrm{DL}}=\left(L_4{\mathrm{EFL}}^4+L_3{\mathrm{EFL}}^3+L_2{\mathrm{EFL}}^2+L_1\mathrm{EFL}+L_0\right)*\left(1\pm 10\%\right);$
wherein,

(21) $L_0=9.82,L_1=-4.91*{10}^{-4},L_2=-2.48*{10}^{-7},L_3=7.24*{10}^{-11},L_4=-3.11*{10}^{-15},\frac{\mathrm{DL}3}{\mathrm{DL}}=\left(M_4{\mathrm{EFL}}^4+M_3{\mathrm{EFL}}^3+M_2{\mathrm{EFL}}^2+M_1\mathrm{EFL}+M_0\right)*\left(1\pm 10\%\right);$
wherein,

(22) $M_0=2.74,M_1=1.32*{10}^{-3},M_2=-8.02*{10}^{-7},M_3=1.53*{10}^{-10},M_4=-9.43*{10}^{-15},\frac{\mathrm{DL}4}{\mathrm{DL}}=\left(N_4{\mathrm{EFL}}^4+N_3{\mathrm{EFL}}^3+N_2{\mathrm{EFL}}^2+N_1\mathrm{EFL}+N_0\right)*\left(1\pm 10\%\right);$
wherein,
N.sub.0=−5.99,
N.sub.1=−1.52*10.sup.−3,
N.sub.2=1*10.sup.−6,
N.sub.3=−1.95*10.sup.−10,
N.sub.4=1.11*10.sup.−14,
EFL is an effective focal length of the catadioptric optical system, and (±10%) means a tolerance allowance range of the present catadioptric optical system under an actual measure.

(23) In the embodiment, a composite diopter of the first lens element and the second lens element is DL12, a composite diopter of the second lens element and the third lens element is DL23, and a composite diopter of the third lens element and the fourth lens element is DL34, and the following conditions are satisfied: DL12

(24) $\frac{\mathrm{DL}12}{\mathrm{DL}}=\left(R_4{\mathrm{EFL}}^4+R_3{\mathrm{EFL}}^3+R_2{\mathrm{EFL}}^2+R_1\mathrm{EFL}+R_0\right)*\left(1\pm 10\%\right);$
wherein,

(25) $R_0=6.05,R_1=-2.7*{10}^{-4},R_2=-1.43*{10}^{-7},R_3=4.21*{10}^{-11},R_4=-1.66*{10}^{-15},\frac{\mathrm{DL}23}{\mathrm{DL}}=\left(S_4{\mathrm{EFL}}^4+S_3{\mathrm{EFL}}^3+S_2{\mathrm{EFL}}^2+S_1\mathrm{EFL}+S_0\right)*\left(1\pm 10\%\right);$
wherein,

(26) $S_0=11.7,S_1=2.38*{10}^{-3},S_2=-1.74*{10}^{-6},S_3=3.46*{10}^{-10},S_4=-1.98*{10}^{-14},\frac{\mathrm{DL}34}{\mathrm{DL}}=\left(T_4{\mathrm{EFL}}^4+T_3{\mathrm{EFL}}^3+T_2{\mathrm{EFL}}^2+T_1\mathrm{EFL}+T_0\right)*\left(1\pm 10\%\right);$
wherein,
T.sub.0=−4.23,
T.sub.1=1.66*10.sup.−4,
T.sub.2=1.16*10.sup.−7,
T.sub.3=−3.25*10.sup.−11,
T.sub.4=1.2*10.sup.−15,
EFL is an effective focal length of the catadioptric optical system, and (±10%) means a tolerance allowance range of the present catadioptric optical system under an actual measure.

(27) Please refer to FIG. 1B, when the incident light projects unto the primary mirror 110, the incident light is reflected and converging to the secondary mirror 120, then reflected again and passing the central hole 112 of the primary mirror 110, and then projecting unto the second corrector lens group 20. The incident light is corrected by the second corrector lens group 20 to become corrected beams with small chief ray angles. Then, the corrected beams with small chief ray angles project unto the first reflective surface 310 and the second reflective surface 320 of the third reflective surfaces group 30. Then, the corrected beams are split and reflected by the first reflective surface 310 and the second reflective surface 320 and being focused unto focal planes of the first image sensing device 40 and the second image sensing device 42. In the implements of the present invention, the first image sensing device 40 can be a linear image sensing device and the second image sensing device 42 can be an area-array image sensing device.

(28) Table VI shows a correlation between field of views vs. chief ray angles of the corrected beams of the present catadioptric optical systems in the implements corresponding to Table I through Table V. FIG. 2 is a relation diagram of the chief ray angles vs. the field of views of the corrected beams. It is clearly seen the present catadioptric optical system has capability to correct the incident light to become corrected beams with chief ray angles less than 3.5 degrees. The present catadioptric optical system is suitable for a Ritchey-Chrétien type telescope with small chief ray angles, which is adaptable for a satellite remote-sensing images instrument.

(29) TABLE-US-00006 TABLE VI FOV CRA- CRA- CRA- CRA- CRA- (degree) Table I Table II Table III Table IV Table V 0.0 0.00 0.00 0.00 0.00 0.00 0.1 0.42 0.43 0.43 0.41 0.38 0.2 0.84 0.87 0.86 0.83 0.76 0.3 1.26 1.30 1.29 1.24 1.15 0.4 1.68 1.73 1.72 1.67 1.54 0.5 2.09 2.17 2.15 2.09 1.94 0.6 2.51 2.60 2.59 2.53 2.36 0.7 2.92 3.03 3.04 2.98 2.80 0.8 3.32 3.47 3.49 3.45 3.27

(30) It is to be noted that Table I through Table V show optical data of the different implements. However, the data of the different implements are obtained from experiments. The implements depicted above and the appended drawings are exemplary and are not intended to be exhaustive or to limit the scope of the present disclosure to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings.