Lens with an extended range of focus

Abstract

The invention relates to a lens which has an extended range of focus, wherein the lens consists of a solid material, the optical surfaces of the lens are transparent and the lens has a focal power distribution. According to the invention, the focal power distribution F.sub.G of the lens (1), in relation to a plane perpendicular to the optical axis (10), changes as a function of the radial height r and of the azimuth angle phi of the aperture between a base value of the focal power F.sub.L not equal to zero and a maximum value F.sub.Smax. Hence, the focal power distribution emerges as
F.sub.G(r,phi)=F.sub.L+F.sub.S(r,phi),
with the spiral focal power component
F.sub.S(r,phi)=F.sub.Smax(r)*w(phi),
where F.sub.Smax(r) depends nonlinearly on the radius and w(phi) is a factor for the focal power component with a spiral profile.

Claims

1. A lens with an extended range of focus, wherein the lens consists of a solid, transparent material and has two manufactured optical surfaces, wherein the lens has a focal power distribution F.sub.G, characterized in that the focal power distribution F.sub.G of the lens, in relation to a plane perpendicular to the optical axis, changes as a function of the radial height r and of the azimuth angle phi of the aperture between a base value of the focal power F.sub.L not equal to zero and a maximum value F.sub.Smax and hence results in the focal power distribution
F.sub.G(r,phi)=F.sub.L+F.sub.S(r,phi), with a spiral focal power component
F.sub.S(r,phi)=F.sub.Smax(r,phi)*w(phi), where F.sub.Smax(r) depends nonlinearly on the radius and w(phi) is a factor for the focal power component with the spiral profile, which, in general, is described by the formula $w\left(\mathrm{phi}\right)=\underset{i=1}{\overset{N}{.Math.}}{I}_i\exp \left[-{a_i\left(\mathrm{phi}-w_i\right)}^2\right],$ and w.sub.i are the peak positions in the angular distribution function; I.sub.i are intensity values of the individual peaks; a.sub.i>0 are damping coefficients for the respective peak positions and i is a counter and Mi is a final value.

2. A lens with an extended range of focus, wherein the lens consists of a solid, transparent material and has two manufactured optical surfaces, wherein the lens has a focal power distribution F.sub.G, characterized in that the focal power distribution F.sub.G of the lens, in relation to a plane perpendicular to the optical axis, changes as a function of the radial height r and of the azimuth angle phi of the aperture between a base value of the focal power F.sub.L not equal to zero and a maximum value F.sub.Smax and hence results in the focal power distribution
F.sub.G(r,phi)=F.sub.L+F.sub.S(r,phi), with a spiral focal power component
F.sub.S(r,phi)=F.sub.Smax(r,phi)*w(phi), where F.sub.Smax(r) depends nonlinearly on the radius and w(phi) is a factor for the focal power component with the spiral profile, which is described as a linear profile by the formula $w\left(\mathrm{phi}\right)=\frac{\mathrm{phi}}{2}.$

3. The lens as claimed in claim 1 or as claimed in claim 2, characterized in that the maximum focal power F.sub.Smax(r) depends nonlinearly on the radius and is described by the polynomial formulae $F_{S\mathrm{ma}x}\left(r\right)=\underset{j=2}{\overset{N}{.Math.}}{c}_j*r^j\mathrm{or}{F}_{S\mathrm{ma}x}\left(r\right)=\underset{j=1}{\overset{N}{.Math.}}{c}_j*r^{2*j},$ with the polynomial coefficients c.sub.j for a refractive focal power and $F_{\mathrm{Sma}x}\left(r\right)=\underset{j=2}{\overset{N}{.Math.}}{k}_j*r^j\mathrm{or}{F}_{\mathrm{Sm}\mathrm{ax}}\left(r\right)=\underset{j=1}{\overset{N}{.Math.}}{k}_j*r^{2*j},$ with the polynomial coefficient k.sub.j for a diffractive focal power, where j is a counter and Nj is a final value.

4. The lens as claimed in claim 1 or as claimed in claim 2, characterized in that the maximum focal power F.sub.Smax(r, phi) depends nonlinearly on the radius and is dependent on the azimuth angle phi of the aperture is described by the polynomial formulae $F_{\mathrm{Sma}x}\left(r,\mathrm{phi}\right)=\underset{j=2}{\overset{N}{.Math.}}{c}_j\left(\mathrm{phi}\right)*r^j\mathrm{or}{F}_{\mathrm{Sma}x}\left(r,\mathrm{phi}\right)=\underset{j=1}{\overset{N}{.Math.}}{c}_j\left(\mathrm{phi}\right)*r^{2*j},$ with the polynomial coefficients c.sub.j for a refractive focal power and $F_{\mathrm{Sma}x}\left(r,\mathrm{phi}\right)=\underset{j=2}{\overset{N}{.Math.}}{k}_j\left(\mathrm{phi}\right)*r^j\mathrm{or}{F}_{\mathrm{Sma}x}\left(r,\mathrm{phi}\right)=\underset{j=1}{\overset{N}{.Math.}}{k}_j\left(\mathrm{phi}\right)*r^{2*j},$ with the polynomial coefficient k.sub.j for a diffractive focal power, where j is a counter and Nj is a final value.

5. The lens as claimed in claim 3, characterized in that the focal power distribution F.sub.G(r, phi) of the lens emerges from a height profile z.sub.G(r, phi) of a second optical surface to be manufactured, which emerges from adding the height profile z.sub.L(r) of a calculated base surface and a height profile z(r, phi), where $\begin{array}{c}{F}_G\left(r,\mathrm{phi}\right)=F_L+F_S\left(r,\mathrm{phi}\right)\\ =z_G\left(r,\mathrm{phi}\right)\\ =z_L\left(r\right)+z\left(r,\mathrm{phi}\right)\end{array}$ applies, where the additive height z(r, phi) changes nonlinearly dependent on the radius, starting from zero to a maximum value z.sub.max(r) which supplies the maximum focal power F.sub.Smax(r), and emerges as a function $z\left(r,\mathrm{phi}\right)=z_{\mathrm{ma}x}\left(r\right)*w\left(\mathrm{phi}\right),\mathrm{with}$ $z_{\mathrm{ma}x}\left(r\right)=\underset{j=2}{\overset{N}{.Math.}}{c}_j*r^j\mathrm{or}{z}_{\mathrm{ma}x}\left(r\right)=\underset{j=1}{\overset{N}{.Math.}}{c}_j*r^{2*j},$ where the radius r changes continuously between 0 and D/2 and the azimuth angle phi of the aperture changes continuously between 0 and 2, as a result of which the optical surface to be manufactured is described by the spiral height profile.

6. The lens as claimed in claim 4, characterized in that the focal power distribution F.sub.G(r, phi) of the lens emerges from a height profile z.sub.G(r, phi) of the second optical surface to be manufactured, which emerges from adding the height profile z.sub.L(r) of a calculated base surface and a height profile z(r, phi), where $\begin{array}{c}{F}_G\left(r,\mathrm{phi}\right)=F_L+F_S\left(r,\mathrm{phi}\right)\\ =z_G\left(r,\mathrm{phi}\right)\\ =z_L\left(r\right)+z\left(r,\mathrm{phi}\right)\end{array}$ applies, where the additive height z(r, phi) changes nonlinearly dependent on the radius and dependent on the azimuth angle phi of the aperture, starting from zero to a maximum value z.sub.max(r, phi) which supplies the maximum focal power F.sub.Smax(r, phi), and emerges as a function $z\left(r,\mathrm{phi}\right)=z_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)*w\left(\mathrm{phi}\right),\mathrm{with}$ $z_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)=\underset{j=2}{\overset{N}{.Math.}}{c}_j\left(\mathrm{phi}\right)*r^j\mathrm{or}{z}_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)=\underset{j=1}{\overset{N}{.Math.}}{c}_j\left(\mathrm{phi}\right)*r^{2*j},$ where the radius r changes continuously between 0 and D/2 and the azimuth angle phi of the aperture changes continuously between 0 and 2, as a result of which the optical surface to be manufactured is described by the spiral height profile.

7. The lens as claimed in claim 3, characterized in that the focal power component with the spiral profile F.sub.S(r, phi) emerges from the effect of an optical grating applied to a manufactured second optical surface with the focal power F.sub.L, where
F.sub.G(r,phi)=F.sub.L+F.sub.S(r,phi)=F.sub.L+Phase(r,phi) applies, and the frequency of the optical grating changes nonlinearly dependent on the radius, starting from a base value zero to a maximum value Phase.sub.max which supplies the maximum focal power F.sub.Smax, wherein the following applies to the spiral focal power profile: $\begin{array}{c}{F}_S\left(r.Math.\mathrm{phi}\right)=F_{S\mathrm{ma}x}\left(r\right)*w\left(\mathrm{phi}\right)\\ =\mathrm{Phase}\left(r,\mathrm{phi}\right)\\ ={\mathrm{Phase}}_{\mathrm{ma}x}\left(r\right)*w\left(\mathrm{phi}\right),\end{array}$ $\mathrm{with}$ ${\mathrm{Phase}}_{\mathrm{ma}x}\left(r\right)=\underset{j=2}{\overset{N}{.Math.}}{k}_j*r^j\mathrm{or}{\mathrm{Phase}}_{\mathrm{ma}x}\left(r\right)=\underset{j=1}{\overset{N}{.Math.}}{k}_j*r^{2*j},$ where the radius r changes continuously between 0 and D/2 and the azimuth angle phi of the aperture changes continuously between 0 and 2, as a result of which the optical grating has a spiral phase profile.

8. The lens as claimed in claim 4, characterized in that the focal power component with the spiral profile F.sub.S(r, phi) emerges from the effect of an optical grating applied to a manufactured second optical surface with the focal power F.sub.L, where
F.sub.G(r,phi)=F.sub.L+F.sub.S(r,phi)=F.sub.L+Phase(r,phi) applies, and the frequency of the optical grating changes nonlinearly dependent on the radius and dependent on the azimuth angle phi of the aperture, starting from a base value zero to a maximum value Phase.sub.max which supplies the maximum focal power F.sub.Smax(r, phi), wherein the following applies to the spiral focal power profile: $\begin{array}{c}{F}_S\left(r,\mathrm{phi}\right)=F_{\mathrm{Sm}\mathrm{ax}}\left(r,\mathrm{phi}\right)*w\left(\mathrm{phi}\right)\\ =\mathrm{Phase}\left(r,\mathrm{phi}\right)\\ ={\mathrm{Phase}}_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)*w\left(\mathrm{phi}\right),\end{array}$ $\mathrm{with}$ ${\mathrm{Phase}}_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)=\underset{j=2}{\overset{N}{.Math.}}{k}_j\left(\mathrm{phi}\right)*r^j$ $\mathrm{or}$ ${\mathrm{Phase}}_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)=\underset{j=1}{\overset{N}{.Math.}}{k}_j\left(\mathrm{phi}\right)*r^{2*j},$ where the radius r changes continuously between 0 and D/2 and the azimuth angle phi of the aperture changes continuously between 0 and 2, as a result of which the optical grating has a spiral phase profile.

9. The lens as claimed in claim 3, characterized in that the focal power component with the spiral profile F.sub.S emerges from an additive or subtractive refractive index distribution n(r, phi), wherein the material of the lens has a refractive index distribution which changes nonlinearly dependent on the radius, starting from a base value n.sub.2 to a maximum value n.sub.max, where
F.sub.G(r,phi)=F.sub.L+F.sub.S(r,phi)=F.sub.L+n(r,phi) applies and the following applies to the spiral focal power profile: $\begin{array}{c}{F}_S\left(r,\mathrm{phi}\right)=F_{\mathrm{Sm}\mathrm{ax}}\left(r\right)*w\left(\mathrm{phi}\right)\\ =n\left(r,\mathrm{phi}\right)\\ =n_{\mathrm{ma}x}\left(r\right)*w\left(\mathrm{phi}\right),\end{array}$ $\mathrm{with}$ $n_{\mathrm{ma}x}\left(r\right)=\underset{j=2}{\overset{N}{.Math.}}{c}_j*r^j\mathrm{or}{n}_{\mathrm{ma}x}\left(r\right)=\underset{j=1}{\overset{N}{.Math.}}{c}_j*r^{2*j},$ where the radius r changes continuously between 0 and D/2 and the azimuth angle phi of the aperture changes continuously between 0 and 2, as a result of which a spiral refractive index distribution of the lens material is described.

10. The lens as claimed in claim 4, characterized in that the focal power component with the spiral profile F.sub.S emerges from an additive or subtractive refractive index distribution n(r, phi), wherein the material of the lens has a refractive index distribution, which changes nonlinearly dependent on the radius and dependent on the azimuth angle phi of the aperture, starting from a base value n.sub.2 to a maximum value n.sub.max, where
F.sub.G(r,phi)=F.sub.L+F.sub.S(r,phi)=F.sub.L+n(r,phi) applies and the following applies to the spiral focal power profile: $\begin{array}{c}{F}_S\left(r,\mathrm{phi}\right)=F_{\mathrm{Sma}x}\left(r,\mathrm{phi}\right)*w\left(\mathrm{phi}\right)\\ =n\left(r,\mathrm{phi}\right)\\ =n_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)*w\left(\mathrm{phi}\right),\end{array}$ $\mathrm{with}$ $n_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)=\stackrel{N}{\underset{j=2}{.Math.}}{c}_j\left(\mathrm{phi}\right)*r^j\mathrm{or}$ $n_{\mathrm{ma}x}\left(r,\mathrm{phi}\right)=\underset{j=1}{\overset{N}{.Math.}}{c}_j\left(\mathrm{phi}\right)*r^{2*j},$ where the radius r changes continuously between 0 and D/2 and the azimuth angle phi of the aperture changes continuously between 0 and 2, as a result of which a spiral refractive index distribution of the lens material is described.

11. A lens system with an extended range of focus, characterized in that the lens with the extended range of focus of claim 1 is arranged in a beam path of the lens system as an imaging element.

12. A lens system with an extended range of focus, characterized in that the lens with the extended range of focus of claim 2 is arranged in a beam path of the lens system as an imaging element.

Description

(1) The invention will be described below on the basis of figures, in which:

(2) FIG. 1 shows a top view of a lens with an extended range of focus in a grayscale image with the spiral focal power profile;

(3) FIG. 2 shows a side view of a lens with an extended range of focus with a depiction of the spiral refractive component;

(4) FIG. 3 shows an optical system of a camera with a lens with the extended range of focus;

(5) FIG. 4 shows a schematic depiction of an intraocular lens in the eye;

(6) FIG. 5 shows an azimuth profile of the spiral component of the focal power profile, modulated thereon, with mainly a linear increase;

(7) FIG. 6 shows an azimuth profile of the spiral component of the focal power profile, modulated thereon, with preference for the zero diopter region;

(8) FIG. 7 shows a much exaggerated depiction of an extended focus lens surface with a spiral height profile modulated thereon;

(9) FIG. 8 shows a top view of a lens with an extended range of focus with a depiction of the spiral diffractive component;

(10) FIG. 9 shows a perspective top view of a lens with an extended range of focus with a depiction of the spiral diffractive component;

(11) FIG. 10 shows an azimuth profile of the additional focal power with extended range for the strong diopter position; and

(12) FIG. 11 shows an azimuth profile of the additional focal power with preference for the zero diopter region.

(13) FIG. 1 shows a lens with an extended range of focus with the spiral focal power profile in a top view as step image of the focal power change. In principle, the illustration applies to the cases:

(14) a) Adding a spiral height profile to one of the optical surfaces of the lens as per step 1, which is the base surface.

(15) b) Adding a spiral diffractive structure to one of the optical surfaces of the lens as per step 1, which is the base surface.

(16) c) Adding a spiral refractive index profile in the material of the lens.

(17) In the example, the lens has conventional spherical optical surfaces and a lens thickness, which form a base system which is designed with a base refractive index of 1.5995 for 0 dpt correction. The additional spiral focal power distribution is realized by a spiral refractive index gradient and begins at phi=0 with the refractive index of 1.5995. Depending on radius and angle, the refractive index increases continuously in a spiral fashion and has, for example, a refractive index of 1.61366 at phi=n and r=D/2. This corresponds to a focal power of 1.0 dpt. The refractive index continues to increase continuously and has a refractive index of 1.64615 at phi=2 and r=D/2, corresponding to a focal power of 3.5 dpt. The difference in refractive index between phi=0 and phi=2 is 0.04665. This corresponds to a usable continuous range of focus between 0 dpt and 3.5 dpt.

(18) FIG. 2 shows a side view of a lens with an extended range of focus with a depiction of the spiral refractive component. The lens 1 is initially determined by its base system with the radius R.sub.1 of the first optical surface 2 and the radius R.sub.2 for the calculated base surface 3, and also by the lens thickness d and the refractive index n.sub.2. These parameters are provided for an envisaged basic magnification. An additional material thickness z is added to the calculated shape of the base surface 3 with the radius R.sub.2, with the additional material thickness being z=0 mm at phi=0, then increasing continuously and having its maximum value in the millimeter range at phi=2. In practice, the maximum value will lie slightly in front of the azimuth angle phi=2 in order to realize a continuous, albeit very steep, transition back to the value zero at phi=0, as indicated by the dashed curve denoted by 4a.

(19) Parameters for a lens are specified as an example:

(20) R.sub.1=15.1411 mm radius to be produced

(21) R.sub.2=22.3164 mm calculated radius

(22) d=0.8 mm

(23) n.sub.1=1 (refractive index outside of the lens)

(24) n.sub.2=1.56 (refractive index of the lens medium)

(25) Hence, from the formula

(26) $f=\frac{1}{\left[\frac{n2-n1}{n1}*\left(\frac{1}{R1}-\frac{1}{R2}\right)+\frac{{\left(n2-n1\right)}^2*d}{n1*n2*R1*R2}\right]},$
the focal length of the base lens emerges as 16.233 mm.

(27) A linear helical increase in accordance with the formula

(28) $\begin{array}{c}z\left(r,\mathrm{phi}\right)=z_{\max }\left(r\right)*w\left(\mathrm{phi}\right)\\ =c_1*r^2*\frac{\mathrm{phi}}{2}\end{array}$
as a continuous, spiral height profile with a linear extent is added to the calculated base surface with the radius R.sub.2=22.3164 mm.

(29) With c.sub.1=0.013, a spiral addition which increases the focal length in air up to 20.57 mm, corresponding to 3.5 dpt, is obtained.

(30) FIG. 3 shows an optical system of a camera with a lens 1 according to the invention, which has the extended range of focus. The optical system consists of the extended focus lens 1 and this is followed in the light propagation direction by an aspherical lens 5 with the optical surfaces 17 and 18; this is then followed by a filter 6 and a sensor 7. On the object side, the extended focus lens 1 has a first optical surface 2. The second optical surface 4 with the spiral design is arranged on the image side.

(31) A lens system of a cellular telephone with a focal length of 5.61 mm is shown as an example. In accordance with the formula for the spiral, linear helical increase

(32) $z\left(r,\mathrm{phi}\right)=c_1*r^2*\frac{\mathrm{phi}}{2},$
the shape of the spiral optical surface 4 over the calculated base surface 3 emerges, analogously to as described in relation to FIG. 2, using the parameters c.sub.1=0.01; phi=0 to 2 (azimuth angle); r=radial height between 0 and D/2. The base surface 3 is concave and spherical in the example, with the radius R.sub.2=5.21369 mm.

(33) The optical surfaces 17 and 18 of the lens 5 and the first optical surface 2 of the extended focus lens 1 are rotationally aspherical. The parameters of the lens system are: focal length f=5.61 mm; design length 6.8 mm; aperture 1:2.8.

(34) Lens 1:

(35) Thickness 1.738 mm; material=Zeonex

(36) First optical surface 2: R.sub.1=1.7668 mm

(37) Asphere coefficients:

(38) K=0.162288

(39) A=0.472171E-04

(40) B=0.225901E-02

(41) C=0.179019E-03

(42) D=0.290228E-03

(43) E=0.131193E-03

(44) Second Optical Surface 4

(45) The calculated radius of the base surface 3 for the basic focal power of the lens F.sub.L is R.sub.2=5.21369 mm (concave, spherical). The basic focal length of the lens is 330 mm, corresponding to an additional focal power of at most 3.0 dpt.

(46) The surface shape of the base surface can be described by the formula z.sub.L(r)=R.sub.2sign(R.sub.2){square root over (R.sub.2.sup.2r.sup.2)}. The additive height emerges from

(47) $\begin{array}{c}z\left(r,\mathrm{phi}\right)=z_{\max }\left(r\right)*w\left(\mathrm{phi}\right)\\ =c_1*r^2*\frac{\mathrm{phi}}{2},\end{array}$
with the coefficient of the polynomial c.sub.1=0.01.

(48) The additive height should be added to each surface point of the base surface such that the overall height profile of the second optical surface is determined by the following formula:

(49) $z_G\left(r,\mathrm{phi}\right)=\left(R_2-\mathrm{sign}\left(R_2\right)\sqrt{R_2^2-r^2}\right)+c_1*r^2*\frac{\mathrm{phi}}{2}.$
Lens 5:
Thickness 2.703 mm; material=polycarbonate
Surface 17: R=3.85282 mm
Asphere coefficients:
K=16.027906
A=0.687655E-01
B=0.676838E-01
C=0.101439E+00
D=0.900331E-02
E=0.345714E-01
F=0.101087E-01
G=0.950453E-16
H=0.443668E-17
J=0.105965E-19
Surface 18: R.sub.4=413.75417 mm
Asphere coefficients:
K=0.238656e57
A=0.200963E-01
B=0.297531E-02
C=0.110276E-02
D=0.209745E-03
E=0.935430E-05
F=0.430237E-05
G=0.434653E-06
H=0.475646E-07
J=0.612564E-08
Distance lens 1 to lens 5: 0.571 mm
Distance lens 5 to filter 6: 0.4 mm
Distance filter to image plane of detector 7: 0.4 mm
Thickness of filter 6: 0.4 mm

(50) The optical system has a design length of 6.8 mm. The aperture is 1:2.8. The lens system supplies a sufficiently good image quality, obtained without refocusing, for an object distance from 330 mm to infinity. It is advantageous that the spiral optical second surface is situated on the rear side of the front lens, wherein the residual surface of the rear side, which is not filled by the spiral optical surface, forms a stop 15.

(51) A further exemplary embodiment describes a lens system for a camera with a focal length of f=6.1 mm, having a design length of 6.8 mm and an aperture of 1:2.8. The illustration corresponds to the one shown in FIG. 3. The lens 1 with the extended range of focus has a first optical surface 2 on the object side. The second optical surface 4 thereof corresponds in terms of its surface shape to the calculated base surface 3 and carries the diffractive optical element 16, which supplies the spiral focal power profile in addition to the focal power of the base system.

(52) All optical surfaces 3, 4, 17 and 18 of the lenses 1 and 5 have a rotationally aspherical basic shape.

(53) Lens 1: lens thickness=1.59 mm, material=Zeonex

(54) Optical surface 2: R.sub.1=1.77985

(55) Asphere coefficients:

(56) K=0.113528

(57) A=0.369422E-02

(58) B=0.497838E-05

(59) C=0.526491E-03

(60) Optical surface 4 (corresponds to calculated surface 3): R.sub.2=4.43773

(61) Asphere coefficients:

(62) K=20.010847

(63) A=0.165668E-01

(64) B=0.598703E-01

(65) C=0.239849E+00

(66) D=0.363395E+00

(67) E=0.231421E+00

(68) The diffractive optical element 16 has the coefficient of the spiral polynomial k.sub.1=2.1350E-03.

(69) The additional spiral focal power component is calculated by

(70) $F_{S\mathrm{diffractive}}=2k_1*\frac{\mathrm{phi}}{2}*\frac{}{\mathrm{wl}}$
and the overall focal power emerges as

(71) $\begin{array}{c}{F}_{G\mathrm{diffractive}}=F_L+F_{S\mathrm{diffractive}}\\ =F_L+2k_1*\frac{\mathrm{phi}}{2}*\frac{}{\mathrm{wl}}.\end{array}$

(72) The lens 5 has a thickness of 2.98 mm, material=polycarbonate

(73) Surface 17:_R.sub.3=4.60229 mm

(74) Asphere coefficients:

(75) K=12.980316

(76) A=0.289939E-01

(77) B=0.193341E-01

(78) C=0.430879E-01

(79) D=0.575934E-01

(80) E=0.345714E-01

(81) F=0.101087E-01

(82) Surface 18: R.sub.4=51.75016 mm

(83) Asphere coefficients:

(84) K=0.238656e57

(85) A=0.128992E-01

(86) B=0.257544E-02

(87) C=0.116486E-02

(88) D=0.176791E-03

(89) E=0.381907E-06

(90) F=0.294503E-05

(91) G=0.250155E-06

(92) H=0.303670E-08

(93) J=0.768736E-09

(94) The distance between lens 1 and lens 5 is 1.05 mm; the distance between lens 5 and filter 6 is 0.4 mm and the distance from filter 6 to the image plane of detector 7 is 0.4 mm, with the filter thickness likewise being 0.4 mm.

(95) The lens system supplies a simultaneous range of focus from 330 mm to infinity.

(96) Here, in particular, the expedient selection of the coefficient c in front of the quadratic term supports the achromatization of the lens system.

(97) FIG. 4 shows a schematic illustration of an intraocular lens 11, which is implanted into the eye as extended focus lens 1. In the example, it replaces the natural lens of the eye and is situated in the light path between the cornea 12 and the retina 14 in the aqueous humor 13.

(98) The intraocular lens 11 has a spherical first optical surface 2 and the spiral second optical surface 4. By way of example, the intraocular lens 11 with the extended range of focus has the following parameters for the base system:

(99) R.sub.1=15.1411 mm (produced first optical surface 2)

(100) R.sub.2=22.3164 mm (calculated base surface 3)

(101) Lens thickness d=0.8 mm

(102) Refractive index outside of the lens n.sub.1=1.33

(103) Refractive index of the lens medium n.sub.2=1.56

(104) Using the formula

(105) $f=\frac{1}{\left[\frac{n2-n1}{n1}*\left(\frac{1}{R1}-\frac{1}{R2}\right)+\frac{{\left(n2-n1\right)}^2*d}{n1*n2*R1*R2}\right]},$
the base focal length f=53.97 mm emerges for the base system of the intraocular lens 11 in the aqueous humor 13.

(106) The additional focal power emerges from the additive height on the base surface using the formula

(107) 0$z\left(r,\mathrm{phi}\right)=c_1*r^2*\frac{\mathrm{phi}}{2},$
where c.sub.1=0.013.

(108) The added spiral surface would extend the value of the base focal length from 16.233 mm to 17.2 mm, corresponding to 3.5 dpt. Accordingly, the extended focus lens supplies a variance in the diopter range between 0 dpt and 3.5 dpt.

(109) FIG. 5 shows the azimuth profile of the spiral component of the focal power profile modulated onto the base surface with a predominantly linear increase corresponding to the formula

(110) $\begin{array}{c}z\left(r,\mathrm{phi}\right)=z_{\max }\left(r\right)*w\left(\mathrm{phi}\right)\\ =c_1*r^2*\frac{\mathrm{phi}}{2}\end{array}$
for the additive component of the focal power.

(111) So that this can be produced in an improved fashion and in order to avoid sharp transitions, the curve profile is smoothed near 2.

(112) FIG. 6 shows the azimuth profile of the spiral component of the focal power profile modulated thereon, with preference for the zero diopter region. In practice, it is often desirable to prefer specific diopter regions such as, for example, the zero diopter position. To this end, it is necessary to depart from the linear dependence of the z-height on the angle. By way of example, by means of the function

(113) $\begin{array}{c}z\left(r,\mathrm{phi}\right)=z_{\max }\left(r\right)*w\left(\mathrm{phi}\right)\\ =\underset{j=1}{\overset{N}{.Math.}}{c}_j*r^{2*j}*\exp \left[-a*{\left(\mathrm{phi}-2\right)}^2\right]\end{array}$
with a=0.25, it is possible to realize a preference for the zero diopter region. The angle-dependent component w(phi)=expa*(phi2).sup.2 is depicted in FIG. 6. The small increase between phi=0 and phi=2 causes a small addition of focal power in this angular range and hence a larger surface component for the zero diopter distance.

(114) FIG. 7 shows an exaggerated illustration of the additive height profile with the spiral extent in accordance with FIG. 2. The spiral optical surface 4 is created by virtue of the fact that the azimuth-dependent polynomial function is added to the spherical base surface 3. What is illustrated is the height z over the diameter of the lens surface, which is being purely added to the spherical base surface 3 as per FIG. 2.

(115) FIG. 8 shows a lens with an extended range of focus, which was calculated according to the diffractive approach in accordance with the variant b), in a top view, wherein all that is visible is the spiral diffractive component. In this case of generating the spiral focal power distribution of the lens by means of the diffractive approach, the phase function is:

(116) $\begin{array}{c}\mathrm{Phase}\left(r,\mathrm{phi}\right)={\mathrm{Phase}}_{\max }\left(r\right)*w\left(\mathrm{phi}\right)\\ =.Math.\underset{j=2}{\overset{N}{.Math.}}{k}_j*r^j.Math.*.Math.\underset{i=1}{\overset{M}{.Math.}}{I}_i*\exp \left[-a_i*{\left(\mathrm{phi}-w_i\right)}^2\right].Math..\end{array}$$\mathrm{Using}$$t=\underset{j=2}{\overset{N}{.Math.}}{k}_j*r^j*\underset{i=1}{\overset{M}{.Math.}}{I}_i*\exp \left[-a_i*{\left(\mathrm{phi}-w_i\right)}^2\right],$
the profile(r, phi) emerges as

(117) $\mathrm{Profile}\left(r,\mathrm{phi}\right)=\left(\frac{t}{\mathrm{wl}}-\mathrm{floor}\left(\frac{t}{\mathrm{wl}}\right)\right)*h$$\mathrm{Profile}\left(r,\mathrm{phi}\right)=\left(\begin{array}{c}\frac{\underset{j=2}{\overset{N}{.Math.}}{k}_j*r^j*\underset{i=1}{\overset{M}{.Math.}}{I}_i*\exp \left[-a_i*{\left(\mathrm{phi}-w_i\right)}^2\right]}{\mathrm{wl}}-\\ \mathrm{floor}\left(\frac{\underset{j=2}{\overset{N}{.Math.}}{k}_j*r^j*\underset{i=1}{\overset{M}{.Math.}}{I}_i*\exp \left[-a_i*{\left(\mathrm{phi}-w_i\right)}^2\right]}{\mathrm{wl}}\right)\end{array}\right)*h,$
where k.sub.i is a coefficient of the diffractive polynomial; r is the radius (radial height); I.sub.i are intensities; a.sub.i are damping coefficients; wl is the design wavelength of the DOE and h is the profile depth.

(118) In the special linear case, the following applies:

(119) $\begin{array}{c}\mathrm{Phase}\left(r,\mathrm{phi}\right)={\mathrm{Phase}}_{\max }\left(r\right)*w\left(\mathrm{phi}\right)\\ =k_1*r^2*\frac{\mathrm{phi}}{2}.\end{array}$$\mathrm{Using}$$t=k_1*r^2*\frac{\mathrm{phi}}{2},$
the following emerges:

(120) $\mathrm{Profile}\left(r,\mathrm{phi}\right)=\left(\frac{t}{\mathrm{wl}}t-\mathrm{floor}\left(\frac{t}{\mathrm{wl}}\right)\right)*h=\left(\frac{k_1*r^2*\mathrm{phi}}{\mathrm{wl}*2}-\mathrm{floor}\left(\frac{k_1*r^2*\mathrm{phi}}{\mathrm{wl}*2}\right)\right)*h.$

(121) Example data are: coefficient of the diffractive polynomial k.sub.1=0.0025, the height r in the range from 0 to 3 mm, the azimuth angle phi in the range from 0 to 2, design wavelength of the DOE wl=550 nm, profile depth h=0.001 mm.

(122) FIG. 9 shows the lens with the extended range of focus in a perspective top view on the diameter of the lens with depiction of the spiral diffractive component.

(123) A profile of the angle-dependent factor w(phi) is depicted in FIG. 10.

(124) Using the following modified formula for the angular dependence:
w(phi)=I.sub.1*expa.sub.1*(phiw.sub.1).sup.2+I.sub.2*expa.sub.2*(phiw.sub.2).sup.2,
where
w.sub.1, w.sub.2: peak positions (between 0 and 2*pi),
I.sub.1, I.sub.2: peak intensities, and
a.sub.1, a.sub.2: damping coefficients for the two peaks,
a profile for the azimuth dependence, in which an extended range is reserved for the strongest diopter position (approximately 3 dpt), emerges using, for example, the values:
I.sub.1=0.9; I.sub.2=0.1; a.sub.1=0.8; a.sub.2=0.1; w.sub.1=1.8; w.sub.2=4.5.

(125) Using the values I.sub.1=0.9; I.sub.2=0.1; a.sub.1=0.8; a.sub.2=0.1; w.sub.1=4.5; w.sub.2=0.5, the zero diopter region is clearly preferred by the formula
w(phi)=I.sub.1*exp[a.sub.1*(phiw.sub.1).sup.2]+I.sub.2*exp[a.sub.2*(phiw.sub.2).sup.2],
which is illustrated in FIG. 11.

LIST OF REFERENCE SIGNS

(126) 1 Lens 2 Manufactured first optical surface (spherical, aspherical, radially symmetric, free-form surface) 3 Calculated base surface (spherical, aspherical, radially symmetric, free-form surface) 4 Manufactured second optical surface (spherical, aspherical, radially symmetric, free-form surface, spiral surface) 5 Aspherical lens 6 Filter 7 Sensor 8 Bundle of light 9 Lens edge 10 Optical axis 11 Intraocular lens 12 Cornea 13 Aqueous humor 14 Retina 15 Stop 16 Spiral diffractive optical element (DOE) 17 Optical surface 18 Optical surface F.sub.G Overall focal power of the lens F.sub.L Focal power of the base system of the lens F.sub.S(r, phi) Focal power which is added to the focal power of the base system by the spiral component F.sub.Smax Maximum focal power f.sub.L Focal length of the base system f.sub.S(r, phi) Focal length of the spiral additional focal power N, M Final values i, j Counters c.sub.j, c.sub.1, c.sub.2 Polynomial coefficients for the refractive case k.sub.j, k.sub.1, k.sub.2 Polynomial coefficients for the diffractive case z.sub.max(r) Maximum height, dependent on the radius z.sub.max(r, phi) Maximum height, dependent on the radius and azimuth angle z(r, phi) Additive height on the base surface z.sub.L(r) Height profile of the calculated base surface z.sub.G(r, phi) Height profile of the manufactured optical surface w(phi) Angle-dependent component of the focal power profile w.sub.i, w.sub.1, w.sub.2 Peak positions of the angular distribution function a.sub.i, a.sub.1, a.sub.2 Damping coefficients for the respective peak positions I.sub.i, I.sub.1, I.sub.2 Intensity values of the individual peaks D Lens diameter r Radius (radial height) phi Azimuth angle R.sub.1 Radius of the first optical surface R.sub.2 Radius of the optical base surface n.sub.1 Refractive index of the surrounding medium n.sub.2 Refractive index of the lens d Lens thickness h Profile depth of the diffractive element Application wavelength wl Design wavelength of the diffractive element t Calculation variable floor(t) Integer component Phase.sub.max(r, phi) Maximum value of the grating frequency, which corresponds to the maximum focal power Phase(r, phi) Phase function Profile(r, phi) Phase function reduced to the height h x, y Cartesian coordinates