# Patent

## Title
Lens having an extended range of focus and method of making the same

## Abstract

A lens having an extended range of focus is made of a transparent material and has two optical surfaces. The lens defines an optical axis and a focal power distribution (Ftot) which, 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 calculated basic value of the focal power (Flens) not equal to zero and a maximum value Fspiral max(r, phi).

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
This application is a continuation application of international patent application PCT/EP2012/004026, filed Sep. 26, 2012, designating the United States and claiming priority from German application 10 2011 114 752.0, filed Sep. 29, 2011, and the entire content of both applications is incorporated herein by reference.


FIELD OF THE INVENTION
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. The invention furthermore relates to a method for producing the lens and to the use thereof for influencing the imaging of an image onto the retina of an eye and to the use thereof in a lens system with an extended range of focus.
BACKGROUND OF THE INVENTION
Multifocal lenses should simultaneously meet a number of demands. Initially, a sufficiently good contrast transfer function in two or more focal planes should be ensured. Furthermore, the contrast transfer function should be independent of the size of the pupil. And finally, it should be easy to make the lens; it should not have projections or edges, and therefore have curves which are as smooth as possible.
Such lenses are used, in particular, for correcting visual defects by means of spectacle lenses or as intraocular lenses (IOLs).
In contrast to the monofocal IOLs, which were already introduced many years ago, multifocal lenses were previously only implemented for the bifocal case since there are significant problems in satisfying the aforementioned demands simultaneously. Here, a variant is based upon a special rotationally symmetric ring system, wherein there is sufficiently good imaging for two discrete object-side focal planes, for example at 0 dpt and at a corrective power of approximately 3 dpt, by skillful matching of ring radii, ring widths and ring depths.
Such a bifocal lens is described in U.S. Pat. No. 5,982,543 A and uses a rotationally symmetric Fresnel-like ring system.
U.S. Pat. No. 6,120,148 A describes a rotationally symmetric diffractive ring system. The bifocal lens from U.S. Pat. No. 6,536,899 B1 likewise utilizes a ring system, wherein each ring consists of two sub-rings, which respectively realize the two desired focal lengths.
In a slightly modified form, solutions are also derived herefrom, in which a single lens covers an extended, continuous range of focus. Such lenses are also known by the term “extended depth of focus lens” or else as “EDoF lens”. In United States patent application publication 2006/0176572 A, use is made of a rotationally symmetric system of rings, wherein the individual focal lengths of the rings lie within the desired continuous focal length range. The “extended depth of focus” effect is created by mixing the various focal lengths.
The system in accordance with United States patent application publication 2011/0279912 consists of sectors (“pie slices”) with a focal power increasing in the azimuth direction. Here, the focal power distribution has discrete steps between the sectors.
United States patent application publication 2010/0002310 A1 describes an optical imaging system for a camera which has an extended depth of field range. The extended depth of field is achieved by a combination of several lenses with aspherical surfaces.
A disadvantage in the case of intraocular lenses in particular is that a strong radius curvature is required when using “normal” spherical or aspherical basic lens shapes due to the relatively short focal length caused by the length of the eye. This creates a large lens thickness, a relatively large lens volume with a correspondingly large weight. Since intraocular lenses are manufactured from organic polymers, the refractive index is usually relatively low, leading to a strong radius curvature and hence also a relatively thick lens shape.
SUMMARY OF THE INVENTION
It is an object of the invention to provide a novel lens with an extended range of focus. The novel lens should provide, either individually, in particular as an intraocular lens, or in conjunction with other optical components, optical systems which, while having a sufficiently good imaging quality, provide a large depth of field range. It should be possible to produce the novel lens in a cost-effective manner.
In particular, the novel lens is to have a reduced lens thickness at a given focal power when used as an intraocular lens.
The lens with an extended range of focus includes a solid, transparent material and has two manufactured optical surfaces. According to the invention, the lens has a focal power distribution Ftot which, in relation to a plane perpendicular to the optical axis, is a function of the radial height r and of the azimuth angle of the aperture phi and changes between a basic value of the focal power Flens not equal to zero and a maximum value Fspiral max. Hence, the focal power distribution emerges as

Ftot(r,phi)=Flens+Fspiral(r,phi),

with the spiral focal power component

Fspiral(r,phi)=Fspiral max(r,phi)*w(phi),

where Fspiral max(r, phi) depends nonlinearly on the radius and w(phi) is a factor for the focal power component with a spiral profile.

An essential further aspect of the invention is that a value of the focal power of the lens Flens is split into a focal power component of a refractive base system of the lens Fbase and a structure-shaped focal power component Fstructure, such that

Flens(r)=Fbase(r) +Fstructure(r)

applies. Here, Fbase is a base focal power of a lens, which is determined by lens radii or free-form surface polynomials and lens thickness, as well as refractive index of the lens material, and Fstructure is a focal power which is not described by lens radii or free-form surface polynomials and lens thickness, as well as refractive index of the lens material. Therefore, the term “structure” and the symbol Fstructure is defined in this document as focal power of a structure which is present as a height profile zFresnel of a Fresnel lens in a first case, is present as a phase profile phasestructure of a diffractive optical element (DOE) in a second case or is present as refractive index gradient Δnstructure of a gradient index lens (GRIN lens) in a third case. Therefore, the focal power distribution of the lens according to the invention emerges in the rotationally symmetric case as

Ftot(r,phi)=Fbase(r)+Fstructure(r)+Fspiral max(r,phi)*w(phi).

However, both the base focal power of the lens Fbase and the focal power of the structure Fstructure may have the focal power profile of a free-form surface, wherein the corresponding polynomials are then to be inserted into the equations.

The invention therefore relates to a special, novel lens shape, by means of which it is possible simultaneously to cover a predetermined focal length range, that is, to generate a sufficiently good image quality over an extended range of focus. What dividing the basic value of the focal power of the lens Flens into the base focal power Fbase of the lens to be manufactured and into the focal power of a structure Fstructure realizes is that the lens to be manufactured can be produced with flatter radii. As a result of this, there is a significant reduction in the lens thickness, hence of the lens volume, and therefore also of the lens weight. Such lenses with an extended range of focus find use in optical systems for a camera, a microscope or in optical measurement apparatuses.
A main field of application is an intraocular lens with a variable focal length range. Using the spiral focal power component, it is possible to realize a focusing range from 0 to approximately 3.5 dpt in relation to a fixed base focal power. Such an intraocular lens is usually implanted into the eye after removing the natural lens. However, it can also be employed in addition to the natural lens.
The lens of the invention is made according to the following steps:

    
    
        Step 1: calculating an initially monofocal, virtual base system, which adopts the focusing for a fixed diopter setting (for example, 60 dpt for the healthy human eye in the case of an IOL). This is the basic value of the focal power Flens, which is set by the surface forms of the optical surfaces, the lens thickness and a material type.
        Step 2: dividing the basic value of the focal power Flens into a base focal power Fbase and into the focal power of a structure Fstructure.
    
    


In practice, it was found to be expedient to realize more than 50% of the basic value of the focal power Flens as refractive base focal power Fbase and to realize less than 50% of the basic value of the focal power Flens as focal power of the structure Fstructure. In respect of the occurrence of defects, it is particularly advantageous to realize more than 70% as refractive base focal power Fbase and less than 30% as focal power of the structure Fstructure. The lens to be manufactured with the base focal power Fbase corresponds to a conventional lens with two optical surfaces, which can be embodied spherically and/or aspherically and/or as a free-form surface. At least one of these optical surfaces serves as base surface for realizing the additional focal power distribution, which will be described in the next step but one, step 4.

    
    
        Step 3: determining the parameters of the additional spiral and structure-shaped focal power FSS by adding the spiral focal power distribution Fspiral to the focal power of the structure Fstructure.
        Step 4: adding or subtracting the spiral and structure-shaped focal power distribution Fss(r, phi)=Fstructure(r)+Fspiral(r, phi) obtained in step 3 to the optical effect of the base system Fbase. As a result, the focal power of the lens changes nonlinearly, depending on the radius, with the azimuth angle of the aperture.
        
            “Adding” the spiral and structure-shaped focal power distribution can be brought about by several variants, which can each be used individually or together in any combination:
            a) “Adding” a spiral and Fresnel-shaped height profile zSF(r, phi), which has the spiral and structure-shaped focal power distribution FSS, to one of the optical surfaces of the lens with the base focal power Fbase calculated in step 2. This determined optical surface is the only calculated base surface with the height profile zbase, to which the spiral and Fresnel-shaped height profile zSF(r, phi) is added and thus the profile to be manufactured of this optical surface is set.
            b) “Adding” a spiral and structure-shaped diffractive structure with the additional focal power FSSdiffractive to one of the calculated and manufactured optical surfaces of the lens with the base focal power Fbase in accordance with step 2.
            c) “Adding” a spiral and structure-shaped refractive index profile ΔnSS in the material of the lens. In this case, the calculated surfaces in accordance with step 2 are not modified and manufactured thus.
        
        
        Step 5: Producing the first optical surface and the second optical surface of the lens with the base focal power Fbase, including the application or the introduction of the spiral and structure-shaped focal power distribution at and/or on and/or inside the lens.
    
    


Production methods for the spiral and structure-shaped focal power distribution are in particular:

    
    
        aa) producing the optical surface by hot stamping or injection molding
        ab) producing the optical surface by diamond turning
        ba) production by lithographic etching methods on the optical surface
        bb) production by diamond turning on the optical surface
        ca) production by centrifugal casting from the liquid state
        cb) production by ion implantation.
    
    


The variants a) and/or b) can be applied to one optical surface or else to both optical surfaces of a lens in a manner splitting the effect. Diffractive optical elements can be used additionally or together with the generation of the focal power distribution for color correction. The scope of the invention also includes other methods and measures, by means of which the spiral and structure-shaped focal power distribution according to the invention can be obtained in a lens, for example by the introduction of nanoparticles.
As a result of the above-described procedure, a continuous variation of the additional spiral focal power Fspiral to the focal power of the base system of between 0 and approximately 3.5 dpt is achieved in e.g. an intraocular lens with, in many cases of application, a sufficiently good image quality. As a result of the focal power component of the structure Fstructure, a reduction in the lens thickness by up to 50% is achieved, leading to a reduction in volume and weight of approximately the same order of magnitude.
The radius-dependent and azimuth angle-dependent focal power Ftot(r, phi) emerges from the sum of a basic focal power of the base system Fbase, from the focal power of the additional structure Fstructure and from the additional spiral focal power Fspiral(r, phi) which is dependent on the radius and the angle. Thus, in the rotationally symmetric case, the following applies:




  
    
      F
      tot
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          F
          base
        
        ⁡
        
          (
          r
          )
        
      
      +
      
        [
        
          
            
              F
              structure
            
            ⁡
            
              (
              r
              )
            
          
          +
          
            
              F
              spiral
            
            ⁡
            
              (
              
                r
                ,
                phi
              
              )
            
          
        
        ]
      
    
    =
    
      
        1
        
          f
          base
        
      
      +
      
        
          [
          
            
              1
              
                f
                structure
              
            
            +
            
              1
              
                f
                spiral
              
            
          
          ]
        
        .
      
    
  




Since standardized optical methods are used for producing the lens with the extended range of focus, this lens can be produced in a cost-effective manner.
In the case a) of “adding” a spiral and Fresnel-shaped height profile to one of the optical surfaces of the lens and thereby realizing a spiral and Fresnel-shaped focal power distribution of the overall system, the following observations apply:
The overall focal power Ftot is composed by adding together the basic focal power of the base system Fbase, the focal power of the Fresnel lens FFresnel Fresnel and the additional spiral focal power Fspiral.

Ftot(r,phi)=Fbase+FFresnel+Fspiral(r,phi),

where, for manufacturing reasons, there is a combination into the base focal power component of the lens Fbase and into the spiral and Fresnel-shaped focal power component

FSF(r,phi)=FFresnel+Fspiral(r,phi).

Since the distribution of the additional focal power is obtained by a height distribution in this case, the following applies:

ztot(r,phi)=zbase+zsF(r,phi).

The height profile, which supplies the spiral and Fresnel-shaped additional focal power, is, in general, described by

zSF(r,phi)=zFresnel+zspiral(r,phi)

The basic focal power of the base system emerges for spherical lenses from the equation




  
    F
    base
  
  =
  
    
      [
      
        
          
            
              
                n
                ⁢
                
                  
                
                ⁢
                2
              
              -
              
                n
                ⁢
                
                  
                
                ⁢
                1
              
            
            
              n
              ⁢
              
                
              
              ⁢
              1
            
          
          *
          
            (
            
              
                1
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
              
              -
              
                1
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
              
            
            )
          
        
        +
        
          
            
              
                (
                
                  
                    n
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                  -
                  
                    n
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                
                )
              
              2
            
            *
            d
          
          
            n
            ⁢
            
              
            
            ⁢
            1
            *
            n
            ⁢
            
              
            
            ⁢
            2
            *
            R
            ⁢
            
              
            
            ⁢
            3
            *
            R
            ⁢
            
              
            
            ⁢
            4
          
        
      
      ]
    
    .
  




Here, R3 is for example the radius of the first optical surface which is produced in reality and R4 is the radius of the calculated base surface, to which the additional spiral and Fresnel-shape focal power FSF in the form of the height profile zFS is “added” (the additive height zSF, which supplies the additional focal power, can also be added to the radius R3 or can be split over both radii R3 and R4; the equations then have to be modified accordingly).
The height profile zbase for the calculated base surface with the radius R4 of the spherical lens emerges as

zbase(x,y)=R4−√{square root over (R42−x2−y2)}, and, with r=√{square root over (x2+y2)},

the data of the base surface in polar coordinates emerge as

zbase(r)=R4−√{square root over (R42−r2)}.

Thus, for the case of a spherical base surface and a rotationally symmetric Fresnel structure, the following applies:

ztot(r,phi)=(R4−√{square root over (R42−r2)})+[zFresnel(r)+zspiral(r,phi)].

The rotationally symmetric, Fresnel-shaped additional focal power is calculated as




  
    
      z
      Fresnel
    
    ⁡
    
      (
      r
      )
    
  
  =
  
    
      
        ∑
        
          l
          =
          2
        
        L
      
      ⁢
      
        
          e
          1
        
        *
        
          r
          1
        
        ⁢
        
          
        
        ⁢
        or
        ⁢
        
          
        
        ⁢
        
          
            z
            Fresnel
          
          ⁡
          
            (
            r
            )
          
        
      
    
    =
    
      
        ∑
        
          l
          =
          1
        
        L
      
      ⁢
      
        
          e
          1
        
        *
        
          
            r
            
              2
              *
              1
            
          
          .
        
      
    
  




To the extent that non-spherical base surfaces underlie the lens, the known polynomials for describing non-spherical surfaces are used for determining the optical surfaces and/or the base surface.
By the additive term zSF(r, phi), the spiral and Fresnel-shaped additional focal power is produced as material height, which is added to or else subtracted from the optical base surface with the radius R4. Analogous considerations also apply to aspherical and free-form surfaces, which cannot be described by a simple radius specification.
The spiral height profile emerges from

zspiral(r,phi)=zspiral max(r)*w(Phi),

where

the radial polynomial for the maximum spiral height component as a function of the radius zspiral max(r), which embodies the maximum diopter number to be obtained, is:





  
    
      
        z
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          c
          j
        
        *
        
          r
          j
        
      
    
  
  ,




where r is the radial height and cj is a coefficient set of the radial polynomial.

In the simplest case,




  
    w
    ⁡
    
      (
      phi
      )
    
  
  =
  
    phi
    
      2
      ⁢
      π
    
  




is the angle-dependent, linear normalized component, with phi as azimuth angle on the base surface of the base system (carrier lens).

The additive term zspiral(r, phi), which is added to the base surface of the lens, emerges from




  
    
      z
      spiral
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          z
          
            spiral
            ⁢
            
              
            
            ⁢
            max
          
        
        ⁡
        
          (
          r
          )
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          c
          j
        
        *
        
          r
          j
        
        *
        
          
            phi
            
              2
              ⁢
              π
            
          
          .
        
      
    
  




In general, the height component of the focal power of the overall system of the lens is obtained as



  
    
      
        z
        tot
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        
          z
          base
        
        ⁡
        
          (
          r
          )
        
      
      +
      
        [
        
          
            
              z
              Fresnel
            
            ⁡
            
              (
              r
              )
            
          
          +
          
            
              z
              spiral
            
            ⁡
            
              (
              
                r
                ,
                phi
              
              )
            
          
        
        ]
      
    
  




  
    
      
        z
        tot
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        z
        base
      
      +
      
        
          [
          
            
              
                ∑
                
                  l
                  =
                  2
                
                L
              
              ⁢
              
                
              
              ⁢
              
                
                  e
                  1
                
                *
                
                  r
                  1
                
              
            
            +
            
              
                ∑
                
                  j
                  =
                  2
                
                N
              
              ⁢
              
                
              
              ⁢
              
                
                  c
                  j
                
                *
                
                  r
                  j
                
              
            
            +
            
              phi
              
                2
                ⁢
                π
              
            
          
          ]
        
        .
      
    
  



For the radial polynomial zspiral max(r), the approach




  
    
      z
      
        spiral
        ⁢
        
          
        
        ⁢
        max
      
    
    ⁡
    
      (
      r
      )
    
  
  =
  
    
      ∑
      
        j
        =
        1
      
      N
    
    ⁢
    
      
    
    ⁢
    
      
        c
        j
      
      *
      
        r
        
          2
          *
          j
        
      
    
  




can also be used in an analogous manner and likewise





  
    
      z
      Fresnel
    
    ⁡
    
      (
      r
      )
    
  
  =
  
    
      ∑
      
        l
        =
        1
      
      L
    
    ⁢
    
      
    
    ⁢
    
      
        e
        1
      
      *
      
        r
        
          2
          *
          1
        
      
    
  




is possible.

In the simplest case, it is therefore already sufficient to realize the additional radial focal power distribution as a product of the normalized azimuth angle and the maximum diopter number to be achieved.
For the simplest case of the radial polynomial

zspiral max(r)=c1*r2,

with c1 as coefficient in front of the quadratic term, the equation for the additive term thus reads





  
    
      z
      spiral
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          z
          
            
              spiral
              ⁢
              
                
              
              ⁢
              max
            
            ⁢
            
              
            
          
        
        ⁡
        
          (
          r
          )
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
    =
    
      
        c
        1
      
      *
      
        r
        2
      
      *
      
        
          phi
          
            2
            ⁢
            π
          
        
        .
      
    
  




The procedure described above represents a linear “helical increase”. In this form, the imaging quality is good with approximately no change over the whole diopter region.
However, it is often desirable to prefer specific diopter regions such as e.g. the zero diopter position. To this end, it is necessary to depart from the linear dependence of the z-height on the angle.
In general, the angle-dependent component can be described by the equation




  
    
      w
      ⁡
      
        (
        phi
        )
      
    
    =
    
      
        ∑
        
          i
          =
          1
        
        M
      
      ⁢
      
        
      
      ⁢
      
        
          I
          i
        
        *
        
          exp
          ⁢
          
            
          
          [
          
            
              -
              
                a
                i
              
            
            *
            
              
                (
                
                  phi
                  -
                  
                    w
                    i
                  
                
                )
              
              2
            
          
          ]
        
      
    
  
  ,




where wi are the peak positions (between 0 and 2π), Ii are the peak intensities and ai>0 are the damping coefficients for the respective peak positions.

By way of example, for M=1; I1=1 and wi=2π, the function




  
    
      z
      spiral
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          z
          
            spiral
            ⁢
            
              
            
            ⁢
            max
          
        
        ⁡
        
          (
          r
          )
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          c
          j
        
        *
        
          r
          j
        
        *
        
          exp
          ⁢
          
            
          
          [
          
            
              -
              
                a
                1
              
            
            *
            
              
                (
                
                  phi
                  -
                  
                    2
                    ⁢
                    π
                  
                
                )
              
              2
            
          
          ]
        
      
    
  




with a1=0.25 allows a preference for the zero diopter region to be implemented. 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.

In the context of optimizing the lens with the extended range of focus, further advantages can be obtained by virtue of further degrees of freedom being available during the design. By way of example, this is brought about if the radial function zspiral max(r) likewise obtains an azimuth-dependent set of coefficients and hence the radial polynomial zspiral max(r, phi) is determined as




  
    
      z
      
        spiral
        ⁢
        
          
        
        ⁢
        max
      
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      ∑
      
        j
        =
        2
      
      N
    
    ⁢
    
      
    
    ⁢
    
      
        
          c
          j
        
        ⁡
        
          (
          phi
          )
        
      
      *
      
        
          r
          j
        
        .
      
    
  




From this, the additive term zspiral(r, phi) emerges in general as




  
    
      z
      spiral
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          z
          
            spiral
            ⁢
            
              
            
            ⁢
            max
          
        
        ⁡
        
          (
          
            r
            ,
            phi
          
          )
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          
            c
            j
          
          ⁡
          
            (
            phi
            )
          
        
        *
        
          r
          j
        
        *
        
          
            ∑
            
              i
              =
              1
            
            M
          
          ⁢
          
            
          
          ⁢
          
            
              I
              i
            
            *
            
              
                exp
                ⁡
                
                  [
                  
                    
                      -
                      
                        a
                        i
                      
                    
                    *
                    
                      
                        (
                        
                          phi
                          -
                          
                            w
                            i
                          
                        
                        )
                      
                      2
                    
                  
                  ]
                
              
              .
            
          
        
      
    
  




Hence, it is possible to specify further variants from the general equation




  
    w
    ⁡
    
      (
      phi
      )
    
  
  =
  
    
      ∑
      
        i
        =
        1
      
      M
    
    ⁢
    
      
    
    ⁢
    
      
        I
        i
      
      *
      
        exp
        ⁡
        
          [
          
            
              -
              
                a
                i
              
            
            *
            
              
                (
                
                  phi
                  -
                  
                    w
                    i
                  
                
                )
              
              2
            
          
          ]
        
      
    
  




for the angle term w(phi), by means of which it is possible to control the “effective period” of the individual azimuth ranges.

The explanations above were all based upon an additive term which is refractive and which is added to one of the optical surfaces of the base system.
The addition term can naturally also be available in a diffractive form, that is, a diffractive optical element (DOE) with a spiral and structure-shaped phase function is applied to the spherical carrier surface of the base system (case b)). This phase function is designed in a completely analogous fashion to the refractive approach. Blaze gratings, sinusoidal gratings and binary gratings are particularly suitable.
In a radial and angle-dependent manner, the grating frequency changes spirally continuously from an initial value to a maximum value corresponding to the maximum focal power.
The spiral phase function emerges as



  
    
      
        phase
        spiral
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        
          
            phase
            max
          
          ⁡
          
            (
            r
            )
          
        
        *
        
          w
          ⁡
          
            (
            phi
            )
          
        
      
      =
      
        
          ∑
          
            j
            =
            2
          
          N
        
        ⁢
        
          
        
        ⁢
        
          
            k
            j
          
          *
          
            r
            j
          
          *
          
            w
            ⁡
            
              (
              phi
              )
            
          
        
      
    
  




  or




  
    
      
        phase
        spiral
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        
          
            phase
            max
          
          ⁡
          
            (
            r
            )
          
        
        *
        
          w
          ⁡
          
            (
            phi
            )
          
        
      
      =
      
        
          ∑
          
            j
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          
            k
            j
          
          *
          
            r
            
              2
              *
              j
            
          
          *
          
            
              w
              ⁡
              
                (
                phi
                )
              
            
            .
          
        
      
    
  



The spiral focal power of the diffractive structure emerges as



  
    
      F
      
        spiral
        ⁢
        
          
        
        ⁢
        diffractive
      
    
    =
    
      2
      ⁢
      
        k
        2
      
      ⁢
      
        λ
        
          w
          ⁢
          
            
          
          ⁢
          1
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
  




  
    or
    ⁢
    
      
    
    ⁢
    as
  




  
    
      
        F
        
          spiral
          ⁢
          
            
          
          ⁢
          diffractive
        
      
      =
      
        2
        ⁢
        
          k
          1
        
        ⁢
        
          λ
          
            w
            ⁢
            
              
            
            ⁢
            1
          
        
        *
        
          w
          ⁡
          
            (
            phi
            )
          
        
      
    
    ,
  



where wl is the design wavelength of the diffractive optical element and λ is the application wavelength. The term w(phi) can be selected from the explanations above and is





  phi
  
    2
    ⁢
    π
  




in the simplest case. With k1 as coefficient of the quadratic term, the maximum focal power emerges as





  
    F
    
      spiral
      ⁢
      
        
      
      ⁢
      max
      ⁢
      
        
      
      ⁢
      diffractive
    
  
  =
  
    2
    ⁢
    
      k
      1
    
    ⁢
    
      λ
      
        w
        ⁢
        
          
        
        ⁢
        1
      
    
  




and the angle-dependent term Fspiral diffractive(phi) emerges as





  
    F
    
      spiral
      ⁢
      
        
      
      ⁢
      diffractive
    
  
  =
  
    2
    ⁢
    
      k
      1
    
    ⁢
    
      λ
      
        w
        ⁢
        
          
        
        ⁢
        1
      
    
    *
    
      
        phi
        
          2
          ⁢
          π
        
      
      .
    
  




In the diffractive embodiment, the structure producing the additional focal power is a phase function. The phase of a rotationally symmetric structure is



  
    
      
        phase
        structure
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          l
          =
          2
        
        L
      
      ⁢
      
        
      
      ⁢
      
        
          g
          1
        
        *
        
          r
          1
        
      
    
  




  or




  
    
      
        phase
        structure
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          l
          =
          1
        
        L
      
      ⁢
      
        
      
      ⁢
      
        
          g
          1
        
        *
        
          
            r
            
              2
              *
              1
            
          
          .
        
      
    
  



In the diffractive embodiment, the focal power of the rotationally symmetric structure is



  
    
      F
      
        structure
        ⁢
        
          
        
        ⁢
        diffractive
      
    
    =
    
      2
      ⁢
      
        g
        2
      
      ⁢
      
        λ
        
          w
          ⁢
          
            
          
          ⁢
          1
        
      
    
  




  
    or
    ⁢
    
      
    
    ⁢
    is
  




  
    
      
        F
        
          structure
          ⁢
          
            
          
          ⁢
          diffractive
        
      
      =
      
        2
        ⁢
        
          g
          1
        
        ⁢
        
          λ
          
            w
            ⁢
            
              
            
            ⁢
            1
          
        
      
    
    ,
  



where wl is the design wavelength of the diffractive optical element and λ is the application wavelength.

In the simplest case, the overall focal power of the lens emerges for N=1 and L=1 from a comparatively strong refractive basic focal power Fbase of the monofocal base system and a relatively small focal power component of the diffractively produced spiral and rotationally symmetric additional focal power FSS diffractive:



  
    
      F
      tot
    
    =
    
      
        
          F
          base
        
        +
        
          [
          
            
              F
              
                structure
                ⁢
                
                  
                
                ⁢
                diffractive
              
            
            +
            
              F
              
                spiral
                ⁢
                
                  
                
                ⁢
                diffractive
              
            
          
          ]
        
      
      =
      
        
          F
          base
        
        +
        
          F
          
            SS
            ⁢
            
              
            
            ⁢
            diffractive
          
        
      
    
  




  
    
      
    
    ⁢
    
      
        F
        tot
      
      =
      
        
          F
          base
        
        +
        
          
            [
            
              
                2
                ⁢
                
                  g
                  1
                
                ⁢
                
                  λ
                  
                    w
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                
              
              +
              
                2
                ⁢
                
                  k
                  1
                
                ⁢
                
                  λ
                  
                    w
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                
                *
                w
                ⁢
                
                  
                
                ⁢
                
                  (
                  phi
                  )
                
              
            
            ]
          
          .
        
      
    
  



In practical terms, the base focal power of the lens Fbase is produced first and the spiral and structure-shaped additional focal power FSS diffractive is applied onto an optical surface of the base lens.
Thus, as a result of the diffractive component, a relatively only small color aberration is created and the lens with the extended range of focus is also suitable for white light.
The spiral and structure-shaped additional focal power FSS diffractive can also be divided onto both optical surfaces of the lens.
However, the spiral and structure-shaped addition term Fss can also be realized by producing a spiral and structure-shaped refractive index gradient ΔnSS (case c)). By way of example, DE 10 2009 033 984 A1 describes how inhomogeneous optical properties can be generated in an optical material. In a development of the method described therein, it is also possible to realize a spiral and structure-shaped refractive index profile. The properties and the design of the refractive index gradient in this case are brought about in a completely analogous fashion to the refractive approach and to the diffractive approach.
The overall focal power Ftot emerges from the base focal power Fbase of the monofocal base system plus the additional focal power FSS which is provided by the spiral and structure-shaped focal power increase.
The spiral and structure-shaped additional focal power FSS(r, phi) is proportional to the refractive index difference ΔnSS(r, phi) according to the equation




  
    Δ
    ⁢
    
      
    
    ⁢
    
      
        n
        SS
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
  
  =
  
    
      
        Δ
        ⁢
        
          
        
        ⁢
        
          n
          structure
        
      
      +
      
        Δ
        ⁢
        
          
        
        ⁢
        
          
            n
            spiral
          
          ⁡
          
            (
            
              r
              ,
              phi
            
            )
          
        
      
    
    =
    
      
        Δ
        ⁢
        
          
        
        ⁢
        
          n
          structure
        
      
      +
      
        Δ
        ⁢
        
          
        
        ⁢
        
          
            n
            
              spiral
              ⁢
              
                
              
              ⁢
              max
            
          
          ⁡
          
            (
            
              r
              ,
              phi
            
            )
          
        
        *
        
          
            w
            ⁡
            
              (
              phi
              )
            
          
          .
        
      
    
  




The refractive index difference ΔnSS(r, phi) increases continuously from 0 (at r=0 and phi=0) to the maximum refractive index increase Δnspiral max(at r=D/2 and phi=22π), wherein the function w(phi) can predetermine the above-described linear or general profile.
Here, Δnspiral max(r, phi) is calculated analogously to the height zspiral max or to the phase function phasespiral max and can be both positive and negative in relation to the base refractive index n2 of the lens.
The subject matter of the present invention therefore also relates to any mixed forms of spiral and/or Fresnel-shaped height profile(s), of spiral and/or rotationally symmetric phase profile(s) and/or of spiral and/or rotationally symmetric refractive index profile(s), which produce the desired additional focal power profile.
The height profile and/or the phase profile can be distributed on one of the optical surfaces and/or on both optical surfaces of a lens, or can be arranged in combination.



BRIEF DESCRIPTION OF THE DRAWINGS
The invention will now be described with reference to the drawings wherein:
FIG. 1 is a side view of a “thick” lens having an extended range of focus according to a solution described in DE 10 2011 101 899 A1;
FIG. 2 is a side view of a “thin” lens having an extended range of focus in accordance with the invention;
FIG. 3 is a schematic of the procedure and the calculation steps leading to design and production of the “thin” lens;
FIG. 4 depicts a spiral focal power component;
FIG. 5 depicts a rotationally symmetric focal power component, made to be a Fresnel-type;
FIG. 6 depicts the added spiral and rotationally symmetric focal power component, made to be a Fresnel-type;
FIGS. 7 to 10 are depictions of the added spiral and rotationally symmetric focal power component, made to be a Fresnel-type, wherein the power of the spiral component increases from figure to figure;
FIG. 11 depicts a diffractive, spiral structure which produces the spiral focal power component;
FIG. 12 depicts a diffractive, rotationally symmetric ring structure;
FIG. 13 depicts the added diffractive, spiral structure and the diffractive, rotationally symmetric ring structure, which corresponds to the focal power component as per FIG. 6;
FIG. 14 shows a schematic depiction of an intraocular lens in the eye;
FIG. 15 shows an optical system of a camera with a “thick” lens; and,
FIG. 16 shows an optical system of a camera with a “thin” lens having the extended range of focus.



DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION
FIG. 1 shows a “thick” lens 1 having an extended range of focus as disclosed in DE 10 2011 101 899 A1, the content of which is incorporated by reference. Shown is a side view with a depiction of the spiral refractive height profile zspiral(r, phi), which produces the spiral focal power distribution Fspiral(r, phi). This lens 1 is initially determined by its base system with the radius R1 of the first optical surface 2′ and the radius R2 for the calculated base surface 3′, and also by the lens thickness d1 and the refractive index n2. These parameters are determined for an envisaged basic magnification. An additional material thickness z is “added” to the calculated shape of the base surface 3′ with the radius R2, with the additional material thickness being z=0 mm at phi=0, then increasing continuously and having a maximum value in the millimeter range at phi=2π. In practice, the maximum value will lie slightly in front of the azimuth angle phi=2π 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. 
Parameters for a lens are specified as an example:

    
    
        R1=−15.1411 mm radius to be produced
        R2=22.3164 mm calculated radius
        d1=0.8 mm
        n1=1 (refractive index outside of the lens)
        n2=1.56 (refractive index of the lens medium) hence, from the equation
    
    






  
    f
    base
  
  =
  
    1
    
      [
      
        
          
            
              
                n
                ⁢
                
                  
                
                ⁢
                2
              
              -
              
                n
                ⁢
                
                  
                
                ⁢
                1
              
            
            
              n
              ⁢
              
                
              
              ⁢
              1
            
          
          *
          
            (
            
              
                1
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              -
              
                1
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
            
            )
          
        
        +
        
          
            
              
                (
                
                  
                    n
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                  -
                  
                    n
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                
                )
              
              2
            
            *
            d
            ⁢
            
              
            
            ⁢
            1
          
          
            n
            ⁢
            
              
            
            ⁢
            1
            *
            n
            ⁢
            
              
            
            ⁢
            2
            *
            R
            ⁢
            
              
            
            ⁢
            1
            *
            R
            ⁢
            
              
            
            ⁢
            2
          
        
      
      ]
    
  




wherein the focal length of the “base lens” emerges as 16.233 mm.

A linear “helical increase” in accordance with the equation




  
    
      z
      spiral
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          z
          
            spiral
            ⁢
            
              
            
            ⁢
            max
          
        
        ⁡
        
          (
          r
          )
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
    =
    
      
        c
        1
      
      *
      
        r
        2
      
      *
      
        phi
        
          2
          ⁢
          π
        
      
    
  




as a continuous, spiral height profile with a linear profile is added to the calculated base surface with the radius R2=22.3164 mm and results in the optical surface 4′.

With c1=−0.013, a spiral addition which increases the focal length in air up to 20.57 mm, corresponding to 3.5 dpt, is obtained.
FIG. 2 shows a “thin” lens 5 according to the invention, which, compared to the lens 1 shown in FIG. 1, has flatter radii R3 and R4 and the central thickness d2 of which is thinner, wherein approximately the same imaging parameters are obtained as in the case of the lens as per FIG. 1: in the case of a basic focal power of approximately 61 dpt, an additional focal power of 3.5 dpt is achieved. The “thin” lens 5 has the peculiarity that the spiral addition contains a rotationally symmetric Fresnel component. This Fresnel component realizes part of the focal power which the “thick” lens 1 as per FIG. 1 obtains from the radii R1 and R2 and also from the lens thickness d1, and so the radii R3 and R4 of the novel lens 5 are flatter and the central thickness d2 thereof is comparatively smaller.
The procedure for designing the novel “thin” lens 5 according to the invention will be explained on the basis of FIG. 3.
The start point is the “thick” lens 1 depicted in the upper row of FIG. 3, which is only calculated. It consists of the refractive base system with the radii R1 and R2 and also the central thickness d1 (depicted on the left) and the spiral focal power component, which is theoretically realized by the height profile zspiral(r, phi) on the radius R2 (depicted on the right). What is then depicted below is that the focal power of the refractive base system is split into a novel “thin” lens 5, with the radii R3 and R4 and also with the central thickness d2, and into a rotationally symmetric Fresnel-shaped focal power component zFresnel(r).
The lowest row depicts that the Fresnel-shaped focal power component zFresnel(r) and the spiral component zspiral(r, phi) are added to form a spiral and Fresnel-shaped additional focal power FSF. The height profile

zSF(r,phi)=zspiral(r,phi)+zFresnel(r)

is added to the only calculated radius R4 of the base lens with the height profile zbase. Now, a lens is produced with the radius R3, with a central thickness d2 and with a height profile zsF(r, phi) on the calculated radius R4. The corresponding height profile of the optical surface 4 to be manufactured emerges as

ztot(r,Phi)=(R4=√{square root over (R42−r2)})+[zFresenel(r)+zspiral max(r,phi)*w(phi)].

FIG. 4 shows only the spiral focal power component Fspiral of the lens as height profile zspiral(r, phi). FIG. 5 shows only the rotationally symmetric focal power component FFresnel, made to be Fresnel-type, of the lens as height profile zFresnel(r). The depiction in FIG. 6 shows the result of adding the spiral focal power component and the rotationally symmetric focal power component, made to be Fresnel-type, as height profile zSF(r, phi), which represents the spiral and Fresnel-shaped focal power component FSF.
This height profile is added to the height profile zbase of the calculated base surface 3 with the radius R4 and manufactured on the lens to be produced.
FIGS. 7 to 10 each show a depiction of the added spiral and rotationally symmetric focal power component FSF, made to be Fresnel-type, wherein the power of the spiral component increases from 1 dpt to 3.5 dpt from figure to figure.
Subsequently, FIGS. 11 to 13 show that a spiral and structure-shaped additional focal power of the lens FSS is transferred in a completely analogous manner onto a diffractive approach starting from the refractive approach (where the structure-shaped additional focal power is realized by a Fresnel structure).
FIG. 11 schematically shows a diffractive, spiral structure which produces the spiral focal power component Fspiral diffractive. FIG. 12 schematically shows a diffractive, rotationally symmetric ring structure which produces the structure-shaped focal power component Fstructure diffractive. FIG. 13 shows the result of adding the two diffractive structures. This superposition of the diffractive, spiral structure and the diffractive, rotationally symmetric ring structure provides as a result a spiral and structure-shaped focal power component FSS, which, in terms of its effect, corresponds to the refractive spiral and Fresnel-shaped focal power component FSF, which is schematically depicted by the spiral and Fresnel-shaped height profile zSF in FIG. 6.
FIG. 14 shows a schematic depiction of an intraocular lens 11, which is implanted in the eye as “thin” lens 5 with extended range of focus. In the example, this lens 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.
The intraocular lens 11 has a spherical first optical surface 2 and the second optical surface 4 carrying the spiral and structure form.
In a first example, the intraocular lens 11 with the extended range of focus has the following parameters for the base system: the base radii of the carrier lens are the produced lens radius R3=−20 mm and the calculated lens radius R4=+20 mm of the base surface 3. The spiral and Fresnel-shaped height profile zSF(r, phi) will be is added onto the base surface 3 and manufactured accordingly as surface 4.
The focal power of the component, made to be Fresnel-type, of the basic focal power of the lens emerges from the height profile of a Fresnel structure




  
    
      z
      Fresnel
    
    ⁡
    
      (
      r
      )
    
  
  =
  
    
      ∑
      
        l
        =
        1
      
      L
    
    ⁢
    
      
    
    ⁢
    
      
        e
        1
      
      *
      
        r
        
          2
          *
          1
        
      
    
  




and, for L=2, provides the coefficients of the rotationally symmetric Fresnel polynomial e1=0.036 and e2=−0.00018398.

The focal power of the spiral additional focal power of the lens emerges from the height profile




  
    
      z
      spiral
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          z
          
            spiral
            ⁢
            
              
            
            ⁢
            max
          
        
        ⁡
        
          (
          r
          )
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
    =
    
      
        ∑
        
          j
          =
          1
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          c
          j
        
        *
        
          r
          
            2
            *
            j
          
        
        *
        
          phi
          
            2
            ⁢
            π
          
        
      
    
  




and, for N=1, provides the coefficients of the spiral polynomial c1=0.025.

Thus, the following emerges:




  
    
      z
      SF
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        
          z
          spiral
        
        ⁡
        
          (
          
            r
            ,
            phi
          
          )
        
      
      +
      
        
          z
          Fresnel
        
        ⁡
        
          (
          r
          )
        
      
    
    =
    
      
        
          c
          1
        
        *
        
          r
          2
        
        *
        
          phi
          
            2
            ⁢
            π
          
        
      
      +
      
        
          e
          1
        
        *
        
          r
          2
        
      
      +
      
        
          e
          2
        
        *
        
          
            r
            4
          
          .
        
      
    
  




The indentation depth of the element p, made to be Fresnel-type, is selected with 0.1 mm and thus the spiral additional focal power, made to be Fresnel-type, emerges by means of the modulus function mod(zSF(r, phi), p).
Here, the corneal radius is assumed to be R5=7.814 mm and the conic constant is assumed to be K=−0.26. The distance between the cornea 12 and the front side of the lens R4 is 4.12 mm; the lens thickness of the intraocular lens is d2=0.65 mm and the distance between the front side of the lens R2 and the retina 14 is 18.1 mm. Benz25 with a refractive index of the lens medium n2=1.56 is used as material.
The refractive index outside of the lens, of the aqueous humor 13, is n1=1.33.
Compared therewith, the intraocular lens described in DE 10 2011 101 899, FIG. 4 in that case, has the following parameters:
R1=−15.1411 mm (produced first optical surface 2)
R2=22.3164 mm (calculated base surface 3)
Lens thickness d1=0.8 mm
As a result, the novel lens according to the invention in accordance with the example in FIG. 14 is thinner by 0.15 mm, caused by the flatter radius R3 compared to R1.
In a second example in respect of FIG. 14, the intraocular lens 11 with the extended range of focus has the following parameters for a diffractive embodiment of the spiral and structure-shaped additional focal power Fss on an optical surface of the base lens:
Cornea: radius R5=7.814 mm, aspherical conic constant K=−0.26, base radii of the lens R3=R4=+/−20.0 mm (spherical); the distance between cornea R5 and the manufactured optical surface 4 with the radius R4 is 4.12 mm,
the thickness of the intraocular lens d2=0.65 mm and the distance between the manufactured optical surface 2 with the radius R3 and the retina is 18.5 mm.
“Benz25” is used as material for the intraocular lens. The diameter of the intraocular lens is 6 mm. The refractive base system of the lens is described by these parameters and the focal power Fbase thereof is set. The spiral additional focal power Fspiral and the structure-shaped additional focal power Fstructure are produced as a spiral and structure-shaped diffractive focal power distribution FSS using a diffractive optical element which is applied onto the surface with the radius R4. Thus, the overall focal power of the intraocular lens 11 emerges as




  
    
      F
      tot
    
    ==
    
      
        F
        base
      
      +
      
        F
        
          SS
          ⁢
          
            
          
          ⁢
          diffractive
        
      
    
  
  =
  
    
      F
      base
    
    +
    
      
        [
        
          
            F
            
              structure
              ⁢
              
                
              
              ⁢
              diffractive
            
          
          +
          
            F
            
              spiral
              ⁢
              
                
              
              ⁢
              diffractive
            
          
        
        ]
      
      .
    
  




Expressed as a phase function, the spiral and structure-shaped additional focal power emerges as



  
    
      
        
          phase
          SS
        
        ⁡
        
          (
          
            r
            ,
            phi
          
          )
        
      
      =
      
        
          phase
          structure
        
        +
        
          phase
          spiral
        
      
    
    ,
    
      

    
    ⁢
    with
  




  
    
      
        phase
        structure
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          l
          =
          1
        
        L
      
      ⁢
      
        
      
      ⁢
      
        
          g
          1
        
        *
        
          r
          
            2
            *
            1
          
        
      
    
  




  and




  
    
      
        Phase
        spiral
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        
          
            Phase
            max
          
          ⁡
          
            (
            r
            )
          
        
        *
        
          w
          ⁡
          
            (
            phi
            )
          
        
      
      =
      
        
          ∑
          
            j
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          
            k
            j
          
          *
          
            r
            
              2
              *
              j
            
          
          *
          
            
              w
              ⁡
              
                (
                phi
                )
              
            
            .
          
        
      
    
  



With L=2, N=1 and




  
    
      w
      ⁡
      
        (
        phi
        )
      
    
    =
    
      phi
      
        2
        ⁢
        π
      
    
  
  ,




the following emerges:





  
    
      phase
      SS
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        g
        1
      
      *
      
        r
        2
      
    
    +
    
      
        g
        2
      
      *
      
        r
        4
      
    
    +
    
      
        k
        1
      
      *
      
        r
        2
      
      ⁢
      
        phi
        
          2
          ⁢
          π
        
      
    
  




and the reduced phase function emerges as





  
    
      
        phase
        
          SS
          ⁢
          
            
          
          ⁢
          reduced
        
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        
          
            phase
            SS
          
          ⁡
          
            (
            
              r
              ,
              phi
            
            )
          
        
        wl
      
      -
      
        floor
        ⁢
        
          
            
              phase
              SS
            
            ⁡
            
              (
              
                r
                ,
                phi
              
              )
            
          
          wl
        
      
    
  
  ,




where phi=0 . . . 2π (azimuth angle), r=radial height on the lens and wl is the design wavelength of the diffractive element (synthetic production wavelength).

For the coefficients of the rotationally symmetric component, made to be Fresnel-type, which in this case is present as symmetric component of a diffractive optical element, the following are set:

g1=0.006109 and g2=−4.92E-5.

For the coefficient of the spiral component of the diffractive optical element, the following applies: k1=−0.003. The profile depth of the diffractive optical element is h=0.0043 mm.
In a third example, the intraocular lens 11 with the extended range of focus has the following parameters for a diffractive embodiment of the additional focal power FSS, split between the two optical surfaces 2 and 4 of the refractive base lens 3: Corneal radius R5=7.814 mm, aspherical conic constant K=−0.26.
The base radii of the intraocular lens are R3=R4=+/−20.0 mm (spherical). Further parameters are: the distance between corneal radius R5 and optical surface 4 with the radius R4 is 4.12 mm; the central thickness d2=0.65 mm and the distance between the optical surface 2 with the radius R3 and the retina is 18.5 mm; the lens material is “Benz25” and the diameter of the intraocular lens is 6 mm.
In this example, one diffractive optical element has been respectively applied to each of the optical surfaces 2 and 4.
Here, the focal power is split in such a way that the spiral focal power component Fspiral lies on the optical surface with the radius R4 and the structure-shaped rotationally symmetric focal power component Fstructure lies on the radius R3.
With L=2, N=1 and




  
    
      w
      ⁡
      
        (
        phi
        )
      
    
    =
    
      phi
      
        2
        ⁢
        
          
        
        ⁢
        π
      
    
  
  ,




the following emerges:





  
    
      phase
      SS
    
    ⁡
    
      (
      
        r
        ,
        phi
      
      )
    
  
  =
  
    
      
        g
        1
      
      *
      
        r
        2
      
    
    +
    
      
        g
        2
      
      *
      
        r
        4
      
    
    +
    
      
        k
        1
      
      *
      
        r
        2
      
      ⁢
      
        phi
        
          2
          ⁢
          
            
          
          ⁢
          π
        
      
    
  




and the reduced phase function emerges as





  
    
      
        phase
        
          SS
          ⁢
          
            
          
          ⁢
          reduced
        
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        
          
            phase
            SS
          
          ⁡
          
            (
            
              r
              ,
              phi
            
            )
          
        
        wl
      
      -
      
        floor
        ⁢
        
          
            
              phase
              SS
            
            ⁡
            
              (
              
                r
                ,
                phi
              
              )
            
          
          wl
        
      
    
  
  ,




where phi=0 . . . 2π (azimuth angle), r=radial height on the lens and wl is the design wavelength of the diffractive element (synthetic production wavelength).

The following applies to the diffractive optical element applied to the optical surface 4:

g1=0 and g2=0 and k1=−0.003.

The profile depth of the diffractive optical element is h=0.0043 mm.
The following applies to the diffractive optical element applied to the optical surface 2:

g1=0.0065 and g2=1.8975E-4 and k1=0.

The profile depth of the diffractive optical element is h=0.0043 mm.
FIG. 15 shows an optical system of a camera in accordance with FIG. 3 from DE 10 2011 101 899 A1 with a “thick” lens 1 which has the extended range of focus. An additional focal power component in the form of a spiral focal power component is added to the base focal power which results from the radii R1, R2, the refractive index n2 and the central thickness d1 of the calculated lens. This spiral focal power component is added to the height profile of the calculated base surface 3′ as height profile zspiral and, in practice, is manufactured as second optical surface 4′.
However, the spiral focal power component also can be manufactured on one or both of the optical surfaces of the lens with the base focal power in a diffractive form as diffractive optical element. Alternatively, the spiral focal power component can also be manufactured as refractive index gradient within the lens with the base focal power. Provision is likewise made for arbitrary mixed forms.
FIG. 16 shows an optical system of a camera with a “thin” lens 5 according to the invention which has the extended range of focus. In the example, an additional focal power component in the form of a spiral and Fresnel-shaped height profile zSF is added to the base focal power of the calculated lens. The height profile is added to the height profile of the calculated base surface 3 with the radius R4 and manufactured as second optical surface 4. Also, the spiral and Fresnel-shaped focal power component can be wholly or in part realized by a diffractive optical element on the optical surface of the base lens (or distributed on the two optical surfaces) or by a refractive index gradient in the lens material.
In the light propagation direction, an aspherical lens 6 with the optical surfaces 17 and 18 follows the “thin” lens 5, and the lens is followed by a filter 15 and a sensor 7.
On the object side, the “thin” lens 5 has a first optical surface 2 with the radius R3. Manufactured on the image side is the second optical surface 4, the height profile of which emerges from the height profile zbase of the calculated radius R4 and the spiral and Fresnel-shaped height profile zSF(r, phi).
A cellular telephone lens system with a focal length of 5.61 mm is shown as an example; it has an installation length of 6.1 mm and an aperture of 1:2.8.
The optical surfaces 2, 17 and 18 of the lenses 5 and 6 have a rotationally aspherical basic form.
Lens 5: lens thickness d2=1.21 mm, material is Zeonex.
Optical surface 2: R3=1.482 mm convex
Asphere coefficients:
K=0.04649
A=−0.698748E-03
B=0.987484E-03
C=−0.119379E-03
D=−0.104254E-02
E=0.323245E-03
The non-manufactured spherical concave base surface 3 has a calculated radius R4=6.303 mm. The spiral and Fresnel-shaped focal power profile in the form of a height profile zSF is added to the height profile zbase of this base surface 3. This height profile is then produced on the lens to be manufactured. In this example, the coefficient of the spiral polynomial c1=−0.00268 and the coefficient of the rotationally symmetric Fresnel component e1=0.03.
The additional spiral focal power component is calculated as




  
    F
    spiral
  
  =
  
    2
    ⁢
    
      
    
    ⁢
    
      k
      1
    
    *
    
      r
      2
    
    *
    
      phi
      
        2
        ⁢
        
          
        
        ⁢
        π
      
    
  




and the additional rotationally symmetric Fresnel component is calculated as

FFresnel=2e1*r2 

and the overall focal power emerges as




  
    
      F
      tot
    
    =
    
      
        
          F
          base
        
        +
        
          F
          SF
        
      
      =
      
        
          F
          base
        
        +
        
          F
          Fresnel
        
        +
        
          F
          spiral
        
      
    
  




  
    
      F
      tot
    
    =
    
      
        F
        base
      
      +
      
        2
        ⁢
        
          
        
        ⁢
        
          e
          1
        
        *
        
          r
          2
        
      
      +
      
        2
        ⁢
        
          
        
        ⁢
        
          k
          1
        
        *
        
          r
          2
        
        *
        
          
            phi
            
              2
              ⁢
              
                
              
              ⁢
              π
            
          
          .
        
      
    
  



The additional focal power added onto the base surface 3 is




  
    
      F
      SF
    
    =
    
      
        
          F
          Fresnel
        
        +
        
          F
          spiral
        
      
      =
      
        
          2
          ⁢
          
            
          
          ⁢
          
            e
            1
          
          *
          
            r
            2
          
        
        +
        
          2
          ⁢
          
            
          
          ⁢
          
            k
            1
          
          *
          
            r
            2
          
          *
          
            phi
            
              2
              ⁢
              
                
              
              ⁢
              π
            
          
        
      
    
  
  ,




or, described as a height profile,





  
    z
    SF
  
  =
  
    
      
        Z
        Fresnel
      
      +
      
        z
        spiral
      
    
    =
    
      
        2
        ⁢
        
          
        
        ⁢
        
          e
          1
        
        *
        
          r
          2
        
      
      +
      
        2
        ⁢
        
          
        
        ⁢
        
          k
          1
        
        *
        
          r
          2
        
        *
        
          
            phi
            
              2
              ⁢
              
                
              
              ⁢
              π
            
          
          .
        
      
    
  




The indentation depth of the Fresnel grooves is 0.008 mm.
The lens 6 has a thickness of 3.0 mm; the material is polycarbonate.
The optical surface 17 has a radius R6=−3.075 mm with the following asphere coefficients:
K=11.058298
A=−0.623991E-01
B=−0.926325E-02
C=0.244030E-01
D=−0.125809E+00
E=0.345714E-01
F=−0.101087E-01
G=−0.221418E-15
H=−0.409672E-17
J=0.991703E-20
The optical surface 18 has the radius R7=44.1377 mm (convex) with the following asphere coefficients:
K=−0.238656e57
A=−0.171783E-01
B=0.462293E-03
C=−0.823963E-03
D=0.227317E-03
E=−0.108925E-04
F=−0.474572E-05
G=0.385353E-06
H=0.475909E-07
J=−0.466662E-08
The distance between the lens 5 and the lens 6 is 0.75 mm; the distance between the lens 6 and the filter 15 is 0.4 mm and the distance between the filter 15 and the image plane of the sensor 7 is 0.4 mm, wherein the filter thickness is likewise 0.4 mm.
The lens system supplies a simultaneous range of focus from 330 mm to infinity.
The installation length of the lens system is only 6.1 mm and therefore 0.7 mm less than described in the examples for FIG. 3 in DE 10 2011 101 899 A1.
Here, in particular, the expedient selection of the coefficients c and e in front of the quadratic term supports the achromatization of the lens system.
It is understood that the foregoing description is that of the preferred embodiments of the invention and that various changes and modifications may be made thereto without departing from the spirit and scope of the invention as defined in the appended claims.
REFERENCE CHARACTERS


    1 “Thick” lens
    2 Manufactured first optical surface (spherical, aspherical, radially symmetric, free-form surface) of a “thin” lens
    2′ Optical surface of a “thick” lens
    3 Calculated base surface of the “thin” lens (spherical, aspherical, radially symmetric, free-form surface)
    3′ Calculated second optical surface of the “thick” lens
    4 Manufactured second optical surface of the “thin” lens (spherical, aspherical, radially symmetric, free-form surface, spiral and structure-shaped surface)
    4′ Manufactured surface of the “thick” lens
    5 “Thin” lens
    6 Aspherical lens
    7 Sensor
    8 Bundle of light
    9 Lens edge
    10 Optical axis
    11 Intraocular lens
    12 Cornea
    13 Aqueous humor
    14 Retina
    15 Filter
    16 Spiral and structure-shaped diffractive optical element (DOE)
    17 Optical surface
    18 Optical surface
    Ftot(r, phi) Overall focal power of the lens
    Flens Basic value of the focal power of the base system of a “thick” lens
    Fbase Focal power of the base system of a “thin” lens
    Fstructure Focal power of a structure which is added to the focal power Fbase of the “thin” lens
    Fspiral(r, phi) Spiral focal power component which is added to the focal power Fbase of the “thin” lens
    Fspiral max(r, phi) Maximum focal power of the spiral component of the focal power
    FSF(r, phi) Spiral and Fresnel-shaped additional refractive focal power
    FSS(r, phi) Spiral and structure-shaped additional focal power
    Fss diffractive(r, phi) Spiral and structure-shaped additional diffractive focal power
    Fstructure diffractive Focal power of the structure in diffractive form
    Fspiral diffractive(r, phi) Spiral focal power in diffractive form
    fbase Focal length of the base system
    fspiral(r, phi) Focal length of the spiral additional focal power
    fstructure Focal length of the additional focal power of a structure
    L, M, N Final values
    i, j, l Counters
    cj, c1, c2 Polynomial coefficients of the spiral for the refractive case
    kj, k1, k2 Polynomial coefficients of the spiral for the diffractive case
    el, e1, e2 Polynomial coefficients of the component, made to be Fresnel-type, for the refractive case
    gl, g1, g2 Polynomial coefficients of the structure-shaped component for the diffractive case
    zspiral max(r) Maximum height of the spiral (radius-dependent)
    zspiral max(r, phi) Maximum height (dependent on the radius and the azimuth angle)
    zspiral(r, phi) Spiral additive height of the base surface
    zbase Height profile of the calculated base surface 3
    zFresnel Height profile of the Fresnel structure
    zSF Spiral and Fresnel-shaped height profile of the calculated base surface 3
    ztot(r, phi) Height profile of the manufactured optical surface 4
    w(phi) Angle-dependent component of the focal power profile
    wi, w1, w2 Peak positions of the angular distribution function
    ai, a1, a2 Damping coefficients for the respective peak positions
    Ii, I1, I2 Intensity values of the individual peaks
    D Lens diameter
    r Radius (radial height)
    phi Azimuth angle
    R1 Radius of the first optical surface of the “thick” lens
    R2 Radius of the optical base surface of the “thick” lens
    R3 Radius of the first optical surface 2 of the “thin” lens
    R4 Radius of the optical base surface 3 of the “thin” lens
    R5 Corneal radius
    R6 Radius of the aspherical lens
    R7 Radius of the aspherical lens
    n1 Refractive index of the surrounding medium
    n2 Refractive index of the lens material
    d1 Central thickness of the “thick” lens
    d2 Central thickness of the “thin” lens
    d3 Central thickness of the aspherical lens
    h Profile depth of the diffractive element
    p Indentation depth of the element made to be Fresnel-type
    λ Application wavelength
    wl Design wavelength of the diffractive element
    phasespiral max(r, phi) Maximum value of the grating frequency, which corresponds the maximum spiral focal power distribution
    phasespiral(r, phi) Phase function of the spiral focal power distribution
    phasestructure Phase function of the additional structural focal power distribution
    phaseSS(r, phi) Phase function of the spiral and structure-shaped focal power distribution
    t Calculation variable
    floor(t) Integer component (floor function)
    Profile(r, phi) Phase function reduced to the height h
    K Aspherical constant
    x, y Cartesian coordinates
    Δnspiral Spiral refractive index distribution
    Δnspiral max Maximum refractive index of the spiral
    Δnstructure Refractive index distribution of the structure
    ΔnSS Spiral and structure-shaped refractive index distribution

## Claims

1. A lens having an extended range of focus, the lens comprising:
said lens defining an optical axis and being made of a transparent material;
said lens having two finished optical surfaces;
said lens having a focal power distribution (Ftot); and,
said focal power distribution (Ftot), in relation to a plane perpendicular to said optical axis, changes as a function of the radial height (r) and of the azimuth angle (phi) between a calculated basic value of the focal power (Flens) not equal to zero and a maximum value Fspiral max (r, phi) so as to cause said focal power distribution (Ftot) to emerge by calculation as:


Ftot(r, phi)=Flens(r)+Fspiral max(r, phi)*w(phi),


wherein Fspiral max (r, phi) depends nonlinearly on the radius and w(phi), which is a factor for the focal power component having the spiral profile, and in that the calculated basic value of said focal power (Flens) is split into a refractive focal power component of a base system (Fbase) and into a focal power component of a structure (Fstructure), furthermore a spiral focal power component


Fspiral(r, phi)=Fspiral max(r, phi)*w(phi)


and the focal power component of the structure (Fstructure) being combined to form a spiral and structure-shaped additional focal power


Fss(r, phi)=Fstructure(r)+Fspiral(r, phi)


such that the overall focal power of the finished lens emerges as


Ftot(r, phi)=Fbase(r)+Fss(r, phi).

2. The lens of claim 1, wherein w(phi) is described as a linear profile using the equation




  
    w
    ⁡
    
      (
      phi
      )
    
  
  =
  
    
      phi
      
        2
        ⁢
        
          
        
        ⁢
        π
      
    
    .

3. The lens of claim 1, wherein the base focal power of the lens (Fbase) and/or the additional focal power of the structure (Fstructure) is/are rotationally symmetric.

4. A lens having an extended range of focus, the lens comprising:
said lens defining an optical axis and being made of a transparent material;
said lens having two finished optical surfaces;
said lens having a focal power distribution (Ftot); and,
said focal power distribution (Ftot), in relation to a plane perpendicular to said optical axis, changes as a function of the radial height (r) and of the azimuth angle (phi) between a calculated basic value of the focal power (Flens) not equal to zero and a maximum value Fspiral max (r, phi) so as to cause said focal power distribution (Flens) to emerge by calculation as:


Ftot(r, phi)=Flens(r)+Fspiral max(r, phi)*w(phi),


wherein Fspiral max (r, phi) depends nonlinearly on the radius and w (phi), which is a factor for the focal power component having the spiral profile, and in that the calculated basic value of said focal power (Flens) is split into a refractive focal power component of a base system (Fbase) and into a focal power component of a structure (Fstructure), furthermore a spiral focal power component


Fspiral(r, phi)=Fspiral max(r, phi)*w(phi)


and the focal power component of the structure (Fstructure) being combined to form a spiral and structure-shaped additional focal power


Fss(r, phi)=Fstructure(r)+Fspiral(r, phi)


such that the overall focal power of the finished lens emerges as


Ftot(r, phi)=Fbase(r)+Fss(r, phi);


Wherein w(phi) is described by the equation





  
    w
    ⁡
    
      (
      phi
      )
    
  
  =
  
    
      ∑
      
        i
        =
        1
      
      M
    
    ⁢
    
      
    
    ⁢
    
      
        I
        i
      
      ⁢
      
        exp
        ⁡
        
          [
          
            -
            
              
                
                  a
                  i
                
                ⁡
                
                  (
                  
                    phi
                    -
                    
                      w
                      i
                    
                  
                  )
                
              
              2
            
          
          ]
        
      
    
  



and wi denotes the peak positions of the angular distribution function; Ii denotes intensity values of the individual peaks; ai>0 denotes damping coefficients for the respective peak positions and i denotes a counter and M≧i denotes a final value.

5. A lens having an extended range of focus, the lens comprising:
said lens defining an optical axis and being made of a transparent material;
said lens having two finished optical surfaces;
said lens having a focal power distribution (Ftot); and,
said focal power distribution (Ftot), in relation to a plane perpendicular to said optical axis, changes as a function of the radial height (r) and of the azimuth angle (phi) between a calculated basic value of the focal power (Flens) not equal to zero and a maximum value Fspiral max(r, phi) so as to cause said focal power distribution (Ftot) to emerge by calculation as:


Ftot(r, phi)=Flens(r)+Fspiral max(r, phi)*w(phi),


wherein Fspiral max (r, phi) depends nonlinearly on the radius and w (phi), which is a factor for the focal power component having the spiral profile, and in that the calculated basic value of said focal power (Flens) is split into a refractive focal power component of a base system (Fbase) and into a focal power component of a structure (Fstructure), furthermore a spiral focal power component


Fspiral(r, phi)=Fspiral max(r, phi)*w(phi)


and the focal power component of the structure (Fstructure) being combined to form a spiral and structure-shaped additional focal power


Fss(r, phi)=Fstructure(r)+Fspiral(r, phi)


such that the overall focal power of the finished lens emerges as


Ftot(r, phi)=Fbase(r)+Fss(r, phi);


wherein the spiral and structure-shaped focal power distribution (Fss) is created by a height profile, wherein the height profile ztot (r, phi) of the second optical surface to be manufactured emerges from adding a height profile (zbase) of a calculated base surface, a Fresnel-shaped height profile (zFresnel) of a Fresnel lens and a spiral height profile zspiral (r, phi), wherein the additive height zspiral (r, phi), starting from zero up to a maximum value (zspiral max) emerges as a function:


zspiral(r, phi)=zspiral max(r, phi)*w(phi)


wherein: the radius (r) changes continuously between 0 and D/2 and the azimuth angle of the aperture (phi) changes continuously between 0 and 2.pi., wherein the spiral height profile zspiral (r, phi) and the Fresnel-shaped height profile (zFresnel) are added to the height profile (zbase) of the calculated base surface, as result of which the optical surface to be manufactured is described by a spiral and Fresnel-shaped height profile (zFS), wherein


ztot(r, phi)=zbase+zFS(r, phi)



with



zFS(r, phi)=zFresnel+zspiral(r, phi)


applies.

6. The lens of claim 5, wherein the forms and/or structures producing the additional spiral and structure-shaped focal power FSS are arranged on one of the optical surfaces of the lens, in each case on their own or combined with one another, and/or also arranged individually or combined with one another and/or in a distributed manner on both optical surfaces of the lens and/or introduced into the material of the lens.

7. The lens of claim 5, wherein the spiral additive height (zspiral) emerges from the product of a polynomial for the maximum height zspiral max(r, phi), which depends nonlinearly on the radius and the angle, and an angle-dependent component w(phi):



  
    
      
        
          z
          spiral
        
        ⁡
        
          (
          
            r
            ,
            phi
          
          )
        
      
      =
      
        
          
            z
            
              spiral
              ⁢
              
                
              
              ⁢
              max
            
          
          ⁡
          
            (
            
              r
              ,
              phi
            
            )
          
        
        *
        
          w
          ⁡
          
            (
            phi
            )
          
        
      
    
    ,
    
      

    
    ⁢
    where
  




  
    
      
        z
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          
            c
            j
          
          ⁡
          
            (
            phi
            )
          
        
        *
        
          r
          j
        
      
    
  




  or




  
    
      
        z
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        ∑
        
          j
          =
          1
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          
            c
            j
          
          ⁡
          
            (
            phi
            )
          
        
        *
        
          r
          
            2
            *
            j
          
        
      
    
  


is the polynomial for the maximum height.

8. The lens of claim 5, wherein the additive height (z) emerges from the product of a polynomial for the maximum height zmax(r), which depends nonlinearly on the radius, and an angle-dependent component w(phi):



  
    
      
        
          z
          spiral
        
        ⁡
        
          (
          
            r
            ,
            phi
          
          )
        
      
      =
      
        
          
            z
            
              spiral
              ⁢
              
                
              
              ⁢
              max
            
          
          ⁡
          
            (
            r
            )
          
        
        *
        
          w
          ⁡
          
            (
            phi
            )
          
        
      
    
    ,
    
      

    
    ⁢
    where
  




  
    
      
        z
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          c
          j
        
        *
        
          r
          j
        
      
    
  




  or




  
    
      
        z
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          j
          =
          1
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          c
          j
        
        *
        
          r
          
            2
            *
            j
          
        
      
    
  


is the radial polynomial for the maximum height.

9. A lens having an extended range of focus, the lens comprising:
said lens defining an optical axis and being made of a transparent material;
said lens having two finished optical surfaces;
said lens having a focal power distribution (Ftot); and,
said focal power distribution (Ftot), in relation to a plane perpendicular to said optical axis, changes as a function of the radial height (r) and of the azimuth angle (phi) between a calculated basic value of the focal power (Flens) not equal to zero and a maximum value Fspiral max(r, phi) so as to cause said focal power distribution (Ftot) to emerge by calculation as:


Ftot(r, phi)=Flens(r)+Fspiral max(r, phi)*w(phi),


wherein Fspiral max (r, phi) depends nonlinearly on the radius and w (phi), which is a factor for the focal power component having the spiral profile, and in that the calculated basic value of said focal power (Flens) is split into a refractive focal power component of a base system (Fbase) and into a focal power component of a structure (Fstructure), furthermore a spiral focal power component


Fspiral(r, phi)=Fspiral max(r, phi)*w(phi)


and the focal power component of the structure (Fstructure) being combined to form a spiral and structure-shaped additional focal power


Fss(r, phi)=Fstructure(r)+Fspiral(r, phi)


such that the overall focal power of the finished lens emerges as


Ftot(r, phi)=Fbase(r)+Fss(r, phi);


wherein the focal power distribution is produced by a diffractive optical element, wherein the calculated base surface is manufactured as a second optical surface and the focal power component with the spiral and structure-shaped profile (Fss diffractive) emerges from the effect of an optical grating, which is applied onto the manufactured second optical surface, furthermore the spiral and structure-shaped additional diffractive focal power (Fss diffractive) is the sum of the focal power of the spiral in diffractive form (Fspiral diffractive) and the focal power of the structure in diffractive form (Fstructure diffractive) and the focal power in phase form is described as


phasess(r, phi)=phasestructure+phasespiral(r, phi)


where the radius (r) changes continuously between 0 and D/2 and the azimuth angle (phi) changes continuously between 0 and 2π, as a result of which the grating manufactured on the optical surface has the spiral and structure-shaped phase profile.

10. The lens of claim 9, wherein the forms and/or structures producing the additional spiral and structure-shaped focal power FSS are arranged on one of the optical surfaces of the lens, in each case on their own or combined with one another, and/or also arranged individually or combined with one another and/or in a distributed manner on both optical surfaces of the lens and/or introduced into the material of the lens.

11. The lens of claim 9, wherein the values for the spiral grating profile are determined by the equation



  
    
      
        phase
        spiral
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        
          phase
          
            spiral
            ⁢
            
              
            
            ⁢
            max
          
        
        ⁡
        
          (
          
            r
            ,
            phi
          
          )
        
      
      *
      
        w
        ⁡
        
          (
          phi
          )
        
      
    
  




  wherein




  
    
      
        phase
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          
            k
            j
          
          ⁡
          
            (
            phi
            )
          
        
        *
        
          r
          j
        
      
    
  




  or




  
    
      
        phase
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        
          r
          ,
          phi
        
        )
      
    
    =
    
      
        ∑
        
          j
          =
          1
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          
            k
            j
          
          ⁡
          
            (
            phi
            )
          
        
        *
        
          r
          
            2
            *
            j
          
        
      
    
  


is the polynomial for the maximum phase value.

12. The lens of claim 9, wherein the values for the spiral grating profile are determined by the equation



  
    
      
        
          phase
          spiral
        
        ⁡
        
          (
          
            r
            ,
            phi
          
          )
        
      
      =
      
        
          
            phase
            
              spiral
              ⁢
              
                
              
              ⁢
              max
            
          
          ⁡
          
            (
            r
            )
          
        
        *
        
          w
          ⁡
          
            (
            phi
            )
          
        
      
    
    ,
    
      

    
    ⁢
    wherein
  




  
    
      
        phase
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          j
          =
          2
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          k
          j
        
        *
        
          r
          j
        
      
    
  




  or




  
    
      
        phase
        
          spiral
          ⁢
          
            
          
          ⁢
          max
        
      
      ⁡
      
        (
        r
        )
      
    
    =
    
      
        ∑
        
          j
          =
          1
        
        N
      
      ⁢
      
        
      
      ⁢
      
        
          k
          j
        
        *
        
          r
          
            2
            *
            j
          
        
      
    
  


is the radial polynomial for the maximum phase value.

13. The lens of claim 11, wherein the forms and/or structures producing the additional spiral and structure-shaped focal power FSS are arranged on one of the optical surfaces of the lens, in each case on their own or combined with one another, and/or also arranged individually or combined with one another and/or in a distributed manner on both optical surfaces of the lens and/or introduced into the material of the lens.

14. A lens having an extended range of focus, the lens comprising:
said lens defining an optical axis and being made of a transparent material;
said lens having two finished optical surfaces;
said lens having a focal power distribution (Ftot); and,
said focal power distribution (Ftot), in relation to a plane perpendicular to said optical axis, changes as a function of the radial height (r) and of the azimuth angle (phi) between a calculated basic value of the focal power (Flens) not equal to zero and a maximum value Fspiral max (r, phi) so as to cause said focal power distribution (Ftot) to emerge by calculation as:


Ftot(r, phi)=Flens(r)+Fspiral max(r, phi)*w(phi),


wherein Fspiral max (r, phi) depends nonlinearly on the radius and w (phi), which is a factor for the focal power component having the spiral profile, and in that the calculated basic value of said focal power (Flens) is split into a refractive focal power component of a base system (Fbase) and into a focal power component of a structure (Fstructure), furthermore a spiral focal power component


Fspiral(r, phi)=Fspiral max(r, phi)*w(phi)


and the focal power component of the structure (Fstructure) being combined to form a spiral and structure-shaped additional focal power


Fss(r, phi)=Fstructure(r)+Fspiral(r, phi)


such that the overall focal power of the finished lens emerges as


Ftot(r, phi)=Fbase(r)+Fss(r, phi);


wherein the focal power component with the spiral and structure-shaped profile (Fss) emerges from an additive or subtractive refractive index distribution Δnss (r, phi) in the material of the lens, which is a sum of a spiral refractive index distribution Δnspiral (r, phi) and a structure-shaped refractive index distribution (Δnstructure):


Δnss(r, phi)=Δnstructure+Δnspiral(r, phi)


and the refractive index distribution emerges, proceeding from a basic value (n2) up to a maximum value (Δnspiral max), as a function


Δnspiral(r, phi)=Δnspiral max(r, phi)*w(phi),


where the radius (r) changes continuously between 0 and D/2 and the azimuth angle (phi) changes continuously between 0 and 2.pi., as a result of which the spiral and structure-shaped refractive index distribution of the lens material is described for Δnss (r, phi).

15. A lens system defining a beam path and having an extended range of focus, the lens system comprising:
A lens with an extended range of focus arranged as an imaging element in said beam path of said lens system:
said lens defining an optical axis and being made of a transparent material:
said lens having two finished optical surfaces;
said lens having a focal power distribution (Ftot); and,
said focal power distribution (Ftot), referred to a plane perpendicular to said optical axis, changes as a function of the radial height (r) and of the azimuth angle (phi) between a calculated basic value of the focal power (Flens) not equal to zero and a maximum value Fspiral max (r, phi) so as to cause said focal power distribution (Ftot) to emerge by calculation as:


Ftot(r, phi)=Flens(r)+Fspiral max(r, phi)*w(phi),


wherein Fspiral max (r, phi) depends nonlinearly on the radius and w (phi), which is a factor for the focal power component having the spiral profile, and in that the calculated basic value of said focal power (Flens) is split into a refractive focal power component of a base system (Fbase) and into a focal power component of a structure (Fstructure), furthermore a spiral focal power component


Fspiral(r, phi)=Fspiral max(r, phi)*w(phi)


and the focal power component of the structure (Fstructure) being combined to form a spiral and structure-shaped additional focal power


Fss(r, phi)=Fstructure(r)+Fspiral(r, phi)


such that the overall focal power of the finished lens emerges as


Ftot(r, phi)=Fbase(r)+Fss(r, phi).