Lens having an extended range of focus and method of making the same
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 (F tot ) 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 (F lens ) not equal to zero and a maximum value F spiral max (r, phi).
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 (F tot ); and,
said focal power distribution (F tot ), 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 (F lens ) not equal to zero and a maximum value F spiral max (r, phi) so as to cause said focal power distribution (F tot ) to emerge by calculation as:
F tot ( r, phi )= F lens ( r )+ F spiral max ( r, phi )* w ( phi ),
wherein F spiral 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 (F lens ) is split into a refractive focal power component of a base system (F base ) and into a focal power component of a structure (F structure ), furthermore a spiral focal power component
F spiral ( r, phi )= F spiral max ( r, phi )* w ( phi )
and the focal power component of the structure (F structure ) being combined to form a spiral and structure-shaped additional focal power
F ss ( r, phi )= F structure ( r )+ F spiral ( r, phi )
such that the overall focal power of the finished lens emerges as
F tot ( r, phi )= F base ( r )+ F ss ( 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 (F base ) and/or the additional focal power of the structure (F structure ) 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 (F tot ); and,
said focal power distribution (F tot ), 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 (F lens ) not equal to zero and a maximum value F spiral max (r, phi) so as to cause said focal power distribution (F lens ) to emerge by calculation as:
F tot ( r, phi )= F lens ( r )+ F spiral max ( r, phi )* w ( phi ),
wherein F spiral 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 (F lens ) is split into a refractive focal power component of a base system (F base ) and into a focal power component of a structure (F structure ), furthermore a spiral focal power component
F spiral ( r, phi )= F spiral max ( r, phi )* w ( phi )
and the focal power component of the structure (F structure ) being combined to form a spiral and structure-shaped additional focal power
F ss ( r, phi )= F structure ( r )+ F spiral ( r, phi )
such that the overall focal power of the finished lens emerges as
F tot ( r, phi )= F base ( r )+ F ss ( 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 w i denotes the peak positions of the angular distribution function; I i denotes intensity values of the individual peaks; a i >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 (F tot ); and,
said focal power distribution (F tot ), 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 (F lens ) not equal to zero and a maximum value F spiral max (r, phi) so as to cause said focal power distribution (F tot ) to emerge by calculation as:
F tot ( r, phi )= F lens ( r )+ F spiral max ( r, phi )* w ( phi ),
wherein F spiral 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 (F lens ) is split into a refractive focal power component of a base system (F base ) and into a focal power component of a structure (F structure ), furthermore a spiral focal power component
F spiral ( r, phi )= F spiral max ( r, phi )* w ( phi )
and the focal power component of the structure (F structure ) being combined to form a spiral and structure-shaped additional focal power
F ss ( r, phi )= F structure ( r )+ F spiral ( r, phi )
such that the overall focal power of the finished lens emerges as
F tot ( r, phi )= F base ( r )+ F ss ( r, phi );
wherein the spiral and structure-shaped focal power distribution (F ss ) is created by a height profile, wherein the height profile z tot (r, phi) of the second optical surface to be manufactured emerges from adding a height profile (z base ) of a calculated base surface, a Fresnel-shaped height profile (z Fresnel ) of a Fresnel lens and a spiral height profile z spiral (r, phi), wherein the additive height z spiral (r, phi), starting from zero up to a maximum value (z spiral max ) emerges as a function:
z spiral ( r, phi )= z spiral 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 z spiral (r, phi) and the Fresnel-shaped height profile (z Fresnel ) are added to the height profile (z base ) 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 (z FS ), wherein
z tot ( r, phi )= z base +z FS ( r, phi )
with
z FS ( r, phi )= z Fresnel +z spiral ( r, phi )
applies.
6. The lens of claim 5 , wherein the forms and/or structures producing the additional spiral and structure-shaped focal power F SS 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 (z spiral ) emerges from the product of a polynomial for the maximum height z spiral 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 z max (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 (F tot ); and,
said focal power distribution (F tot ), 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 (F lens ) not equal to zero and a maximum value F spiral max (r, phi) so as to cause said focal power distribution (F tot ) to emerge by calculation as:
F tot ( r, phi )= F lens ( r )+ F spiral max ( r, phi )* w ( phi ),
wherein F spiral 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 (F lens ) is split into a refractive focal power component of a base system (F base ) and into a focal power component of a structure (F structure ), furthermore a spiral focal power component
F spiral ( r, phi )= F spiral max ( r, phi )* w ( phi )
and the focal power component of the structure (F structure ) being combined to form a spiral and structure-shaped additional focal power
F ss ( r, phi )= F structure ( r )+ F spiral ( r, phi )
such that the overall focal power of the finished lens emerges as
F tot ( r, phi )= F base ( r )+ F ss ( 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 (F ss 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 (F ss diffractive ) is the sum of the focal power of the spiral in diffractive form (F spiral diffractive ) and the focal power of the structure in diffractive form (F structure diffractive ) and the focal power in phase form is described as
phase ss ( r, phi )=phase structure +phase spiral ( 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 F SS 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 F SS 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 (F tot ); and,
said focal power distribution (F tot ), 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 (F lens ) not equal to zero and a maximum value F spiral max (r, phi) so as to cause said focal power distribution (F tot ) to emerge by calculation as:
F tot ( r, phi )= F lens ( r )+ F spiral max ( r, phi )* w ( phi ),
wherein F spiral 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 (F lens ) is split into a refractive focal power component of a base system (F base ) and into a focal power component of a structure (F structure ), furthermore a spiral focal power component
F spiral ( r, phi )= F spiral max ( r, phi )* w ( phi )
and the focal power component of the structure (F structure ) being combined to form a spiral and structure-shaped additional focal power
F ss ( r, phi )= F structure ( r )+ F spiral ( r, phi )
such that the overall focal power of the finished lens emerges as
F tot ( r, phi )= F base ( r )+ F ss ( r, phi );
wherein the focal power component with the spiral and structure-shaped profile (F ss ) emerges from an additive or subtractive refractive index distribution Δn ss (r, phi) in the material of the lens, which is a sum of a spiral refractive index distribution Δn spiral (r, phi) and a structure-shaped refractive index distribution (Δn structure ):
Δ n ss ( r, phi )=Δ n structure +Δn spiral ( r, phi )
and the refractive index distribution emerges, proceeding from a basic value (n 2 ) up to a maximum value (Δn spiral max ), as a function
Δ n spiral ( r, phi )=Δ n spiral 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 Δn ss (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 (F tot ); and,
said focal power distribution (F tot ), 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 (F lens ) not equal to zero and a maximum value F spiral max (r, phi) so as to cause said focal power distribution (F tot ) to emerge by calculation as:
F tot ( r, phi )= F lens ( r )+ F spiral max ( r, phi )* w ( phi ),
wherein F spiral 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 (F lens ) is split into a refractive focal power component of a base system (F base ) and into a focal power component of a structure (F structure ), furthermore a spiral focal power component
F spiral ( r, phi )= F spiral max ( r, phi )* w ( phi )
and the focal power component of the structure (F structure ) being combined to form a spiral and structure-shaped additional focal power
F ss ( r, phi )= F structure ( r )+ F spiral ( r, phi )
such that the overall focal power of the finished lens emerges as
F tot ( r, phi )= F base ( r )+ F ss ( r, phi ).