Lens having extended depth of focus, method for designing the same, and optical system having the same
The lens includes a plurality of lens layers, each lens layer being axi-symmetric and having an extended depth of focus to focus light in a corresponding section of a focal curve in the form of a straight line located on an optical axis. In the optical system, light is focused on an optical axis to obtain a clear image in a wide distance range between a camera and an object. The optical system has a point spread function that is simpler and more symmetric. That is, the optical system provides improved continuity of a lens surface and easiness and flexibility in optical designing.
1. An optical system comprising:
a lens including a plurality of lens layers, each lens layer being axi-symmetric and having an extended depth of focus to focus light in a corresponding section of a plurality of sections of a focal curve in a form of a straight line located on an optical axis, the plurality of lens layers include a plurality of first lens layers, wherein
at least one of the first lens layers is configured to focus light in a section from any one of both ends of the focal curve to a first focal distance, and
at least one of the first lens layers is configured to focus light in a section from the other one of both ends of the focal curve to a second focal distance;
an image sensor configured to detect an image formed by the lens having an extended depth of focus; and
an image processor configured to restore an image detected by the image sensor.
2. The optical system of claim 1 , wherein the plurality of lens layers include a plurality of first lens layers located outside a radius from the optical axis, and the plurality of first lens layers focus light in a section from each of both ends of the focal curve to at least one focal distance.
3. The optical system of claim 2 , wherein the plurality of lens layers further include a plurality of second lens layers located within the radius from the optical axis, and a light field formed by a corresponding one of the plurality of second lens layers is coherently mixed with a light field formed by the first lens layers.
4. The optical system of claim 3 , wherein a thickness of each of the corresponding at least one lens layer of the plurality of lens layers controls a distribution of intensity of a light field of any one of the plurality of sections of the focal curve.
5. The optical system of claim 3 , wherein the lens layers have instant focal lengths with respect to radii of the plurality of lens layers that define a phase function of the lens having an extended depth of focus.
6. The optical system of claim 5 , wherein the instant focal length defines the phase function of the lens having an extended depth of focus corresponding to the following mathematical expression,
F
(
r
)
=
{
F
1
(
r
1
)
,
for
the
first
lens
layer
F
2
(
r
2
)
,
for
the
second
lens
layer
,
where F(r) denotes the instant focal length of a lens layer having a radius r,
r 1 denotes the radius of the first lens layer, and
r 2 denotes the radius of the second lens layer.
7. The optical system of claim 3 , wherein the lens layers have optical phase delays with respect to radii of the plurality of lens layers that define the phase function of the lens having an extended depth of focus.
8. The optical system of claim 7 , wherein the optical phase delay define the phase function of the lens having an extended depth of focus corresponding to the following mathematical expression,
Φ
(
r
)
=
π
×
r
2
λ
×
F
(
r
)
,
where Φ(r) denotes an optical phase delay,
r denotes the radius of a lens layer,
λ denotes the wavelength of light, and
F(r) denotes the instant focal length of the lens layer.
9. The optical system of claim 1 , wherein the plurality of first lens layers are located outside a radius from the optical axis.
10. The optical system of claim 9 , wherein the plurality of lens layers further include a plurality of second lens layers located within the radius from the optical axis, and the plurality of second lens layers include,
at least one first-type second lens layer that forms a light field to be coherently mixed with the light field formed by the at least one first lens layer that is configured to focus light in a section from any one of both ends of the focal curve to a first focal distance; and
at least one second-type second lens layer that forms a light field to be coherently mixed with the light field formed by the at least one first lens layer that is configured to focus light in a section from the other one of both ends of the focal curve to a second focal distance.
11. A lens having an extended depth of focus, the lens comprising:
a plurality of first lens layers located outside a radius from an optical axis, wherein
at least one of the first lens layers is configured to focus light in a section from any one of both ends of the focal curve to a first focal distance, and
at least one of the first lens layers is configured to focus light in a section from the other one of both ends of the focal curve to a second focal distance; and
a plurality of second lens layers located within the radius from the optical axis, wherein the plurality of first lens layers focus light in a section from each of both ends of a focal curve in a form of a straight line located on the optical axis to at least one focal distance.
12. The lens of claim 11 , wherein a corresponding lens of the plurality of second lens layers forms a light field and is coherently mixed with a light field formed by the first lens layers.
13. The lens of claim 12 , wherein a thickness of each of the corresponding at least one lens layer of the plurality of lens layers controls a distribution of intensity of a light field of any one of the plurality of sections of the focal curve.
14. The lens of claim 12 , wherein the lens layers have instant focal lengths with respect to radii of the plurality of lens layers that define a phase function of the lens having an extended depth of focus.
15. The lens of claim 14 , wherein the instant focal length defines the phase function of the lens having an extended depth of focus corresponding to the following mathematical expression,
F
(
r
)
=
{
F
1
(
r
1
)
,
for
the
first
lens
layer
F
2
(
r
2
)
,
for
the
second
lens
layer
,
where F(r) denotes the instant focal length of a lens layer having a radius r,
r 1 denotes the radius of the first lens layer, and
r 2 denotes the radius of the second lens layer.
16. The lens of claim 12 , wherein the lens layers have optical phase delays with respect to radii of the plurality of lens layers that define the phase function of the lens having an extended depth of focus.
17. The lens of claim 16 , wherein the optical phase delay defines the phase function of the lens having an extended depth of focus corresponding to the following mathematical expression,
Φ
(
r
)
=
π
×
r
2
λ
×
F
(
r
)
,
where Φ(Kr) denotes an optical phase delay,
r denotes the radius of a lens layer,
λ denotes the wavelength of light, and
F(r) denotes the instant focal length of the lens layer.
18. The lens of claim 11 , wherein the plurality of second lens layers include,
at least one first-type second lens layer that forms a light field to be coherently mixed with the light field formed by the at least one first lens layer that is configured to focus light in a section from any one of both ends of the focal curve to a first focal distance, and
at least one second-type second lens layer that forms a light field to be coherently mixed with the light field formed by the at least one first lens layer that is configured to focus light in a section from the other one of both ends of the focal curve to a second focal distance.
19. A method for designing an extended depth of focus lens, the method comprising:
dividing the focal curve of the lens into a plurality of sections;
focusing both ends of the focal curve using one or more first lens layers located outside a radius from an optical axis, wherein
at least one of the first lens layers is configured to focus light in a section from any one of both ends of the focal curve to a first focal distance, and
at least one of the first lens layers is configured to focus light in a section from the other one of both ends of the focal curve to a second focal distance;
focusing the focal curve using one or more second lens layers located within the radius from the optical axis, wherein
the plurality of first lens layers focus light in a section from each of both ends of a focal curve in the form of a straight line located on the optical axis to a focal distance, and
the focusing of the one or more second lens layers generates a coherent mixing with the one or more first lens layers;
calculating the lens phase function; and
manufacturing the lens.
20. The method of claim 19 , wherein the phase function is defined by an instant focal length corresponding to the following mathematical expression,
F
(
r
)
=
{
F
1
(
r
1
)
,
for
the
first
lens
layer
F
2
(
r
2
)
,
for
the
second
lens
layer
,
where F(r) denotes the instant focal length of a lens layer having a radius r,
r 1 denotes the radius of the first lens layer, and
r 2 denotes the radius of the second lens layer.
21. The lens of claim 19 , wherein the phase function of the lens is defined by an optical phase delay corresponding to the following mathematical expression,
Φ
(
r
)
=
π
×
r
2
λ
×
F
(
r
)
,
where Φ(r) denotes an optical phase delay,
r denotes the radius of a lens layer,
λ denotes the wavelength of light, and
F(r) denotes the instant focal length of the lens layer.