U.S. patent application number 17/190031 was filed with the patent office on 2022-09-29 for solid state electrically variable-focal length lens.
This patent application is currently assigned to HRL Laboratories, LLC. The applicant listed for this patent is HRL Laboratories, LLC. Invention is credited to Richard KREMER, Jeong-Sun MOON, Ryan G. QUARFOTH, Kyung-Ah SON.
Application Number | 20220308419 17/190031 |
Document ID | / |
Family ID | 1000006588889 |
Filed Date | 2022-09-29 |
United States Patent
Application |
20220308419 |
Kind Code |
A9 |
KREMER; Richard ; et
al. |
September 29, 2022 |
SOLID STATE ELECTRICALLY VARIABLE-FOCAL LENGTH LENS
Abstract
A solid state electrically variable focal length lens includes a
plurality of concentric rings of electro-optical material, wherein
the electro-optical material comprises any material of a class of
hydrogen-doped phase-change metal oxide and wherein each respective
concentric ring further includes a transparent resistive sheet on a
first face of the respective concentric ring, wherein the
transparent resistive sheet extends along the first face, and a
first voltage coupled between a first end and a second end of the
transparent resistive sheet, wherein the first voltage may be
varied to select an optical beam deflection angle.
Inventors: |
KREMER; Richard; (Ramona,
CA) ; SON; Kyung-Ah; (Moorpark, CA) ; MOON;
Jeong-Sun; (Moorpark, CA) ; QUARFOTH; Ryan G.;
(Los Angeles, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
HRL Laboratories, LLC |
Malibu |
CA |
US |
|
|
Assignee: |
HRL Laboratories, LLC
Malibu
CA
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20210364884 A1 |
November 25, 2021 |
|
|
Family ID: |
1000006588889 |
Appl. No.: |
17/190031 |
Filed: |
March 2, 2021 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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63027838 |
May 20, 2020 |
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63027844 |
May 20, 2020 |
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63027847 |
May 20, 2020 |
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63027849 |
May 20, 2020 |
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63027841 |
May 20, 2020 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G02F 1/294 20210101 |
International
Class: |
G02F 1/29 20060101
G02F001/29 |
Claims
1. A solid state electrically variable focal length lens
comprising: a plurality of concentric rings of electro-optical
material, wherein the electro-optical material comprises any
material of a class of hydrogen-doped phase-change metal oxide and
wherein each respective concentric ring further comprises: a
transparent resistive sheet on a first face of the respective
concentric ring, wherein the transparent resistive sheet extends
along the first face; and a first voltage coupled between a first
end and a second end of the transparent resistive sheet; wherein
the first voltage may be varied to select an optical beam
deflection angle.
2. The solid state electrically variable focal length lens of claim
1 wherein: the electro-optical material comprises NdNiO.sub.3,
SmNiO.sub.3, PrNiO.sub.3, EuNiO.sub.3, or GdNiO.sub.3, or any
combination of NdNiO.sub.3, SmNiO.sub.3, PrNiO.sub.3, EuNiO.sub.3,
and GdNiO.sub.3.
3. The solid state electrically variable focal length lens of claim
1 further comprising: a transparent electrode on a second face of
the respective concentric ring, wherein the transparent electrode
extends along the second face, and wherein the second face is
opposite the first face; and a second voltage coupled between the
first end of the transparent resistive sheet and the transparent
electrode; wherein the second voltage may be varied to apply a beam
forming phase-shift.
4. The solid state electrically variable focal length lens of claim
3 wherein: the first voltage and the second voltage are direct
current (DC) voltages.
5. The solid state electrically variable focal length lens of claim
1 wherein: the first voltage is set for each respective concentric
ring so that the solid state electrically variable focal length
lens has a desired focal length.
6. The solid state electrically variable focal length lens of claim
1 wherein: the first voltage is set for each respective concentric
ring so that the solid state electrically variable focal length
lens has a focal length at a far focal range; or the first voltage
is set for each respective concentric ring so that the solid state
electrically variable focal length lens has a focal length at a
close focal range; or the first voltage is set for each respective
concentric ring so that the solid state electrically variable focal
length lens has a focal length between the far focal range and the
close focal range.
7. The solid state electrically variable focal length lens of claim
1 wherein: a different radial voltage gradient is applied across
each respective ring of the plurality of concentric rings so that a
radial gradient in the index of refraction steers light toward an
optical axis of the solid state electrically variable focal length
lens.
8. The solid state electrically variable focal length lens of claim
1 further comprising: a Fresnel lens coupled to and adjacent to the
solid state variable focal length lens; wherein the Fresnel lens
has a plurality of Fresnel rings and wherein each respective
Fresnel ring of the plurality of Fresnel rings has a radius
matching and aligned to a respective concentric ring of the
plurality of concentric rings.
9. The solid state electrically variable focal length lens of claim
8 wherein: the Fresnel lens has a focal length between a farthest
focal length or focus for the solid state variable length lens and
a closest focal length or focus to reduce a steering angle for the
solid state electrically variable focal length lens.
10. The solid state electrically variable focal length lens of
claim 1: wherein the solid state electrically variable focal length
lens operates in transmission; or wherein the solid state
electrically variable focal length lens further comprises: a mirror
on the first face of the respective concentric ring; wherein the
solid state electrically variable focal length lens operates in
reflection.
11. A solid state zoom lens comprising: a first plurality of first
concentric rings of first electro-optical material, wherein the
first electro-optical material comprises any material of a class of
hydrogen-doped phase-change metal oxide and wherein each respective
first concentric ring further comprises: a first transparent
resistive sheet on a first face of the respective first concentric
ring, wherein the first transparent resistive sheet extends along
the first face; and a first voltage coupled between a first end and
a second end of the first transparent resistive sheet; and wherein
the first voltage may be varied to select a beam deflection angle;
and a second plurality of second concentric rings of second
electro-optical material, wherein the second electro-optical
material comprises any material of a class of hydrogen-doped
phase-change metal oxide and wherein each respective second
concentric ring further comprises: a second transparent resistive
sheet on a first face of the respective second concentric ring,
wherein the second transparent resistive sheet extends along the
first face; and a second voltage coupled between a first end and a
second end of the second transparent resistive sheet; wherein the
second voltage may be varied to select a beam deflection angle; and
wherein the first plurality of first concentric rings is optically
coupled to the second plurality of second concentric rings.
12. The solid state zoom lens of claim 11 further comprising: a
first transparent electrode on a second face of the respective
first concentric ring, wherein the first transparent electrode
extends along the second face, and wherein the second face is
opposite the first face; and a third voltage coupled between the
first end of the first transparent resistive sheet and the first
transparent electrode; wherein the third voltage may be varied to
apply a beam forming phase-shift.
13. The solid state zoom lens of claim 11 further comprising: a
second transparent electrode on a second face of the respective
second concentric ring, wherein the second transparent electrode
extends along the second face, and wherein the second face is
opposite the first face; and a fourth voltage coupled between the
first end of the second transparent resistive sheet and the second
transparent electrode; wherein the fourth voltage may be varied to
apply a beam forming phase-shift.
14. The solid state zoom lens of claim 11 wherein: a distance
between the first plurality of concentric rings and the second
plurality of concentric rings is the sum of a far focal length for
the first plurality of concentric rings and a near focal length for
the second plurality of concentric rings; or a distance between the
first plurality of concentric rings and the second plurality of
concentric rings is the sum of a near focal length for the first
plurality of concentric rings and a far focal length for the second
plurality of concentric rings.
15. The solid state zoom lens of claim 11 further comprising: a
solid state optical tip-tilt-phased element optically coupled to
the second plurality of concentric rings to provide a solid state
pan-tilt-zoom "gimbal" with no moving parts.
16. The solid state zoom lens of claim 15 wherein the solid state
optical tip-tilt-phased element further comprises: a body of
electro-optical material, wherein the body of electro-optical
material comprises any material of a class of hydrogen-doped
phase-change metal oxide; a third transparent resistive sheet on a
first face of the body of electro-optical material, wherein the
third transparent resistive sheet extends along the first face; and
a fourth transparent resistive sheet on a second face of the body
of electro-optical material, wherein the fourth transparent
resistive sheet extends along the second face, and wherein the
second face is opposite the first face; a third voltage coupled
between a first end and a second end of the third transparent
resistive sheet; and a fourth voltage coupled between a first end
and a second end of the fourth transparent resistive sheet; wherein
the first end and the second end of the third transparent resistive
sheet are opposite each other; wherein the first end and the second
end of the fourth transparent resistive sheet are opposite each
other; wherein the third voltage biases the third transparent
resistor sheet in a first direction; and wherein the fourth voltage
biases the fourth transparent resistor sheet in a second
direction.
17. The solid state zoom lens of claim 16 wherein the second
direction is orthogonal to the first direction.
18. The solid state zoom lens of claim 16 wherein the third voltage
and the fourth voltage are direct current (DC) voltages.
19. A method of providing a solid state electrically variable focal
length lens comprising: providing a plurality of concentric rings
of electro-optical material, wherein the electro-optical material
comprises any material of a class of hydrogen-doped phase-change
metal oxide and wherein providing each respective concentric ring
further comprises: providing a transparent resistive sheet on a
first face of the respective concentric ring, wherein the
transparent resistive sheet extends along the first face; and
providing a first voltage coupled between a first end and a second
end of the transparent resistive sheet; wherein the first voltage
may be varied to select a optical beam deflection angle.
20. The method of claim 19 wherein: the electro-optical material
comprises NdNiO.sub.3, SmNiO.sub.3, PrNiO.sub.3, EuNiO.sub.3, or
GdNiO.sub.3, or any combination of NdNiO.sub.3, SmNiO.sub.3,
PrNiO.sub.3, EuNiO.sub.3, and GdNiO.sub.3.
21. The method of claim 19 further comprising: providing a Fresnel
lens coupled to and adjacent to the solid state variable length
lens; wherein the Fresnel lens has a plurality of Fresnel rings and
wherein each respective Fresnel ring of the plurality of Fresnel
rings has a radius matching and aligned to a respective concentric
ring of the plurality of concentric rings.
22. A method of providing a solid state zoom lens comprising:
providing a first plurality of first concentric rings of first
electro-optical material, wherein the first electro-optical
material comprises any material of a class of hydrogen-doped
phase-change metal oxide and wherein providing each respective
first concentric ring further comprises: providing a first
transparent resistive sheet on a first face of the respective first
concentric ring, wherein the first transparent resistive sheet
extends along the first face; and providing a first voltage coupled
between a first end and a second end of the first transparent
resistive sheet; and wherein the first voltage may be varied to
select a beam deflection angle; and providing a second plurality of
second concentric rings of second electro-optical material, wherein
the second electro-optical material comprises any material of a
class of hydrogen-doped phase-change metal oxide and wherein
providing each respective second concentric ring further comprises:
providing a second transparent resistive sheet on a first face of
the respective second concentric ring, wherein the second
transparent resistive sheet extends along the first face; and
providing a second voltage coupled between a first end and a second
end of the second transparent resistive sheet; wherein the second
voltage may be varied to select a beam deflection angle; and
wherein the first plurality of concentric rings are optically
coupled to the second plurality of concentric rings.
23. The method of claim 22 wherein: the first electro-optical
material comprises NdNiO.sub.3, SmNiO.sub.3, PrNiO.sub.3,
EuNiO.sub.3, or GdNiO.sub.3, or any combination of NdNiO.sub.3,
SmNiO.sub.3, PrNiO.sub.3, EuNiO.sub.3, and GdNiO.sub.3; and the
second electro-optical material comprises NdNiO.sub.3, SmNiO.sub.3,
PrNiO.sub.3, EuNiO.sub.3, or GdNiO.sub.3, or any combination of
NdNiO.sub.3, SmNiO.sub.3, PrNiO.sub.3, EuNiO.sub.3, and
GdNiO.sub.3.
24. The method of claim 22 further comprising: providing a solid
state optical tip-tilt-phased element optically coupled to the
second plurality of concentric rings to provide a solid state
pan-tilt-zoom "gimbal" with no moving parts.
25. The method of claim 24 wherein providing the solid state
optical tip-tilt-phased element further comprises: providing a body
of electro-optical material, wherein the body of electro-optical
material comprises any material of a class of hydrogen-doped
phase-change metal oxide; providing a third transparent resistive
sheet on a first face of the body of electro-optical material,
wherein the third transparent resistive sheet extends along the
first face; and providing a fourth transparent resistive sheet on a
second face of the body of electro-optical material, wherein the
fourth transparent resistive sheet extends along the second face,
and wherein the second face is opposite the first face; providing a
third voltage coupled between a first end and a second end of the
third transparent resistive sheet; and providing a fourth voltage
coupled between a first end and a second end of the fourth
transparent resistive sheet; wherein the first end and the second
end of the third transparent resistive sheet are opposite each
other; wherein the first end and the second end of the fourth
transparent resistive sheet are opposite each other; wherein the
third voltage biases the third transparent resistor sheet in a
first direction; wherein the fourth voltage biases the fourth
transparent resistor sheet in a second direction; and wherein the
second direction is orthogonal to the first direction.
26. (canceled)
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is related to and claims the benefit of
U.S. Provisional Patent Application Ser. No. 63/027,838, filed May
20, 2020, and entitled "Solid State Electrically Variable-Focal
Length Lens", which is hereby incorporated herein by reference.
[0002] This application is also related to and claims the benefit
of U.S. Provisional Patent Application Ser. No. 63/027,844, filed
May 20, 2020, and entitled "Solid State Tip-Tilt Phased Array",
which is hereby incorporated herein by reference.
[0003] This application is also related to and claims the benefit
of U.S. Provisional Patent Application Ser. No. 63/027,841, filed
May 20, 2020, and entitled "Solid-state Electrically-Variable
Optical Wedge", which is hereby incorporated herein by
reference.
[0004] This application is also related to and claims the benefit
of U.S. Provisional Patent Application Ser. No. 63/027,847, filed
May 20, 2020, and entitled "Method to Grow IR Optical Materials
with Extremely Small Optical Loss", which is hereby incorporated
herein by reference.
[0005] This application is also related to and claims the benefit
of U.S. Provisional Patent Application Ser. No. 63/027,849, filed
May 20, 2020, and entitled "Method to Grow Thick Crystalline
Optical Films on Si Substrates", which is hereby incorporated
herein by reference.
[0006] This application is also related to U.S. patent application
Ser. No. 16/296,049, filed 7 Mar. 2019, and entitled "Electrically
Reconfigurable Optical Apparatus Using Electric Field", which is
hereby incorporated herein by reference.
[0007] This application is also related to U.S. Provisional Patent
Application Ser. No. 63/094,756, filed Oct. 21, 2020, and entitled
"Electric Field-Tunable IR Devices with Very Large Modulation of
Refractive Index and Methods to Fabricate Them", which is hereby
incorporated herein by reference.
STATEMENT REGARDING FEDERAL FUNDING
[0008] None
TECHNICAL FIELD
[0009] This disclosure relates to variable focal-length lenses.
BACKGROUND
[0010] Prior art zoom lenses have been used in photography for over
100 years. A conventional zoom lens achieves the zoom with three or
more standard, fixed focal-length lenses, at least one of which
moves to provide a variable optical magnification. Disadvantages of
these prior art zoom lenses include slow to change zoom settings
due to the need to mechanically move the movable lens or lenses,
and the need for a finely-machined complex mechanism, which results
in a mechanism that is costly and not rugged.
[0011] Another prior art zoom lens uses a liquid crystal variable
lens. The University of Arizona has been developing such a variable
lens. In this prior art a layer of liquid crystal is used to change
the optical path length between two lenses such that the focal
length changes. This is further described by Mike Hanlon in
"Eyeglasses with Adaptive Focus", New Atlas, Health and Well Being,
Apr. 15, 2006, which may also be found at
https://newatlas.com/eyeglasses-with-adaptive-focus/5516/, which is
incorporated herein by reference.
[0012] Drawbacks of liquid crystal variable lenses include: changes
in zoom are still slow, but faster than a mechanical zoom lens; the
temperature range is limited, because at low temperature the liquid
may freeze and stop working; the index change is limited, which
limits the achievable change in magnification; and it is an
immature technology that is still in development.
[0013] A related prior art lens is a Fresnel lens, which has a flat
optical design. A Fresnel lens is composed of concentric rings that
are blazed at angles that change with radius such that the light
passing through is deflected toward the focal point. However, a
Fresnel lens has a fixed focal length, so it is not an adjustable
focus or zoom lens.
[0014] Also in the prior art are beam steering systems that have
utilized mechanically actuated mirrors. Milanovic, V., et al.,
describes such a mechanically actuated mirror in "Tip-tilt-piston
Actuators for High Fill-Factor Micromirror Arrays",
www.adriaticresearch.org/Research/pdf/HHH04.pdf, which is
incorporated herein by reference.
[0015] What is needed is an improved variable focal length lens
that has no moving parts, and that can be rapidly configured for
different focal lengths, and also steered with no moving parts. The
embodiments of the present disclosure answer these and other
needs.
SUMMARY
[0016] In a first embodiment disclosed herein, a solid state
electrically variable focal length lens comprises a plurality of
concentric rings of electro-optical material, wherein the
electro-optical material comprises any material of a class of
hydrogen-doped phase-change metal oxide and wherein each respective
concentric ring further comprises a transparent resistive sheet on
a first face of the respective concentric ring, wherein the
transparent resistive sheet extends along the first face, and a
first voltage coupled between a first end and a second end of the
transparent resistive sheet, wherein the first voltage may be
varied to select an optical beam deflection angle.
[0017] In another embodiment disclosed herein, a solid state zoom
lens comprises a first plurality of first concentric rings of first
electro-optical material, wherein the first electro-optical
material comprises any material of a class of hydrogen-doped
phase-change metal oxide and wherein each respective first
concentric ring further comprises a first transparent resistive
sheet on a first face of the respective first concentric ring,
wherein the first transparent resistive sheet extends along the
first face; and a first voltage coupled between a first end and a
second end of the first transparent resistive sheet, and wherein
the first voltage may be varied to select a beam deflection angle,
and a second plurality of second concentric rings of second
electro-optical material, wherein the second electro-optical
material comprises any material of a class of hydrogen-doped
phase-change metal oxide and wherein each respective second
concentric ring further comprises a second transparent resistive
sheet on a first face of the respective second concentric ring,
wherein the second transparent resistive sheet extends along the
first face, and a second voltage coupled between a first end and a
second end of the second transparent resistive sheet, wherein the
second voltage may be varied to select a beam deflection angle, and
wherein the first plurality of concentric rings are optically
coupled to the second plurality of concentric rings.
[0018] In yet another embodiment disclosed herein, a method of
providing a solid state electrically variable focal length lens
comprises providing a plurality of concentric rings of
electro-optical material, wherein the electro-optical material
comprises any material of a class of hydrogen-doped phase-change
metal oxide and wherein providing each respective concentric ring
further comprises providing a transparent resistive sheet on a
first face of the respective concentric ring, wherein the
transparent resistive sheet extends along the first face, and
providing a first voltage coupled between a first end and a second
end of the transparent resistive sheet, wherein the first voltage
may be varied to select a optical beam deflection angle.
[0019] In still another embodiment disclosed herein, a method of
providing a solid state zoom lens comprises providing a first
plurality of first concentric rings of first electro-optical
material, wherein the first electro-optical material comprises any
material of a class of hydrogen-doped phase-change metal oxide and
wherein providing each respective first concentric ring further
comprises providing a first transparent resistive sheet on a first
face of the respective first concentric ring, wherein the first
transparent resistive sheet extends along the first face, and
providing a first voltage coupled between a first end and a second
end of the first transparent resistive sheet, wherein the first
voltage may be varied to select a beam deflection angle, and
providing a second plurality of second concentric rings of second
electro-optical material, wherein the second electro-optical
material comprises any material of a class of hydrogen-doped
phase-change metal oxide and wherein providing each respective
second concentric ring further comprises providing a second
transparent resistive sheet on a first face of the respective
second concentric ring, wherein the second transparent resistive
sheet extends along the first face, and providing a second voltage
coupled between a first end and a second end of the second
transparent resistive sheet, wherein the second voltage may be
varied to select a beam deflection angle, and wherein the first
plurality of concentric rings are optically coupled to the second
plurality of concentric rings.
[0020] These and other features and advantages will become further
apparent from the detailed description and accompanying figures
that follow. In the figures and description, numerals indicate the
various features, like numerals referring to like features
throughout both the drawings and the description.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] FIG. 1A shows concentric rings of the electro optic material
and FIG. 1B shows a detailed view of a section of one of the rings
showing electrical controls for achieving a desired deflection
angle and for applying a beam forming phase shift in accordance
with the present disclosure.
[0022] FIG. 2A shows an example section through the diameter of the
concentric ring array where the radial gradients for each ring are
set for a far focal range f.sub.f in accordance with the present
disclosure, and FIG. 2B shows an example section through the
diameter of the concentric ring array where the radial gradients
for each ring are set for a close focal range f.sub.c in accordance
with the present disclosure.
[0023] FIG. 3A shows an example section through the diameter of the
concentric ring array in which the variable length lens is paired
with a Fresnel lens, and where the radial gradients for each ring
are set for a far focal range f.sub.f in accordance with the
present disclosure, and FIG. 3B shows an example section through
the diameter of the concentric ring array in which the variable
length lens is paired with a Fresnel lens and where the radial
gradients for each ring are set for a close focal range f.sub.c in
accordance with the present disclosure.
[0024] FIG. 3C is a side elevation view of a reflective embodiment
for steering an optical plane wave using a solid state
electrically-variable optical wedge in accordance with the present
disclosure.
[0025] FIG. 4 shows a first variable focal length lens in
accordance with the present disclosure paired with a second
variable focal length lens in accordance with the present
disclosure to form a solid state zoom or variable focus lens in
accordance with the present disclosure.
[0026] FIG. 5 shows an example change in bandgap (eV) and
refractive index of material as a function of hydrogen doping
density in accordance with the present disclosure.
[0027] FIG. 6 shows a first variable focal length lens in
accordance with the present disclosure paired with a second
variable focal length lens in accordance with the present
disclosure with an adjacent solid state Tip-Tilt-Phased array to
form a solid state pan-tilt-zoom gimbal with no moving parts in
accordance with the present disclosure.
[0028] FIG. 7 depicts a two dimensional array of elements, in which
each element may direct its beamlet in a same direction (Om) and
provides up to 2.pi. phase lag to cohere all beamlets into a single
beam in accordance with the present disclosure.
[0029] FIG. 8 shows a plan view of a single element of the two
dimensional array of elements shown in FIG. 7 and showing the
orientations 2A and 2B of the element in accordance with the
present disclosure.
[0030] FIGS. 9, 10 and 11 show the elements of the array in greater
detail and show the voltages applied to each element in accordance
with the present disclosure.
[0031] FIG. 12 is a side elevational view a portion of the array of
elements with a plane-wave incident from below becoming many
beamlets that are made to cohere into one beam in accordance with
the present disclosure.
DETAILED DESCRIPTION
[0032] The following description is presented to enable one of
ordinary skill in the art to make and use the invention and to
incorporate it in the context of particular applications. Various
modifications, as well as a variety of uses in different
applications will be readily apparent to those skilled in the art,
and the general principles defined herein may be applied to a wide
range of embodiments. Thus, the present invention is not intended
to be limited to the embodiments presented, but is to be accorded
the widest scope consistent with the principles and novel features
disclosed herein.
[0033] In the following detailed description, numerous specific
details are set forth in order to provide a more thorough
understanding of the present invention. However, it will be
apparent to one skilled in the art that the present invention may
be practiced without necessarily being limited to these specific
details. In other instances, well-known structures and devices are
shown in block diagram form, rather than in detail, in order to
avoid obscuring the present invention.
[0034] The reader's attention is directed to (i) all papers and
documents which are filed concurrently with this specification and
which are open to public inspection with this specification (the
contents of all such papers and documents are incorporated herein
by reference) and (ii) all papers and documents which are otherwise
incorporated by reference herein (but not physically filed with
this specification).
[0035] All the features disclosed in this specification, (including
any accompanying claims, abstract, and drawings) may be replaced by
alternative features serving the same, equivalent or similar
purpose, unless expressly stated otherwise. Thus, unless expressly
stated otherwise, each feature disclosed is one example only of a
generic series of equivalent or similar features.
[0036] Furthermore, any element in a claim that does not explicitly
state "means for" performing a specified function, or "step for"
performing a specific function, is not to be interpreted as a
"means" or "step" clause as specified in 35 U.S.C. Section 112,
Paragraph 6. In particular, the use of "step of" or "act of" in the
claims herein is not intended to invoke the provisions of 35 U.S.C.
112, Paragraph 6.
[0037] The present disclosure describes a solid state electrically
variable focal length lens that has concentric rings 12, as shown
in FIG. 1A, of an electro-optical (E/O) material 14, which may be
of a class of hydrogen-doped phase-change metal oxide (H-PCMO)
materials typified by neodymium nickelate (NdNiO.sub.3). This
material is the subject of U.S. Provisional Patent Application Ser.
No. 63/027,847, filed May 20, 2020, entitled "Method to Grow IR
Optical Materials with Extremely Small Optical Loss", and U.S.
Provisional Patent Application Ser. No. 63/027,849, filed May 20,
2020, entitled "Method to Grow Thick Crystalline Optical Films on
Si Substrates", which are incorporated herein by reference. The
electro-optical material 14 may, in addition to NdNiO.sub.3, be
SmNiO.sub.3, PrNiO.sub.3, EuNiO.sub.3, and GdNiO.sub.3. These
materials may be used individually or combined to form the E/O
material 14 utilized in the embodiments described herein. The E/O
H-PCMO material 14 is essentially transparent over the infrared
wavelength range, and may have an extremely small optical loss, for
example, an optical extinction coefficient k less than 0.001.
[0038] The E/O material 14 changes its index of refraction when an
electric field is applied to the E/O material 14. FIG. 5 shows the
change in bandgap (eV) and refractive index as a function of
hydrogen doping density for SmNiO.sub.3. The refractive index (RI)
is a complex number usually written RI=n+i*k. The left axis of FIG.
5 shows the bandgap in eV, RI (n) the real part of the refractive
index, and RI(k) the imaginary part of the refractive index. The
real part n indicates the phase velocity, while the imaginary part
K is called the extinction coefficient. For the material
SmNiO.sub.3, FIG. 5 shows that it is desirable to have a hydrogen
doping density of up to about 10{circumflex over ( )}21 hydrogen
ions/cm{circumflex over ( )}3 to achieve a desired refractive index
change.
[0039] The concentric rings 12, as shown in FIG. 1A, may be
configured in such a way that a radial voltage gradient applied
across a ring 12 results in a radial gradient in the index of
refraction to steer light passing through the ring 12 toward an
optical axis of the device. The totality of the concentric rings 12
can be made to result in a spherical wave converging toward a
desired focal point. A variable focal-length lens is achieved by
changing a radial voltage gradient applied across each ring 12. The
radial voltage gradient for a respective ring 12 may be different
than a radial voltage gradient applied across another respective
ring 12.
[0040] The solid state electrically variable focal length lens of
the present disclosure may be thought of and described as a
variable focal length Fresnel lens that forms a coherent spherical
wave, which is the sum of the contributions from each of the rings
12. The solid state electrically variable focal length lens of the
present disclosure has flat rings 12, which are arranged
concentrically. The deflection angle of each ring 12 can be varied
to change the focal length of the overall lens. Further the phase
emitted from each ring of the present disclosure may be adjusted to
produce coherence in the focused spherical wave. In contrast, a
Fresnel lens has a fixed focal length, and a conventional Fresnel
lens can be regarded as an array of prisms arranged in a circular
fashion, with steeper prisms on the edges, and a flat or slightly
convex center.
[0041] The solid state electrically variable focal length lens of
the present disclosure can replace slow moving, mechanical lenses
and has a much greater range of variable focus than a liquid
crystal variable lens. The advantages of the solid state
electrically variable focal length lens include that the lens is
solid state and therefore has no moving parts, that the lens can be
grown so no grinding and polishing of a lens is required, and that
the lens can be rapidly reconfigured for different focal
lengths.
[0042] FIG. 1A shows a solid state electrically variable focal
length lens 10, which has concentric rings 12 of the
electro-optical material 14 described above. FIG. 1B shows a
detailed view of a section of one of the rings 12 showing the
electro-optical material 14, a transparent resistive sheet 16 on a
first face 17 of the ring 12, and a transparent electrode 18 on a
second face 19 of the ring 12. The first face 17 and the second
face 19 of the ring 12 are on opposite sides of the ring 12. The
transparent resistive sheet 16 extends along a width 21 of the
first face 17 of the ring 12. A voltage V.sub.1 20 is applied
across the transparent resistive sheet 16 from an outer radius 31
of the ring 12 to an inner radius 23 of the ring 12. The
transparent electrode 18 extends along a width 21 of the second
face 19 of the ring 12. A second voltage V.sub.3 22 may be applied
to the transparent electrode 18. The voltage V.sub.1 20 and the
voltage V.sub.3 22 may be DC voltages. The negative terminal of
voltage V.sub.1 20 and the negative terminal of V.sub.3 22 are
connected by conductor 15, as shown in FIG. 1B. The resistive sheet
16 may be made of any suitable material, such as vanadium oxide,
tin oxide, a nanowire grid, graphite sheets, or other materials
known in the art. The transparent electrode 18 is a sheet with as
low of a resistance as is consistent with it being mostly
transmissive to photons. The transparent electrode 18 operates like
a constant voltage plane as a reference to the resistive sheet (16)
whose value of Ohms/square is selected to provide an acceptable
operating point with low power operation and high speed
operation.
[0043] The voltage V.sub.1 20 may be varied to steer an optical
beam to a desired deflection angle. The second variable voltage
V.sub.3 22 may be varied to apply a beam forming phase-shift.
[0044] The voltage V.sub.1 20 applied across the transparent
resistive sheet 16 applies a radial electric field gradient along a
respective ring 12. The radial electric field gradient along the
respective ring 12 deflects the incident optical beam 24 on the
respective ring 12 toward an optical axis as shown by outgoing
light wave 26 in FIG. 1B. The magnitude of the voltage V.sub.1 20
determines where the focus is along the optical axis.
[0045] The voltage V.sub.3 22, for each ring 12, is selected such
that the peaks and valleys of the outgoing light wave 26 align
spatially and temporally to outgoing light waves 26 from other
rings 12 to form a single focused and phase coherent beam. Aligning
the multiple beam elements in this way produces phase coherence
among the contributions. A conventional Fresnel lens has a further
disadvantage of not being able to form a coherent light beam.
Algorithms for determining the appropriate phase-shifts to produce
coherence have appeared in the literature, for example, as
described by Christopher T. Phare, Min Chul Shin, Steven A. Miller,
Brian Stern, and Michal Lipson, in "Silicon Optical Phased Array
with High-Efficiency Beam Formation over 180 Degree Field of View"
Department of Electrical Engineering, Columbia University, New
York, N.Y. 10027, USA, which may be found at arXiv:1802.04624
[physics.app-ph), and which is incorporated herein by
reference.
[0046] FIG. 2A shows an example section through the diameter of the
concentric ring array where the radial electric field gradient for
each respective ring 12 of the solid state electrically variable
focal length lens 10 is set for a focal length or focus at far
focal range f.sub.f 27 by adjusting the voltage V.sub.1 20 for each
respective ring 12. FIG. 2B shows an example section through the
diameter of the concentric ring array where the radial electric
field gradient for each respective ring 12 of the solid state
electrically variable focal length lens 10 is set for a focal
length or focus at close focal range f.sub.c 28 by adjusting the
voltage V.sub.1 20 for each respective ring 12. The numbers 0, 1, 2
. . . n in FIGS. 2A and 2B refer to different rings 12 with the
ring with number 0 being in the center of the lens, 1 being the
next ring 12 from the center, 2 being the next ring 12 from the
center, and so on to the nth ring 12.
[0047] The ring with number 0 is a disk in FIGS. 2A and 2B, and
does not need a ramped voltage distribution--only a constant
voltage applied across the two faces. This allows adjustment of the
phase of the light passing through ring 0 to end up in-phase with
light from the other rings light and to apply an overall phase
shift to the focused light.
[0048] In an alternate embodiment, ring 0 could be a void--without
an ability to adjust its phase. This would require the void to be
the reference phase for the phase settings on all other rings. The
overall phase of the resulting focus is the same as the phase of
the center of the beam, so there is no capability to apply an
overall phase shift relative to, for example, another beam in an
interferometer.
[0049] In short ring 0 could be either a disk or a void--but the
disk version, as shown in FIGS. 2A and 2B has more flexibility and
more employment options.
[0050] The control voltages V.sub.1 20 and V.sub.3 22 for each
respective ring shaped element 12 are determined by the desired
focal length and are specific to that respective ring element 12.
As shown in FIGS. 2A and 2B, the more central ring elements 12
(e.g. 0, 1, 2, . . . ) require only a small deflection angle while
the outer ring elements 12 (e.g. . . . , n-2, n-1, n) require the
largest deflection angle to focus to a focal length along the
optical axis 29. To vary the focal length of the lens, the voltages
V.sub.1 20 and V.sub.3 22 are varied for all ring elements 12.
[0051] As described above, the magnitude of the voltage V.sub.1 20
for each ring element determines where the focus is along the
optical axis 29. The voltage V.sub.3 22, for each ring 12, is
selected such that the peaks and valleys of the outgoing light
waves 26 align spatially and temporally to form a single focused
and phase coherent beam.
[0052] FIGS. 3A and 3B show an embodiment, showing an example
section through the diameter of the concentric ring array in which
the solid state variable length lens 10 is paired with a standard
Fresnel lens 30. In FIG. 3A the radial gradients for each ring 12
of the solid state electrically variable focal length lens 10 are
set for a focal length or focus at far focal range f.sub.f27. In
FIG. 3B the radial gradients for each ring 12 of the solid state
electrically variable focal length lens 10 are set for a focal
length or focus at the close focal range f.sub.c 28.
[0053] Each ring 32 of the Fresnel lens 30 has a radius and width
that matches the radius and width of the adjacent ring 12. Further,
the rings 32 in the Fresnel lens 30 are aligned to the rings 12 of
the solid state variable length lens 10. If the Fresnel lens 30 has
a focal length midway between the farthest focal range f.sub.f 27
for the solid state variable length lens 10 and the closest focal
range f.sub.c 28 for the solid state variable length lens 10, then
the required steering angle for the solid state electrically
variable focal length lens 10 can be minimized.
[0054] For any specific ring shaped element design, the material
properties of the electro-optical material 14 place a practical
limit on the maximum deflection angle attainable. By pairing each
ring element 12 to a Fresnel lens ring 32 that provides a constant
or fixed offset angle equal to the mean of the angles of the
desired far and close focal points, the dynamic deflection
capability and variable focusing of the solid state variable length
lens 10 can be used to provide the difference between the mean
angle provided by the Fresnel lens and the desired deflection
angles. Using a Fresnel lens in this way enables construction of
larger diameter variable lenses and allows a broader range of
materials to be used. Further, using a Fresnel lens enables lenses
with a smaller f-number. The combination of the variable focal
length lens 10 with the standard Fresnel 30 results in a lens that
can achieve, for a given set of voltages V.sub.1 20, a smaller
closest focal range f.sub.c 28 than can be achieved without the
standard Fresnel lens 30.
[0055] The embodiments of the preceding figures show each ring 12
with a solid state electrically-variable optical wedge (SSEVOW)
steering an optical beam being transmitted through the ring 12.
Instead the solid state electrically-variable optical wedge
(SSEVOW) may be configured and used in a reflective embodiment, as
shown in FIG. 3C, which shows a solid state electrically-variable
optical wedge (SSEVOW) 90 with the E/O material 14. SSEVOW 90 is a
cross-section of a ring 12 shown in FIG. 1A. The solid state
electrically-variable optical wedge (SSEVOW) 90 has a mirror 92 at
the output to reflect the incident light wave 94 back into the E/O
material 14. The reflected light 96 exits the through the E/O
material 14 with a phase shift. Because the light wave travels two
times through the E/O material 14, the same steering effect as the
transmissive configuration of, for example FIG. 1A, may be obtained
with one-half the thickness of E/O material 14. The voltage
necessary to achieve a particular electric field level inside the
E/O material 14 may be reduced at the expense of a limited field of
regard due to self-shadowing and a higher element capacitance which
results in a slower temporal response. Note that the voltage
V.sub.0 in FIG. 3C corresponds to voltage V.sub.1 shown in FIG.
1B.
[0056] FIG. 4 shows an embodiment in which a first solid state
variable focal length lens 40 (VFLL') is paired with a second solid
state variable focal length lens 42 (VFLL) to form a solid state
zoom or variable focus lens. In this embodiment, the sum of the
focal lengths of the two lenses 40 and 42 must equal the fixed
spacing 44 between the lenses (coincident focal points). The dashed
lines 46 represent the case in which the left lens 40 is focused to
its "far" f.sub.f focal length 70 (located a distance f.sub.f to
the right of lens 40) and the right lens 42 is focused to its
"near" or "close" f.sub.n focal length 72 (located a distance
f.sub.n to right of lens 42). The lenses are spaced by distance 44
d=f.sub.f+f.sub.n. The solid lines 48 represent the opposite case
in which the left lens 40 is focused to its "near" f.sub.n' focal
length 74 (located a distance f.sub.n to the right of lens 40) and
the right lens 42 is focused to its "far" f.sub.f focal length
76.
[0057] It is standard in optics drawings to have the light incident
from the left. The largest magnification in FIG. 4 is max
magnification=fan, which for example is represented by lines 48 in
FIG. 4. The max demagnification is f.sub.n/f.sub.f, which for
example is represented by lines 48 in FIG. 4. So the magnification
ratio is the ratio of these two values, or
f.sub.f*f.sub.f/f.sub.n*f.sub.n. Any magnification between the
extremes may be achieved by adjusting the coincident focal point at
a selected common point between f.sub.f and f.sub.n.
[0058] FIG. 6 shows yet another embodiment showing the solid state
zoom or variable focus lenses 40 and 42 of FIG. 4 combined with a
solid state optical tip-tilt-phased (TTP) array 50, which is the
subject of U.S. Provisional Patent Application Ser. No. 63/027,844,
filed May 20, 2020, which is incorporated herein by reference. This
embodiment provides a solid state pan-tilt-zoom (PTZ) "gimbal" with
no moving parts. The solid state TTP array 50 provides steering to
the pan and tilt angles while the solid state zoom or variable
focus lenses 40 and 42 provide the zoom feature. The use of a solid
state TTP 50 has several benefits. A very high reconfiguration
speed (.about.microseconds), and a large angular throw (45 degrees
being typical) can be achieved.
[0059] FIG. 7 depicts a two dimensional array 100 of elements 102,
which together form a solid-state tip-tilt-phased array 50. FIG. 8
is a plan view of a single element 102. The two dimensional array
100 may have N.times.N elements 102; however, a solid-state
tip-tilt-phased array 50 may also be formed with a single element
102. Each element includes the electro-optical (E/O) material 14
which as described above may be of a class of hydrogen-doped
phase-change metal oxide (H-PCMO) materials typified by neodymium
nickelate (NdNiO.sub.3). As further described above, H-PCMO
materials in addition to NdNiO.sub.3 may be used, including
SmNiO.sub.3, PrNiO.sub.3, EuNiO.sub.3, and GdNiO.sub.3. These
materials may be used individually or combined to form the E/O
material 14 utilized in the embodiments described herein. The E/O
H-PCMO material 14 is essentially transparent over the infrared
wavelength range, and may have an extremely small optical loss, for
example, an optical extinction coefficient k less than 0.001.
[0060] FIG. 11 is a three dimensional view showing how control
voltages V.sub.1 120, V.sub.2 124, and V.sub.3 122 are applied.
Control voltages V.sub.1 120 and V.sub.2 124 are applied across
transparent resistive sheets 16 and 156, which are arranged across
opposite sides of the E/O material 14. The voltage fields created
by V.sub.1 120 and V.sub.2 124 are set at a right angle to each
other, as best shown in FIG. 11. FIGS. 9 and 10 are side
elevational views taken at a right angle to each other. With
reference to FIG. 7, FIG. 9 is a cross sectional view of element
102 along the cut 2A-2A and FIG. 10 is a cross sectional view of
element 102 along the cut 2B-2B. In FIGS. 9 and 11 control voltage
V.sub.1 120 is applied across transparent resistive sheet 16, while
in FIGS. 10 and 11 control voltage V.sub.2 124 is applied across
transparent resistive sheet 156 in a direction at a right angle to
the control voltage V.sub.1 120 applied across transparent
resistive sheet 16. Control voltage V.sub.3 122 is further
discussed below. FIGS. 9 and 10 show the control lines 150, 152 and
154 that control voltages V.sub.1 120, V.sub.3 122, and V.sub.2
124, respectively.
[0061] FIG. 11 is a three dimensional view showing the voltages
applied to the resistive sheets 16 and 156. The resistive sheets 16
and 156 may be made of any suitable material, such as vanadium
oxide, tin oxide, a nanowire grid, graphite sheets, or other
materials known in the art. The value of the sheet resistance in
Ohms/square of sheets 16 and 156 may be selected for good device
design noting that the overall resistance sets the current
necessary to maintain a set voltage and, hence, establishes overall
power consumption by the element 102.
[0062] One side of each sheet 16 and 156 may have a conductive bus
bar disposed at one edge thereof while the voltage to be applied is
applied to a conductive bus bar disposed at the opposing edge
thereof. The conductive bus bar 106 may be a conductive bus bar 106
directly coupled to ground 170, while the conductive bus bar 104 of
sheet 16 may be coupled to ground via control voltage V.sub.3 122.
If control voltage V.sub.3 122 is zero volts, then the conductive
bus bar 104 is directly coupled to ground. The corner where the
control voltage V.sub.3 122 is applied may be thought of as a
common ground corner 140, especially when control voltage V.sub.3
122 has a voltage of zero volts or control voltage V.sub.3 122 is
not utilized, in which case the control voltage V.sub.3 122 shown
in the figures would be replaced with a wire connection.
[0063] Consider the top resistive sheet 16. Applying V.sub.1 120 to
its bus bar results in a linear voltage gradient between V.sub.1
120 and the conductive bus bar 104. Likewise, V.sub.2 124 results
in a similar smooth gradient in the cross-direction in bottom
resistive sheet 156 between V.sub.2 124 and the ground bus bar 106.
Together these two voltages steer the beam of incident light 24 to
outgoing light 26, as shown in FIGS. 9, 10 and 12. The voltage
V.sub.3 122 is needed at the pinned corner between resistive sheets
16 and 156 only if there is a desire to apply an over-all phase
adjustment to the light passing through the E/O material 14. If
there is only a single-element 102 for solid-state tip-tilt-phased
array 50, then the voltage V.sub.3 122 is replaced with a short
circuit that grounds sheets 16 and 156 at the common ground corner
140 of the element 102. All voltages are referenced to
wafer-ground, so only a single control line is required for each.
The gradient across the bottom resistive sheet 156 is V.sub.2/w,
where w is the width of the element 102. The gradient across the
top resistive sheet 16 is then (V.sub.1-V.sub.3)/w, again where w
is the width of the element 102.
[0064] Each element 102 directs an outgoing beamlet 26 in the same
direction (.theta., .phi.) and provides up to 2.pi. phase lag to
cohere all beamlets 26 into a single beam. Relative to the x, y,
and z axes in FIG. 7, with the array 100 in the x-y plane, then
.theta. is the angle between the z-axis and the projection of
beamlet 26 onto the x-z plane, and .phi. is the angle between the
z-axis and the projection of beamlet 26 onto the x-y plane.
[0065] Each E/O material 14 has transparent resistive sheet 16
disposed at or on a first face 17 of the body 102 and a transparent
electrode 18 disposed at or on a second face 19 of the body 102.
Each element 102 has a control line to each voltage V.sub.1 120,
V.sub.2 124, and V.sub.3 122, to apply a .theta. angle modifying
voltage V.sub.1 120 to transparent resistive sheet 16, a .phi.
angle modifying voltage V.sub.2 124 to transparent resistive sheet
156, and a phase-voltage V.sub.3 122 between sheets 16 and 156.
[0066] The first two voltages V.sub.1 120 and V.sub.2 124 are
preferably common for all elements 102 in the array 100. The
phase-voltage V.sub.3 122 is preferably unique to each element 102
depending upon the desired output angles. If all of the voltages
V.sub.1 120 and V.sub.2 124 in the array are the same, then one
beam is produced. This single beam embodiment may well be the most
useful embodiment. On the other hand, if instead half of the
voltages V.sub.1 120 and V.sub.2 124 in the array 100 are different
than the other half, then two beams may be produced. In this
embodiment each beam has a higher divergence than the single beam
embodiment. It should be apparent that this may be generalizable to
a many beam embodiment and dissimilar beam embodiments, when such
embodiments are desired.
[0067] Each element 102 may be wired with three control lines 150,
154, and 152 for the three voltages, V.sub.1 120, V.sub.2 124, and
V.sub.3 122, respectively, as shown in FIGS. 9, 10 and 11. The
orientation of the voltage gradients generated by V.sub.1 120 and
V.sub.2 124 are preferably at right angles to each other or
orthogonal to each other and orthogonal to the nominal optical axis
110 of the element 102, as shown in FIGS. 10 and 11 of the element
102. The third voltage, V.sub.3, 122 is used to adjust the overall
phase of the beamlet such that its phase is spatially aligned with
its neighbors. This phase-matching process is called "beamforming"
in that it combines the array of N.times.N beamlets 26 from array
100 into a single beam that behaves as if it were emitted from the
whole aperture 100. The phase-match is obtained by adjusting
voltage V.sub.3 122 until the gap marked .DELTA..PHI..sub.n 108 in
FIG. 12 becomes zero. The gap .DELTA..PHI..sub.n 108 corresponds to
the element-to-element phase mismatch. It changes depending on
output angle. In order to `cohere` a beam, that element-to-element
phase mismatch is driven to zero by adjusting the voltage V.sub.3
122.
[0068] FIG. 7 shows the elements 102 spaced apart by small gaps
160. Those gaps 160 may be used to run the control wires 150, 154
and 152 for the voltages V.sub.1 120, V.sub.2 124 and V.sub.3 122,
respectively, applied to each element 102.
[0069] FIG. 12 shows a portion of the two dimensional array 100 of
elements 102, shown in FIG. 7, in a side-view with a plane-wave 24
incident from below becoming many beamlets 26 deflected by angle
.theta..sub.n (where n refers to the nth ring from the center) 130
and further indicating the phase adjustment .DELTA..PHI..sub.n 108
that must be made to cohere the beamlets 26 into a single point at
a distance fin order to perform as a lens with focal length f. The
phase lag between elements is given by Phase
Lag=.DELTA..PHI..sub.n=(8*.pi.*s.sup.2/.lamda.)*(n-1/2)/sqrt(f.sup.2+4n.s-
up.2s.sup.2), but it is only necessary to apply the phase
difference within the nearest 2.pi.: Applied Phase Lag=modulo
(Phase Lag, 2.pi.). This set of relative phase lags results in a
piece-wise approximation to a spherical wavefront converging on a
point at distance f, i.e the action of a lens. Each angle
.theta..sub.n and phase adjustment .DELTA..PHI..sub.n is unique to
each ring of the structure, set by the desired focal length of the
lens assembly.
[0070] Having now described the invention in accordance with the
requirements of the patent statutes, those skilled in this art will
understand how to make changes and modifications to the present
invention to meet their specific requirements or conditions. Such
changes and modifications may be made without departing from the
scope and spirit of the invention as disclosed herein.
[0071] The foregoing Detailed Description of exemplary and
preferred embodiments is presented for purposes of illustration and
disclosure in accordance with the requirements of the law. It is
not intended to be exhaustive nor to limit the invention to the
precise form(s) described, but only to enable others skilled in the
art to understand how the invention may be suited for a particular
use or implementation. The possibility of modifications and
variations will be apparent to practitioners skilled in the art. No
limitation is intended by the description of exemplary embodiments
which may have included tolerances, feature dimensions, specific
operating conditions, engineering specifications, or the like, and
which may vary between implementations or with changes to the state
of the art, and no limitation should be implied therefrom.
Applicant has made this disclosure with respect to the current
state of the art, but also contemplates advancements and that
adaptations in the future may take into consideration of those
advancements, namely in accordance with the then current state of
the art. It is intended that the scope of the invention be defined
by the Claims as written and equivalents as applicable. Reference
to a claim element in the singular is not intended to mean "one and
only one" unless explicitly so stated. Moreover, no element,
component, nor method or process step in this disclosure is
intended to be dedicated to the public regardless of whether the
element, component, or step is explicitly recited in the Claims. No
claim element herein is to be construed under the provisions of 35
U.S.C. Section 112, as it exists on the date of filing hereof,
unless the element is expressly recited using the phrase "means for
. . . " and no method or process step herein is to be construed
under those provisions unless the step, or steps, are expressly
recited using the phrase "comprising the step(s) of . . . ."
[0072] Modifications, additions, or omissions may be made to the
systems, apparatuses, and methods described herein without
departing from the scope of the invention. The components of the
systems and apparatuses may be integrated or separated. Moreover,
the operations of the systems and apparatuses may be performed by
more, fewer, or other components. The methods may include more,
fewer, or other steps. Additionally, steps may be performed in any
suitable order. As used in this document, "each" refers to each
member of a set or each member of a subset of a set.
* * * * *
References