ACOUSTICALLY-CONTROLLED DYNAMIC OPTICAL LENSES AND GRATINGS
AND METHODS RELATED THERETO
RELATED APPLICATIONS AND CLAIM OF PRIORITY [0001] This application claims priority to, and incorporates by reference, U.S. provisional patent application number 60/423,912, filed November 5, 2002.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH [0002] The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of Contract No. F49620-03-C-002 awarded by the Defense Advanced Research Project Agency (DARPA) through the Air Force Office of Scientific Research (AFOSR).
TECHNICAL FIELD [0003] The present invention relates generally to the field of adaptive optics. More specifically, the present invention relates to acoustically controlled programmable lenses and gratings for optical instruments. Additionally, the present invention relates to programmable axicon lenses.
BACKGROUND [0004] Adaptive optics has been used in various applications in the past decade, such as optical switching and phase contrast for satellite imaging. Current approaches to achieving adaptive optics include rotatable mirrors, liquid crystal spatial light modulators, and piezoelectric-driven devices with limited behaviors.
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[0005] Rotatable mirrors technology for micron-scale mirrors involves electro-static pulse driven thin films, whereas rotatable mirrors technology for larger mirrors involves electro-mechanical devices, such as motors and hydraulic actuators. These technologies have drawbacks inherent to physical mechanical systems, such as failure of their components. For micron-sized rotatable mirrors technology, the primary problem is thin film fatigue that results in mirror rupture. For larger-size rotatable mirrors technology, the primary problem is mechanical system failure, such as with motors and actuators.
[0006] Liquid crystal spatial light modulator technology is limited to certain application domains due to its narrow operating temperature range. Further, liquid crystal spatial light modulators cannot be used in phase contrast correction, phase shift mask, and maskless lithography applications due to optical resolution limits of the device.
[0007] Current piezoelectric-driven device technology (See e.g., U.S. Patent No. 4,516,838 to Bademian) for adaptive optics has a limited range of applicability due to limitations in device design. This technology requires pre-computation of the shape, configurations and arrangements of the piezo-transducers that results in a fixed set of behaviors.
[0008] These technologies all present various shortcomings and thus create manufacturing difficulties and increased manufacturing costs.
[0009] One application of adaptive optics involves creating a Bessel beam, which is an optical beam with a Bessel function profile. Bessel beams are useful for materials processing and micromanipulation of micron-scale particles and single cells. A Bessel profile, such as the one shown in FIG. 1 , includes a bright central spot surrounded by rings of decreasing intensity. When an object is placed between the beam source and the display medium so as to block the center of the beam, energy from outer rings of the Bessel beam are focused to the central spot. Thus, the energy from the outer rings heals the Bessel beam at a
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position further along the beam axis. In addition, a Bessel beam is diffraction-free in that diffraction is not observed at the edges of such an obstruction.
[0010] Previously, an annular aperture and a converging lens have been used to create Bessel beams, as shown in FIG. 2. Such a system can be used to create a Bessel beam profile that exhibits diffraction-free behavior up to about 800 cm. For distances greater than about 800 cm, the central beam intensity diminishes rapidly. Alternatively, a gradient index lens has been produced by creating a circular disk of glass with a gradient of ion density that is high at the edges and lower at the center. The gradient index lens can be formed by injecting ions into the disk to produce the ion density gradient. The ion density gradient creates a corresponding gradient in the refractive index of the lens, which permits the production of the Bessel beam.
[0011] Typically, axicon lenses are used to create Bessel beams (or "pseudo-Bessel beams"). An axicon lens usually is a cone-shaped lens, but any optical device with a line focus may be used. For example, a spherically aberrating lens may be used as an axicon lens. A conical lens has been used to produce a Bessel beam profile for a distance up to 24 meters.
[0012] Each of these previously developed technologies is limited to producing a lens with a particular focal length. In other words, the means for creating the Bessel beam is fixed and not programmable. As such, if a lens having a different focal length were required, these technologies would require a new structure to be created.
SUMMARY [0013] In view of the above shortcomings associated with the current approaches to adaptive optics, there is a need for programmable optical devices with versatility for use in a variety of applications.
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[0014] It is, therefore, an object of the present invention to provide programmable optical devices for use in a wide range of applications, including phase contrast correction, phase shift mask, maskless lithography, optical switching, acousto-optic holography, cryptographic keys, and optical memory devices.
[0015] It is another object of the present invention to provide methods for constructing acoustically controlled programmable optical lenses and gratings, which can be enhanced in power by using acoustophoresis.
[0016] It is a further object of the present invention to provide methods for generating programmable lenses and gratings whose line spacing can be modulated by changing the acoustic drive frequency.
[0017] It is a still further object of the present invention to provide methods for generating an axicon lens that produces a Bessel beam at a dynamically programmable distance.
[0018] It is an additional object of the present invention to create programmable axicon lenses for a wide range of applications including laser beam shaping, maskless lithography, foveated optics, and tunable wavefront sensors.
[0019] The present invention pertains to acoustically controlled programmable optical lenses and gratings. The programmable optical lenses and gratings are produced by placing one or more acoustic transducers on a transparent medium that may, or may not, have high index of refraction nanoparticles suspended therein. Electrical signals are then sent to the acoustic transducer where the electrical signals induce modulations in the refractive index of the medium. These refractive index modulations can be gratings and/or lenses, depending on the spacing between the modulations and the amplitude of the modulations. The electrical signals can be frequency or amplitude modulated. The acoustic transducer may be ring shaped. Alternatively, an array of flat or shaped transducers may be used.
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[0020] The above summary of the present invention is not intended to describe each illustrated embodiment or every implementation of the present invention. The figures and the detailed description which follow more particularly exemplify these embodiments.
BRIEF DESCRIPTION OF THE FIGURES
[0021] The invention may be more completely understood in consideration of the following detailed description of various embodiments of the invention in connection with the accompanying drawings, in which:
[0022] FIG. 1 depicts an exemplary Bessel function profile.
[0023] FIG. 2 depicts a prior art embodiment used to create Bessel beams.
[0024] FIG. 3 schematically illustrates a simple acousto-optic lens according to an embodiment of the present invention;
[0025] FIG. 4 illustrates examples of several acoustic patterns induced in a transparent media according to an embodiment of the present invention;
[0026] FIG. 5 illustrates examples of GRIN lenses with different focal lengths according to an embodiment of the present invention;
[0027] FIG. 6 illustrates an embodiment of the present invention for producing a programmable GRIN lens;
[0028] FIG. 7 illustrates an exploded view of an exemplary programmable lens according to an embodiment of the present invention;
[0029] FIG. 8 illustrates a graph of an exemplary calculated time-average refractive index profile according to an embodiment of the present invention;
[0030] FIG. 9 illustrates the operation of the programmable lens with the refractive index profile according to the graph in FIG. 8;
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[0031] FIG. 10 illustrates a graph of the front and back focus of the central spot according to an exemplary embodiment of the present invention.
[0032] FIG. 11 graphically and pictorially illustrates the focus of outer rings as a function of the distance from the lens according to an exemplary embodiment of the present invention.
[0033] FIG. 12 illustrates the self-healing nature of an exemplary Bessel beam according to an embodiment of the present invention.
[0034] FIG. 13 illustrates the article distribution for an asymmetric drive programmable GRIN lens according to an embodiment of the present invention; ι [0035] FIG. 14 schematically illustrates a 3-dimensional lens with acoustic transducers attached to faces of the prism according to an embodiment of the present invention. Only one face having transducers is shown; and
[0036] FIG. 15 schematically illustrates a more complex 3-dimensional lens having acoustic transducers on the edges of a polyhedral prism and light paths through the faces of the prism according to an embodiment of the present invention.
[0037] While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS [0038] The present invention involves constructing programmable optical lenses and gratings by placing one or more acoustic transducers on a transparent medium that may, or
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may not, have high index of refraction nanoparticles suspended therein. Electrical signals are then sent to the acoustic transducers whereby the electrical signals induce modulations in the refractive index of the medium. These refractive index modulations can be gratings and/or lenses, depending on the spacing between the modulations, the amplitude of the modulations, and the way in which the modulations vary in time. The electrical signals can be frequency or amplitude modulated. The acoustic transducer may be ring shaped. The programmable lenses are produced by carefully controlling the acoustic vibrations in the media. Transparent nanoparticles may be contained within the media.
[0039] The transparent medium of the present invention can be any solid or liquid material. Suitable solid media for use herein include glass and polymers, such as polyacrylic acid, polyacrylamide, polymethylmethacrylate, polysiloxane, and polyethylene glycol. Suitable liquid media for use herein include water and organic liquids such as glycerin or carbon tetrachloride. The refractive index of the nanoparticles may be higher or lower than the refractive index of the medium. Suitable high refractive index nanoparticles for use herein include but are not limited to titanium dioxide and other oxides with a high refractive index, gold, silver, and cadmium sulfide.
EXAMPLES [0040] Having generally described the invention, a more complete understanding thereof may be obtained by reference to the following examples that are provided for purposes of illustration only and do not limit the invention.
Example 1 : Grating Optics
[0041] Traveling or standing waves, such as acoustic waves, in a medium may vary the refractive index in space (and time) as they pass. Modulating the refractive index may allow the medium to act as an optical grating. One well-known variation of this phenomenon
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is called Brillouin scattering, which can be used to modulate light. 1 he time vanation ot the acoustic signal is not important for this type of behavior.
[0042] A Fresnel zone plate is a device which utilizes diffraction of a fixed pattern to create lensing by occluding all the rays that contribute to destructive interference. In a two-dimensional array, acoustically created gratings may be used to create a Fresnel zone plate. Fresnel zones may be induced in a transparent medium by using a series of acousto- optic transducers, as shown in FIG. 3. By modulating the frequency and/or amplitude of the acoustic pulses, complex gratings or Fresnel lenses may be constructed for diffraction, Fourier transformation, and other optical operations commonly carried out by simple lenses or gratings. Two or more of these programmable lenses may be stacked to add to the complexity of the optical transform, as shown in FIG. 4. Complex Fresnel zone plates may be created by overlapping two or more distorted polygonal Fresnel zone plates. The Fresnel plates shown in FIGs. 4B-4E are created from distorted octagonal Fresnel zone plates.
Example 2: GRLN Optics from the Static Density Field
[0043] At high amplitudes, the acoustic standing wave includes time-average or time-invariant components of the pressure and density (and velocity). Since the refractive index varies with density, the static density component may be exploited to create a gradient index (GRLN) lens which is designed to refract light rather than diffract it like a grating. Depending on the shape of the index gradient, converging, diverging, or axicon lenses may be created. The input to the acoustic transducers may be used to control properties of the lens such as the focal length.
Example 3: Enhanced Index Contrast by Acoustophoresis
[0044] Diffraction or lensing due to static index gradients can be enhanced by employing the principle of acoustophoresis. Acoustophoresis is a separation process whereby
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particles in suspensions are separated based on their response to acoustic radiation. The acoustic radiation force is another high-amplitude phenomenon that tends to push particles toward or away from regions of maximum displacement, depending on the physical properties of the particles and the fluid in which the particles are suspended. For standing plane waves, this force is proportional to the particle volume and the square of the sound amplitude. In most cases, particles that are denser and less compressible than the fluid migrate to the pressure nodes of the standing wave whereas less dense and more compressible particles migrate to the anti-nodes of the standing wave.
[0045] A converging continuously graded index (GRIN) lens, embodiments of which are shown in FIG. 5, can be made by varying the concentration of high refractive index particles (e.g., titania) suspended in an organic liquid medium. This can be achieved by using acoustic pulses to increase the concentration of particles in the lens' center. Standing waves in circular devices have pressure antinodes at the center and naturally tend to push particles away from the center and create diverging lenses. In order to push particles to the center, a pressure release surface, such as a thin hollow plastic tube, may be used to create a pressure node near (but not precisely at) the center of the device. Alternatively, multiple transducers may be used to excite more complicated three-dimensional waveforms which allow pressure nodes in the center. A simple programmable lens having a ring shaped transducer and two transparent cover plates is shown in FIG. 6. The cavity between the plates is filled with a transparent medium of suspended nanoparticles.
[0046] Diffraction optics can also be utilized to focus light, taking advantage of the nodal patterns of the acoustic standing wave, rather than relying solely on the GRIN lens effect from amplitude modulation.
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[0U47J Diverging lenses, with the nanoparticle concentration being higher at the edge of the lens and lower at the center of the lens, are also produced in a similar manner by exploiting the standing wave effects.
[0048] FIG. 7 illustrates an exploded view of an exemplary programmable lens according to an embodiment of the present invention. Preferably, cylindrical cavities may be used to produce, for example, a programmable GRLN lens. In an embodiment, the lens body may include a PZT ring transducer with a diameter of, for example, approximately 4 cm. Such a PZT ring, with a height of 1.27 cm and a wall thickness of 0.32 cm, is produced by a number of companies, such as Channel Industries of Santa Barbara, CA. The ring may preferably have electrodes on the inner and outer radial surfaces. Circular glass plates may be placed on the top and bottom surface to enclose the cavity and supply a viewing window. A flanged metal ring may be used to supply electrical contact. The flanged metal ring is preferably soldered to the inner electrode. Upon construction, the lens may be filled with fluid through a gasket by a syringe.
[0049] The refractive index gradient in the operating device can occur as a result of finite-amplitude sound waves in the medium. In particular, a time-invariant density field superposed on the linear (sinusoidal) motion of the acoustic standing wave may produce local compression and expansion with a corresponding change in the refractive index. For a liquid medium, the density may be related to the pressure by the following equation:
where P is the total pressure, P
0 is the ambient pressure, p is the density, c
0 is the sound
speed, and ^(for liquids) is an empirical constant.
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[0050] Expanding Eqn. 1 in a Taylor series about P0 and po provides the following
equation:
p - p
0 = (P - P
0)
2 + ..., (2)
[0051] Under adiabatic conditions and for irrotational flow, the pressure terms may be estimated by again expanding the total pressure in a Taylor series and grouping the second-order terms. Time-averaging the result eliminates the first-order terms and yields the
time-invariant component of the density, pϊ.
»> H-PJ^J)- H) (3)
where u andp are the first-order acoustic velocity and pressure (solutions of the linear wave equation which vary sinusoidally in time), and the angular brackets signify a time average.
[0052] For an axially symmetric standing wave described by p(r,t) = AJ (kr)sϊn( ot)
the density may be described by the following equation:
P2 (r) = -^[( - γ)j 0 2 {kr)- ? (kr)], (4)
in which A is the pressure amplitude of the linear acoustic signal of frequency ω, k is the
dispersion- free wave number ( O/CQ), r is the radial coordinate, and J, are Bessel functions of
the first kind.
[0053] Radial modes may be excited in the acoustic lens by applying an amplified AC electrical signal, such as a signal of approximately 140 Vpp, across the electrodes. The magnitude of A may be estimated based on the optical behavior of the lens.
[0054] The density is related to the refractive index n by the Lorentz-Lorenz equation,
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Qp = (n2-\)/(n2+2) (5) where Q is the molar refractivity of the material.
[0055] Linearizing this about po (w0 is the refractive index at po) and time-averaging,
such that
< -Λ>-Λ -((*-".(£) J. (6)
yields a convenient expression for the refractive index profile when combined with Eqn. 4:
[0056] Preferably, an operating fluid with a low vapor pressure, such as glycerin, may be used to minimize cavitation. The calculated time-average index profile of a glycerin-
filled cell (po= 1260 kg/m3, c0= 1904 m/s, n0 = 1.4746, Q = 2.23 x 10"4 m3/kg at po, and γ=
10.0) operated at ωl2π= 700 kHz and A = 150 MPa is shown in FIG. 8.
[0057] FIG. 9 illustrates the operation of the programmable lens with the refractive index profile according to the graph in FIG. 8. As illustrated in FIG. 9, the programmable lens may be modeled optically as a GRIN lens of thickness L with a refractive index profile described by Eqn. 4. In the model, light rays may be assumed to follow straight paths within the lens, and refraction at the glass/air interface may be neglected. A ray that passes through the lens at position r may be retarded proportionally to the local refractive index relative to the center. The transmitted wavefront may be defined by z(r) = L[n(0)-n(r)]. The slope of a ray at r may be normal to the wavefront and may cross the main optical axis at a focal length The slope is described by -z' = rl(f-z), where z' = dz/dr. (Similar solutions may be found for a locus of rays passing through some radial position other than the main axis. Other radial
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positions may appear as visible rings in the projected image.) Using the index profile expressed in Eqn. 7, the focus may now be expressed as a function of r (assuming small z),
[0058] Collimated light, collinear with the ring's axis, may be focused through the acoustic lens onto a screen. The screen may be moved along the main axis on a rail, and the region where a concentric ring pattern remains in focus may be recorded. As the screen is moved away from the lens, rays may start to converge on the center axis at a certain point (the "front focus," which is equal to the first positive value of/produced by Eqn. 8), and elements should remain in focus indefinitely as the screen continues to move back. In practice, however, a range of distances may be evident over which a focused central spot is observed, as illustrated in FIG. 10. The location of the front focus may be used to estimate
the magnitude of the refractive index disturbance (An). The refractive index disturbance
may, in turn, yield an estimate for the sound pressure A at these resonance conditions. The
value of 30 cm at 360 kHz may correspond to An of approximately 0.1% and a pressure
amplitude of approximately 200 MPa.
[0059] Eqn. 8 does not predict the presence of a back focus. The back focus may be the point at which fine diffraction patterns appear to blur the primary ring pattern. Lenses with line foci - axicons - may be used to create close approximations of Bessel beams over some distances. The axicons may exhibit self-healing and may not diverge diffractively.
[0060] FIG. 11 shows how non-central rings come into and out of focus as a function of the distance from the lens. The "primary" ring pattern, which is caused by a focusing effect of multiple annular regions of the appropriate refractive index gradient, may exhibit self-similarity over some distance and approximates a Bessel-fiinction shaped profile.
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[0061] FIG. 12 shows an experiment demonstrating the self-healing nature of the central beam. The top figure shows the lens and the image produced without a rod blocking the center. The bottom figure shows the image produced with a rod blocking the center. The central region of the interference pattern, and particularly the central spot, is still present in this case. As shown in FIG. 12, the shadow of the rod is only present at the top and bottom of the lens.
Example 4: Dynamic Lenses Based on Multiple-Transducer Drive
[0062] Pure radial modes in a lens are described in linear combinations of zero- order Bessel functions, which have maximum amplitude in the center. Other modes of vibration, where nodes form along diameters, may be used to alleviate this problem. There are two modes of the vibrating lens, as illustrated in FIG. 13. These configurations of nanoparticles will result in significant distributions at the radial lines as shown in FIG. 13. Transducers can be driven asynchronously to minimize the radial nodes while maintaining the central node only.
Example 5: Dynamic Optical Gratings
[0063] Besides the simple two-dimensional gratings and zone plates shown in FIG. 4, 3-dimensional gratings that act as programmable holograms can also be constructed. FIGs. 14 and 7 illustrate such 3-dimensional gratings of the programmable optical device. In FIG. 14, there are transducers on the faces of the prism and light passes through the ends of the prism. In FIG. 15, acoustic transducers are on the edges and light passes through the faces of the prism.
[0064] As noted above, the present invention is applicable to programmable optical lenses and gratings. The present invention should not be considered limited to the particular examples described above, but rather should be understood to cover all aspects of the
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invention as fairly set out in the attached claims. Various modifications, equivalent processes, as well as numerous structures to which the present invention may be applicable will be readily apparent to those skilled in the art to which the present invention is directed upon review of the present specification. The claims are intended to cover such modifications and devices.
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