Patent Application
20210080907
The invention relates to a volume holographic optical element WHOP suitable for imaging applications in one or more wavelength bands and the fabrication thereof. The invention recreates holographically, the properties of refractive or reflective optics to produce a lightweight, thin film, lens. The holographic optical elements can be thinner, lighter, and less expensive than the corresponding refractive or reflective optical elements that they replace. The holographic optical elements can he designed to minimize aberrations in the output wavefront while maintaining high diffraction efficiencies to improve the performance of the imaging system.
Holography is the science and practice of making holograms. Typically, a hologram is a recording of the interference pattern created by the interaction of two light fields (typically called the reference and object beams), rather than of an image formed by a lens. The hologram contains both the amplitude and relative phase of the light fields as opposed to a photograph that contains only the intensity of the recorded light field. The developed hologram works as a diffraction grating that when illuminated by the reference beam generates an output beam that contains the exact wavefront of the object beam. The object beam can be light from a physical object or a computer-generated scene. When the reference beam illuminates the hologram the diffracted light reconstructs a full 3D image of the scene with its full parallax. If the wavefront of the object beam is chosen to have a particular geometric property e.g., spherical or cylindrical shape then the hologram will work as a lens e.g., a spherical or cylindrical lens, thus allowing the hologram to function as an optical element that provides optical power for magnification (larger or smaller).
A Holographic Optical Element (HOE) is a thin film optical device that functions as traditional optical component. HOEs can operate in either transmission replacing and enhancing traditional refractive optics such as lenses, or in reflection replacing and enhancing traditional reflective optics such as mirrors, beam splitters and beam combiners. HOEs can also be designed to generate waveforms not available to traditional refractive and reflective optics including: multi-focus lenses, power mirrors with see-through functionality, etc. especially holographic lenses are widely used in the art and become particularly useful in the wavelength range where refractive optics becomes opaque. The examples of such applications are X-ray and deep UV contact-less photolithography.
The underlying physics of the diffraction of light from a hologram is different depending on the thickness of the recording media. A thin hologram is one where the thickness of the recording medium is much less than the spacing of the interference fringes that make up the holographic recording. In a thin hologram, light scatters into multiple orders where each order corresponds to a particular angle. A thick or volume hologram is one where the thickness of the recording medium is greater than the spacing of the fringes of the interference pattern. The recorded hologram is now a three dimensional structure and HOEs recorded in this fashion are often called Volume Holographic Optical Elements or VHOEs. In a thick hologram, light scatters into primarily one diffraction order. VHOEs can be fabricated using a wide variety of materials including: Dichromated gelatin, photopolymers, and photoemulsions. The scattering of light from VHOE is governed by the Bragg Equation
2{tilde over (n)}Λ sin(θ+ϕ)=λ (1)
where ñ is a positive integer and is used to enumerate the diffraction order, λ is the wavelength, Λ is the average grating period, θ is the angle between the incident beam and the normal and ϕ is the angle between the normal and the grating vector.
The diffraction efficiency of the TE mode of the diffraction grating is calculated [Blanche et al, Opt. Eng. 43(11) 2603-2612 (November 2004)] as
ηTE=sin2[πΔnd/(λ cos θ1)] (2)
where η is the diffraction efficiency Δn is the change in refractive index of the VHOE material, d is the thickness of the VHOE, λ is the wavelength and θi is the angle of incidence. The first order spectral and angular bandwidth (full width half maximum, FWHM) can be approximated by
ΔλFWHM/λ≈(Λ/d)cot θi (3)
and
ΔθFWHM≈Λ/d (4)
where Λ is the average grating period of the VHOE. Similar equations can be derived for the TM mode.
VHOEs are fabricated by interfering the object and reference beams in a recording medium. The object beam contains the desired output waveform that will be created when the VHOE is illuminated by the reference beam. The VHOE can operate in transmission mode where the light enters on one side of the VHOE and exits on the other side with the desired wavefront. In reflection mode, the light enters on one side of the VHOE and exits on the same side.
When used in transmission mode, current embodiments of VHOEs suffer from either low diffraction efficiency (light within the desired bandwidth directed to the desired angle or angles divided by the total light in that bandwidth) or chromatic aberration (where a lens is either unable to bring all wavelengths to a focus in the same focal plane, and/or when wavelengths are focused at different positions in the focal plane) and astigmatism (where rays that propagate in two perpendicular planes have different foci).
Previous studies of Holographic Optical Elements [D. H. Close. “Holographic Optical Elements”, Optical Engineering, Vol 14, No 5 pp 409-419, 1975] concluded that the strong dependence of the HOE's imaging properties on the operating wavelength due to their diffractive nature makes it more difficult to design achromatic optical systems with HOE than conventional optics. This difficulty has resulted in HOE used only in quasi monochromatic or narrowband (Δλ<10 nm) applications.
For imaging applications, traditional refractive and reflective optical elements and their holographic replacements accept input light and relay that light to an image conjugate plane. In many imaging applications, a particular instantiation of a HOE called a zone plate is used for in-line focusing. [Zone Plates and Their Aberrations: M. Young, Electro-physics and Electronic Engineering, Rensselaer Polytechnic Institute, NY, OSA Vol. 62 No. 8, pages 972-976.]. The ideal zone plate can be considered as a hologram of coaxial collimated and spherical beams also called a Gabor plate. Such a holographic optical element works as an on-axis lens and provides diffraction-limited performance in the paraxial approximation in narrowband wavelength (Δλ≤10 nm) range. Other examples of the applications where the zone plates show superior performance compared to regular refractive optics are: image projection in the deep UV spectral range where regular optics become opaque or multi-focus lens made by stacking of zone plates in single film [Banyai, William Charles et al. “Composite holographic multifocal lens”, US 20010050751], wide field of view projection using segmented zone plates [Spitz, Eric, et al., “High-resolution, wide-field holographic lens”, U.S. Pat. No. 4,094,577, and Close D., “Extended-field holographic lens arrays”, U.S. Pat. No. 3,807,829]. However the biggest disadvantage of the zone plate is that the light is diffracted into multiple diffraction orders, which results in both low diffraction efficiency (DE <40%) in the desired diffraction order and low image contrast because of crosstalk (unwanted signal or noise introduced by one optical signal onto another optical signal) with unwanted diffraction orders.
Other known attempts to address the low diffraction efficiency in narrowband imaging applications have been explored including shaping the grooves of the zone plates (Fresnel lens, blazed diffraction structure, etc.,) allowing them to direct input light energy to only one diffraction order. However, these approaches significantly complicate the manufacturing process and makes fabrication of large HOEs problematic [D. H. Close, “Holograpihic Optical Elements”, Optical Engineering, Vol 14, No 5 pp 409-419, 1975].
Other authors [Pernick, Benjamin J., “In-line holographic lens arrangement”, U.S. Pat. No. 4,810,047] have suggested making an on-axis zone plate with suppressed strait light of 0-th diffraction order by combining it with a polarization rotator and polarization filter, and using the fact that polarization rotation of diffracted focusing beam is different than that of collimated 0-th order beam. However, such a structure further decreases the amount of light in the focusing beam due to absorption of the polarizers and the angular dependence of the polarization rotation results in non-uniformity in the focusing beam passing through the polarization filter.
Other attempts [D. L. Dickensheets, “Imaging performance of off-axis planar diffractive lenses”, Vol. 13, No. 9/September 1996/J. Opt. Soc. Am. A, pp 1849-1858] to improve the diffraction efficiency in transmission VHOE systems have explored off-axis focusing. Single order volumetric holograms working in the Bragg regime have been fabricated which resolve the issues of low contrast due to the cross-talk between multiple diffraction orders seen in Gabor zone plates. To operate in the Bragg regime, off-axis angles should be larger than θmin derived from the following formula [Coupled Wave Theory for Thick Hologram Gratings, Herwig Kogelnik, Bell System Technical Journal, Volume 48, Issue 9, pages 2909-2947, November 1969]
This condition corresponds to 100% diffraction of the input beam to the first diffraction order. The high diffraction angles introduce significant astigmatism due to the asymmetry in the diffraction pattern. The large diffraction angles also increase the chromatic aberration according to the Bragg equation. In addition to introducing astigmatism and chromatic aberration, the off-axis VHOE requires a more complicated design architecture to accommodate the off-axis constraints and cannot be used as a direct replacement for an on-axis refractive optical element.
While numerous attempts have been made to fabricate a volume holographic optical element capable of providing on-axis imaging, there are no reports of a VHOE capable of working in on-axis geometry while providing high diffraction efficiency (>75% and preferably greater than 95%) for desired diffraction order and suppressing the unwanted diffraction orders (<0.1%) and reducing the chromatic aberrations and astigmatism. Current attempts to expand reflection VHOE to broadband operation (>10 nm) show significant chromatic aberration and astigmatism making them impractical for imaging applications.
The following is a summary of the invention in order to provide a basic understanding of some aspects of the invention. This summary is not intended to identify key or critical elements of the invention or to delineate the scope of the invention. Its sole purpose is to present some concepts of the invention in a simplified form as a prelude to the more detailed description and the defining claims that are presented later.
This invention describes the design and fabrication of single element and composite reflection mode VHOEs that provide high diffraction efficiency and reduce chromatic aberrations and astigmatism in imaging and other applications. These VHOE can be used for imaging at one or more wavelengths in applications such as telescopes, image projection, and other optical systems. The lens can provide optical power (magnification) within the bandwidth centered relative to several wavelengths to either focus or collimate light and is transparent for the rest of the image spectrum. The size of each bandwidth can be controlled by proper choice of VHOE parameters in order to keep the lens aberrations within acceptable range. Each bandwidth may be narrowband (<10 nm) or broadband (>10 nm). These VHOEs can be used in a significant number of applications which employ broadband sources such as light emitting diodes (LED), organic light emitting diodes (OLED), supercontinuum sources (SLD/SLED) and silicon optical amplifiers (SOA) without the need for safety and regulatory issues associated with laser sources. For the invention to achieve high diffraction efficiency and to correct for inherent aberrations caused by large diffraction angles and broadband sources, the traditional VHOE designs must be modified.
In a single element configuration, the VHOE is configured to act as a mirror at the specified wavelength(s) and bandwidth(s) and to form an image. The reflection from the “mirror” is equivalent to the 0th order diffraction in which the VHOE is designed to reflect light (or diffract light in the 0th order) in a principal ray at an angle equal to the angle of incidence according to Snell's Law. At this condition, all of the desired wavelengths are reflected at the same angle. No angular dispersion occurs and chromatic aberration is minimized.
A method of fabricating a single element reflection mode lens comprises interfering a collimated reference beam and a non-collimated object beam configured with optical power at equal but opposite angles with respect to a surface normal of a recording media on opposite sides of the recording media to record a diffraction pattern on the recording media with fringes of the diffraction pattern substantially parallel to a top surface of the recording media to form a reflection mode VHOE. The diffraction pattern is configured to reflect light achromatically at a known wavelength and bandwidth and transmit other wavelengths to form an output beam from the reflected light with a principal ray at an angle equal to an angle of incidence of broadband light and to magnify through diffraction the output beam to form an image. The bandwidth of the reflection VHOE can be controlled by proper choice of hologram thickness and index modulation. The equal but opposite angles for recording the diffraction pattern are equal to the angle of incidence and the reflected angle.
In a composite configuration, the input and output VHOEs are configured to diffract light into an Nth order where N is not zero. The input and output VHOEs are positioned in parallel to and offset from each other such that the filtered Nth order beam exits the composite lens on a path at the angle of incidence and parallel to the broadband light and the unwanted 0th order beam is discarded at each VHOE. The output VHOE compensates for and cancels the angular dispersion induced by the input VHOE. The composite lens improves suppression of unwanted wavelengths while achieving minimal chromatic aberration.
Various embodiment of the composite lens are possible. In one embodiment, parallel light is incident on the input VHOE and is focused by the second VHOE. In another embodiment, light from a point source at the focal distance of the input VHOE is incident on the input VHOE and exits the composite lens at the focal distance of the output VHOE where the focal distances of the input VHOE and output VERDE need not be the same distance. In a third embodiment, broadband parallel light enters and exits the composite lens but is filtered into to one or more narrow wavelength ranges.
A method of fabricating a composite lens comprises fabricating two complementary VHOE elements. The input VHOE (also called VHOE1) is fabricated by interfering a collimated reference beam and (depending on the application) a non-collimated object beam (
The output VHOE (also called VHOE2) is fabricated interfering a collimated reference beam and (depending on the application) a non-collimated object beam (
For a color system, multiple (e.g., three) color holograms can be printed simultaneously on a common recording media at different wavelengths (e.g., RGB) with a common focal point while the unwanted portions of the while light spectrum pass through the HOE undiffracted since they do not satisfy the Bragg condition.
The reflective mode VHOEs may also be configured for applications other than traditional imaging such as multi-focus lenses and lens arrays in which the object beam for recording the diffraction grating is selected to perform an optical function such as multiplexing in the axial or lateral dimensions. In this case, the diffraction grating would be configured to more generally shape the direction and wavefront of the output beam as opposed to the specific application of forming an image. The improved performance of the VHOEs in the form of higher diffraction efficiency and lower chromatic aberrations and astigmatism over the bandwidth would have the beneficial effect in these other applications.
These and other features and advantages of the invention will be apparent to those skilled in the art from the following detailed description of preferred embodiments, taken together with the accompanying drawings, in which:
This invention describes the design and fabrication of two types of VHOEs (transmission and reflection) that can be used in traditional imaging and other applications. These VHOE provide high diffraction efficiency with minimal aberrations and can be used for imaging at one or more wavelengths in applications such as telescopes, image projection, and other optical systems. The VHOE lenses provide optical power (magnification) within the bandwidth centered relative to several wavelengths and is transparent for the rest of the image spectrum. The size of each bandwidth can be controlled by proper choice of VHOE parameters in order to keep the lens aberrations within acceptable range. Each bandwidth may be narrowband (<10 nm) or broadband (>10 nm). These concepts are further extended to create VHOEs that operate with high diffraction efficiency at multiple wavelengths (colors) with each wavelength having a separate bandwidth. These VHOEs can be used in a significant number of applications which employ broadband sources such as light emitting diodes (LED), organic light emitting diodes (OLED), supercontinuum sources (SLD/SLED) and silicon optical amplifiers (SOA) without the need for safety and regulatory issues associated with laser sources.
To achieve high diffraction efficiency and to correct for inherent aberrations introduced in imaging applications with broadband sources, the traditional VHOE designs must be modified to achieve high-resolution imaging and improved performance in other non-imaging applications.
As previously described, in transmission mode traditional on-axis VHOE designs employ a single zone plate or a Gabor pate that is fabricated using coaxial collimated and spherical beams. The on-axis VHOE exhibits low diffraction efficiency (≤40%) into the focal spot and deliver low image contrast because of crosstalk with unwanted diffraction orders. A traditional off-axis VHOE design operates in the Bragg regime to improve DE (>90%) but introduces high levels of chromatic aberration and astigmatism.
In the present invention, two VHOEs are designed and fabricated in such a way as to provide high diffraction efficiency and introduce compensating adjustments that minimize the astigmatism and chromatic aberrations. Two VHOEs that form a “composite lens” (CL) are required to provide an on-axis imaging system to magnify light to form an image and reduce the chromatic aberrations and astigmatism across the bandwidth while maintaining high diffraction efficiency (DE) and low noise.
In reflection mode, the traditional VHOE designs provide high diffraction efficiency but introduce significant aberrations when used in imaging applications due to Fresnel refraction.
In the present invention, a single reflective VHOE is configured to act as a mirror at the specified wavelength and bandwidth (i.e., reflects the specified wavelength and bandwidth at an angle equal to the angle of incidence (0th diffraction order)) and to magnify light to form an image and, consequently, has minimal level of astigmatism and chromatic aberration. This is accomplished by fabricating the single VHOE with recording and object beams at equal and opposite angles to the surface normal so that the fringes of the diffraction pattern are parallel to the surface of the recording media and by using a spherical object beam to record the diffraction pattern to magnify the light. The equal recording angles are also equal to the angle of incidence/angle of reflection.
In a composite configuration, a complementary pair of input and output reflection mode VHOEs are configured to diffract light into an Nth order where N is not zero. The input and output VHOEs are positioned in parallel to and offset from each other such that the Nth order beam exits the composite lens on a path at the angle of incidence and parallel to the broadband light while the unwanted 0th order beam is discarded. The composite lens improves suppression of unwanted wavelengths while achieving minimal chromatic aberration. The composite lens may be configured as a filter only or a bi-convex or planoconvex lens equivalent. The suppression of unwanted wavelengths and producing a beam with minimal chromatic aberration is accomplished by fabricating two complementary VHOE with the same thickness and index modulation with the interference beams at complementary angles. The input VHOE is fabricated with the reference beam at the angle of incidence and the object beam at the selected internal diffraction angle. The output VHOE is fabricated with the reference beam at the selected internal diffraction angle and the object beam at the angle of incidence. When the two lenses are parallel to each other, this configuration ensures that any angular and chromatic dispersion introduced by the input VHOE is compensated by the output VHOE.
The transmissive composite lens and the reflective VHOE lens, as all optical lenses, perform different but related transforms on the input light depending on the direction light traverses the lens. For the transmission lens, collimated light entering from the same side as the reference beam used for recording is brought to a focus. Conversely, input light diverging from the focal point will pass through the composite lens and be collimated. The same symmetry is present in the reflective lens where collimated light reflecting from the surface is brought to a focus and light diverging from the focal point is collimated. In either case, a diffraction pattern is recorded to include optical power to magnify light (larger or smaller) to focus or collimate the output beam to form the image.
As shown in
The two VHOE are configured to introduce compensating adjustments that minimize the chromatic aberrations introduced by the bandwidth of the input light and astigmatism. VHOE1 compensates for aberrations induced by VHOE2. The pair of VHOEs is required to provide an on-axis imaging system to focus light to form an image and reduce the chromatic aberrations across the bandwidth and reduce the astigmatism while maintaining high diffraction efficiency (DE) and low noise.
This on-axis geometry achieves diffraction efficiencies of >75% can be achieved over the lens' bandwidth and suppresses unwanted diffraction orders to <1%. The remaining light in the bandwidth is either scattered or absorbed. The light outside of the bandwidth passes through the VHOE. In many cases, the DE >95% over the bandwidth can be achieved and unwanted diffraction orders can be suppressed to <0.1%. The lens' bandwidth can be increased to greater than 10 nm depending on the requirements of the resolution of the VHOE by varying the incidence angles of the reference beam and choosing the holograms thickness and index modulation. Furthermore, the on-axis geometry minimizes chromatic aberrations and astigmatism over the bandwidth.
As shown in
VHOE2 is fabricated by applying a holographic recording media 32 (which can be the same type of media used in VHOE1 or a different media) to the surface of VHOE1. Diffraction pattern 34 (shown in
When these two VHOEs are used in combination, they function as an on-axis lens as shown for a single λ. Equation 6 [D. H. Close, “Holographic Optical Elements”, Optical Engineering, Vol 14, No 5 pp 409-419, 1975] the shows relationship between the principal input angle 24 (θ1 ) and output angle (θ2) and the wavelength of the CL.
Large input or diffraction angles introduce significant chromatic aberration. For the on-axis transmission CL, θ1=0 for the collimated input beam and principal ray θ2 of the output beam is also zero. θ2 for the marginal rays 36 are a function of the f-number of the system. The chromatic aberrations for the VHOE would be the same as for the zone plate but with much higher DE and much lower noise. The on-axis geometry of this composite lens (CL) will have minimal chromatic aberration and negligible astigmatism since it minimizes the diffraction angles, which results in minimal dispersion.
Decreasing astigmatism further is possible by minimizing the distance between HOE1 and HOE2 to less than 100 microns by shortening the path of the image that propagates in the off-axis geometry. The aberrations in the CL system can be further minimized by placing VHOE1 and VHOE2 in contact with one another on the surface of a glass/plastic substrate.
The resolution of transmission mode CL 10 can be estimated by noting that the diffraction pattern of CL is similar to that of the hologram recorded using coaxial planar and spherical beams [Zone Plates and Their Aberrations: M. Young, Electro-physics and Electronic Engineering, Rensselaer Polytechnic Institute, NY, OSA Vol. 62 No. 8, pages 972-976.] that represents a zone plate. Thus, without sacrificing accuracy, we can apply the formulism of a Zone Plate to derive CL parameters.
According to [Young], chromatic aberration will not be noticeable if the radius r of the imaging lens is equal to or less than:
where f is focal length, λ is the central design wavelength, and Δλ is interpreted as FWHM (full width half maximum) of the illumination source.
Combing Eq. 7 with Rayleigh resolution criteria:
provides an estimate of the maximum. spectral width of image beam Δλ to keep resolution of such a lens better than Δl. The spectral width of the image can be controlled by the bandwidth of the HOEs, which obeys equation 9 [Fabrication of Diffractive Optical Elements. Springer, E. Di Fabrizio, L. Grella, M. Baciocchi, M. Gentili, p, 149-160. 1997.],
where Λ is the average period of the holographic grating, d is the film thickness, and θ is the Bragg angle. By choosing proper grating parameters, one can fix the resolution of CL better than Δλ of Eq. 9.
Although the diffractive properties are similar, transmission mode CL 10 has four significant advantages over that of a single element narrow band Zone Plate:
The concepts used to minimize aberrations in single wavelength CL can be expanded to VHOEs operating at multiple wavelengths to design and fabricate a CL that can be used in multi-wavelength or “color” applications. For most visible commercial applications, the imaging sources comprise three sources emitting at different wavelengths roughly corresponding to the tri-stimulus values of the human eye. The devices typically emit at the red, green, and blue (RGB) wavelengths in the visible spectrum. For applications in the infrared (IR) or ultraviolet (UV) multiple wavelengths will be selected depending on the sources and detectors available.
For multi-color transmission and reflection applications, the traditional fabrication technique is to fabricate and combine multiple holograms, one of each color, or to simultaneously record the holograms for each color in the recording media. Both the combination and simultaneous recording techniques have been unsuccessful due to the crosstalk that occurs when multiplexing multiple holograms in a single film layer or layer stack. The crosstalk reduces the contrast of the image because light at one wavelength is scattered by the diffraction grating recorded to diffract another wavelength.
As shown in
The present invention overcomes the crosstalk problem by designing the diffraction gratings for each wavelength to diffract the light at a different angle relative to the surface normal. As shown in
The fabrication for the multi-wavelength CL systems follows the same sequence of operations as described above but with the reference beam used to fabricated VHOE1 and VHOE2 rotated about the surface normal by 360°/N (where N is the number of wavelengths). The N object beams for VHOE1 and VHOE2 are all co-axial and parallel to the surface normal.
As shown in
Using a well-known formula for combined focal length f of two lenses with focal length f1 and f2,
and noting that the focal length of the VHOE is inversely proportional to wavelength λ, the separation d 306 between the CLs can be determined that corresponds to their achromatic performance over a wavelength range between λ1 and λ2 by requiring same combined focal length f 310 at the two extreme wavelengths λ1 and λ2.
Straight-forward calculation shows that a combination of two CL 302 and 304 with the same focal length f1=f2 separated at the distance d=0.67 f, an output beam 308 becomes achromatized to the first order. This technique can be used to extend the range of achromatization to 100 nm thus covering a much wider spectral range than each CL can on its own [Spectral Diffraction Efficiency Characterization of Broadband Diffractive Optical Elements Junoh Choi, Alvaro A. Cruz-Cabrera, Anthony Tanbakuchi, Sandia National Laboratories, March/2013] producing an achromatic holographic lens.
As shown in
Diffraction fringes parallel to the surface of the recording media acts as a bandpass filter centered at the known wavelength that reflects the wanted wavelengths in the bandwidth like a mirror and passes unwanted wavelengths 119 outside the defined bandwidth. The diffraction pattern 106 and fringes 108 include in the design a first component that is parallel to the surface to provide the achromatic reflection over the specified bandwidth and a second compute that is not parallel to the surface to provide the optical power or magnification that provides the focusing. The power of the lens or “f-number” determine how much deviation there is in the fringes from parallel. The stronger the lens the more the deviation.
As shown in
The equal angular illumination during the holographic recording creates a VHOE 104 with diffraction fringes 108 substantially parallel to the surface of the holographic film. This parallelism is modified to some extent by the optical power induced by the focusing object beam. The amount of deviation from parallel is determined by the power or f-number of the lens. This holographic fringe pattern acts as a high diffraction efficiency (DE >95%) mirror at the design wavelength and bandwidth. The reflective nature of the diffraction ensures the system has a minimal level of chromatic aberration when used for imaging. Chromatic aberration for such a HOE is minimal also because of the narrowband nature of reflection volumetric holograms and their bandwidth can be controlled by proper choice of hologram thickness and index modulation [Coupled Wave Theory for Thick Hologram Gratings, Herwig Kogelnik, Bell System Technical Journal, Volume 48, Issue 9, pages 2909-2947, November 1969]. Recording and reconstruction geometry for such a VHOE is shown in
The reflection lens 100 as designed and fabricated as described above provides distortion-free see-through functionality where light can pass from the backside of the VHOE since light is traveling at angles that do not satisfy the Bragg equation and are not diffracted. This functionality is combined with a VHOE that provides optical power to create an image combiner with capabilities can't be achieved using standard refractive or reflective optics. Other embodiments of image combiners use semitransparent metallic coatings to integrate the pass through light and the reflected light but these embodiments cannot provide image magnification or minification without introducing considerable distortion by adding a curved reflecting surface.
While there are significant similarities between the function of reflection and transmission VHOEs, reflection VHOEs have two advantages:
The reflective lens can be extended to multiple wavelength system by using techniques to simultaneously record the holograms associated with each of the wavelengths during a single exposure as a diffraction pattern on a single recording media. This design will enable the reflective VHOE to combine multiple wavelengths in a way that can achieve the resolution equivalent to the single bandwidth lens described above. The design and fabrication process can also compensate for any decrease in DE by increasing An and/or film thickness.
As shown in
As described, the single element reflective lens is designed to maximize DE in the 0th order to reflect a band of light around a center frequency at the angle of incidence of the broadband light and suppress light in all other diffraction orders. The reflection is specular, all wavelengths in the band are reflected at the same angle. The VHOE does not induce any angular dispersion, hence the axial chromatic aberration is minimized. The lens acts as a filter to remove via transmission the unwanted wavelengths outside the band. However, the filtering of light is not perfect. Light outside the band of interest still exists and the DE tappers off according to Eq. 2 to a floor set by the bulk reflection. In some applications, a more aggressive taper and lower floor is desirable.
In a composite configuration, a complementary pair of input and output reflection mode VHOEs is configured to diffract light into an Nth order where Nis not zero. The input and output VHOEs are positioned in parallel to and offset from each other such that the filtered Nth order beam exits the composite lens on a path at the angle of incidence and parallel to the broadband light while the unwanted 0th order beam is discarded at each VHOE. Processing light in a non-zero diffraction order improves the suppression of unwanted wavelengths by increasing the taper and lowering the floor according to Eq. 2. Furthermore, processing the light through both input and output VHOEs serves to narrow the transmission bandwidth of the composite lens by successive applications of Eq 2. The successive application of Eq. 2 in the composite lens narrows the spectral FWHM (Eq. 3) and further suppresses the signal intensity in wavelengths outside of the region of interest. But processing light in a non-zero diffraction order induces angular dispersion according to Eq. 2. The output VHOE compensates for the induced angular dispersion under certain precise conditions. The composite lens improves suppression of unwanted wavelengths while still achieving minimal chromatic aberration. The composite lens may be configured as a filter only or a bi-convex or plano-convex lens equivalent.
The spectral FWHM of the output signal experiences equation 3 twice effectively multiplying the sin2 function by itself.—[one example is the diffraction efficiency in Eq 2 is 1.0 at the desired wavelength, 0.5 at wavelengths 1 nm to either side of the desired wavelengths, and 0.1 at wavelengths 2 nm on either side of the desired wavelength. The FWHM of this system would be 2 nm. Two applications of this equation would yield a diffraction efficiency of 1.0 at the desired wavelength, 0.25 at wavelengths one nanometer on either side of the desired wavelength, and 0.01 at 2 nm on either side of the desired wavelength. The spectral FWHM would be less than 2 nm after 2nd lens and the background signal would be reduced from 0.1 to 0.01. The exact shape and reduction in FWHM would depend on the design of the VHOE.
The input VHOE and output VHOE are fabricated as a complementary pair in which because the angles of the object and reference beam and exchanged between the two VHOEs. If the two VHOE are fabricated with the same thickness and refractive index modulation and placed parallel to each other, this configuration ensures that the angular and spectral dispersion (Eq 2) imparted to the beam exiting the input VHOE is compensated by the output VHOE. The spectral and angular compensation occurs because the θ and φ angles in Eq 1 are define by orientation of the reference and object beam. In the composite lens configuration, the beam exists the input VHOE as the object beam but enters the output VHOE as the reference beam this changes the sign of the angle and reverses the direction of the angular and spectral dispersion since the sin function in Eq 1 is an odd function sin θ=−θ.
Referring now to
Light 900 with a central wavelength λ and a bandwidth Δλ, where is Δλ<<λ, (e.g., <<means less than 10×) is incident on input VHOE1 901 at an angle of incidence angle θi 907 relative to the surface normal. Input VHOE1 diffracts the incoming light 900 at a diffraction angle θd 911 that is different from the angle of incidence θr=θi 908 that would be reflected via Snell's law. The diffracted light 910 is diffracted in a range of angles θd±Δθ according to Equation 2 and 4. The diffracted light 910 travels to output VHOE2 903 that is aligned parallel to and offset from input VHOE1 901. The principal ray of diffracted light 910 is incident at a diffraction angle θd 904 and is diffracted at angle θi 909 as light 905 which is parallel to the original light ray 900 and not along the path θr=θd. Light 902 is also reflected from input VHOE1 according to Snell's law along the path θr=θd. The input and output VHOEs are arranged such that light 902 bypasses output VHOE2 903. Similarly light 906 is reflected from output VHOE according to Snell's law along the path θr=θd along a different path than light 905. The output VHOE introduces the same magnitude angular dispersion but of the opposite direction than the input VHOE to exactly compensate for and cancel the angular dispersion introduced by the input VHOE such that the light 905 diffracted from both VHOEs has minimal axial chromatic aberration.
Three different configurations of “multiple wavelength” or “color” composite lenses are illustrated in
Referring now to
Parallel broadband light 1000 with a center wavelength λ and a bandwidth where Δλ is comparable (about 2×) to λ, is incident on input VHOE1 1001 at an angle of incidence θi 1002 relative to a surface normal 1009. Input VHOE1 1001 is composed of multiple diffraction gratings, each of the multiple diffraction gratings diffracting a narrow band of wavelengths around a center wavelength and passing the other unwanted wavelengths 1004. VHOE1 1001 diffracts the incident light 1000 into diffracted light 1006 at a diffraction angle θd 1012 that is different from the θr=θi 1013 that would be reflected via Snell's law. The grating spacing parameter is varied among the multiple diffraction gratings so that they all diffract the principal ray at a common diffraction angle. The principal ray 1005 reflected at θr=θi 1013 bypasses the output VHOE2. The diffracted light 1006 at λ1±δλ1, λ2±δλ2, λ3±δλ3 from each of the multiple gratings in VHOE1 1001 is diffracted in a range of angles θ1±δθ1, θ2±δθ2, θ3±δθ3 according to Equations 2 and 4. The diffracted light 1006 travels to output VHOE2 1007 that is aligned parallel to the input VHOE. Some of the incoming light 1006 is reflected into light 1008 at angle θd 1012 relative to surface normal 1010 and exits the composite lens. The output VHOE2 exactly compensates for the angular dispersion introduced by the input VHOE1. The output VHOE also contains optical power and the multiple wavelengths diffracted from VHOE2 into beam 1014 are all focused to the same focal point (achromatic focus) 1011. This configuration is equivalent to a plano convex refracting lens but provides an achromatic focus free of axial chromatic aberration.
See-Through System with Reflective VHOE
As shown in
The embodiment of the reflection VHOE capability to simultaneously provide both a see through capability for a broad spectrum of light as well as optical magnification from a second source for one or more narrow band wavelengths each with a separate bandwidth enables the development of low cost, light weight and low profile optical elements that can create optical systems that are not achievable with traditional refractive or reflection optics.
A particular embodiment that shows the advantages of the reflective VHOE 200 would be the ability to construct a simple optical system inside a car allowing the driver to see the content of his smartphone or other display (i.e. object 201) without having to adjust their focus from the far field (i.e. real scene 202).
In this example, the reflective VHOE is designed to take a diverging beam from a cell phone or other image source and project a magnified image of one or more colors with bandwidths to the far field of the driver's view. The transparent reflective VHOE 200 is attached to windshield or visor of a vehicle. An image source 201 projects a diverging image toward the reflective lens at a distance di. The reflective VHOE combines an enlarged image of driver's phone placed on dashboard with the scene of the road in front of the vehicle. One example would be the projection of a mobile phone image in such a way that driver would not have to shift his sight from the road nor refocus his eyes to see the phone content.
While several illustrative embodiments of the invention have been shown and described, numerous variations and alternate embodiments will occur to those skilled in the art. Such variations and alternate embodiments are contemplated, and can be made without departing from the spirit and scope of the invention as defined in the appended claims.
This application is a continuation-in-part of and claims priority to U.S. patent application Ser. No. 15/720,349 entitled “Volume Holographic Optical Elements for Imaging With Reduced Aberrations”, filed Sep. 29, 2017, which claims benefit of priority under 35 U.S.C. 119(e) to U.S. Provisional Application No. 62/403,584 entitled “Broadband High Resolution Diffraction Optics” and filed on Oct. 3, 2016, the entire contents of which are incorporated by reference.
| Number | Date | Country | |
|---|---|---|---|
| 62403584 | Oct 2016 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 15720349 | Sep 2017 | US |
| Child | 17102513 | US |
