WO2017176389A1 - Miroirs de déviation holographiques à grand champ de vue - Google Patents

Miroirs de déviation holographiques à grand champ de vue Download PDF

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Publication number
WO2017176389A1
WO2017176389A1 PCT/US2017/020087 US2017020087W WO2017176389A1 WO 2017176389 A1 WO2017176389 A1 WO 2017176389A1 US 2017020087 W US2017020087 W US 2017020087W WO 2017176389 A1 WO2017176389 A1 WO 2017176389A1
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WO
WIPO (PCT)
Prior art keywords
grating
medium
holographic
wavelength
angle
Prior art date
Application number
PCT/US2017/020087
Other languages
English (en)
Inventor
Mark R. Ayres
Adam URNESS
Kenneth E. Anderson
Friso Schlottau
Original Assignee
Akonia Holographics Llc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from US15/174,938 external-priority patent/US10180520B2/en
Priority to US16/089,965 priority Critical patent/US20190179063A1/en
Priority to EP17779483.1A priority patent/EP3420415A4/fr
Priority to JP2018550324A priority patent/JP7001613B2/ja
Priority to CN201780020765.3A priority patent/CN109074026A/zh
Priority to KR1020187028192A priority patent/KR102123174B1/ko
Application filed by Akonia Holographics Llc filed Critical Akonia Holographics Llc
Priority to TW106134401A priority patent/TW201825932A/zh
Priority to TW106134790A priority patent/TW201823773A/zh
Priority to CN201780063137.3A priority patent/CN110073252B/zh
Priority to US16/339,297 priority patent/US11774657B2/en
Priority to PCT/US2017/056404 priority patent/WO2018071714A1/fr
Publication of WO2017176389A1 publication Critical patent/WO2017176389A1/fr
Priority to US18/453,243 priority patent/US20230393320A1/en

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Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/18—Diffraction gratings
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/04—Processes or apparatus for producing holograms
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/01—Head-up displays
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/32—Holograms used as optical elements
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/02—Details of features involved during the holographic process; Replication of holograms without interference recording
    • G03H1/024—Hologram nature or properties
    • G03H1/0248—Volume holograms
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/04—Processes or apparatus for producing holograms
    • G03H1/0402—Recording geometries or arrangements
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/04—Processes or apparatus for producing holograms
    • G03H1/0402—Recording geometries or arrangements
    • G03H1/0408—Total internal reflection [TIR] holograms, e.g. edge lit or substrate mode holograms
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/26—Processes or apparatus specially adapted to produce multiple sub- holograms or to obtain images from them, e.g. multicolour technique
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/26—Processes or apparatus specially adapted to produce multiple sub- holograms or to obtain images from them, e.g. multicolour technique
    • G03H1/2645—Multiplexing processes, e.g. aperture, shift, or wavefront multiplexing
    • G03H1/265—Angle multiplexing; Multichannel holograms
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/26—Processes or apparatus specially adapted to produce multiple sub- holograms or to obtain images from them, e.g. multicolour technique
    • G03H1/28—Processes or apparatus specially adapted to produce multiple sub- holograms or to obtain images from them, e.g. multicolour technique superimposed holograms only
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/01—Head-up displays
    • G02B27/0101—Head-up displays characterised by optical features
    • G02B27/0103—Head-up displays characterised by optical features comprising holographic elements
    • G02B2027/0105—Holograms with particular structures
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/01—Head-up displays
    • G02B27/0101—Head-up displays characterised by optical features
    • G02B27/0103—Head-up displays characterised by optical features comprising holographic elements
    • G02B2027/0109—Head-up displays characterised by optical features comprising holographic elements comprising details concerning the making of holograms
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/18—Diffraction gratings
    • G02B5/1861—Reflection gratings characterised by their structure, e.g. step profile, contours of substrate or grooves, pitch variations, materials
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/04—Processes or apparatus for producing holograms
    • G03H1/0402—Recording geometries or arrangements
    • G03H2001/0415—Recording geometries or arrangements for recording reflection holograms
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/04—Processes or apparatus for producing holograms
    • G03H1/0402—Recording geometries or arrangements
    • G03H2001/0439—Recording geometries or arrangements for recording Holographic Optical Element [HOE]
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/22—Processes or apparatus for obtaining an optical image from holograms
    • G03H1/2202—Reconstruction geometries or arrangements
    • G03H2001/2223—Particular relationship between light source, hologram and observer
    • G03H2001/2226—Edge lit holograms
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/22—Processes or apparatus for obtaining an optical image from holograms
    • G03H1/2286—Particular reconstruction light ; Beam properties
    • G03H2001/2289—Particular reconstruction light ; Beam properties when reconstruction wavelength differs form recording wavelength
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H2223/00—Optical components
    • G03H2223/18—Prism

Definitions

  • a holographic skew mirror is a holographic optical element that reflects incident light about a reflective axis that need not be perpendicular to the surface upon which the incident light impinges.
  • a holographic skew mirror's reflective axis does not have to be parallel to or coincident with the surface normal of the holographic optical element.
  • the angle between the reflective axis and the surface normal is referred to as the reflective axis angle and can be selected based on the desired application of the holographic skew mirror.
  • Embodiments of the present technology include holographic optical elements, including but not limited to holographic skew mirrors, holographic input/output couplers, and other holographic optical reflective devices.
  • an optical reflective device that includes a grating structure residing in a grating medium. This grating structure is structured to principally reflect incident light as reflected light, where the incident and reflected light both include a first wavelength. The incident light of the first wavelength and the reflected light of the first wavelength form an angle bisected by a reflective axis, which varies by less than 1 degree where the incident light is incident upon the grating medium at a range of internal angles of incidence spanning at least 15 degrees.
  • the reflective axis differs from a surface normal of the grating medium by at least 2.0 degrees.
  • the reflective axis varies by less than 1 degree where the incident light is incident upon the grating medium at a range of internal angles of incidence spanning at least 30 degrees.
  • the grating structure may include one or more holograms having a grating frequency (
  • the incident and reflected light both include a second wavelength that differs from the first wavelength by at least about 50 nm (e.g., the first wavelength may be 50 nm, 60 nm, 70 nm, 80 nm, 90 nm, 100 nm, or more greater than the second wavelength).
  • the incident and reflected light includes a third wavelength that differs from each of the first wavelength and the second wavelength by at least about 50 nm (e.g., the first wavelength may be 50-100 nm greater than the second wavelength, which in turn may be 50 - 100 nm greater than the third wavelength).
  • the first wavelength may reside in the red region of the electromagnetic spectrum
  • the second wavelength may reside in the green region
  • the third wavelength may reside in the blue region.
  • the grating structure in the optical reflective device may include one or more holograms having a grating frequency (
  • the grating structure may include one or more holograms having grating frequencies (
  • the grating structure includes at least nine holograms.
  • of these holograms may reside in a range between 5.0 ⁇ 10 3 rad/m and 1.0 ⁇ 10 7 rad/m.
  • the optical reflective device may be configured or structured to act as an output coupler, with the incident light is incident upon the grating structure from inside the optical reflective device and the reflected light exiting the optical reflected device.
  • the optical reflective device may further comprise at least one substrate adjacent to the grating medium.
  • the optical reflective device may include two substrates with the grating medium disposed between the two substrates.
  • the grating medium may comprise a photopolymer medium at least 100 ⁇ thick, and the two substrates may transmit at least 60% of the incident light and at least 60% of the reflected light.
  • the refractive indices of the grating medium and the two substrates may be within about 0.1 of each other.
  • Other embodiments of the present technology include a method of using an optical reflective device. This method comprises illuminating a grating structure residing in a grating medium with incident light at a first wavelength.
  • This incident light reflects off the grating structure to produce reflected light at the first wavelength.
  • the incident and reflected light form an angle bisected by a reflective axis tilted by at least about 2.0 degrees with a surface normal of the grating medium.
  • This reflective axis varies by less than 1 degree where the incident light is incident upon the grating structure within the grating medium at a range of internal angles of incidence spanning at least 15 degrees. In some cases, the reflective axis varies by less than 1 degree where the incident light is incident upon the grating medium at a range of internal angles of incidence spanning at least 30 degrees.
  • illuminating the grating structure comprises coupling the incident light into the grating medium, e.g., via a holographic input coupler, prism, or edge coupling, and totally internally reflecting the incident light within the grating medium.
  • the grating medium may guide the incident light at least partway to the grating structure.
  • the incident and reflected light may comprise a second wavelength different from the first wavelength by at least about 50 nm.
  • the incident and reflected light may also comprise a third wavelength different from each of the first wavelength and the second wavelength by at least about 50 nm.
  • Examples of this method may also include coupling the reflected light out of the grating medium at an angle of about 25 degrees with respect to the surface normal of the grating medium.
  • the grating medium may couple this reflected light towards a human eye in optical communication with the grating medium such that the reflected beam at least partially illuminates the human eye.
  • illuminating the grating structure may comprise illuminating the grating structure with an image such that a reflected image appears visible to the human eye.
  • Another example of the present technology includes a method of imaging. This method comprises disposing a grating medium containing a grating structure in optical communication with a human eye. This grating medium has a proximate surface defining a surface normal.
  • a visible image is coupled into the grating medium and guided to the grating structure via at least one total internal reflection within the grating medium.
  • the grating structure reflects the visible image about an axis of reflection forming an angle of at least about 2 degrees with respect to the surface normal.
  • the visible image is coupled out of the grating medium via the proximate surface towards the human eye. This visible image spans a field of view in free space of at least about 30 degrees.
  • Yet another example of the present technology includes a method of writing holographic gratings in a photosensitive medium.
  • This method includes disposing the photosensitive medium between an oblique face of a first prism and an oblique face of a second prism.
  • a first beam is coupled into the photosensitive medium via a first surface of the photosenstive medium and the oblique face of the first prism. This first beam forms a first angle with respect to a surface normal of the first surface.
  • a second beam is coupled into the photosensitive medium via a second surface of the photosenstive medium and the oblique face of the second prism. This second beam forms a second angle with respect to a surface normal of the second surface with a magnitude substantially equal to that of the first angle.
  • this method also includes interfering a third beam and a fourth beam in the photosensitive medium to form a second holographic grating within the photosensitive medium.
  • Still another example of the present technology includes a device with a holographic optical element having at least one grating structured to reflect visible light over a field of view of at least about 50° in a first dimension.
  • the field of view is measured outside the holographic optical element and is substantially centered on a surface normal of the holographic optical element.
  • the grating has a grating vector oriented at an angle of at least about 15° to about 45° with respect to the surface normal.
  • the holographic optical element includes a single grating structured to reflect visible light at wavelengths in a range from about 400 nm to about 700 nm over the field of view.
  • the holographic optical element includes a plurality of gratings, each structured to reflect incident light at one wavelength of the visible light at a different angle within the field of view.
  • the device may also include at least one light source, in optical communication with the holographic optical element, to illuminate the plurality of gratings with the visible light.
  • the field of view may be at least about 30° in a second dimension orthogonal to the first dimension.
  • the angle formed by the axis of reflection and the surface normal may be about 20° to about 40°.
  • the holographic optical element may be substantially free of photo- initiators sensitive to visible light.
  • Another instance of the present technology includes a method of reflecting light.
  • This method comprises illuminating at least one grating in a holographic optical element with visible light.
  • the grating reflects at least a portion of the light over a field of view of at least about 50°. This field of view is centered on an axis of reflection that forms an angle of at least about 15° to about 45° with respect to a surface normal of the holographic optical element.
  • Still another instance of the present technology includes method of making a holographic optical element (and the resulting holographic optical element).
  • This method comprises interfering a first beam and a second beam inside a holographic recording medium to form a first grating.
  • the holographic recording medium has a planar surface.
  • the first grating is structured to reflect incident light at a first visible wavelength over a field of view of at least about 50°. This field of view is centered on an axis of reflection that forms an angle of at least about 15° to about 45° with respect to a surface normal of the planar surface of the holographic optical element.
  • interfering the first beam and the second beam comprises coupling the first beam into the holographic recording medium via an oblique surface of a first prism and coupling the second beam into the holographic recording medium via an oblique surface of a second prism.
  • Yet another instance of the present technology includes device comprising a holographic optical element having a plurality of reflection gratings.
  • Each reflection grating in the plurality of reflection gratings has a grating vector KG forming an angle of about 15° to about 45° with a surface normal of the holographic optical element and a grating frequency (
  • FIG. 1 shows a holographic skew mirror with a relatively narrow field of view.
  • FIGS. 2A and 2B show a k-space representation of the holographic skew mirror shown in FIG. 1 without and with an incident beam, respectively.
  • FIGS. 3 A and 3B show an in-plane holographic recording system suitable for making holographic skew mirrors.
  • FIGS. 4A and 4B show k-space representations of making a holographic skew mirror using the in-plane holographic recording geometry of FIGS. 3A and 3B, respectively.
  • FIGS. 5A and 5C show real-space perspective views of an out-of-plane holographic skew mirror writing geometry.
  • FIGS. 5B and 5D show k-space representations of the real-space views shown in FIGS. 5A and 5C, respectively.
  • FIG. 6 is a plot that shows the angular recording bands achievable with both in-plane and out-of-plane holographic skew mirror recording geometries.
  • FIGS. 7A-7C show different views of a holographic recording medium sandwiched between Total Internal Grazing-Extension Rotation (TIGER) prisms for writing holographic skew mirrors with wide fields-of-view.
  • TIGER Total Internal Grazing-Extension Rotation
  • FIG. 7D shows a perspective view of the TIGER prisms used in the holographic recording geometry of FIGS. 7A-7C.
  • FIGS. 8A-8C shows a holographic recording system with TIGER prisms and the out-of- plane holographic recording geometry shown in FIGS. 7A-7C.
  • FIG. 9 illustrates angle-correction using pairs of wedges.
  • FIG. 10 shows a plan view of a holographic skew input/output coupler with a 60° diagonal field of view (53.4° horizontal field-of-view, 31.6° horizontal field-of-view, and 16:9 aspect ratio) made using an out-of-plane holographic recording system.
  • FIG. 11 shows a k-space representation of the recording beams for the first and 228 th gratings in the holographic skew mirror of FIG. 10.
  • FIG. 12 is a plot of skew mirror internal angle recording bands for a 53.4° field-of-view holographic skew mirror output coupler.
  • FIG. 13 illustrates an experimentally realized holographic skew output coupler with a 53.4° horizontal field of view and a 31.6° vertical field of view coupled to a waveguide.
  • FIG. 14 is a mosaic of modulation transfer function (MTF) plots of the holographic skew mirror of FIG. 13.
  • MTF modulation transfer function
  • FIG. 15 shows a head-mounted display with a wide field-of-view holographic skew mirror.
  • FIG. 1 shows a real-space representation of a holographic skew mirror 100.
  • This holographic skew mirror 100 includes a grating structure 120 recorded in a holographic grating medium 110, such as Tapestry ® holographic photopolymer media from Akonia Holographies LLC of Longmont, Colorado, or Bayfol ® HX200 light-sensitive, self-devel oping photopolymer film from Covestro AG of Leverkusen, Germany.
  • the grating structure 120 may comprise many discrete holographic gratings, each of which reflects light over a narrow range of angles and/or wavelengths.
  • the grating structure 120 includes many holographic gratings that define both a skew axis 121 and a reflective axis.
  • the grating vector for each holographic grating is parallel to or coincident with the skew axis 121, which forms a skew angle ⁇ with respect to a surface normal 111 of the holographic grating medium 110.
  • each holographic grating reflects light at a particular wavelength or range of wavelengths over a particular range of internal angles of incidence, which are incidence angles on the grating structure 120 as measured within the holographic grating medium 110.
  • the axis about which each holographic grating reflects incident light is called the reflective axis.
  • Each holographic grating's reflective axis may vary slightly from the skew axis 121 with wavelength, e.g., by about less than 0.1°, less than 0.01°, less than by 0.001°, etc.
  • a skew axis / reflective axis may be called a skew axis when referring to making a skew mirror (for example when describing recording a hologram in a skew mirror grating medium), and as a reflective axis when referring to light reflective properties of a skew mirror.
  • a mean skew angle for a hologram (including a mean skew angle for a collection of holograms) can be substantially identical to a reflective axis angle, meaning the skew angle or mean skew angle is within 1.0°, 0. ⁇ , 0.05°, 0.02°, 0.0167° (1 arcmin), or less of the reflective axis angle.
  • the skew angle and reflective axis angle can be theoretically identical.
  • the skew angle or mean skew angle as measured or estimated based on recording beam angles may not perfectly match the reflective axis angle as measured by incidence angles and reflection angles of light reflected by a skew mirror. This variation occurs at the single hologram level and is inversely proportional to the hologram's thickness.
  • a skew angle determined based on recording beam angles can be within 1.0°, 0.1°, 0.05°, 0.02°, 0.0167°, or less of the reflective axis angle determined based on angles of incident light and its reflection, even where medium shrinkage and system imperfections contribute to errors in estimating skew angle and reflective axis angle.
  • an incident beam 101 ' of visible light impinges on a surface 112 of the holographic grating medium 110 at an angle 6F with respect to the skew axis 121.
  • This beam 101 ' may be a monochromatic, polychromatic, or broadband visible beam of light.
  • the holographic grating medium 110 has a higher refractive index than the surrounding air, so the incident beam 101 ' refracts at the surface 112 to form a refracted incident beam 101.
  • the refracted incident beam 101 illuminates the volume hologram 120 at an angle ⁇ with respect to the skew axis 121.
  • the angle ⁇ is also called the internal angle of incidence because it is the angle of incidence on the volume hologram 120 measured inside the holographic grating medium 110.
  • the volume hologram 120 reflects at least a portion of the refracted incident beam 101 at an angle & with respect to the skew axis 121.
  • the angle & is also called the internal angle of reflection and is equal to the internal angle of incidence ⁇ as shown in FIG. 1.
  • the skew axis 121 bisects an angle equal to twice the internal angle of incidence &.
  • the reflected portion of the refracted incident beam 101 is called the principal reflected beam 103.
  • the principal reflected beam 103 impinges on the surface 112 of the holographic grating medium 110. It refracts at this boundary to form a refracted principal reflected beam 103' at an angle 6 with respect to the skew axis 121.
  • the holographic skew mirror's field-of-view, as measured in free space outside the holographic grating medium 1 10, is determined by the range of external angles of reflection & ' .
  • FIGS. 2A and 2B show a k-space representation of the holographic skew mirror 100 shown in FIG. 1 with and without the incident beam 101 and principal reflected beam 103, respectively.
  • this k-space representation includes multiple concentric circles, each of which is a two-dimensional projection of a k-sphere representing the optical propagation vectors, or wave vectors, for light at a particular wavelength in the holographic medium.
  • the length of the wave vector can be represented as:
  • n is the refractive index and ⁇ is the wavelength.
  • the wave vectors are longer for shorter wavelengths.
  • the innermost circle 290 represents wave vectors for red light in the holographic grating medium 1 10
  • the second innermost circle 291 represents wave vectors for green light in the holographic grating medium 1 10
  • the second outermost circle 292 represents wave vectors for blue light in the holographic grating medium 1 10
  • the outermost circle 293 represents wave vectors at the recording wavelength in the holographic grating medium 1 10.
  • FIGS. 2A and 2B also show the volume hologram 120, which appears in k-space as a line segment-like distribution whose distribution of grating vectors KG is parallel to the
  • FIG. 2B also shows the wave vectors of the incident refracted beam 101 and the principal reflected beam 103 with respect to the volume hologram' s grating vector.
  • the wave vector of the principal reflected beam 103 is the vector sum of the volume hologram' s grating vector and the wave vector of the incident refracted beam 101.
  • FIGS. 3A and 3B illustrate a skew mirror recording system 300 that uses in-plane recording prisms 330a and 330b (collectively, in-plane recording prisms 330) to couple light into a holographic recording medium 310, which is disposed between a pair of transparent substrates (not shown).
  • the recording medium 310 and substrates are sandwiched between the in-plane recording prisms 330 so that a signal beam 331a and a reference beam 33 lb, also called recording beams 331, can be introduced into the holographic recording medium 310 at angles that would produce total internal reflection (TIR) at the substrate-air boundary were the in-plane recording prisms 330 not present.
  • TIR total internal reflection
  • the in-plane recording prisms are typically index-matched to the substrates, and an index-matching fluid may be applied at a boundary between the prisms 330 and substrates (not shown) to reduce reflection and refraction at the prism/substrate boundaries.
  • index-matching may mean that the refractive indices of the holographic recording medium 310, substrates, and prisms 330 are within about 0.1 or less.
  • Mirrors 350a and 350b reflect the recording beams 331a and 33 lb, respectively, into the holographic recording medium 310 via the prisms 330a and 330b, respectively.
  • Each mirror 350a, 350b is oriented to direct the corresponding recording beam 331a, 33 lb such that it illuminates a base of the corresponding prism 330a, 330b.
  • the recording beams 331 may refract at the air/base interface, then propagate into the holographic medium 310, where they interfere to produce a (reflection) grating recorded by the holographic recording medium 310.
  • the holographic recording medium 310 and prisms 330 are translated back and forth along the ZG axis with respect to the mirrors 350 using a translation stage (not shown) and the mirrors 350 are rotated to record the series of gratings that make up the skew mirror as shown in FIG. 3B.
  • FIGS. 3 A and 3B also illustrate global, or recorder, coordinates (XG, yc, ZG) for the case of in-plane prisms.
  • the origin of the global coordinates shown in FIGS. 3A and 3B is defined to be in the center of the output coupler in the center of the recording layer of the holographic recording medium 310.
  • the Global Angle for recording, 0G is defined as the angle of the recording beam 331a with respect to the XG axis within the holographic recording medium 310/prism 330a. Note that the nominal angle of the other recording beam 33 lb is 180° - 0G (not marked), so that recorded grating vectors are aligned substantially with the XG axis.
  • the angle between the recordings beams 331, or interbeam angle, within the holographic recording medium 310/prism 330a is marked as a.
  • the global skew angle is the angle between the XG and z axes and is marked as ⁇ .
  • the surface normal of the holographic recording medium 310 forms an angle ⁇ (the global skew angle) with respect to the ZG axis.
  • ⁇ the global skew angle
  • the angle between the holographic recording medium 310 and the ZG axis sets the skew axis of the holographic skew mirror.
  • This skew axis can be changed, e.g., by rotating the holographic recording medium 310 and prisms 330 with respect to the recording beams 331 using an appropriate combination of stages and mounts.
  • in-plane recording systems generally cannot be used to make holographic skew mirrors with wide fields of view. This is due to constraints on the geometry and wavelengths of the beams used to record the volume holographic gratings for the holographic skew mirror. These constraints include the skew angle, the grating frequency, which determines the angle of reflection, and the difference between the recording beam wavelength, which is usually in the deep blue region of the electromagnetic spectrum (e.g., 400 nm to 430 nm), and the reading beam wavelength, which is usually in the visible region of the electromagnetic spectrum.
  • the recording beam wavelength which is usually in the deep blue region of the electromagnetic spectrum (e.g., 400 nm to 430 nm)
  • the reading beam wavelength which is usually in the visible region of the electromagnetic spectrum.
  • a holographic grating's grating frequency which can be expressed as the magnitude of the grating wave vector,
  • the holographic recording medium' s refractive index and the skew angle both limit the range of recording angles that can be accessed via in-plane prisms like those shown in FIGS. 3A and 3B.
  • one or both of the recording beams may become parallel to the holographic recording medium surface, making it difficult if not impossible to interfere the recording beams within the holographic recording medium.
  • one recording beam 33 lb' makes a grazing angle that is steeper (higher) with respect to surface of the recording medium 310 than that made by the other recording beam 331a' .
  • Snell' s Law may limit the maximum grazing angle (the exact limit depends on the recording wavelength, the refractive indices of the recording medium and surrounding media, and the skew angle). Above this limit, the recording beam 33 lb' may reflect off the holographic recording medium 310 instead of coupling into it.
  • the upper bound on the grazing angle may limit the ability to record lower frequency holograms, which may limit the skew mirror's field of view for some colors, particularly for large skew angles.
  • FIGS. 4A and 4B show k-space representations of the in-plane recording geometries in FIGS. 3 A and 3B, respectively.
  • the recording beams 331a and 331b are incident on the holographic recording medium such that their wave vectors form an interbeam angle a and record a holographic grating with a grating vector KG that is parallel to the skew axis 421.
  • FIG. 4A the recording beams 331a and 331b are incident on the holographic recording medium such that their wave vectors form an interbeam angle a and record a holographic grating with a grating vector KG that is parallel to the skew axis 421.
  • the recording beams 331a' and 331b' are incident on the holographic recording medium such that their wave vectors form an interbeam angle a ' and record a holographic grating with a grating vector KG' that is also parallel to the skew axis 421.
  • the size of the grating vector determines the internal incidence angle(s) over which the corresponding holographic grating reflects incident light.
  • Holographic gratings with smaller gratings reflect light at larger internal incidence angles as measured from the skew axis, and holographic gratings with larger gratings reflect light at smaller internal incidence angles as measured from the skew axis.
  • the largest possible grating vector is recorded when the recording beams' wave vectors are antiparallel and aligned with the skew axis 421.
  • the corresponding holographic grating retro-reflects light incident on the grating medium along the skew axis 421 ("normal incidence" for a holographic skew mirror).
  • the interbeam angle a also shrinks, reducing the size of the grating vector KG and increasing the possible field of view.
  • the angle between the recording beam 33 lb' and the x axis becomes so small that the recording beam 33 lb' becomes parallel to the surface of the holographic recording medium 310 instead of refracting into the holographic recording medium 310.
  • the limit occurs when the grating vector of the recording beam 33 lb' is aligned with k x , i.e., when the recording beam 33 lb' is parallel to the surface of the holographic recording medium 310.
  • the recording beam 33 lb' no longer interferes with the other recording beam 331a' within the holographic recording medium 310 to record a reflection grating. This limits the smallest size of the grating vector and hence the field of view. Although rotating the skew axis may compensate for this effect, it also limits the range of permissible skew angle/field of view combinations.
  • FIGS. 3A, 3B, 4A, and 4B illustrate the tradeoff between permissible skew angle and permissible field of view in the in-plane recording geometry: generally, it is possible to have a large skew angle or a large field of view with in-plane recording, but not both.
  • the smallest accessible angular difference between recording beams depends in part on the wavelengths of the recording beams and the reading beams and dispersion of the holographic recording medium.
  • Most holographic recording media is optimized to record gratings at deep blue wavelengths, e.g., 405 nm, and to be insensitive to visible light at longer wavelengths. But it is difficult to impossible to interfere deep blue beams within a holographic recording medium at angular differences small enough to generate reflective gratings at spatial frequencies low enough to produce a wide field-of-view at visible wavelengths in an in-plane recording system.
  • Increasing the recording beam wavelength would alleviate this problem, but would also require a holographic recording medium sensitive to longer-wavelength light. But increasing the holographic recording medium's sensitivity to longer- wavelength light would make the holographic recording medium more susceptible to incomplete bleaching at visible wavelengths. This is because holographic recording media with photo-initiators sensitive to visible light may polymerize when exposed to visible light and is therefore less suitable for making holographic optical elements that operate at visible wavelengths. Moreover, photo-initiators sensitive to visible light can cause undesirable visible light absorbance in the grating medium. This would make the holographic recording medium less suitable for use in a skew mirror that reflects light at visible wavelengths.
  • FIGS. 5A-5D show how rotating recording beams 531a and 531b (collectively, recording beams 531) about the_yG axis, which is in the x-z plane of the holographic recording medium 310, makes it possible to record shorter holographic gratings than is possible with an in-plane recording geometry.
  • FIGS. 5A and 5C show real-space views from different perspectives of the recording beams 531 incident on a holographic recording medium 510 that is tilted about the ZG axis of the recording system's coordinate frame (i.e., the .y axis of the holographic recording medium 510).
  • the recording beams 531 are rotated within the XG - ZG plane to record grating vectors that also lie in the XG - ZG plane.
  • FIGS. 5B and 5D are k-space representations of the real-space views shown in FIGS. 5A and 5C, respectively.
  • the wave vectors of the recording beams 531 lie within the XG - ZG plane, which forms an off-axis slice of a k-sphere 591 representing the recording beams' momentum within the holographic recording medium 510.
  • changing the interbeam angle between the recording beams 531 changes the length of the grating vector.
  • ) is written when the recording beams 531 are counter-propagating along the XG axis, and the smallest grating vector (minimum
  • FIGS. 5A-5C show just one of the many possible orientations of recording beams and skew angles.
  • the skew angle and each recording beam can be adjusted as desired, within the constraints imposed by the writing wavelength and the holographic recording medium's refractive index, to record holographic gratings at a wide variety of spatial frequencies.
  • the exact number and spatial frequencies of holographic gratings depend on the desired field of view of the holographic skew mirror, among other things.
  • FIG. 6 is a plot illustrating the capabilities of out-of-plane vs. in-plane recording prisms for a specific recording geometry.
  • the horizontal axis is grating frequency (in rad/m), and the vertical axis shows the Bragg-matching angle with respect to the grating vector/skew axis.
  • curve 690 is for the wavelength at which the holograms are recorded (405 nm); curve 691 is for 463 nm (blue); 692 is for 522 nm (green); curve 693 is for 622 nm (red); and curve 694 is for 860 nm.
  • the horizontal lines at 47.75° and 12.75° demark the range of spatial grating frequencies required for the red, green, and blue wavelengths, coded by color.
  • FIGS. 7A-7C show different perspectives of an out-of-plane holographic recording system 700 that can record holographic skew mirrors with wide fields of view.
  • a holographic recording medium 710 is disposed between a pair of total internal grazing-extension rotation (TIGER) prisms 730a and 730b (collectively, TIGER prisms 730).
  • the holographic recording medium 710 may also be sandwiched between a pair of transparent substrates (not shown) with index-matching fluid disposed on the surfaces of the transparent substrates contacting the prisms 730. These substrates may transmit 60%, 70%, 80%), 90%), or more of light at visible wavelengths.
  • the TIGER prisms 730 enable introducing recording beams into the holographic recording medium 710 at angles that are inaccessible using in-plane recording geometries because of total internal reflection (TIR) and grazing angles constraints.
  • TIR total internal reflection
  • FIG. 7A-7C (and FIGS. 5A-5D) also show the symmetry of the recording beams 731a and 73 lb (531a and 53 lb in FIGS. 5A-5D). More specifically, these figures show that the magnitudes angles between the recording beams and the surface normals of the holographic recording medium 710 are substantially equal. Put differently, if recording beam 731a forms a first angle (e.g., 32°) with respect to the holographic recording medium's surface normal, then recording beam 731b and the holographic recording medium's surface normal form an angle with the same magnitude (e.g. ,-32°).
  • a first angle e.g. 32°
  • recording beam 731b and the holographic recording medium's surface normal form an angle with the same magnitude (e.g. ,-32°).
  • the recording beams 731 are incident on surfaces of the holographic recording medium 710 that are parallel and therefore have coincident/parallel surface normals. This holds as the recording beams 731 are rotated with respect to the holographic recording medium 710 as shown in FIGS. 5A-5D.
  • each TIGER prism 730 has a prism primary face 732a, 732b (collectively, primary faces 732) that is oblique to the prism base.
  • the primary face 732 of each TIGER prism 730 is a hexagonal face residing parallel to and immediately proximate the holographic recording medium 710 where the prism 730 and the holographic recording medium 710 reside in a skew mirror recording system.
  • the obliqueness of the primary faces 730 makes it possible to access out-of-plane recording beam angles and skew angles like those illustrated in FIGS. 5A-5D.
  • the TIGER prisms 730 can be visualized by imagining a cutting a glass cuboid, or rectangular prism, into two sections.
  • the cut in the cuboid is along a plane that joins a diagonal line connecting adjacent sides of one of the cuboid's faces (prism faces 734a and 734b) with another diagonal line connecting the other two sides of the opposite face of the cuboid (prism faces 736a and 736b).
  • the resulting sections of the cuboid form a matched pair of TIGER prisms 730.
  • TIGER prisms can be of any suitable shape, so long as they have oblique faces or facets angled to enable access of out-of-plane recording angles.
  • a TIGER prism may be formed as a section of any suitable polyhedra, including parallelepipeds and regular right (geometrical prisms).
  • the face/facet may oriented or angled as desired and does not necessarily have to result in a symmetric division of a polyhedron.
  • the face (and the holographic recording medium) could also be curved, e.g., to form at least a portion of a spherical, cylindrical, or conical surface. Other surfaces are also possible, including arbitrarily curved or warped surfaces.
  • the TIGER prisms' oblique primary faces 732 and other faces can be used to define the two different coordinate systems shown in FIGS. 7A-7C show.
  • axes XG, yc, and ZG are Cartesian coordinates in the frame of reference of the TIGER prisms 730.
  • axes x, y, and z are Cartesian coordinates in the frame of reference of the TIGER prisms 730.
  • Cartesian coordinates (aka standard coordinates) in the frame of reference of the holographic recording medium 710, with the z axis extending normal to the surface of the holographic recording medium 710.
  • the axes x, y, and z are the real-space equivalents of the k-space axes k x , k y , and kz shown in FIGS. 5A-5D.
  • the TIGER prisms 730 allow the recording medium 710 to be rotated about the XG axis, "splitting the difference" between the recording beams 73 la and 73 lb grazing angles.
  • Both the TIGER prism configuration 700 and the in-plane configuration 300 can record grating vectors aligned with the XG axis, and hence result in equivalent written skew mirrors.
  • the TIGER prism configuration 700 can also access smaller recording angles and thus can record gratings of lower spatial frequency than the in- plane configuration.
  • FIGS. 7A-7C show a TIGER prism-based skew mirror recorder 800 that uses TIGER prisms 730 to implement the recording geometry 700 shown in FIGS. 7A-7C for making wide- field-of-view holographic skew mirrors. It includes mirrors 850a and 850b (collectively, mirrors 850) that directed the recording beams 73 la and 73 lb, respectively, to the holographic recording medium 710, which is mounted between the TIGER prisms 730 in a mount 860.
  • the TIGER prism-based skew mirror recorder 800 also includes stages to adjust the angular and translational alignment of the recording beams 731 with respect to the holographic recording medium 730.
  • These stages may include three goniometers 870a-870c (collectively, goniometers 870), a vertical translation stage 880, a rotation stage 872a and 872b (collectively, rotation stages 872) for each mirror 850, and a horizontal translation stage (not shown) for moving the mounted holographic recording medium 710 and TIGER prisms 730 back and forth.
  • refraction correction and other adjustments are typically performed by rotating the mirrors 350 and translating the holographic recording medium.
  • TIGER prisms there may be desired out-of-plane angle adjustments that cannot be made by rotating the mirrors 850 or translating the holographic recording medium.
  • the TIGER prism skew recorder 800 may be equipped with other actuators, such as the goniometers 870 and vertical stage 880, to perform out-of-plane angle adjustments.
  • the first goniometer 870a is situated on top of the first rotating stage 872a, beneath rotating mirror 850a, to allow rotation of the mirror 850a about an axis substantially aligned to the horizontal mid-line of the mirror surface. Actuation of the first goniometer 870a allows recording beam 73 la to be reflected up or down by up to several degrees out of the XG - ZG plane. Similarly, the second goniometer 870b is situated so as to allow recording beam 73 lb to also be reflected up or down independently by mirror 850b. The third goniometer 870c similarly allows a mirror (not labeled) upstream of rotating mirror 850a to tip up and down so that, in
  • the first and third goniometers 870a, 870c can produce any desired beam 731a height and vertical angle combination (within mechanical limits).
  • the vertical stage 880 can raise or lower the height (yc coordinate) of the entire prism package 860, including the recording medium 710.
  • An additional method for performing the correction would be to add an additional goniometer (not shown) for adjusting the path of recording beam 73 lb to produce any desired height and vertical angle combination in much the same manner as the first and third goniometer (not shown) for adjusting the path of recording beam 73 lb to produce any desired height and vertical angle combination in much the same manner as the first and third goniometer (not shown) for adjusting the path of recording beam 73 lb to produce any desired height and vertical angle combination in much the same manner as the first and third goniometer (not shown) for adjusting the path of recording beam 73 lb to produce any desired height and vertical angle combination in much the same manner as the first and third goniometer (not shown) for adjusting
  • goniometers 870a, 870c produce the desired height and vertical angle combination.
  • FIG. 9 illustrates another method for achieving this refraction correction uses a pair of optical wedges in rotation mounts which can be aligned with respect to each other to achieve angles within a cone of twice the magnitude that one wedge achieves.
  • this configuration will allow small arbitrary vertical angle components to be introduced into each recording beam, while also maintaining overlap between the beams and the recording medium. For instance, one may set a desired vertical angle component of reference beam 73 lb using goniometer 870b, and then set the vertical stage height so that the reference beam 73 lb passes through the desired recording region. Then, one may set goniometers 870a and 870c so that the signal beam 73 la is introduced at a desired vertical angle at a height matching that set by the vertical stage. Typically, only a few degrees of vertical angle range and a couple centimeters of vertical motion will be sufficient to implement desired refraction correction and other adjustments.
  • the out-of-plane skew mirror recorder 800 shown in FIGS. 8A-8C can be used to make wide field-of-view holographic skew mirror by recording one or more volume holograms within the volume of the holographic recording medium.
  • the interbeam and skew angles chosen to record these holograms depend on the desired field of view and operating wavelength range of the holographic skew mirror.
  • the out-of-plane skew mirror recorder 800 may be used to record many discrete gratings, each of which principally reflects light at one or more wavelengths over a different, narrow range of incident angles. If these ranges of incident angles overlap or are close to each other, the gratings will reflect light over a wide range of incident angles to provide a wide field of view.
  • the holographic skew mirror may include a holographic grating that is written by continuously recording the interference between a pair of recording beams as the interbeam angle is varied. This continuously recorded grating reflects light over wide range of incident angles to provide a wide field of view.
  • Other combinations of grating are also possible, e.g., to produce a holographic skew mirror that reflects light over certain ranges of angles of incidence but not others, or certain ranges of wavelengths but no others.
  • the vector form of Snell's law may be used to calculate the direction of a recording beam upon refraction at an internal boundary between a recording medium and a prism.
  • the vector form of Snell's law describes what happens to light rays that impinge on an optical boundary, such as a prism surface, at an angle that includes non-zero components in more than one coordinate axis.
  • the vector form of Snell's law gives the resulting refraction at such a surface as:
  • N is the unit normal vector of the optical boundary
  • l and s 2 are the normalized incident and refracted ray direction vectors
  • ni and are the refractive indices of the first and second materials.
  • a refraction typically includes non-zero components in more than one axis of the global coordinate system.
  • refractive index mismatches between optical elements such as a recording medium and a recording prism are corrected using Snell's law.
  • an internal ray direction vector s s int might be desired for a signal beam within recording medium 710 (FIGS. 7A-7D and 8A-8C) during a recording exposure.
  • Snell's law may be applied at the internal boundary between recording prism 730a and recording medium 710 to determine s jsm , the ray direction vector within prism 730a (note that even a small index mismatch may produce significant refraction).
  • Snell's law may be may be again applied at the external surface of recording prism 730b to determine the external ray direction vector s S ext from s S prjsm .
  • External ray direction vector s S ext thus directly determines 6b, which may be set by rotating mirror 850b.
  • the angle for rotating mirror 850a may be determined from the desired reference ray direction vector 3 ⁇ 4 int by tracing through the internal and external surfaces of recording prism 730a.
  • adjustments to recording angles may be performed for reasons other than refraction correction.
  • other adjustments include dispersion compensation, media shrinkage pre-compensation, and empirical adjustments to improve the modulation transfer function (MTF) or color plane separation.
  • MTF modulation transfer function
  • these adjustments may be made to compensate for instrument error, shrinkage, index mismatch, etc.
  • error can be determined empirically by writing a complete test skew mirror with (imperfect) holograms and ascertaining the holograms' imperfections by measuring the test skew mirror's angular dispersion as a function of wavelength. These measurements can be used to adjust the design angles. Once the design angles have been adjusted, it is possible to record holographic skew mirrors that are virtually free of imperfections.
  • an out-of-plane skew mirror recorder can create a holographic skew mirror with a wide field of view by recording one or more (e.g., tens, hundreds, or thousands) of holographic gratings within a holographic recording medium.
  • Writing a discrete set of gratings over a series of exposures as opposed to a single grating in a single continuous exposure with angularly scanning beams offers several advantages. First, it reduces the need to suppress or compensate vibration during exposure.
  • discrete gratings preserve the change in refractive index
  • An at the expense of spectrally sub sampling incoming light (the discrete gratings apply a reflective comb function to light illuminating skew mirror).
  • picking the grating spacing to match the light source's spectrum makes the device more efficient.
  • FIG. 10 shows a wide field-of-view holographic input/output coupler 1000 made using an out-of-plane writing geometry.
  • the holographic skew input/output coupler 1000 comprises a holographic grating structure 1020 recorded in a holographic grating medium 1010, which may be about 100 microns thick or thicker.
  • the grating structure 1020 comprises 228 gratings, each of which is recorded with a different interbeam recording beam angle and hence has a different grating frequency (
  • skew angles may range from about 15.0° to about 45.0° (e.g., about 20.0° to about 40.0°, about 25.0° to about 35.0°, about 27.5° to about 32.5°, and so on).
  • This corresponds to a field of view as measured in air outside the holographic grating medium of about 6>FOV 54.3°.
  • the grating structure 1020 principally reflects this light into shaded region 1003, which spans the same angular range (-13.1° to -47.6°) on the other side of the skew axis 1021.
  • the principally reflected light with the third shaded region 1003 refracts at the surface 1020 into a fourth shaded region 1003 ' spanning a horizontal field of view of about 54.3°.
  • FIG. 10 shows a k-space representation of the grating vectors for a first grating
  • KGI and a 228 TH grating KG228 along with the wave vectors for the recording beams used to record the gratings.
  • the grating and wave vectors are shown with respect to k-sphere 1 191 for the holographic grating medium 1020, which has a refractive index of about 1.5471 at a recording wavelength of 405 nm.
  • the tips of the grating and wave vectors lie on an ellipse.
  • First and second recording beam wave vectors for the first grating, Rl i and R2i, respectively, form angles in the holographic grating medium of 32.0° and 148.0°, respectively, with respect to the reflective axis 1021 to produce a first grating with a grating frequency of about 4.1 x 10 7 rad/m.
  • the wave vectors for the 228 TH grating, RI228 and R2228, form angles in the holographic grating medium of 64. 1 ° and 1 15.9°, respectively, with respect to the skew axis 1021 to produce a 228 TH grating with a grating frequency of about 2. 1 x 10 7 rad/m.
  • Each grating vector is angled at -30.25° relative to the surface normal 101 1.
  • This grating vectors in the grating structure 1020 of FIG. 10 span a range of grating frequencies that extends about 2.0 ⁇ 10 7 rad/m. Other grating frequencies and ranges of grating frequencies are also possible; in practice, range of grating frequencies, or difference between the maximum and minimum grating frequency, may be about 2.00 x 10 5 radians per meter to about 3.
  • the gratings may be spaced uniformly or non-uniformly in k-space. For about
  • the grating frequencies may be selected based on the spectrum of the incident light and/or the range of expected incidence angles for increased efficiency.
  • each grating reflects light from a different incident angle to a different principally reflected angle.
  • the range of possible angles of incidence depends on the range of grating frequencies and determines the field of view.
  • each grating may reflect light at one wavelength (e.g., 460 nm, 518 nm, or 618 nm), two wavelengths (e.g., 460 nm and 518 nm or 518 nm and 618 nm), three wavelengths (e.g., 460 nm, 518 nm, and 618 nm), or more.
  • Gratings may reflect light at visible wavelengths, near infrared (NIR) wavelengths, near ultraviolet wavelengths, or combinations thereof. This enables the skew mirror to reflect narrowband light (e.g., light from a laser), broadband light (e.g., light from an organic light-emitting diode (OLED)), and even natural light (e.g., sunlight).
  • narrowband light e.g., light from a laser
  • broadband light e.g., light from an organic light-emitting diode (OLED)
  • natural light e.g., sunlight
  • the skew axis may be selected to couple light into or out of the grating medium at angles near the surface normal, e.g., as shown in FIG. 10.
  • Table 1 lists recording beam angles and grating frequencies for each of the 228 uniformly spaced gratings.
  • First recording beam angle 0RI and second recording beam angle 0R2 are relative to a skew axis having a skew angle of -30.25 degrees relative to surface normal of the recording medium.
  • grating vectors listed in Table 1 are oriented at -30.25 degrees relative to surface normal of the recording medium, which is referred to as a grating medium after all 228 gratings are recorded.
  • 0RI and 0R2 are analogous to 0GRI and 0GR2 respectively, as illustrated in FIG. 7B, except that 0RI and 0R2 are measured within medium 710, no prism 730.
  • the gratings can be grouped into three overlapping subsets, each of which is structured to reflect incident light of a specified wavelength about the reflective axis, at a range of incidence angles. [00114] Subset 1, comprising gratings 1 through 146, is structured to reflect incident light
  • Gratings 1 through 228 i.e., all of the gratings in Table 1
  • collectively can reflect incident light at 460 nm about the substantially constant reflective axis, at angles of incidence ranging from 13.1 to 59.8 degrees (a range of 46.7 degrees) relative to the reflective axis.
  • the range from 13.1 to 47.6 degrees is of interest for the skew mirror structured to reflect blue, green, and red light at common incidence angles relative to the substantially constant reflective axis.
  • Subset 2 comprising gratings 53 through 182, is structured to reflect incident light at 518 nm about the substantially constant reflective axis, at angles of incidence ranging from 12.8 to 47.7 degrees relative to the reflective axis.
  • gratings 43 through 228 can reflect incident light at 518 nm about the substantially constant reflective axis, at angles of incidence ranging from 3.1 to 55.6 degrees (a range of 52.5 degrees) relative to the reflective axis. The range from 13.1 to 47.6 is of interest for purposes of the present discussion.
  • Subset 3 comprising gratings 120 through 228, is structured to reflect incident light at 618 nm about the substantially constant reflective axis, at angles of incidence ranging from 12.5 to 47.6 degrees relative to the reflective axis.
  • Gratings 112 through 228 are structured to reflect incident light at 618 nm about the substantially constant reflective axis, at angles of incidence ranging from 3.0 to 47.6 degrees (a range of 44.6 degrees) relative to the reflective axis. The range from 13.1 to 47.6 is of interest for purposes of the present discussion.
  • At least gratings 198 through 228 cannot be recorded using in-plane recording such as illustrated in FIGS. 3 A and 3B because the in-plane recording geometry results in impermissible recording beam angles of 90 degrees and greater relative to surface normal of the recording medium. Practically speaking, even gratings 115 through 198, although theoretically possible, would likely problematic using in-plane architecture because recording beam angles approach a grazing condition (i.e., approach 90 degrees). Out-of-plane recording using TIGER prisms, such as illustrated in FIGS. 7A-7C, enables writing all gratings in Table 1. [00118] Selecting Recording Beam Angles and Exposure Times
  • Computer code can be used to compute the writing beam angles and exposure times for making a holographic skew mirror with an out-of-plane writing geometry.
  • the following snippet of computer code calculates the horizontal and vertical fields of view from the diagonal field of view.
  • this holographic skew mirror 1000 has a 60° diagonal field of view (measured outside the holographic recording medium 1020).
  • g. height g.dia * sin( atan ( g. aspect) );
  • a 60° diagonal field of view and a 16:9 aspect ratio correspond to a 53.4° horizontal field of view and a 31.6° vertical (Bragg degenerate) field of view (again, as measured outside the holographic recording medium).
  • the choice of orientation is arbitrary and could be reversed, i.e., the horizontal field of view could be 31.6° and the vertical field of view could be 53.4°.
  • the range of horizontal incident angles on the holographic gratings measured inside the medium is about 35° (e.g., 34.17°).
  • FIG. 12 illustrates a set of curves, produced by a different computer code, illustrating the holograms (holographic gratings) for each color band.
  • These curves represent the skew mirror internal angle wavelength bands 1201a-1201e for a holographic output coupler with a 53.4° horizontal field-of-view.
  • the left bands 1201a represent holograms that reflect red light.
  • the middle bands 1201c represent holograms that are used for all three color bands.
  • the middle- left bands 1201b represent holograms that are shared for the green and red band.
  • the middle- right bands 1201d represent holograms shared for the blue and green bands.
  • the right bands 1201e represent holograms that reflect blue light.
  • the code also produced a table of recording parameters, shown below in Table 1. The parameters were selected to support the 53.4° horizontal field-of-view for an output coupler at the red-green-blue (RGB) color bands centered at 620 nm, 520 nm, and 460 nm, respectively.
  • RGB red-green-blue
  • the 228 rows of Table 1 correspond to 228 exposures for programming the skew mirror using the out-of-plane writing geometry and system shown in FIGS. 7A-7D and 8A-8C.
  • the first column, Global Angle indicates the angle 0G of signal beam 731a (FIG. 7A) with respect to the XG axis inside the medium, which is set by rotating mirror 850a (FIG. 8A).
  • Rotating mirror 850b is set to deliver reference beam 73 lb at an angle of 180° - 0G inside the medium.
  • Column 3 Adjustment Angle is used to set the goniometers 870 to produce the indicated out-of-plane angular components for both beams 731 inside the medium.
  • a linear stage and the vertical stage 880 are set to center the recording medium 710 at the intersection of the recording beams 731. Then a shutter is opened to expose the recording medium 710 for the time indicated in column 2. All exposures in Table 1 are so recorded, and then the recording medium 710 is removed from the skew mirror recorder and post-cured with an incoherent UV LED source immediately after exposure.
  • beam angles are relative to the skew axis, which is oriented -30.25° relative to surface normal
  • FIG. 13 shows a slab waveguide 1350 with a holographic skew mirror output coupler 1300 (e.g., like the output coupler 1000 shown in FIG. 10) that was fabricated according to the parameters shown in Table 1.
  • the holographic skew output coupler 1300 had a 53.4° horizontal field-of-view and a 31.6° vertical (Bragg degenerate) field-of-view.
  • the skew mirror output coupler was programmed into the recording media according to the parameters of Table 1.
  • An optically flat waveguide package was fabricated using two 1" ⁇ 2" 500 ⁇ thick Eagle XG glass substrates 1354 with a 500 ⁇ recording layer 1310 of Akonia formulation AK291 photopolymer medium.
  • a TIGER prism skew recorder delivered collimated signal and reference beams approximately 40 mm in diameter at an optical power of approximately 2 mW/cm 2 for each beam. Each beam was apodized by a rectangular aperture measuring 25 ⁇ 21 mm (width by height).
  • the resulting waveguide 1350 and output coupler 1300 were tested to verify their properties.
  • a coupling prism was affixed to left (x ⁇ 0) end of the waveguide 1350 using an optical adhesive, and an image 1301 was projected into the waveguide through the coupling prism using an off-the-shelf picoprojector.
  • This image was guided within the recording layer via total internal reflection at the substrate boundaries to the gratings within the output coupler 1300. These gratings reflect the image out of the coupler 1300 (e.g., towards an eye) about an axis of reflection forming an angle of about -30.25 degrees with respect to the surface normal.
  • the output image 1303' was visually inspected to approximately confirm the 53.4° horizontal field- of-view (the picoprojector had only a -30° field of view, so it was manually rotated to examine both ends of the waveguide range).
  • FIG. 14 depicts a mosaic of nine plots of the MTF measured across the field of view, where the position of the plot within the figure corresponds to the position in the field of view (i.e., the top left plot corresponds to the top left of the field, the center corresponds to the center, etc.).
  • the horizontal axis of each plot in FIG. 14 is spatial frequency (cycles/degree) and the vertical axis is contrast ratio (CR).
  • the darker lines correspond to vertical MTF and lighter lines to horizontal MTF.
  • a large portion of the degradation is due to the projector lens, demonstrated by the low CR of the vertical MTF, which is not deleteriously effected by the output coupler.
  • FIG. 15 shows a head-mounted display 1500 with wide field of view skew mirror- based couplers for projecting images to an eye 1599 of a viewer.
  • An image source 1502 such as a microdisplay illuminated by one or more lasers or light-emitting diodes (LEDs), disposed in or along an eyewear temple 1504 emits image light 1501 at one or more colors (e.g., red, green, and blue light) in a direction substantially parallel to the eyewear temple 1504.
  • a skew input coupler 1510 which comprises a grating structure recorded in a grating medium sandwiched between a pair of transparent substrates 1512, couples the light into a slab waveguide 1520. (A prism or edge coupling can also be used to couple the light 1501 from the image source 1502 into the slab waveguide 1520.)
  • the slab waveguide 1520 guides this light 1511 to a skew output coupler 1530 like the one shown in FIG. 10.
  • This skew output coupler 1530 comprises another grating structure recorded in more grating medium sandwiched between the transparent substrates 1512.
  • the skew output coupler 1530 couples this light 1531 out towards to the viewer over a wide field of view, e.g., a field of view spanning about 50 degrees horizontally and about 30 degrees vertically as perceived by the viewer. This causes the viewer to perceive an image with a wide field of view.
  • the skew input coupler 1510 has a skew angle of about +30.25 degrees and the skew output coupler 1530 has a skew angle of about -30.25 degrees (e.g., like, the skew input/output coupler shown in FIG. 10).
  • inventive embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed.
  • inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein.
  • embodiments of designing and making the technology disclosed herein may be implemented using hardware, software or a combination thereof.
  • the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers.
  • the various methods or processes may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine.
  • inventive concepts may be embodied as a computer readable storage medium (or multiple computer readable storage media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory medium or tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above.
  • the computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above.
  • program or "software” or “code” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computer or other processor to implement various aspects of
  • one or more computer programs that when executed perform methods of the present invention need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present invention.
  • Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices.
  • program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types.
  • functionality of the program modules may be combined or distributed as desired in various embodiments.
  • data structures may be stored in computer-readable media in any suitable form.
  • data structures may be shown to have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a computer-readable medium that convey relationship between the fields.
  • any suitable mechanism may be used to establish a relationship between information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationship between data elements.
  • inventive concepts may be embodied as one or more methods, of which an example has been provided.
  • the acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.
  • a reference to "A and/or B", when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.
  • the phrase "at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements.
  • This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase "at least one" refers, whether related or unrelated to those elements specifically identified.
  • At least one of A and B can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

Abstract

Un miroir de déviation holographique présente un axe de réflexion, ou un axe de déviation, qui peut être incliné par rapport à sa normale à la surface. L'inclinaison de l'axe de déviation dans deux dimensions par rapport à la normale à la surface élargit le champ de vue possible du miroir de déviation holographique, par exemple, à 60 ou plus. On peut accéder à ces angles supplémentaires en utilisant une géométrie d'écriture hors plan au moyen de prismes de rotation à extension de l'angle rasant interne total (TIGER) appariés.
PCT/US2017/020087 2015-08-24 2017-03-01 Miroirs de déviation holographiques à grand champ de vue WO2017176389A1 (fr)

Priority Applications (11)

Application Number Priority Date Filing Date Title
US16/089,965 US20190179063A1 (en) 2015-08-24 2017-03-01 Wide field-of-view holographic skew mirrors
EP17779483.1A EP3420415A4 (fr) 2016-04-06 2017-03-01 Miroirs de déviation holographiques à grand champ de vue
JP2018550324A JP7001613B2 (ja) 2016-04-06 2017-03-01 広視野のホログラフィックスキューミラー
CN201780020765.3A CN109074026A (zh) 2016-04-06 2017-03-01 宽视场全息偏斜镜
KR1020187028192A KR102123174B1 (ko) 2016-04-06 2017-03-01 광시야 홀로그래픽 스큐 미러
TW106134401A TW201825932A (zh) 2016-10-13 2017-10-05 光瞳等化
TW106134790A TW201823773A (zh) 2016-10-13 2017-10-11 廣視角全像偏斜鏡
CN201780063137.3A CN110073252B (zh) 2016-10-12 2017-10-12 空间变化的倾斜镜
US16/339,297 US11774657B2 (en) 2016-10-12 2017-10-12 Spatially varying skew mirrors
PCT/US2017/056404 WO2018071714A1 (fr) 2016-10-12 2017-10-12 Miroirs obliques à variation spatiale
US18/453,243 US20230393320A1 (en) 2016-10-12 2023-08-21 Spatially Varying Skew Mirrors

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US201662318917P 2016-04-06 2016-04-06
US62/318,917 2016-04-06
US15/174,938 2016-06-06
US15/174,938 US10180520B2 (en) 2015-08-24 2016-06-06 Skew mirrors, methods of use, and methods of manufacture
USPCT/US2016/048499 2016-08-24
PCT/US2016/048499 WO2017035283A1 (fr) 2015-08-24 2016-08-24 Miroirs à effet d'obliquité, procédés d'utilisation, et procédés de fabrication
US201662407994P 2016-10-13 2016-10-13
US62/407,994 2016-10-13
US201662435676P 2016-12-16 2016-12-16
US62/435,676 2016-12-16

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US16/339,297 Continuation-In-Part US11774657B2 (en) 2016-10-12 2017-10-12 Spatially varying skew mirrors
PCT/US2017/056404 Continuation-In-Part WO2018071714A1 (fr) 2016-10-12 2017-10-12 Miroirs obliques à variation spatiale

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JP7001613B2 (ja) 2022-01-19
CN109074026A (zh) 2018-12-21
JP2019514049A (ja) 2019-05-30

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