Shearing Bragg Gratings for Slim Mixed Reality

Adrian Travis*, James Clegg**, Jinsoo Jeong***, Andreas Georgiou** *Clare College, Cambridge CB2 1TL, UK

** Microsoft Research Cambridge, 21 Station Road, Cambridge CB1 2FB, UK *** School of Electrical and Computer Engineering, Seoul National University, Gwanak-Gu Gwanakro 1,

Seoul 08826, South Korea

Abstract We suggest a mixed reality display in which the eye-box follows the eye’s pupil by shearing of the holographic combiner. Tests on Bragg gratings show a switching extinction ratio of 35:1 for an extrapolated shear of several microns and switching energy of milliJoules or less.

Author Keywords Gratings; virtual reality; mixed reality; holograms; wedge guides.

1. Introduction Pioneers of virtual reality and their successors emphasize how helpful it is to have a wide field of view such as can be achieved by reflecting a display off a large curved optic [1,2]. Designers, however, insist on a device that has the compact elegance of a pair of spectacles [3]: “if the user will not wear the product in the first place, nothing else matters”. It is difficult to get such elegance and also have a wide field of view. This is because the pupil of a virtual image, i.e. the area over which the virtual image is visible, needs to be big, typically with a diameter of 15 to 20 millimeters if rotations of the orbit (i.e. eye-ball) and ill-fitting headgear are to be tolerated [4]. Even with no constraint on size, it would be hard to handle the enormous etendue of such an image pupil with the >120° field of view and high resolution that can be seen by a single human eye.

Instead, otherwise small pupils have been expanded by tiling replicates of the virtual image [5-8]. This allows the etendue of the virtual image at launch to be low enough that it can be transported via a slim light-guide. However, pupil expansion works only if replicates of the virtual image match with great precision. In practice, this means that the virtual image is focused at infinity and the tiling surface flat. It follows that images visible to the wearer’s peripheral vision cannot be displayed while for mixed reality, the virtual image cannot be made to overlay objects at various distances near the wearer.

It is possible nowadays to track the position of the pupil of an eye so that at least in principle, a virtual image with a very small pupil might be steered so that image rays always enter the pupil of the eye. This would not only eliminate the need for pupil expansion but also permit a system that need display full resolution only to the fovea, with progressively poorer focus being imperceptible at increasing angles from the fovea [9].

Pupil steering is also a strategy for the display of three dimensional images [10] and many solutions have been proposed [11]. But for mixed reality, the pupil-steerer must be transparent so that virtual images can be superposed on the outside world. Ideally, transparency should also allow others to see the wearer’s eyes (so that the device can be used for teleconferencing) and should leave intact light from bright sources such as the sun so that the user is not dazzled. The angle of deflection from the pupil steerer should be variable by

perhaps 45° and it should use very little power.

Liquid crystals use minimal power and liquid crystal gratings with variable pitch and high contrast have been demonstrated [12]. But any grating risks diffracting bright sources into the eye unless its pitch is high enough to avoid this. Such a high pitch is fundamental to the architecture of avionic head up displays and pupil expansion and both technologies do indeed have excellent transparency. A good aim, therefore, would be to make small variations of pitch about the large value desirable for transparency, but this seems beyond the present capabilities of addressable liquid crystal devices [13]. Although high pitch gratings can be recorded in liquid crystal/monomer mixtures [14,15], the pitch is fixed. Even so, the component of spatial frequency perpendicular to the surface of these devices could in principle be altered by modulation of the liquid crystal if the device were thick.

The combiner in an avionics display is a Bragg grating and since the transparency of these is proven, it would be excellent if they could be made variable. Stretchable versions of such gratings have been used to tune laser wavelengths [16] but stretch distances would be too long on a surface as wide as an eye-piece.

Recently it was shown [17] that if the pupil is small, the classic arrangement of a projector reflected off a holographic combiner might be folded into a guide that can be curved round the head of the viewer, as shown in figures 1 and 2. It was proposed that the pupil be steered by shearing the holographic combiner so as to switch between multiple holograms recorded within the holographic film. Recording many holograms in a film is common-place but shearing is a new concept: this paper reports tests showing a contrast ratio of 35:1 and explains why higher contrast ratios at low switching energies are expected.

Figure 1. Slim mixed reality looks plausible if we can steer the pupil of the virtual image by shearing a Bragg grating.

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Figure 2. Trace of rays from the eye back to the input that predicts the predistortion needed in the projector.

2. Theory We plan to store many holograms in a film, each producing an eye-box at a unique position and we will make only one of the holograms active at any time. We will make all the other holograms inactive by ensuring that they do not meet the Bragg condition for rays of the virtual image that, due to the small etendue, are very nearly collimated. Although this change in Bragg condition could perhaps be effected in a liquid crystal/monomer mixture, it proves easier to do it by shearing holographic film, i.e. by moving the front surface of the film relative to the rear.

Figure 3. A grating in its relaxed state diffracts a ray if the Bragg condition is met

Figure 4. If we shear the grating of Figure 3 so that the Bragg condition is not met, there will be no diffraction

The left-hand side of figure 3 depicts a Bragg grating that diffracts the input because partial reflections off each layer of the grating superpose constructively. In the right-hand side of figure 3, the volume grating is represented by a vector whose length is proportional to the spatial frequency of the grating and whose direction is perpendicular to the planes of the grating. If

is the vector of incident light (with length given by ) then

light is efficiently diffracted in the direction if . This is known as the Bragg condition. If the Bragg condition is not met then the incident light is unaffected by the grating. Now, let lie in the plane of the film and be perpendicular to the plane of the film. Figure 4 shows that when the film is sheared along then ( ) must alter because the planes of the Bragg grating must undergo collective rotation and there can be no change to

because the film is not stretched in any way. If the film is sheared along , then by geometry of Figures 3 and 4 we see that the change in is given by

(1)

where is the distance moved by the front of the film versus the rear of the film when it undergoes shear and is the film thickness. So, for a fixed incident on a grating with a that satisfies the Bragg condition, then as the grating shears the Bragg condition is broken and light is no longer diffracted; it is as if the grating switches off. Of course, shear can also have the opposite effect, of causing a grating to diffract that did not diffract when relaxed.

Switching energy and extinction ratio

The classic paper on volume holograms by Kogelnik [18] gives diffraction efficiency in transmission as:

(2)

The coefficient (all variables as defined by Kogelnik) and in a well-made hologram, the index modulation is such that . Here we mean well-made in the sense that

when the Bragg condition is met (i.e. when ). is defined by Kogelnik as

(3)

Now we turn our attention to investigating how changes when we shear the hologram. Beginning when , we can write

(4)

Neglecting the higher-order terms, we just need to calculate .

This is given by

(5)

Now, we have (from equation 1) and also because

and is a constant. Therefore does not depend on , i.e.

as the hologram is sheared, the value of does not depend on the hologram thickness.

If this prediction seems surprising, consider that if the thickness of a slab doubles, its Q factor also doubles so the shear angle needed to reach a particular efficiency halves, thereby cancelling out the doubling of thickness.

The effect of shear on a Bragg grating derived from the equations of Kogelnik is shown in figure 5. This predicts that the diffracted power will decrease by a factor of 85 if the front surface moves 2.7 microns relative to the rear surface.

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Figure 5. Modeled diffraction efficiency vs. displacement of the front versus rear of a film such as that in figure 4.

3. Experiment We holographically recorded a transmission Bragg grating in a 40 mm by 40 mm sample of 70 µm thick photopolymer. Wavelength was 532 nm and when relaxed, the grating diffracted at an input angle of 10°±0.5° to the surface normal with output at -39°±0.5° to the surface normal. The grating was glued between two glass plates and placed in a rig containing a piezo electric device as shown in Figure 6.

Figure 6. Shearing rig. This rig is used to apply shear to the photopolymer film.

Figure 7. The total diffracted power as a function of input angle for three different applied shears: 0, 50 and 75 µm.

The polymer was peeled away from the glass slide used for the recording step and optical adhesive was used to reattach the polymer to this slide. Optical adhesive was then spread onto the top face of the photopolymer and the upper glass plate was placed on top. This gluing process was carried out in a custom-made jig that allowed the offset between the glass plates to be controlled. Shear was applied using a piezo-electric and the results are shown in Figure 7.

Extinction ratio is 35:1 for an applied shear of 75 microns, a much larger distance than predicted by figure 5. This is because the active layer of the photopolymer is sandwiched between layers of glue and protective plastic that are much thicker, perhaps a few hundred microns. We therefore measured the angle of the Bragg planes with and without an applied shear of 50 µm by illuminating the film at a range of angles and seeing which led to diffraction (measurements in Table 1). Such a small change in the difference between two angles does not give great accuracy but we deduced a shear of 2.9 µm, consistent with Kogelnik theory.

Table 1. Input and diffracted ray angles versus the normal of the film with and without shear

Applied shear

Input angle in film at Bragg condition

Output angle in film at Bragg condition

0 µm 4.7° -28°

50 µm 2.5° -31°

4. Discussion It is remarkably fortunate that many of the materials used to record holograms such as dichromated gelatin and photopolymer are very flexible (G=200 kPa), both three times more flexible than rubber (G=600 kPa). The force, F, required to shear a film is therefore tolerable, equal to F=G×A× where area A might be 50 mm by 30 mm for an eyepiece and angle =2.7/70 radians in order to switch between two holograms, i.e. 12 N. Switching energy is therefore expected to be 12×2.7= 31 µJ but this figure will increase by a factor equal to the square of the number of holograms recorded. Both the forces and displacements required are within the capabilities of piezoelectric transducers but lower forces would permit a less stiff frame and perhaps lower drive voltages.

Switching force scales with the inverse of film thickness so could easily be reduced by using thicker film and >1 mm thick films have been demonstrated [19]. It may also be possible to reduce material stiffness, for example ultra-violet holograms can be recorded in a mixture of polysilicone and benzophenone [20] and the stiffness of polysilicone can reduce to a few kiloPascals [21].

5. Conclusions The Bragg gratings in holographic combiners are a proven way of superposing virtual images on images of the real world with excellent transparency. We have shown that the gratings can be switched on and off by shearing the film with little motion and little use of energy. It is known that many Bragg gratings can be holographically recorded in a single film while the pupil of a wearer’s eye can move to only a limited range of independent positions, perhaps thirty or forty. We therefore hope to use this effect to steer the pupils of a pair of virtual images into the pupils of the wearer’s eyes.

The potential advantages of pupil-steering are manifold. Very little light is needed from the projector if all is to enter the wearer’s eyes so we can hope for small projectors and batteries. Etendue is low so

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the optics can be folded into a light-guide. Absent the rigors of pupil expansion, thickness tolerance is sufficiently lax for the guide to be plastic and curve round the head, giving large fields of view. The projectors could go near the ears, with variable lenses giving variable image depth.

6. Acknowledgements The authors would like to thank Tripletake Holographics for performing preliminary experiments in dichromated gelatin on our behalf.

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