# Analysis of Display Resolution of Volume Holographic Waveguide and High Resolution by Line-Symmetric Image Input

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## Abstract

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## 1. Introduction

## 2. Mathematical Model of Off-Bragg Diffraction in the Waveguide

**δK**) and the volume of the illuminated holographic areas [30,31]. Thus, the diffraction light intensity, (I

_{g}_{diff}) including the Bragg and off-Bragg diffractions, is given by

**r**is the position vector, Δn is the holographic strength, E

_{in}is the amplitude of the electric field of the readout light, and V is the illuminated volume of the hologram, which is determined by the position and size of the eye’s pupil and the diffraction light’s direction [29]. Notably, if the illuminated volume hologram is split into several areas, each diffracted electrical field should be summed up to account for the phase differences, as in the reported model [29]. The off-Bragg vector,

**δK**, is defined by

_{g}**K**is the grating vector, and

_{g}**k**,

_{s}**k**,

_{r}**k**, and

_{p}**k**are the wave vectors inside the waveguide for the signal, reference, readout, and diffracted (reproduced) light, respectively. For the Bragg-matching condition,

_{d}**k**=

_{d}**k**, and

_{s}**k**=

_{p}**k**; thus,

_{r}**δK**becomes zero. Considering the coordinate axis (Figure 2), the wave vector of the readout light,

_{g}**k**, is expressed as

_{p}_{Vcalc}and θ

_{Hcalc}are the vertical and horizontal ray angles of the input image outside the waveguide, respectively, and n

_{gl}is the refractive index of the waveguide.

**k**, of the diffracted light is given by

_{d}_{V}and θ

_{H}are the vertical and horizontal ray angles outside the waveguide, respectively. They also represent the viewing angles of the observed virtual image.

**K**, is written as

_{g}**δK**is transformed as follows:

_{g}**r**. In our calculation, the eye relief, E

_{r}(the distance from the output surface of the waveguide to the eye’s pupil along the x-axis), was set to 22 mm, and the eye position, E

_{p}(the distance from the input edge surface of the waveguide to the eye’s pupil along the z-axis), was 25 mm. The diameter of the eye’s pupil generally varied according to the brightness of the surrounding environment [36]. An intermediate size of 3 mm was used. The light-source wavelength was assumed to be a single wavelength of 555 nm. The refractive index of the waveguide was 2.3, characteristic of an ideal photorefractive material.

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**HMD optical system with volume holographic waveguide and conceptual diagram of degraded image resolution by off-Bragg diffraction.

**Figure 2.**(

**a**) Schematic of analytical model of the waveguide with off-Bragg diffraction; (

**b**) Geometric definition of ray angles of readout light (θ

_{Hcalc}and θ

_{Vcalc}).

**Figure 3.**Calculation results of display resolution by conventional volume holographic waveguide with one-sided image input.

**Figure 4.**Calculation results of ray-angle dependence of display resolution (red circle dots) and luminance distribution according to each ray angle (background shading) with conventional one-sided image input.

**Figure 5.**Schematic of (

**a**) line-symmetric image input; (

**b**) light-propagation pass and output-light intensity at each position of the waveguide.

**Figure 7.**Waveguide thickness and FOV-dependence of display resolution with line-symmetric image input.

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**MDPI and ACS Style**

Nakamura, T.; Fujimura, R.
Analysis of Display Resolution of Volume Holographic Waveguide and High Resolution by Line-Symmetric Image Input. *Photonics* **2022**, *9*, 649.
https://doi.org/10.3390/photonics9090649

**AMA Style**

Nakamura T, Fujimura R.
Analysis of Display Resolution of Volume Holographic Waveguide and High Resolution by Line-Symmetric Image Input. *Photonics*. 2022; 9(9):649.
https://doi.org/10.3390/photonics9090649

**Chicago/Turabian Style**

Nakamura, Toshiteru, and Ryushi Fujimura.
2022. "Analysis of Display Resolution of Volume Holographic Waveguide and High Resolution by Line-Symmetric Image Input" *Photonics* 9, no. 9: 649.
https://doi.org/10.3390/photonics9090649