# Development of a Holographic Waveguide with Thermal Compensation for Augmented Reality Devices
## 2 Methods
This study can be useful for augmented reality systems, in which clear positioning of the output information relative to real-world objects should be provided, for example, in the field of medicine for surgical operations, for displaying contextual prompts during assembly and repair of complex products, for displaying navigation labels and arrows. As a result of a change in the wavelength of the source by an amount of even 10 nm, the angle of radiation propagation in the waveguide during diffraction at DOE2 (with a period different from DOE1) changes, and therefore the angles of radiation diffraction will change when output from the waveguide. Having solved the system of equations and substituting into it the calculated parameters of the waveguide with a displaced \(\lambda\) = 0.66, we get an angle \(\gamma\) = \(1^{\circ}42^{\prime}\) with a normal to the surface of the substrate (Figure 5a). This is due to the fact that the periods DOE1 and DOE2, in Figure 1, are different, and the angular dispersion (change in the diffraction angle) of the first element cannot be compensated by the similar dispersion of the second. Based on the analysis of literary and patent sources, it has been established that this problem can be solved by using hologram compensators, but they have significant weight and size parameters [25]. Another possibility to compensate for the change in the direction of the line of sight and the displacement of the output image when the temperature changes is the use of an alternative structure of the waveguide substrate gratings (Figure 6). \[L\ =\ 2d\cdot tg(\alpha_{TIR}), \tag{2}\]0 (**a**) The angular displacement of the beams in the absence of thermal compensation. (**b**) The displacement of the beams when the wavelength changes by \(\pm 20\) nm in the scheme with thermal compensation. \[L\ =\ 2d\cdot tg(\alpha_{TIR}), \tag{2}\]1 Propagation of radiation inside a waveguide with thermal compensation. In this case, thermal compensation of the holographic waveguide is achieved due to the equality of periods and a change in the orientation of the gratings. DOE1 consists of two diffraction gratings superimposed on each other at angles of 60 and 120 degrees. The left DOE3 and right DOE2 parts of relay DOE are located, respectively, at the conjugate angles of 120 and 60 degrees DOE1. When radiation hits the input area of the DOE1 waveguide, the radiation diffracts on the superimposed structure of DOE1 (superimposed relief-phase gratings) and is divided into 2 parts, one of which spreads along the left side of DOE3, and the other along the right--DOE2. This implementation is widely used in augmented reality devices, because due to the separation of radiation at the input to the waveguide, it allows you to almost double the size of the working angular field of the device compared, for example, with the structure shown in \[L\ =\ 2d\cdot tg(\alpha_{TIR}), \tag{2}\]2  
The angles of inclination of the gratings in DOE 1 and DOE 2 (DOE3) are equal to 60 and 120 (or minus 60) degrees, because in this case, when the radiation is diffracted, a kind of \"equilateral triangle\" is obtained, in which the step of the radiation inside the substrate does not change when diffracted on the intermediate DOE 2 (DOE3). Due to this fact, the periods of the structure are the same on all DOE. If we consider the situation proposed in Figure 1, then due to the fact that DOE2 (relay grating) is located at an angle of 45 degrees, the step of the sequence changes by a factor of \(\surd 2\), therefore, in order to compensate for it, it is necessary to change the period of DOE2. In all cases, except when the angles of the input and relay gratings are 60 and 120 degrees, the periods of the structures will be different. From the point of view of manufacturing the substrate, it is most rational to use the option when all periods are equal, since there is no need to rebuild the stand and the recording scheme.