## 4 Experimental Results and Discussion  
After the recording, the HOEs were certified, i.e., underwent the measurement of the surface period according to the method proposed in [14]. The method is based on measuring the angle of incidence of the readout beam with respect to the normal to the grating surface, at which the diffracted beam returns back to the light source. In this case, the value of the surface period and the angle of incidence of the readout beam are related as follows:  
\[d=\frac{\lambda}{2\sin\frac{\theta}{2}}, \tag{22}\]  
where \(d\)--the surface period of the grating; \(\lambda\)--the readout wavelength (outside the medium); \(\theta\)--the angle of incidence of the readout beam with respect to the normal to the grating surface. A CrystalLaser DL445-025 laser with a wavelength of 445 nm was used as a readout radiation source; a rotation sensor (LIR-510M.01, with the declared accuracy of \(<\)0.025\({}^{\circ}\)) was used to control the rotation angle. The estimated accuracy of measuring the surface period was \(\pm\) 1 nm. An HOE was certified at 29 points along the direction of the grating vector with a step of 1 mm between measurements. Then, the period values obtained from experimental measurements of the diffraction angles (Figure 14a), were approximated by a fourth-order polynomial in the MatLAB software, which made it possible to reject erroneous measurements and improve the accuracy of the measured dependence. The obtained function was subtracted from the required law of variation of the period (Figure 14b). From the above results, it follows that in the experiment it was possible to obtain an HOE with a maximum deviation of the surface period from the required values in the range of \(\pm\) 0.8 nm. Thus, it can be seen that in the experimentally recorded HOEs, the law of variation of the  
Figure 13: A mold for bending the waveguides and a workpiece of such a waveguide inside it. period is close to the calculated one. The largest discrepancy between the calculated and experimentally implemented periods is observed for the end parts of the HOEs. Then, the difference between the diffraction angles for the measured and required distributions of the periods of the HOEs over the aperture was found using Formula (18). The estimate showed that the detected error in the period leads to a deviation in the propagation angles of the out-coupled rays \(<\) 0.5 arcmin, which is an acceptable result for observing systems. The recorded in-coupling and out-coupling HOEs were laminated onto prepared curved waveguides. A prototype of a fabricated waveguide is shown in Figure 15. We made such waveguide prototypes for red, green and blue colors of a virtual image. Figure 14: Comparison of the required and implemented dependences of the surface period of an HOE for red color waveguide on the coordinate \(L\). The required dependence of the period and the results of the experimental measurement of the period of the HOE on the coordinate (**a**), the difference between the required dependence of the period and the result of the approximation of the experimental measurements of the period of the HOE (**b**). Figure 15: A prototype of a curved waveguide with a curvature radius of 150 mm based on PMMA with a thickness of 1 mm. The in-coupling grating is on the right, and the out-coupling grating is on the left. Test images (templates) were generated by the projector, and at the output of the optical system the horizontal FOV of the transmitted images [15] were measured, and also their quality was visually (with the eye and with the help of the camera) assessed--namely, intensity uniformity over the FOV, sharpness, scattering. Examples of transferred images are shown in Figures 16 and 17. Different monochrome templates were used to evaluate the quality of in-coupling-propagation-out-coupling of images in the optical system under consideration. RGB (white color) image was not used to test the waveguides, since the assembly of the waveguide stack for transmitting white color image was not the task of this work.