## 3 Optical Fabrication of the Designed System
The equivalent angle of the reference beam in the air (\(\beta_{a}\)) was found using Formula (19) derived from [PERSON]'s relation for the case of light passing through the wedge, for the propagation angle of the reference beam in the medium (\(\beta_{f}\)):  
\[\beta_{a}=\arcsin\left(n_{p}\sin\left(\gamma_{p}-\arcsin\left(\frac{n_{f}\sin \left(\beta_{f}\right)}{n_{p}}\right)\right)\right), \tag{19}\]  
where \(n_{p}\)--the prism refractive index, \(\gamma_{p}\)--the angle at the base of the prism. Then, the value \(y_{d}\)--the projection onto the \(OY\) axis of the distance from the edge of the HOE to the point of intersection of the ray with the input face of the prism--was calculated according to the Formula (20), for each ray in a geometric approximation:  
\[y_{d}(L)=L+h_{p}\text{tg}\big{(}\alpha_{p}\big{)}, \tag{20}\]  
where \(h_{p}\)--the prism height. Figure 11: A scheme representing the path of rays in a prism (**a**) and symbols for the key values in the calculation (**b**). The distance (\(S\)) from the prism along the optical axis of the object beam to the point of intersection of each ray with the optical axis, i.e., the focal length for each ray in the beam, was calculated using Formula (21):  
\[S(L)=\frac{-(y_{d}(L)-y_{d}(L_{c}))\sin(90-\ \alpha(L))}{\sin(|\alpha(L)-\ \alpha(L_{c})|)}, \tag{21}\]  
where \(L_{c}\)--the coordinate of the center of the HOE. The arithmetic mean value of the array of the values \(S\) was chosen as the location of the lens focus point. Then, inverse modeling was carried out: according to the algorithm described above, the period of the HOE formed in the case of using the common focus of all rays in the beam was calculated. The deviation of the period of the HOE from the required dependence, obtained at the chosen position of the lens, was analyzed. By selecting the value of the angle \(\beta_{f}\), the deviation was minimized. The HOE was recorded using the Bayfol HX holographic film photopolymer [13] consisting of a photosensitive layer with a thickness of \(\approx\)5 \(\upmu\)m, deposited on a flexible polyamide (PA) substrate with a thickness of 60 \(\upmu\)m. This photopolymer is sensitive in the spectral region from 430 to 670 nm. Due to its high adhesion, it can be laminated to glass or plastic surfaces. Thus, during holographic recording, the film was laminated onto the prism and then transferred onto the plastic waveguide. The HOEs were recorded in a two-ray interferometer. The scheme of recording is shown in Figure 12. A single-frequency TEM\({}^{00}\) DPSS laser Cobolt Bolero with vertical polarization and a wavelength of 639.6 nm was used as a radiation source. In the interferometer, the initial laser beam was divided into two rays with a ratio of 50:50 by using a beam-splitting cube. After the beam-splitting cube, there were electromechanical shutters that ensured the simultaneous opening of the rays for a given time interval with an accuracy of 0.1 s. Then each of the rays passed through the telescope with a magnification of \(\approx\)100\(\times\) to increase the aperture of the recording beams. A central part, 30 mm in diameter, with uniform intensity, was cut out from each beam. The beams were converged at a given angle using mirrors mounted on electromechanical turntables (Newport URS100 BCC). A glass prism was installed in the region of beam convergence, which ensured the recording of TIR holograms in a photopolymer film laminated on it. A diverging cylindrical lens was installed in the object beam in such a way that its focus was located at the calculated distance \(S\) from the prism. The radiation power density in each channel in the recording region was \(\approx\) 0.5 mW/cm\({}^{2}\). The exposure time varied from 10 to 12 s, which enabled achieving a diffraction efficiency of 10-15% when readout by a non-monochromaic projector was used in the present work. Figure 12: The scheme of recording of the in-coupling and out-coupling HOEs. The waveguides were fabricated using a sheet of PMMA with a thickness of 1 mm.