## 1 Introduction  
Augmented reality (AR) displays and augmented reality glasses based on them are currently being developed both by a number of well-known companies (Google, Apple, Microsoft, Meta, Zeiss) and numerous startups (Waveoptics, Dispelix, Lumus, LetinAR, TruLife, etc.). The key component of such devices is a combiner--an optical device that provides the user with a combination of light streams of a virtual image and the environment. To date, a fairly large number of designs of displays have been proposed using different physical principles and manufacturing technologies for optical combiners. However, designs with free-form combiners, as well as waveguide combiners with micromirrors, microprisms, diffractive or holographic optical elements (DOEs, HOEs) have become the most common [1; 2; 3; 4].  
Despite this, none of the prototypes have been converted into mass production to date; however, individual models are available to a limited circle of test engineers or are made by order of the military. At the same time, a discussion continues about the tasks solved by such devices, about the technical characteristics and aesthetic criteria that they must satisfy in order to be attractive to a wide range of consumers [3; 5]. In particular, it is proposed to create AR glasses with curved waveguide combiners instead of the traditionally used flat ones. It is assumed that this approach will make it possible to create a device that can be worn for a long time with the proper level of comfort, give the glasses a more familiar form factor of ordinary glasses, and in the future provide the vision correction function for users with imperfect vision (due to combining a spectacle lens and an image combiner) [6; 7; 8; 9].  
In the present paper, we propose a method for calculating an image combiner based on a curved concentric cylindrical waveguide and holographic optical elements, and also describe and experimentally implement an optical system of such a combiner. The proposed solution demonstrates the possibility of creating AR devices with curved waveguide combiners and can serve as a basis for further work on the design and implementation of such devices.  
The paper is structured as follows.  
Section 2 describes the propagation of rays in a curved concentric cylindrical waveguide and formulates the principles for constructing the optical system of a combiner for aberration-free propagation of rays inside it. Coupling of radiation into/out of a curved waveguide in cases of a point or extended radiation source are considered in detail. Formulas are derived that describe the laws of variation of periods of in-coupling and out-coupling DOEs to obtain a virtual image without aberrations (in case of a point source) or with minimized aberrations (in case of an extended source). In Section 3, we calculate the recording conditions and describe the experimental scheme for recording in-coupling and out-coupling HOEs with variable grating periods over the aperture to implement a waveguide combiner for a virtual image. Moreover, a method for manufacturing plastic concentric cylindrical waveguides with a radius of 150 mm, used in the present paper, is described. Section 4 presents and discusses the experimental results of testing the obtained waveguide combiner. Conclusions of the paper are given in Section 5.