## 1 Introduction  
Rotary encoders are widely used to detect the rotation angle of motors and gear shafts. State-of-the-art encoders mostly operate on potentiometric, capacitive, magnetic, or optical principles [1]. Magnetic and optical encoders are most common in use with an annual growth rate of 11%, whereby the optical technology dominates the global industrial encoder market. The market of encoders is segmented into automotive (35%), electronics (28%), machines (21%), and others (16%) [2]. It is expected that, by 2021, the global market size of the encoders will reach $760 million [3]. The common approach of magnetic encoders is to use a magnetic rotor and to detect the position of the rotor with a hall sensor. In contrast, the common structure of optical encoders is to use a chrome structured encoder disc made of glass. The position of the rotor is then detected with a light barrier. Both operating principles are shown in Figure 1. The advantages of magnetic encoders are their high robustness and low fabrication costs, whereas optical encoders show high accuracy and high dynamics. A distinction is made between incremental and absolute encoders. While absolute encoders deliver the angular position immediately after switching on the encoder, incremental encoders firstly need a reference run. Otherwise only relative position measurement is possible. This article deals solely with absolute optical encoders. As a result of the extensive topic which comprises optical design, injection molding, ultra-precision machining, application-specific integrated circuit (ASIC) design and micro assembly, not all details can be presented in this article. Absolute encoder discs contain the angle information typically as a Gray code pattern, which is read out in accordance with a transmission principle. Every position of an absolute encoder is unique. Figure 2a shows the Gray code pattern for an encoder disc with \(n=6\) tracks (6-bit resolution) and its optical path. This results in \(2^{n}=64\) positions per revolution of the encoder disc. This means that, for a higher resolution, there are more tracks necessary. The tracks consist of opaque and transparent parts. Each track is read out optically with a light barrier as shown in Figure 2b. This means that, for a resolution of \(n\) bits, there are \(n\) tracks with \(n\) light barriers necessary. As a result, the dimensions of optical encoders increase with their resolution, and the effort for assembling increases due to elaborate alignment processes between the optical device and the encoder disc [4]. However, the smaller the encoder is, the lower its resolution and the higher its costs will be, because, on small discs, there is less space for the Gray code patterns and the associated light barriers; additionally, the expense for the assembly increases due to the complicated fine mechanical-optical system [5; 6]. For example, an optical high-end encoder with a diameter of 13 mm delivers a resolution of only 256 increments, while the costs are on the order of several hundreds of euros [7; 8]. Also, the accuracy decreases with smaller diameters because the influence of the angular error due to eccentricity between encoder disc and encoder shaft increases for smaller diameters of the encoder disc [9]. Table 1  
Figure 1: (**a**) Operating principle of a magnetic encoder with a magnetic rotor and hall sensor; (**b**) operating principle of an optical encoder with a light source, encoder disc, aperture, and detector. Figure 2: (**a**) Encoder disc of an absolute optical encoder with Gray code patterns of opaque and transparent parts; (**b**) cross-section of the optical path. shows two examples of high-end state-of-the-art-encoders with comparatively very small dimensions. Especially for small devices such as finger prostheses, miniaturized drives, or miniaturized robots, the need for small encoders with high resolution is obvious.