## 2 A New Approach for Optical Encoders  
### Main Principle of the Encoder  
The physical basis of the optical encoder was the diffraction of light using a reflective phase grating. The approach was to use a reflective phase grating as an encoder disc for an optical encoder. Figure 3 shows the mechanism of diffraction schematically. After reflection of the light at the phase grating, destructive and constructive interference occurs because of the path difference \(\Delta\) of the light, which is caused by the grating. If \(\Delta\) is equal to \(\lambda\), constructive interference occurs and, if \(\Delta\) is equal to 0.5\(\lambda\), destructive interference occurs. The relationship between the grating constant and the angle of diffraction is described by the so-called grating equation as follows:  
\[-sin\ \alpha_{e}-sin\ \alpha_{m}=\ \frac{m\lambda}{g},\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature/Series** & **CUI MAS10** & **CUI MES6** \\ \hline Method & Absolute & Incremental \\ Resolution & 256 positions & 500 positions \\ Speed & 6000 rpm & 6000 rpm \\ Interface & Digital & Digital \\ Temperature & 0... +60 \({}^{\circ}\)C & 0... +60 \({}^{\circ}\)C \\ Size & \(\O\) 13 mm \(\times\) 16 mm & \(\O\) 8 mm \(\times\) 11 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examples of high-end state-of-the-art encoders. where \(\alpha_{e}\) is the angle of the incident light and \(\alpha_{m}\) is the angle of the diffracted light. With a given wavelength \(\lambda\) and grating constant \(g\), the angle of the diffracted light can be calculated for each diffraction order \(m\) (\(m=0\), \(\pm 1\), \(\pm 2\),... ) using this equation. The concept for the optical encoder was to use a light source on top of a photo detector that transmits light through a lens to the encoder disc. The disc contains micro structures forming the grating. The light is then diffracted at the encoder disc and reaches the photo detector. While laminar gratings result in two beams of equal intensity with the zero order of the beam being reflected into the light source [10; 11; 12; 13; 14; 15], a blazed grating diffracts two beams of different intensities. This is due to the fact, that the zero order is diffracted into the +1 st order beam. When the disc rotates, the two diffracted light spots also rotate on the photo detector. In this way, it is possible to detect the rotational movement of the encoder disc. This circulation was detected by a ring of photodiodes on an opto-ASIC. While the beams were of different intensity, an unambiguous assignment of the disc angle over 360\({}^{\circ}\) was accomplished. Figure 4 shows the functional principle of the optical encoder and the underlying concept for the arrangement of the individual components [16; 17]. To detect the rotational angle of the diffracted beams on the photodiode ring, different concepts for the photodiodes were investigated and designed. The first concept consists of a segmented arrangement of photodiodes as shown in Figure 5a. This approach leads to a simple focusing lens to form circular spots, but requires 1024 photodiodes on the opto-ASIC for an encoder resolution of 10 bits. Thus, the signal processing unit had to be designed to read out 1024 photodiodes. The second concept consists of a Gray code arrangement of the photodiodes as shown in Figure 5b. This approach requires a number of tracks of photodiodes of significantly bigger size, but a more complex lens, as the diffracted beam has to be additionally expanded in the radial direction to illuminate all photodiode tracks. For 10-bit resolution, 10 tracks of photodiodes with the most significant bit (MSB) on the inner track and the least significant bit (LSB) on the outer track are required. Figure 4: Functional principle of the optical encoder. Figure 3: Diffraction of light by a reflective phase grating. By using photodiodes for the dark and bright parts of the Gray code, differential signals can be obtained leading to a higher signal-to-noise ratio (SNR) and offset compensation.