Optical Encoder with Pitch-Modulated Photodiode Array

Because of its simple optical configuration, the Moiré encoder shown in Figure 4.7, in which two gratings are superimposed with an air gap, is still important in many practical applications. Recently, for this simple Moiré encoder it was proposed that the pitch-modulated gratings be used to suppress the harmonic noise [Ohashi et al., 1999]. The output of the encoder measured as a function of the lateral displacement includes some higher order distortions in addition to the sinusoidal signal. The harmonic noise is attributed to the harmonic components of the grating transmittance. Therefore, these harmonic noises cause a considerable measurement error when we obtain a displacement smaller than the pitch of the grating by the interpolation, assuming that the signal is sinusoidal.

It has been proposed that an index grating with a modulated pitch can be used for decreasing the higher order distortions in the output of the encoder. In the demonstration, the third- and fifth-order distortions of the displacement signal were decreased by a factor of more than 10.

A schematic diagram of the proposed index grating is shown in Figure 4.20. The encoder consists of a periodic grating with a constant pitch, p, as the main scale and a pitch-modulated grating with an FIGURE 4.18 (a) Displacement x, and (b) y measured as a function of stage position.

FIGURE 4.19 Angular deviation as a function of position.

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averaged pitch p as the index scale; these are fixed parallel to the main scale. The schematic diagram of the pitch-modulated grating, which actually employs a unit structure of photodiodes with different phases, is shown in Figure 4.20. This unit structure is repeated by the phase differences of p/6, p/10, and p/15 with respect to the averaged pitch p. The phase difference between the set of the grating lines (1) and that of (2) is designed to be p + p/6 to compensate the third-order harmonics by inverting their phases. Similarly, the sets of grating lines of (3) and (4) are also arranged to have a phase difference of p + p/6. Furthermore, the phase difference between the combination of ([1] + [2]) and that of ([3] + [4]) is set to be 2p + p/10, thereby eliminating their fifth harmonics. Therefore the pitch-modulated grating shown in Figure 4.20, which is used as an index grating, suppresses both the third and fifth harmonics noises in the encoder signals as a function of displacement.

The pitch-periodic and pitch-modulated photodiode arrays with multichannels were fabricated for the encoder experiment by using integrated circuit process technology. The multichannels were used for obtaining four photocurrent signals of the phase-shifted photodiodes independently. Figure 4.21 shows a photomicrograph of the pitch-modulated photodiode array with the four electrodes for respective FIGURE 4.20 Schematic diagram of a pitch-modulated grating.

FIGURE 4.21 Photomicrograph of the pitch-modulated photodiode array.

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channels. The substrate was a 300-µm-thick, n-type (100) silicon wafer. The p–n junction of the photo-diodes was formed by doping boron ions. Then, aluminum metal film was patterned and etched for electrodes. The electrodes are fabricated as three-dimensional wiring. The width of the photodiodes in the index grating is 40 µm, with an averaged pitch of 80 µm.

The air gap z between the scale and index gratings is equal to 2.8 mm, and the typical light intensities of the two types obtained from the encoder experiment are shown in Figure 4.22. The intensity curve for the pitch-periodic type was the quasi-sinusoidal containing some higher harmonics, while the inten-sity curve for the pitch-modulated type was approximated by the sinusoidal. The Fourier spectra of the intensity from the encoder experiment are shown in Figure 4.23. The third- and fifth-order distortions for the pitch-modulated type were much smaller than those for the pitch-periodic type. Moreover, for the pitch-periodic type, the change of the air gap had a large effect on the third- and fifth-order distortions.

Thus, high resolution can be obtained in the interpolation with the proposed encoder system.

The interpolation error was estimated as follows. The photocurrents can be transformed into voltages, which are approximated by sine and cosine curves. Then, the phase angle, i.e., the relative position between the scales, is directly calculated from these two voltages by applying the arc tangent function.

The maximum third- and fifth-order distortions in the experiment using pitch-periodic type grating are 4.35 and 1.45%, respectively. On the other hand, when we use the pitch-modulated type, the maximum third- and fifth-order distortions are 0.44 and 0.17%, respectively, in the experiment. Then the interpolation errors are calculated at 0.11 and 0.043 µm. Moreover, the third- and fifth-order distortions are almost independent of the air gap. Thus the pitch-modulated photodiode array can reduce the interpolation errors by a factor of more than ten.

The optical encoder with the slit-like pitch-modulated photodiode array as the index scale has been developed to integrate the gratings and the detectors. The photodiode array was specially designed to decrease higher harmonics distortions of the displacement signal and to obtain four signals simulta-neously. Subsequently, the photodiode array for the index grating was fabricated using integrated circuit process technology. The third- and fifth-order distortions have been reduced by a factor of more than ten in this new system. Moreover, these distortions were found to be independent of the air gap between the index scale and main scales.

FIGURE 4.22 Light intensity with relative displace-ment.

FIGURE 4.23 Fourier spectrums of light intensity.

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