Integrated Grating-Image-Type Encoder

In an optical system that is similar to the conventional Moiré encoder, the grating imaging effect was used previously for a precise displacement measurement [Hane and Grover, 1987a]. In the encoder, the signal was insensitive to the change of the air gap between the two gratings under incoherent illumination.

The grating imaging effect was further investigated on the basis of the optical transfer function for the displacement measurement [Hane and Grover, 1987a,b].

More recently, an integrated grating-image-type encoder was proposed, in which the transmission grating was fabricated by silicon micromachining [Hane et al., 2001, 2002]. Two gratings, photodetectors (two line photodiodes on each grid), LEDs, and a preamplifier circuit chip were integrated by stacking them. The integrated optical encoder is described below.

Figure 4.24 shows the proposed integration of the encoder. Compared with the conventional grating image encoder shown in Figure 4.9, the optical system is integrated. The five components of the con-ventional encoder are stacked. The integrated encoder consists of the two gratings, an incoherent light source, and the photodetectors. The photodiodes are installed in the respective grids of the index grating.

The scale grating is assumed to be an amplitude-reflection grating. The optical configuration in reflection makes the encoder system as compact as the conventional Moiré encoders. The light source used in the proposed encoder is assumed to be polychromatic and incoherent as an LED. The index grating is fabricated from a silicon wafer and consists of transmission grids. In each grid, which is a thin silicon beam, photodiodes are installed using semiconductor microfabrication technology.

Figure 4.25 shows the schematic front views of the designed index grating. The Si substrate is etched through to form the index gratings. Figure 4.25 shows two kinds of phase-shifted line photodiodes as installed in each grid, which is a thin Si beam. In all, four 90° phase-shifted photodiodes, in which the spatial phase differences are 90°, are needed to obtain four sinusoidal signals. They are used for eliminating

FIGURE 4.24 Schematic diagram of the grating-image-type optical encoder.

FIGURE 4.25 Designed index gratings consisting of Si grids with line photodiodes.

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DC offset of signals, for sensing direction, and for interpolating the signal. As shown in Figure 4.25, because the two kinds of 90° phase-shifted photodiodes are installed in each Si beam alternately and closely in space, the photodiode sensitivities are nearly equal and the average intensities of signals are not affected by the light intensity distribution in the large region. The index grating is illuminated from behind and the light passes through the slits of the grating. The grating periods used in the experiment were 80 and 40 µm.

Figure 4.26 shows the schematic diagram of the encoder cross-section (in which the scale grating is not shown). The index grating fabricated from the Si substrate is fixed to the LED holder to encapsulate the LED. The electrodes for the LED are patterned on the surface of the LED holder. Light is emitted from the LED through the Si index grating. The light reflected from the scale grating is detected by the photodiode fabricated on the Si grating. A chip of signal amplifier is fixed to the LED holder with a polymer spacer. The electronic circuits may be fabricated on the side area of the index grating if the fabrication facility can accept both processes.

As shown in Figures 4.9 and 4.10, the three gratings placed in tandem describe an equivalent optical system for this encoder. When the first grating (object grating) is irradiated with spatially incoherent light, the object-grating pattern is transferred by the center grating (reflection scale grating) onto the image plane (which is equal to the plane of the object and the index gratings). The center grating of the three gratings works as a pupil for imaging. The encoder optics has been analyzed by using optical transfer function. Based on the results of the analysis [Hane and Grover, 1987b], the grating period and distance between the gratings have been determined.

The grating imaging for this encoder receives a brief theoretical explanation below. The essential optical system of the encoder is described by the three gratings placed in tandem at the same distances z between the gratings, as shown in Figure 4.10. The grating-like image is formed by the slit array of the pupil grating under Fresnel diffraction. To understand the grating imaging, it may be easier to consider that each slit of the pupil grating images the object grating on the plane of the index grating, and the superposition of the images generated by the respective slits of the grating produces a grating-like image, if they are in phase. The optical transfer function of the pupil grating is obtained under our experimental conditions as follows [Hane and Grover, 1987b],

(4.8)

for

(4.9)

for .

FIGURE 4.26 Cross-sectional view of the designed encoder.

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Optical Sensors and Their Applications 4-17 Here, σ is the image frequency; p and 2ε are, respectively, the pitch and slit width of the pupil grating;

z is the distance between the gratings; λ is the wavelength of light; and m is an integer. The function Π(x) represents a comb function, which becomes a unit when x is equal to integers. When the image frequency is equal to the object frequency (σ = 1/p) and the slit width is assumed to be half of the pitch (ε = p/4), then Eqs. 4.8 and 4.9 are simplified to the periods of the three gratings are equal to each other corresponds to the second imaging condition (x = 2). The image contrast calculated as a function of the normalized distance ξ is shown in Figure 4.27.

As shown in Figure 4.27, the image contrast is always positive under the optical conditions, although the contrast varies periodically with increasing ξ. The period of the image contrast as a function of z is equal to p²/(2λ) (i.e., ξ = 1), which is dependent on the wavelength λ of light. Therefore, in the case of polychromatic illumination (white light), the images generated by the respective wavelengths are super-imposed constructively, and the image contrast is not degraded by the polychromaticity of the light source when x = 2. The contrast under white light illumination is schematically shown in Figure 4.27.

Moreover, the maximum value of the image contrast does not decrease when the distance between the gratings increases, thus the displacement can be measured at a distance z larger than that used in the conventional Moiré encoder.

Because the imaging effect of the grating is used in the encoder, the relative displacement d of the object grating generates that of an image on the plane of the index grating in the opposite direction.

Therefore, the encoder signal varies by two periods for the relative displacement of the grating equal to a single grating period. The sensitivity of the displacement detection in this encoder is improved by a factor of two by this phenomenon over the conventional Moiré encoder.

FIGURE 4.27 Image contrast calculated as a function of normalized distance for a single wavelength.

F p _m m m

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Figure 4.28 shows the lithographic processes for fabricating the index grating. Starting from an n-type Si substrate (200 µm thick and 1 to 10 Ω-cm), a 500-nm-thick SiO2 film is formed by wet oxidation (1).

From the rear surface, the wafer is etched with TMAH (2). The etched area is 3.5 mm × 5.7 mm and 40 µm thick. Next, the line photodiode is fabricated on the etched area by implanting B ions (2 × 10¹⁴/cm³ at 120 keV) (3). After annealing (4) at a temperature of 1000°C, the Al electrode is patterned (5). The gratings with the line photodiodes are then fabricated by etching them through with inductively coupled reactive plasma (6).

A spatially incoherent light source is needed for this encoder and a 3-mm-long and 1-mm-wide GaAlAs LED was specially designed for this purpose. For further integrating the encoder, a preamplifier was designed for obtaining the two phase-shifted signals without DC offset from the four channel photodiodes, which consisted of eight operational amplifiers. Because all the operational amplifiers were fabricated on one chip and the photodiodes for sensing the light intensities were located closely in space, a signal intensity nearly equal to each other was obtained, which was effective for a high-precision interpolation.

The fabricated index grating with a period of 80 µm is shown in Figure 4.29. As shown in Figure 4.29, the duty ratio between the widths of Si grid and the slit is nearly unity. The two line photodiodes are installed as shown in the magnified image of the grating in Figure 4.29. The photocurrent of the diode was measured to be 500 nA with a 10-nA dark current using a standard light source of 12.5 lx. The cut-off frequency response of the fabricated photodiode was around 200 kHz.

Figure 4.30 shows the encoder signals measured as a function of displacement and the Lissajour figure of the two 90° phase-shifted signals. The gap between the index grating and the scale grating is 3 µm under experimental conditions. In this experiment, the index grating shown in Figure 4.29 was illuminated with the white light from a halogen lamp through a fiber bundle. The light reflected from the scale grating is detected with the photodiodes installed on the grids of the index grating. Therefore, the areas of light emission and detection are nearly the same. Two line photodiodes are installed on one grating line to FIGURE 4.28 Lithographic process for fabricating the index grating.

FIGURE 4.29 Fabricated index grating.

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obtain the 90° phase-shifted signals. Another set of the phase-sifted signals is obtained from the index grating located below, as shown in Figure 4.29. As shown in Figure 4.30, two sinusoidal signals are obtained and the phase difference between the signals is nearly 90°. Because the Lissajour figure is almost a circle, the signal includes little harmonic noise. The signal contrast was measured as a function of the gap between the index and the scale gratings. The signal contrast was kept constant at large air gaps from 1 mm to 30 mm.

After testing the fabricated index grating as described above, the integrated encoder sensor was tested.

The index grating, LED, LED holder, and the IC chip were integrated, as shown in Figure 4.26, by stacking them with epoxy resin. The integrated encoder sensor was 1.2 mm thick. Figure 4.31 shows the optical micrograph of the light emission from the fabricated encoder sensor. As shown in Figure 4.31, a grating-like emission through the Si grating is obtained. Therefore, the Si grating on which photodiodes are installed works simultaneously as a transmission object grating. Figure 4.32 shows the encoder signals FIGURE 4.30 Encoder signal measured as a function of displacement and its Lissajour figure.

FIGURE 4.31 Light emission from the integrated sensor.

FIGURE 4.32 Encoder signals from an integrated sensor.

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from the two channels. Although some noise is superimposed on the signals, sinusoidal encoder signals are obtained, as shown in Figure 4.32. The low signal-to-noise ratio is mainly due to the low intensity of the fabricated LED. No significant influence of the heat generated by the LED and IC chip on the encoder signal was observed in the experiments.