Optoelectronic device for the measurement of the absolute ... - CiteSeerX

Optoelectronic device for the measurement of the absolute linear position in the micrometric displacement range Tomás Morlanesa, José Luis de la Peñaa, Luis Miguel Sanchez-Breab, Jose Alonsob, Daniel Crespob, José Bienvenido Saez-Landetec, Eusebio Bernabeub a

Fagor Automation S. Coop. R+D Department, Mondragón, Guipúzcoa (Spain) Universidad Complutense de Madrid, Departamento de Optica, Madrid (Spain) c Universidad de Alcalá, Departamento de Teoría de la Señal y Comunicaciones, Alcalá de Henares, Madrid (Spain) b

ABSTRACT In this work, an optoelectronic device that provides the absolute position of a measurement element with respect to a pattern scale upon switch-on is presented. That means that there is not a need to perform any kind of transversal displacement after the startup of the system. The optoelectronic device is based on the process of light propagation passing through a slit. A light source with a definite size guarantees the relation of distances between the different elements that constitute our system and allows getting a particular optical intensity profile that can be measured by an electronic post-processing device providing the absolute location of the system with a resolution of 1 micron. The accuracy of this measuring device is restricted to the same limitations of any incremental position optical encoder. Keywords: Optical encoder, absolute position, optoelectronic device.

1.

INTRODUCTION

An encoder is a device that transforms a linear or angular displacement into one or several electric signals which, after a post-processing, allows determining the position of a moving part with respect to a fixed element. There exists a great variety of position encoding devices based on different physical phenomena. Within the machine-tool enviorement, most common commercial devices are based on Magnetic (inductive, magnetorresistive, magnetostrictive) or Optical (interferometric, with a reticle) effects. Each of them is useful in a determinate application field. Thus, magnetic encoders are insensitive to dirty although they are very sensitive to magnetic external fields, while optical encoders are generally preferred because of its accuracy and resolution. Interferometric encoders are the most precise with resolutions up to 1 nm. However, they are only used in calibration of machines and research laboratories since they need a strict control of the ambience (temperature, humidity, pressure). Optical encoders using reticles (diffraction gratings) are normally applied to machines with CNC or to simpler machines devoted to the visualization of cotes. Currently, the period of the fringes of the optical gratings used is of around 10-20 microns for common machine-tool applications and 0.5-10 microns for high resolution applications (lithography, large telescopes, etc.). With such periods, a resolution of 10 nm or less is possible. Optical encoders can be classified in incremental, which provide the relative displacement between the scanning head and the fixed scale, and absolute, where it is possible to determine the position of the scanning head with respect to an absolute position of the scale. Incremental encoders consist of periodic diffraction gratings engraved on both parts of the encoder, it means, on the reticles of the scanning head and on fixed scale (Fig. 1a). Every relative translational a T.M. & J.L.P.: Email: [email protected], Telephone: 943 71 92 00Address: Fagor Automation S. Coop., Departamento de I+D, Bº. San Andrés, 19 , 20500, Mondragón, Guipúzcoa (Spain) b L.M.S.B., J.A. & E.B.: Email: [email protected], Telephone: (+34) 91 394 5110. Address: Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Óptica Ciudad Universitaria s.n., 28040, Madrid (Spain) c J.B.S.L.: Email: [email protected]. Telephone: (+34) 91 394 5110 Address: Departamento de Teoría de la Señal y Comunicaciones, Universidad de Alcalá, Escuela Politécnica. Campus Universitario, 28871, Alcalá de Henares, Madrid (Spain)

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Photonic Materials, Devices, and Applications, edited by Gonçal Badenes, Derek Abbott, Ali Serpengüzel, Proc. of SPIE Vol. 5840 (SPIE, Bellingham, WA, 2005) · 0277-786X/05/$15 · doi: 10.1117/12.628135

movement between both parts produces a periodic light modulation which is converted into electrical signal by the use of photodetectors. There exist several optical techniques and configurations to modulate the light, known in the literature as Moiré effect, Lau effect, Generalized Grating Imaging etc. [1-8]. Commonly, several reading reticles, shifted 90 electrical degrees each other, are placed in the scanning head, providing two sinusoidal signals (called A and B) (see Fig. 1b). By considering the arctan algorithm B ,  A

ϕ = arctan 

(1)

it is possible to get a complete information of the displacement by means of the following expression: pos = ( N + ϕ / 2π) p

(2)

where p is the period of the diffraction grating at the scale and N is the number of whole displaced periods. Obviously sinusoidal signals are required to minimize errors [9-11]. By using only these incremental signals, one is not able to provide information about the absolute position of the scanning head with respect to the scale. The knowledge of the absolute position is important for several reasons: physical limits of the movement, the application of the calibration errors to the processing unit, etc. For that, a third signal, called the reference mark signal, is required. Usually, this signal shows a narrow and steeped peaky shape centered on a certain position of the scale. Therefore, the absolute position is obtained by adding or subtracting the incremental values provided by the incremental signals to this reference mark signal. It is very important to remark that this technique requires, after the start-up of the machine, a previous movement of the scanning head with respect the fixed scale in order to locate the reference mark. In many situations this initial extra displacement is available. However, there are situations where this previous movement is not possible (for instance under breakdowns of the machine in the middle of a process or in linear motors environments). For that, techniques for determining the absolute position of the encoder at any time and position are required. One possibility is to include a new scale where the slits are not placed regularly, but with a ‘random’ distribution. In rotary encoders “Gray codes” are common. However they cannot be used for linear encoders since the length of these can be very long (up to 3 meters) and pseudorandom algorithms [13] are normally applied. Since the light signal that collects the information of the absolute position is quite complex, normally arrays of photodiodes are required to capture it. When several of these marks are read, a mathematical algorithm or a look-up table transforms the read data into the absolute position. For this, microprocessors can be used. Obviously, the information for each position cannot be repeated in all the length of the scale. Normally the pixel size is much lower than the width of the slits of the absolute code. Then this code is overdetermined since many pixels at the photodetector present the same information. In addition to the absolute position provided by the pseudorandom code, an interpolation for this position can be performed using the pixels that collect light at transitions ’01’ or ‘10’ of the absolute code by a simple linear fitting. The resolution at this interpolation is given by the accuracy of the analog digital converter that transforms this analog signal in a digital data. The best estimation of the interpolation is given by the mean of the values obtained for the different transitions. With this technique, it is intended that the edges between illuminated and dark slits be as abrupt as possible, giving rise, in an ideal situation, to a square-shaped signal. However, it happens that most of commercial light sources show a certain degree of divergence, therefore every square shaped signal is altered and smooth (see Fig. 1c and 1d). In this work we take advantage of this effect and we propose a technique that increases the number of pixels used for the interpolation, without eliminating the information of the absolute code. For this we use a light source with a definite size. Normally the resolution required in tool-machine is much lower (around 0.1-1 micron, which is the resolution provided by incremental encoders), thus a normally both synchronized incremental and absolute scales are required in parallel to obtain such resolutions. Also an optical device that uses this technique is described.

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2.

THEORETICAL ANALYSIS

2.1. Optical principle of operation Let us consider an absolute optical encoder as described in Fig. 2. A punctual light source (1) illuminates a pseudorandom grating scale composed of slits with different size (3). Within a geometrical approach, light propagates in straight lines and as a consequence, the image after propagating is the geometrical shadow of the pseudorandom grating scale (5). The image at this plane is collected with an array of photodetectors. Normally the distance between photodetectors d is smaller than the width p of the slits that form the pseudorandom grating. Then, the basic resolution in determining the position is d.

(a)

(b)

(d) (c) Fig. 1. (a) Example of a periodical diffraction grating engraved on the reticles and the scale for an Incremental Encoder; (b) Sinusoidal signals shifted 90 electrical degrees; (c) Example of a random distribution of slits engraved over the scale to provide the absolute position; (d) Profile obtained at a certain distance In a given image, there will be several (N) edges and the interpolated position can be obtained with any of these edges. The best estimation for the interpolation is the mean value, and the standard deviation in the determination of the interpolated position is s=

d N

.

(3)

This resolution is not enough for many machine-tool applications. As a consequence, more refined techniques that allow a lower resolution are required. For this we will take advantage of the blurring effects at the edges of a slit when it is illuminated with an extended light source. Up to this point it has been only made considerations based on a geometrical treatment of the problem. However, when the light is passing through a slit, diffraction effect appears and light distribution at a plane after the slit is not abrupt, but a Fresnel diffraction pattern is obtained [12]. This is an undesired effect that can be avoided using an extended light source and working at a defined distance.

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Fig. 2. Scheme of a absolute encoder within a geometrical approach for a punctual source. 1 Punctual Light source, 2 Light beams, 3 Plane of reading code, 4 Plane of photosensors arrays, 5, theoretical signal When the light source is punctual, there is not a control of the slope of the edge. For this, we can use a light source with a given width l, as it is shown in Fig. 3. In order to increase the number of pixels in a transition zone, the optimal size of the light source is given by the following relationship, p l = s2 s1 + s2

(4)

where p is the width of the fringes, s1 is the distance between the light source and the slits s2 is the distance between the slits and the array of photodetectors. The optical intensity profile at this optimal position will not be triangular like it is shown in Fig. 3. It should be smooth due to the diffraction effects. The slope at the edge can be used for interpolating the relative position between the scanning head and the fixed pseudorandom grating since the intensity for a given pixel at this edge present a certain discrete value. A linear interpolation of all the pixels at the transition zone can be performed. The estimation of the interpolated value is computed in a similar way than in the case of abrupt edges. Nevertheless, the number of points at the edges increases (k pixels at each transition). As a consequence the standard deviation with this technique results s=

d N ⋅k

.

(5)


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Fig. 3. Scheme of a absolute encoder for an extense light source with a finite size. 1 is the extense light source, 2 are the extreme light beams, 3 is the plane of the reading code, 4 is the plane of the photosensors array, 5 is the generated light distribution at the plane of the array of photodetectors.

3.

NUMERICAL AND EXPERIMENTAL RESULTS

3.1. Diffraction by a slit and experimental evaluation of the absolute position We have considered a slit of 80 microns illuminated by different extended light sources and we have experimentally measured the propagation patterns obtained at different distances from the slit (Fig. 4 show an example). For small distances between the slit and the plane of observation, the edges of the slit are quite abrupt. For larger distances the edges smooth, the light spreads out different. A compromise between both situations is obtained when the slit shows a triangular profile, that means, non diffraction effects are present, the edge are still abrupt enough and the maximum intensity is still high.

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Fig. 4. Experimental images obtained of a slit with a width of 80 microns for several distances of the observartion plane (a) aprox. 100 microns, (b) 0.95 mm, (c) 1.9 mm, and (d) 2.85 mm. In this case, the light source is an IR led of Photonics detector (PDI-E825) where the emission area is around 90 microns diameter. The slit shows an approximately triangular profile for z=1.9 mm. This kind of profile is used to perform the interpolation. We have also measured the intensity distribution for a pseudo-random grating where the slits also have a size of 80 microns. The transition zones are around 12 pixels wide and with them it is possible to obtain the interpolation. To detect this image we have used a CCD linear array with 1024 pixels. The size of these pixels is 7.4 microns. As a consequence, the number slits shown is approximately 1024*7.8 / 80 ≈ 100 . Since the track is pseudo-random, there are approximately 50 transitions. Then, the resolution in the determination of the absolute position is, for the case of abrupt transitions d N

=

7.8 50

≈ 1.1µm

(6)

Fig. 5. Experimental of a pseudo-random code obtained with the proposed technique. The upper and lower parts of the signal allow determining the absolute position. The transition zones are around 12 pixels wide and with them it is possible to obtain the interpolation.


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When all the pixels at the transition zone are considered then the resolution in the interpolation is improved. For the case shown in Fig. 5, the number of pixels at the transition is approximately k=12. Then, the resolution at the interpolation is d N ⋅k

3.2.

=

7.8 50 ⋅12

≈ 0.3 µm

(7)

Design of the device

The final device is an absolute linear encoder with two tracks: one is intended for incremental signals and the other for absolute signal (Fig. 7). The incremental measuring is based on moire effect. The absolute measuring is based in the previously described principle and does not make use of the incremental track in order to give the position. The position controller for the feedback of the machine uses the incremental signal. The components for the absolute device are: A led with a square surface output of 250 × 250 µm, The absolute pseudorandom track, A CCD sensor with 1024 pixels and a pitch of 7.8 µm, A microcontroller device which contains an AD converter. The width of the bits engraved in the absolute track is 80 µm. The process of calculus consists in the determination of two quantities. The first one is obtained with the binarization of the code given by the CCD. The result is a set of zeros and ones that gives the position that can be directly correlated with the pseudorandom code. This quantity is know as integer part and has a resolution of 80 µm. The second quantity is known as fractional part and consists in an interpolation of the position in the width of a code bit. Although the theoretical resolution can be 0.3 µm, due to restrictions associated to the calculus mediums in our device, the final resolution for the position is 1 µm.

Fig. 6. In the left side it is shown a photograph of the device while in the right one it is a magnification of the engraving.

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Fig. 7. Scheme of the optical encoder developed for the absolute measurement of the position. An incremental grating has been included for compatibility with other numeric controls and to determine the accuracy of the absolute technique

4.

CONCLUSIONS

In this work we propose a technique for determining the absolute position of one moving part with respect to a fixed pattern scale where there is not a need to perform a previous transversal displacement after the start-up of the device. The absolute position is obtained processing the ‘pseudorandom’ binary code of the track and using known mathematical algorithms. With this technique the resolution of the measurement is just the size of the photodiodes of the CCD linear array, which is too high for many tool-machine applications. To improve such a resolution, we perform an interpolation. For this we use a light source with a finite size so that the image of a slit at the plane of the photodetectors does not present an abrupt edge, but an edge with a linear transition between light and darkness. With this particular light profile many pixels can be used for the interpolation and the resolution of the interpolation decreases substantially. Experimental measurements have been performed and we have also designed an optical device that allows us to obtain resolutions better than 1 micron.

ACKNOWLEDGMENTS This works was partially supported by the Proyecto de Investigación Complutense PR1/05-13381 “Mejora de las tolerancias mecánicas en sistemas de posicionamiento óptico de alta precisión”. Sanchez-Brea is currently contracted by the Universidad Complutense de Madrid under the "Ramón y Cajal" research program.

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