High-precision absolute linear encoder based on a standard calibrated scale

This paper presents the full research and development cycle of a high-precision absolute linear encoder based on a standard calibrated scale. Already available and used in industry standard scales of invar alloy were employed in the study. The scales have incremental indexes with 1 mm spacing intervals without an absolute code. However, the existing technical task is to measure the absolute position in the range of 2 m with accuracy less than 5μm. For that, the developed encoder rationally combines magnetic measuring channel for the index numbering and an optical channel for the precise estimation of the encoder position. First, for the development, a simulation was performed to synthesize and analyze an image of an index. This image was used to develop a real-time double-threshold image processing algorithm to estimate the index position. Later the developed image processing algorithm was verified by preliminary testing and supported by a presented three-stage calibration procedure. The final measurements proved that the designed and developed encoder has the accuracy of 1.65μm (3 standard deviations) at the speed up to 3 m/s. The possibility of use of standard calibrated scales with the presented encoder to solve existing and new industrial tasks forms the value of this paper. A possible use of the existing scales also provides unification and compatibility with conventional metrology equipment.

1. Introduction

The rapid development of new industrial technologies determines constant growth in complexity and accuracy of machining operations. This increase in accuracy of positioning of a tool relatively to a workpiece is directly linked to monitoring of their relative position, often in real-time. Linear encoders are effective means of solving such problems, providing high measuring accuracy, speed and reliability together with various options of mathematical and logical signal processing [1]. The variety of linear encoders includes digital calipers, coordinate measuring machines and stages, laser scanners, mobile equipment, manufacturing gantry tables and semiconductor steppers [2].

All linear encoders are conventionally divided into incremental and absolute classes by their principle of operation and, as a consequence, by the output signal [3]. Incremental encoders determine the displacement by consistently counting the number of discrete pulses, which normally does not require complex signal processing. One or several reference marks can be used for zero indexing if specified by an application. The main disadvantage of incremental encoders is the output reset in case of power outage or reset delay [4]. A re-initialization by the reference mark re-search can be done; however, such re-initialization may affect manufacturing process. In contrast, an output signal of absolute encoders is linear and can be unambiguously interpreted as the sought linear displacement [4]. Reference marks are also redundant for absolute encoders. Since the result of the measurement is an estimation of absolute position, such encoders are not affected by power breaks. In addition, the probability of counting additional pulses or pulses lost during shocks, vibrations or direction reverses is excluded. This is quite important in production of large-size structures when processing or machining takes a long time and there is a high probability of occurrence of a non-regular situation or of an external impact [5].

 

When linear encoders are categorized by the physical principle, the main types are optical, magnetic, capacitive, resistive, ultrasonic, inductive and mechanical. Optical encoders provide the highest accuracy without contact with the object [6]. Most of the optical encoders use imaging [7–9] or interferometric [10–13] schemes. Interferometric encoders have high positional sensitivity and large measuring range, however, their operating principle defines incremental measurements. In addition, the maximum speed of movements is limited by processing of interference pattern [14]. Furthermore, air fluctuations affect the measuring beam and the respective signal output [14]. Therefore, use of interferometric encoders in real production conditions is limited up to individual cases. On the contrary, image-based encoders have a Table 1

Typical technical requirements for absolute optical linear encoders.

 

Parameter	Value
Travel distance	up to 2 m
Resolution	<0.5 μm
Positioning accuracy (3 standard deviations)	<5 μm
Maximum speed	up to 0.5 m/s
Calculation time	<10 μsec
Time of the signal output	<10 μsec

lower resolution with higher resistance to changes in external conditions. Image-based encoders are more flexible in use and allow implementation of absolute measurements using absolute scales [9,15,16]. Based on a survey, typical technical requirements for optical encoders for precision positioning are summarized in Table 1 [2,3,9].

The vast majority of absolute encoders use specially designed absolute scales with a pseudo-random set of indexes or several groups of indexes with different interspaces [9,10,17]. Production of such scales of a large length with high-precision requires unique fabrication equipment, only available at limited facilities. Often such scales are more expensive than a reading head of the encoder. As a compromise, we suggest using already available standard scales of invar alloy, as shown in Fig. 1(a, b).

Invar alloy is used as a base material because of its relatively lowtemperature coefficient of linear expansion in the extended temperature range of operation from −50 to +100° [18]. Some of these scales (as in Fig. 1(a, b)) have regional standards [19]. According to literature [19], these indexes are made mechanically with 1 mm spacing interval and thickness varying from 18 to 23μm. The inter-index spacing intervals may deviate from the nominal value of 1 mm by up to 20μm. However, as the indexes are of equal nature, there is no absolute code or reference marks, therefore the scales are incremental.

The scope of this paper includes the full research and development cycle of an absolute scale-based imaging linear encoder from an initial design up to a prototype development with preliminary testing. The first stages of the development were previously reported by the authors [16].

 

First, in this work, a simulation was performed to synthesize and analyze an image of an index. This image was used to develop a realtime double-threshold image processing algorithm to estimate index position. Later the developed image processing algorithm was verified by preliminary testing and supported by a developed three-stage calibration procedure. Final measurements proved that the designed and developed image-based encoder has the accuracy of 1.65μm (3 standard deviations) at speed up to 3 m/s.

 

The possibility to use standard calibrated scales with the developed imaging encoder to solve existing and new industrial tasks forms the value of this paper. A possible use of existing scales also provides unification and compatibility with conventional metrology equipment.

2. Absolute measurements: the proposed concept

The proposed encoder is based on the presented incremental scale (Fig. 1) which does not have information on indexes numbering. A rational approach is to employ a combination of a precise measuring channel based on indexes image processing, acting as a vernier, and an additional rough measuring channel for fast absolute index numbering.

The allowable error for index numbering falls within ±0.5 mm, which is feasible with modern magnetic, ultrasonic, optical scale-based or pulsed laser sensors. Possible use of a second optical scale or an optical distance sensor with open optical path is not rational [8,20]. The same limitation of open path is valid for ultrasonic sensors [21,22]. Unlike others, magnetic sensors combine large measuring range together with compact dimensions and fast operation. Modern magnetic scales are robust and used widely in industry [23,24]. Their accuracy is relatively low to solve the task solely (Table 1); however, it is quite sufficient for real-time numbering of scale indexes. As a result, a magnetic sensor was used in the design for indexes numbering.

When the rough and the precise channels are used together, the overall performance of the encoder is defined by the precise measuring channel. According to the task definition (Table 1) the most critical parameters are high resolution (less than 0.5μm) and accuracy (less than 5μm) at scale lengths up to 2 m. As it was proposed earlier [15], such high resolution and accuracy can be achieved with image-based approach using modern megapixel digital cameras with adapted image processing algorithms. Fig. 2 summarizes the dual-channel approach and presents the structure of the developed encoder.

In operation, the reference scale is fixed on a stationary element of machine. The encoder is mounted on the moving part and travels together with a work item relative to the reference scale. A laser diode beam passing through an optical system is projected on the linear scale surface to capture well illuminated and high contrast images of indexes. The light reflected from the linear scale passes back through the optical system and forms the image of analyzed section of the reference scale on a digital camera sensor. In case of external trigger, the computing device estimates the current encoder position based on the output from both channels, including the absolute index number x_abs acquired from the rough channel and the precise displacement estimation x_prec based on index image processing. The output signal is given in scale coordinate system which is associated with the first index.

 

In accordance with the foregoing, the output signal of the encoder is formed as follows:

X = xprec {K x[ abs (Czero),Cspacing,KFOV]},

 

where X is the resulting position of the encoder relative to the reference scale, x_prec is formation function of the precise position of index, K is calibration function, which takes into account systematic errors K_FOV of the encoder, an error C_spacing of inter-index spacing and the value x_abs obtained from the rough channel relative to zero position C_zero.

2.1. Optical simulation

Optical simulation of the precise channel was performed to investigate the dependence of measurement results on various factors. These factors, which are difficult to simulate independently in real setup, include optical and mechanical issues (e.g. possible wedge of a protective glass and laser light interference) and environmental affection, including possible dust and scratches on the protective glass. The optical encoder model included the following components:

•the linear scale with modeled reflective properties of the scale surface, indexes and indexes edges represented with Boolean (sub) models;

•the camera model with internal (focal length, size and skew of pixels) and external (spatial position and orientation) parameters, which defines the relationship between global coordinate system of the encoder and local camera coordinate system;

•the optical system with a beam splitter and the protective glass.

Optical modeling was carried out using non-sequential regime in Zemax. Fig. 3 shows the ray tracing as well as the simulated image of an index.

The linear scale modeled as Boolean object by geometrical subtraction of triangular grooves (indexes) from a rectangular box. The reflective properties were set for each (sub) model as follows: the scale surface was simplified to mate aluminum with reflection coefficient of 0.7 at 655 nm, absorbing inner part of indexes and indexes edges scattering the light according to Lambert law with scatter factor of 0.55 and 1000 scattered rays per one incident.

According to the model, the optical system forms a shadow image; therefore the dark index image is formed on a light background. The laser module illuminates the scale through the beam splitter. The reflected light passed through the beam splitter is focused on the camera detector. The mirror is introduced to reduce overall encoder dimensions. Optical scheme uses two beams paths:

•Collimated laser beam which is directly reflected from the polished surface of the scale. The lens forms a defocus cross-section of this beam on the detector that acts as a bright background (see outer areas in the simulated image in Fig. 3).

 

•Divergent beam from index edges. Edges scatter laser beam into arbitrary directions. The lens conjugates the scale surface with the detector, so the images containing shape of index edges can be acquired. The sharper the edges, the better conditions for the image analysis algorithm can be achieved.

2.2. Image processing algorithm

The use of the encoder in high speed or real-time applications limits the possible duration of the image processing and, as a consequence, the complexity of the processing. Some papers propose high-accuracy algorithms of index position calculation. Several algorithms [15,25] provide submicron accuracy, but do not satisfy the real-time processing requirement due to iterative nature and computational complexity. Other method [26] based on cross-correlation of the scale surface image is very sensitive to any change of the surface or operating conditions. The algorithm presented further is adapted for high-speed processing using the full power of parallel data processing with FPGA. As shown later, it allows obtaining the information about the current encoder position simultaneously with the transmission of the last image pixel.

 

Since the indexes of the scale are oriented in one (vertical) direction, an assumption can be made that they will remain vertical in the image under the condition of a proper encoder orientation. Therefore, the index position estimation can be reduced from the initial 2D case to 1D with estimation of the horizontal coordinate (see 1D representation in Fig. 4 processed from Fig. 3). The 2D to 1D conversion of the image is made by element-wise summing the columns, the result of which is a 1D signal with a high-level amplitude. This solution allows eliminating the influence of small defects on images or defects directed along the scale both on the detection capabilities of the algorithm and its accuracy.

At the next step, index coordinate C is estimated by search of local minimum corresponding to the index. For this search, a doublethreshold algorithm can be used to identify four key points A_1..4 in the 1D image (Fig. 4).

 

During the 1D image processing any signal is recognized as an index if the signal level from all four points satisfies the following threshold criteria {T T₁, ₂} taking into account the pre-defined sequential order of the thresholds:

 

⎧A₁ = x S x, ( ) < T₁ ∧ S x( −1) > T₁;

⎪A₂ = x S x, ( ) < T₂ ∧ S x( −1) > T₂; ⎨A₃ = x S x, ( ) > T₂ ∧ S x( −1) < T₂;

^⎪⎩A₄ = x S x, ( ) > T₁ ∧ S x( −1) < T₁                                                                                                        (2)

where T₁ and T₂ are the actual threshold levels. Later it was empirically found that the acceptable threshold values ensuring reliable recognition of the index on synthesized image are T₁ = 0.5 and T₂ = 0.25. Once the locations of four key points A_1..4 are defined, index center C can be found as a mean value of outer points A_1,4 :

_{C =} A1 + A4

 

             2                                                                                                                    (3)

This approach allows determination of index position C with accuracy up to 0.5 pixels. Other methods to calculate the center C are based on one-dimensional centroid, which provides higher accuracy. If a bicubic interpolation is used [27,28], the error up to 2·10⁻³ pixel can be achieved, however, the needed computational power may not be feasible in real-time applications. A rational alternative is to use the golden mean method which uses weighted summation, has low computational complexity and can achieve accuracy up to 10⁻² pixel [29,30]. The index center coordinate C can be found as:

C′

(4)

where S x( ) is the signal level at pixel x between points A_1..4,x = ±A_i 1 means adding one pixel to each side of the range to reduce the influence of background component [31].

The developed image processing algorithm was tested on a set of images simulated in Zemax. Images of indexes were synthesized with a virtual step of 0.01 mm in range of 0.5 mm. The results of simulation are shown in Fig. 5.

Maximal deviations of estimated index center location with predefined locations were less than ±0.3 pixels or ±0.9μm as 1 pixel in the image space corresponds to 0.3μm in the scale space.

•manufacturing errors and position deflection of optical components (including the lens focal length error and optical elements misalignment), influence of the protective glass and the beam splitter (including wedge shape, scratches);

•position errors of the camera sensor due to the error of its initial setting;

•motion image blur;

•deviations of inter-index spacing intervals from the nominal value of

1 mm;

• influence of external factors (e.g. temperature, vibrations).

Deflections and displacements of optical elements, as well as geometrical inhomogeneity of camera sensor, do not significantly affect total measurement error [32]. The most affecting errors were taken into account in the following calibration of the encoder (Section 4).

Beam splitter orientation affects index position on the image as shown in Fig. 6.

The encoder optical system is not sensitive to any shifts and tilts around X axis of the beam splitter, as the indexes images are long enough. Small tilts around Z axis do not affect the measurements as well

because of 1D representation of the image. However, a small tilt β around Y axis causes a systematic error Δ_ty, which can be represented as follows:

Δ_ty = f d β( , )                                                                                                                (5)

where d is the distance between the lens and the reference scale along the optical axis.

For optical model used, the index position error Δ_ty caused by beam splitter tilt β was simulated. The image was processed as described in Section 2.2 and index position was estimated for each position of the beam splitter rotated in range of 2 degrees with step of 0.1 degree

According to Fig. 7, the error Δ_ty does not exceed 0.05μm in realistic case of beam-splitter misalignment by 1 degree. In addition, Δ_ty obeys Eq. (5) and, therefore, it can be eliminated during the calibration procedure.

Possible nonlinearity of camera field of view and wedge of the protective glass are also included in the systematic error components which can be eliminated during the calibration procedure.

Deviations of inter-index spacing intervals from 1 mm result in the error, which is also systematic and individual for each scale. Further, the calibration procedure will be shown to eliminate the systematic errors (Section 4).

3. The prototype design: mechanical, optical and electrical parts

Developed mechanical design of the prototype is presented in Fig. 8.

A magnetic strip is attached to the scale, as well as the cover glass to protect the surface from contamination and scratches. Optical scheme of the encoder is shown in Fig. 9(a). All elements of the encoder are installed in a protective housing (Fig. 9(b)).

For the rough channel, a magnetic encoder M10A S5 528V by GIVI MISURE was used with resolution up to 50μm. The magnetic strip is fixed at the reference scale from non-working side. The magnetic encoder is integrated into the designed encoder housing and provides reliable indexes numbering. The shadow image obtained by the encoder is shown in Fig. 10(a) together with its 1D representation (Fig. 10(b)). The field of view is about 2.5 mm to ensure observation of at least two indexes. The working distance from the beam splitter up to the scale is 12.5 mm which is defined by the mechanical design. The lens focal distance is 20 mm. The IMPERX ICL-B1921 camera is used with 1952× 1112 pixels of 5.5× 5.5μm. Camera effective resolution was 1952× 140 pixels due to 8× vertical binning realized on the camera sensor for faster image continuously. Total dimensions and weight of the prototype are 220× 94× 82 mm and 2.44 kg, respectively.

 

The difference between the real image and the simulated one (Fig. 3 vs. Fig. 10(a)) is essential: the scale surface has defects, scratches and contamination, which are perfectly focused. Moreover, illumination is not uniform across the field of view. As a result, the threshold coefficients shown in Section 2.2 are valid only for the center of the field of view. Average level of illumination was taken into account to calculate the threshold coefficients across the field of view (Fig. 11) which must be stored in the encoder memory.

 

Image processing together with the rough channel output is performed by the computing device based on a developed processing board including Cyclone IV FPGA by Altera driven at the 50 MHz clock frequency. The use of parallel computing with FPGA leads to a high processing speed to ensure minimal processing time. The image conversion from 2D to 1D was released during the image acquisition which effectively does not take additional time. Following processing of the 1D image including thresholding, recognition and calculation of index position, recalculation from pixels to millimeters by the scale factor takes no more than 3μs. As a result of a relatively long image readout time and of additional service operations (including interrogation of the magnetic sensor, reading the correction factors from an internal memory, camera triggering and output SSI/BiSS package formation) the total time of the position output is about 9.6μs. It is important to mention that output position is captured with 1μs delay after an external trigger arrival with minimal available camera exposure time of 2μs. The remaining processing delay, which is constant, can be taken in account by external master equipment.

 

4. Calibration and experiments

 

The prototype calibration was performed on a developed laboratory test setup using a laser interferometer XD6 by API as a working reference to control encoder position and orientation (including 3 linear and 3 angular coordinates) (Fig. 12). The XD6 interferometer has a linear accuracy of 0.5μm with a resolution of 0.02μm at maximum velocity of 3 m/s. During the experiments, the encoder was traveling along the scale with help of a motor stage. The interferometer reflector was placed on the moving stage together with the encoder.

 

The calibration procedure was developed to eliminate systematic errors including variations of inter-index spacing intervals and zero index position. Therefore, the calibration procedure consisted of three steps:

 

(i)     nonlinearity of the camera field of view;

 

(ii)    zero index calibration;

 

(iii)   estimation the deviations of inter-index spacing intervals.

Before calibration, the repeatability of the encoder output was experimentally tested to estimate possible distribution of results and to limit the number of experiments or measurements needed for the following calibration. For that, the encoder was mounted on a static basement to measure an index position for 250 times. The measurements were made for 10 different indexes along the scale. The standard deviation for each index did not exceed 0.02 pixels which corresponds to 0.018μm (3 standard deviations).

The first calibration step eliminates systematical error, which includes nonlinearity of the camera field of view and wedge shape of the protective glass. The procedure is based on regression analysis of the relationship between the encoder output and the interferometer data. For that, the encoder was moved with minimal available step of 200μm over 10 indexes one after another. Fig. 13(a) shows experimental results with the deviation of the encoder output compared with the interferometer. Fig. 13(b) shows the same experimental data with a fitted polynomial function (K_FOV ( )d = −7.94d³ + 0.33d²− −d 1.48, where d is the distance).

The fitted polynomial function served as the calibration of systematic component of nonlinearity across the camera field of view. According to Fig. 13(b), residual errors within 1 mm range do not exceed 0.4μm.

The second step of the calibration procedure aimed to estimate the zero index position. For this, the encoder was placed right in front of the first index to measure its position for 1000 times. The resulting mean value is taken as the zero index position C_zero, which is then stored in the encoder memory.

The calibration of inter-index spacing intervals deviations and the following experiments were performed using a certified test setup (Fig. 14). The reason is that room air temperature drift and environmental vibrations significantly affected long experimental measurements.

The certified experimental test setup consists of a significant basement with rails where a motorized carriage can travel with speeds up to 4 m/s in range up to 4 m. As shown in Fig. 14, the encoder was fixed on the carriage above the scale. The rails and the carriage design limit any tilts of the carriage up to arc second values. Renishaw XL-80 interferometer with an extended reference arm was used as a working reference to control the carriage position. The experiments were carried out under the following controlled conditions:

•air temperature 25.0 ± 0.2 °C;

•humidity 70 ± 5%;

•air pressure 101.7 ± 0.5 kPa;

supply voltage 5 ± 0.05 V;

 

•vibration amplitude of the basement was not more than 0.01 mm with frequencies less than 0.0005 Hz.

Vibration isolation of test bench components was provided by the use of active aerostatic supports. Since room temperature affects all elements of the test setup and directly influences the experimental results, the room was thermally stabilized. To ensure stability and accuracy of the laser interferometer, the stability of air parameters (temperature, humidity and pressure changes) along the optical path was carefully monitored with high accuracy. All measurements were controlled remotely with no personnel in the room.

 

The calibration of inter-index spacing intervals was done by moving the encoder along the scale with 1 mm stops when the index was at the center of the field of view. The operation was repeated 3 times in both directions, resulting in 6 passes in total. The difference of the nominal step of 1 mm was compared with the interferometer output. The averaged deviations of inter-index spacing intervals are presented in Fig. 15.

 

According to the results, the inter-index spacing deviations have a cumulative nature with absolute value reaching 8μm. Later, the measured deviations are stored in the encoder memory as a reference profile C_spacing for this specific scale.

 

Final measurements were carried out at two different speeds of 1 and 3 m/s with 10 and 30 passes of the carriage both ways (forward and back) at each speed. The encoder moved along the entire length of the scale (2000 mm). Synchronously, the values of the encoder and laser interferometer were taken at 100 Hz with strict timing start for each pass. Consequently, an assumption can be made that different indexes were captured in different parts of the encoder field of view from pass to pass. The results obtained during the final measurements are presented in Fig. 16.

 

Absolute value of the deviations does not exceed 1.5μm at full measurement range of 2 m at both speeds. There is also no meaningful systematic error component, which experimentally proves the effect of the calibration procedure. The distributions of deviations are close to normal distribution with standard deviation of 0.58 and 0.6μm for the speeds of 1 and 3 m/s, respectively.

 

5. Discussion

 

A proper metrological approach is needed to treat the final experimental results (Fig. 16) when deviations of 1μm are measured over 2 m at speeds up to 3 m/s. The interferometer used here (Renishaw XL-80) was certified before the experiments with an absolute error of ± 0.7μm in 2m range (3 standard deviations σ_int of 0.23μm with a systematic component close to 0). To estimate the accuracy of the encoder, a practical assumption can be made that both the encoder and the interferometer had normally distributed affecting errors without meaningful systematic components. In this case, standard deviation σ_sum of deviations in the data presented in Fig. 16 can be treated as a quadratic sum σ_int² + σ_sum² of standard deviations of the encoder σ_enc and the interferometer σ_int, so given σ_int = 0.23 μm, the standard deviation of the encoder σ_enc is 0.55μm.

 

Since maximum deviations and the distributions are similar at both speeds of motion (1 and 3 m/s, Fig. 16), the performance and the error of the developed encoder does not depend on the speed of motion (with speeds up to 3 m/s). This also means that possible influence of image blurring is negligible at these speeds. An improvement can be done in the future by using pulsed laser illumination instead of the continuous mode to decrease the effective exposure time from 2μs to the ns time scale.

 

A special comment has to be made on how the environment affects the measurement accuracy for such experiments. According to our experience obtained during the development and the experimental phase, it is not possible to validate the encoder output in non-controlled environment. This experience resulted in move from the laboratory setup (Fig. 12) to the certified one (Fig. 14). Otherwise, it is quite difficult to isolate all affecting parameters to reliably interpret the results.

 

The encoder was developed as a proof of concept with certain initial requirements (see Table 1). The summarized technical specification of the developed encoder is presented in Table 2.

As the research and development of any product in real life takes more than one iteration, the developed prototype can be improved in the future to make it smaller (current dimensions are 220× 94× 82 mm) and faster. On a more important note, there are operational parameters, which effectively define a possible use of the encoder, such as the requirements on the position tolerance and long term stability:

5.1. Position tolerance

For an optimal operation of the encoder with a given error, it is necessary to position the encoder relative to the scale with a tolerance of 0.1 mm over the entire length of the scale. Larger gaps lead to defocusing of the acquired image. To reduce and eliminate this effect, future work is planned to increase the power of the laser module and to reduce the lens aperture. Doing so will increase the depth of sharply depicted space and effectively release the requirements on the encoder position tolerance.

5.2. Long term stability

During the laboratory tests, the influence of the encoder temperature on the measurement accuracy was also studied. After powering on, the encoder was continuously interrogated for 90 min in a static position being controlled by the interferometer. The temperature of the encoder was monitored by an infrared camera FLIR A320. As the experiment showed, the temperature of some electronic components (Fig. 17(b)) reached 60 °C (Fig. 17(a)). This leads to an additional error (Fig. 17(c)) caused by displacement of optical components of the encoder due to thermal expansion of the housing.

According to Fig. 17(c) the error has an increasing character and almost reaches the value of 0.03μm. As a result, the developed prototype has an additional operational requirement for temperature stabilization. The influence of dissipating heat can be lowered if the computing device is taken out of the housing. Furthermore, a modification of the optical unit can be proposed by combining it with a video camera or an image sensor. These modifications will simplify the process of assembling and optical adjusting and increase the rigidity of the optical unit.

6. Conclusion

This paper presented the full research and development cycle of the high-precision absolute linear encoder based on the standard calibrated scale. The main feature of the developed encoder is the principle of operation, based on a rational combination of magnetic and optical channels, which resulted in possibility of absolute linear measurements with an existing incremental scale. Experimental tests showed that the developed encoder has the accuracy of 1.65μm (3 standard deviations of 0.55μm) and calculation time of 3 μsec. For industrial application, some of the encoder parameters including overall calculation time, dimensions and thermal stability have to be improved.

Acknowledgements

The work is partially financially supported by the Government of the Russian Federation, Grant 074-U01.

 

1. Introduction

The rapid development of new industrial technologies determines constant growth in complexity and accuracy of machining operations. This increase in accuracy of positioning of a tool relatively to a workpiece is directly linked to monitoring of their relative position, often in real-time. Linear encoders are effective means of solving such problems, providing high measuring accuracy, speed and reliability together with various options of mathematical and logical signal processing [1]. The variety of linear encoders includes digital calipers, coordinate measuring machines and stages, laser scanners, mobile equipment, manufacturing gantry tables and semiconductor steppers [2].

All linear encoders are conventionally divided into incremental and absolute classes by their principle of operation and, as a consequence, by the output signal [3]. Incremental encoders determine the displacement by consistently counting the number of discrete pulses, which normally does not require complex signal processing. One or several reference marks can be used for zero indexing if specified by an application. The main disadvantage of incremental encoders is the output reset in case of power outage or reset delay [4]. A re-initialization by the reference mark re-search can be done; however, such re-initialization may affect manufacturing process. In contrast, an output signal of absolute encoders is linear and can be unambiguously interpreted as the sought linear displacement [4]. Reference marks are also redundant for absolute encoders. Since the result of the measurement is an estimation of absolute position, such encoders are not affected by power breaks. In addition, the probability of counting additional pulses or pulses lost during shocks, vibrations or direction reverses is excluded. This is quite important in production of large-size structures when processing or machining takes a long time and there is a high probability of occurrence of a non-regular situation or of an external impact [5].

Received 4 September 2017; Received in revised form 3 March 2018; Accepted 29 March 2018 Available online 30 March 2018

0263-2241/ © 2018 Elsevier Ltd. All rights reserved.

When linear encoders are categorized by the physical principle, the main types are optical, magnetic, capacitive, resistive, ultrasonic, inductive and mechanical. Optical encoders provide the highest accuracy without contact with the object [6]. Most of the optical encoders use imaging [7–9] or interferometric [10–13] schemes. Interferometric encoders have high positional sensitivity and large measuring range, however, their operating principle defines incremental measurements. In addition, the maximum speed of movements is limited by processing of interference pattern [14]. Furthermore, air fluctuations affect the measuring beam and the respective signal output [14]. Therefore, use of interferometric encoders in real production conditions is limited up to individual cases. On the contrary, image-based encoders have a

Table 1

Typical technical requirements for absolute optical linear encoders.