Scanning laser triangulation sensor geometry maintaining imaging condition

8th IFAC Symposium on Mechatronic Systems 8th IFAC Symposium on Mechatronic Systems Vienna, Sept. on 4-6, 2019 8th IFACAustria, Symposium Systems Vienna, Austria, Sept. 4-6,Mechatronic 2019 Available online at www.sciencedirect.com 8th IFACAustria, Symposium Systems Vienna, Sept. on 4-6,Mechatronic 2019 Vienna, Austria, Sept. 4-6, 2019

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IFAC PapersOnLine 52-15 (2019) 301–306

Scanning laser triangulation sensor Scanning laser triangulation sensor Scanning laser triangulation sensor geometry maintaining imaging condition Scanning laser triangulation sensor geometry maintaining imaging condition geometry maintaining imaging condition geometry maintaining imaging condition Johannes Schlarp ∗∗ Ernst Csencsics ∗∗ Georg Schitter ∗∗

Johannes Schlarp ∗∗ Ernst Csencsics ∗∗ Georg Schitter ∗∗ Johannes Schlarp Ernst Csencsics Georg Schitter ∗ Johannes Schlarp ∗ Ernst Csencsics ∗ Georg Schitter ∗ ∗ Christian Doppler Laboratory for Precision Engineering for ∗ Christian Doppler Laboratory for Precision Engineering for ∗ Automated In-Line Metrology, Automation and Control Christian Doppler Laboratory for Precision for Automated In-Line Metrology, Automation andEngineering Control Institute Institute ∗ Christian Doppler Laboratory for Precision Engineering for (ACIN), TU Wien, Vienna A-1040, Austria Automated In-Line Metrology, Automation and Control Institute (ACIN), TU Wien, Vienna A-1040, Austria Automated In-Line Metrology, Automation and Control Institute (e-mail: [email protected]). (ACIN), TU Wien, Vienna A-1040, Austria [email protected]). (ACIN),(e-mail: TU Wien, Vienna A-1040, Austria (e-mail: [email protected]). (e-mail: [email protected]). Abstract: This This work work deals with with the the system system design, design, control control and and the the experimental experimental results results of of a Abstract: Abstract: This workindeals deals with the system design, control and thehigh experimental results of aa scanning laser sensor which the optical path is scanned by a novel performance compact scanning laser sensor indeals whichwith the the optical pathdesign, is scanned by aand novel performance compact Abstract: This work system control thehigh experimental results of a fast steering steering mirror (FSM). The system design satisfies the Scheimpflug condition even though scanning laser sensor in which thesystem optical path issatisfies scanned byScheimpflug a novel high performance compact fast mirror (FSM). The design the condition even though scanning laser sensor in which the optical path is scanned by a novel high performance compact only the illumination path is scanned, such that an FSM with a small aperture size and high fast steering mirror (FSM). The system design satisfies the Scheimpflug condition even though only the path scanned, such that an with a small size high fast steering mirror (FSM). system design satisfies the Scheimpflug condition evenand though only the illumination illumination pathTois isThe scanned, such that an FSM FSM with small aperture aperture size and high bandwidth can be used. used. scan the area area of interest with thea FSM, FSM, raster trajectories are bandwidth can be To scan the of interest with the raster trajectories are only the illumination path scanned, suchresolution that an FSM with a FSM, small aperture sizetrajectory and high bandwidth can be used. Tois scan the area of interest with the raster trajectories are employed, which provide an uniform spatial over the scan area. To track the employed, which provide an uniform spatial resolution over the scan area. To track the trajectory bandwidth can be used. Touniform scanusing the areaH of interest with FSM, raster trajectories are a feedback feedbackwhich controller is designed designed the such that aa closed loop bandwidth of employed, provide an spatial resolution over the the scan To track trajectory ∞ -approach, thatarea. closed loop the bandwidth of a controller is using the H ∞ -approach, employed, which provide an uniform spatial resolution oversuch theup scan area. To with track the trajectory kHz is achieved. The FSM can follow triangular signals to 200 Hz the maximum a1.4 feedback controller is designed using the H such that a closed loop bandwidth of ∞ -approach, ∞ 1.4 kHz is achieved. The FSM can follow triangular signals up to 200 Hz with the maximum a1.4 feedback controller is◦◦ .designed using the H∞ -approach, such a closed loopthe bandwidth of kHz isrange achieved. The FSMenables can follow triangular signals upthat to 200 Hz second with maximum actuation of ±3 This a framerate of up to two frames per for an image actuation of ±3The enables a framerate of up to two frames per formaximum an image ◦ ◦ . This 1.4 kHz isrange achieved. FSM can follow triangular signals up to 200 Hz second withofthe with 100x100 pixels. With the scanning system a maximum spatial resolution 60 µm and actuation range of ±3 . This enables a framerate of up to two frames per second for an image with 100x100 pixels. theenables scanning system a of maximum spatial resolution of 60 and aa ◦ actuation range of ±3With . This a framerate up to two frames per second for µm an image scan range of 25 mm can be achieved. with 100x100 pixels. With the scanning system a maximum spatial resolution of 60 µm and a scan range of 25 mm With can be achieved. with 100x100 pixels. scanning system a maximum spatial resolution of 60 µm and a scan range of 25 mm can bethe achieved. © 2019, IFAC Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. scan range of (International 25 mm can be achieved. Keywords: Sensor, Laser Keywords: Absolute Absolute measurement, measurement, Precision Precision measurements, measurements, 3D 3D Sensor, Laser Sensor, Sensor, Fast Fast Keywords: Absolute measurement, Precision measurements, 3DScheimpflug Laser Sensor, Fast Steering Mirror, Optical Sensing and Sensors, System Design, Condition Sensor, Steering Mirror, Optical Sensing and Sensors, System Design, Scheimpflug Condition Keywords: Absolute measurement, Precision 3DScheimpflug Sensor, Laser Sensor, Fast Steering Mirror, Optical Sensing and Sensors,measurements, System Design, Condition Steering Mirror, Optical Sensing and Sensors, System Design, Scheimpflug Condition 1. 1. INTRODUCTION INTRODUCTION image 1. INTRODUCTION intersection image plane plane intersection line line image plane 1. INTRODUCTION intersection line A key technology for the production of the future is the image of the future is the A key technology for the production image plane plane image plane intersection line A key technology for the production in-line metrology [Schmitt and Moenning of the(2006); future Kunzis the image plane a‘ in-line metrology [Schmitt and Moenning (2006); Kunza‘ A key et technology forThis the requires production the future is the in-line metrology [Schmitt and Moenning (2006); KunzM�' mann al. (2005)]. fast of and high resolution image plane a‘ M�' M�' mann al. This requires fast high resolution in-lineet [Schmitt andpreferably Moenning (2006); KunzM�' M�' mann etmetrology al. (2005)]. (2005)]. Thiswhich requires fast and and generate high resolution ff measurement systems, three a‘ measurement systems, which preferably generate three M�' M�' mann et al. (2005)]. This requires fast and high resolution measurement systems, which preferably generate three f dimensional (3D) (3D) images images [Leopold [Leopold et et al. al. (2003)]. (2003)]. State State of of M�' dimensional f measurement systems, preferably generate three dimensional (3D) imageswhich [Leopold et mechanical al. (2003)]. State of the art 3D 3D measurement measurement systems are scanning the art systems are mechanical scanning object lens ff dimensional (3D) images systems [Leopold et mechanical al.machines (2003)]. scanning State of the art 3Dlike measurement are systems, coordinate measurement [Pfeifer object plane plane lens plane systems, like coordinate measurement machines [Pfeifer lens object plane lens f the art 3D measurement systems are mechanical scanning plane systems, like coordinate measurement machines [Pfeifer lens plane plane (2013)]. These systems manipulate the position of the samplane (2013)]. These systems manipulate the position of samobject plane lensaa f lens plane systems, like coordinate measurement machines [Pfeifer (2013)]. These systems manipulate theprobe position of the the sample or sensor, which can be a tactile [Weckenmann plane lens plane ple or sensor, which can be a [Weckenmann a M� (2013)]. These or systems manipulate theprobe position of theet sample or (2004)] sensor, which can be point a tactile tactile probe [Weckenmann et al. an optical optical sensor [Schwenke al. a M� M� et al. (2004)] or an point sensor [Schwenke et al. ple or sensor, which can be a tactile probe [Weckenmann et al. (2004)] or an optical pointAssensor [Schwenke (2002)], with external external actuators. described in [Yu [Yu et et al. M� (2002)], with actuators. As described in et M� object et al. (2004)] or an optical point [Schwenke (2002)], with external actuators. Assensor described in [Yu et et al. al. M� (2017)], the achievable scan speed of such an mechanical object plane plane (2017)], the achievable scan speed of such an mechanical M� object plane equa(2002)], with external actuators. Asof described [Yu et al. (2017)], the achievable scanrestrained speed such an in mechanical (a) Thin-lens (b) Scheimpflug condition scanning system is by moving (a) Thin-lens scanning system is strongly strongly restrained by the the large large moving object plane equa- M� (b) Scheimpflug condition (2017)], the achievable scanrestrained speed of such mechanical tion scanning system is strongly bygenerally theanlarge moving (a) Thin-lens equa(b) Scheimpflug condition mass. If a higher throughput is required cameration mass. If a higher throughput is required camerationThin-lens equa(a) (b) Scheimpflug condition scanning is strongly restrained bygenerally the largeare moving mass. Ifsystems, asystem highere.g. throughput is structured required generally camerabased based on light, used based systems, e.g. based on structured light, are used tion Fig. 1. Schematic illustration mass. If a higher throughput is required generally camerabased systems, e.g. based on structured light, are used [Leach (2011)]. (2011)]. This This optical optical surface surface sensors, sensors, however, however, suffer suffer Fig. 1. Schematic illustration of of (a) (a) the the thin-lens thin-lens equation equation [Leach (b) the Scheimpflug condition, which is a baseda systems, e.g. optical basedofsurface on structured light, are suffer used Fig. and 1. Schematic illustration of (a) the thin-lens equation [Leach (2011)]. This sensors, however, from limited resolution about 10 µm [Keferstein and and (b) the Scheimpflug condition, which is a genergenerfrom a limited resolution of about 10 µm [Keferstein and 1. Schematic illustration of (a) the thin-lens (b)form the of Scheimpflug condition, which is equation a generalized the equation for tilted planes. [Leacha (2011)]. This opticalofsurface however, suffer from limited resolution about sensors, 10 µm [Keferstein and Fig. and Dutschke (2010)]. alized form of the equation for tilted planes. Dutschke (2010)]. and (b)form the of Scheimpflug condition, is a generfrom a limited resolution of about 10 µm [Keferstein and alized the equation for tiltedwhich planes. Dutschke (2010)]. precisely the distance between sample and In et alizedobtain form of equation for tilted planes. obtain thethe distance between sample and sensor, sensor, Dutschke (2010)]. In [Schlarp [Schlarp et al. al. (2018d)] (2018d)] two two optical optical scanning scanning systems systems precisely obtain the distance between sample and sensor, the diffusely scattered laser light spot from the sample In [Schlarp et al. only (2018d)] two optical systems which manipulate the optical optical path of ofscanning a line line sensor sensor are precisely the diffusely scattered laser light spot from the sample which manipulate only the path a are precisely obtain the distance between sample and sensor, must be projected sharply onto the detector [Keferstein In [Schlarp et al. (2018d)] two optical scanning systems the diffusely scattered laser light spot from the sample which manipulate only the optical of a line sensor are must be projected sharply onto the detector [Keferstein presented. Since the the moving mass of ofpath an integrated integrated compact presented. Since moving mass an compact the diffusely scattered laser light spot from the sample and Dutschke (2010)]. To project an object on the which manipulate only the optical path of a line sensor are must be projected sharply onto the detector [Keferstein presented. Since the moving mass of an integrated compact optical scanning scanning system system can can be be significantly significantly smaller smaller as as and Dutschke (2010)]. To project an object on the object object optical be projected sharply onto the detector plane correctly onto the image plane, as illustrated in presented. Since the moving mass ofsignificantly an integrated compact and Dutschke (2010)]. To project an object on [Keferstein the object optical scanning system can be scanning smaller as must compared to external mechanical systems, higher plane correctly onto the image plane, as illustrated in compared to external mechanical scanning systems, higher Dutschke (2010)]. To project an object on the object plane correctly onto the image must plane, assatisfied, illustrated in Fig. 1(a), the thin-lens equation be which optical scanning system canwithout be scanning significantly smaller as and compared tocan external mechanical systems, higher scan speeds be achieved, impairing the lateral Fig. 1(a), the thin-lens equation must be satisfied, which without impairing the lateral scan speeds can be achieved, plane correctly onto the image plane, as illustrated in can be given by compared to external mechanical scanning systems, higher Fig. 1(a), the thin-lens equation must be satisfied, which scan speedsofcanthe be achieved, resolution measurement system [Schlarp et al. al. can be given by without impairing the lateral resolution of the measurement system [Schlarp et Fig. 1(a), the thin-lens equation must be satisfied, which 1 1 1 scan speeds can be achieved, without impairing the lateral can be given by resolution of the measurement system [Schlarp et al. (2018c)]. Due Due to to their their high high resolution resolution of of down down to to 30 nm nm and and 1 = 1 + 1, (1) (2018c)]. (1) 1 + a1 , resolution of to the measurement system [Schlarp et and al. can be given by (2018c)]. Due their highrange resolution of to 30 30 nm a ff1 = their large measurement of up to down 1 m, m, triangulation + = , (1) a a their large measurement range of up to 1 triangulation 1 1 1   (2018c)]. Due resolution down to 30 nm and with the focal length off the their large measurement range of up of sensors are onetoof oftheir the high most commonly used optical sensors distance between toused 1 m,optical triangulation + aff,,, the = alens (1) with the focal length of the lens the distance between sensors are one the most commonly sensors af ,distance alens fathe theirquality large range of et upal. toused 1 m,optical triangulation sensors are measurement one of the most commonly sensors for control tasks [Brosed (2010)]. The main lens and object plane and the between lens with the focal length of the distance between lens and objectlength plane andlens thef ,distance between lens for quality tasks [Brosed et al. (2010)]. The main  ofa sensors are control one of the most commonly optical sensors the focal the distance between for quality control tasks [Brosed al.used (2010)]. The main with lens and object plane athe and the distance between lens components of these these sensors are aa et laser source, an imaging thin-lens equation is, however, and image plane a  . The . The thin-lens equation is, however, and image plane a components of sensors are laser source, an imaging   for quality control [Brosed et al.(2015)]. (2010)].In The main lens and object plane aplanes and the distance between lens components of thesetasks sensors are aNoll laser source, an imaging lens and a detector [Donges and order to only valid, if all three are parallel, which is . The thin-lens equation is, however, and image plane a lens and and to only image valid, if all three planes are parallel, is not not components of these[Donges sensors are laser(2015)]. source, In an order imaging thin-lens equationwhich is, however, a . The lens and a a detector detector [Donges andaNoll Noll (2015)]. In order to and only valid, plane if all three planes are parallel, which is not lens and a© detector and Federation Noll (2015)]. In order to only if allLtd. three planes are parallel, which is not 2405-8963 2019, IFAC[Donges (International of Automatic Control) Hostingvalid, by Elsevier All rights reserved.

Copyright © 2019 IFAC 826 Copyright © under 2019 IFAC 826 Control. Peer review responsibility of International Federation of Automatic Copyright © 2019 IFAC 826 10.1016/j.ifacol.2019.11.691 Copyright © 2019 IFAC 826

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Johannes Schlarp et al. / IFAC PapersOnLine 52-15 (2019) 301–306

the case for the components of a triangulation sensor. In order to generate a sharp projection, the components of the triangulation sensor are aligned according to the Scheimpflug condition [Blais et al. (1988)], which is a generalized form of the thin-lens equation for non parallel planes. The Scheimpflug condition is fulfilled, if the object, the lens and the image plane intersect in a single line (intersection line), as depicted in Fig. 1(b). In a recently published design of a scanning triangulation sensor [Schlarp et al. (2018d)] both optical paths of the sensor are manipulated by a fast steering mirror (FSM), such that the basic measurement geometry of the sensor is not affected and the Scheimpflug condition is maintained. Another system design [Schlarp et al. (2018d)] manipulates only the illumination path of the sensor by an FSM, which leads to a violation of the Scheimpflug condition and introduces a related additional measurement error [Schlarp et al. (2018b)]. A benefit of this design is, however, that an FSM with a smaller aperture size can be used, if only the illumination path is scanned, such that even higher scan speeds can be achieved. Furthermore, the FSM can generally be positioned closer to the sensor, such that a larger lateral scan range can be achieved as compared to a scanning system which manipulates both optical paths. The contribution of this paper is the system design of a scanning triangulation sensor system, which manipulates only the illumination path of the sensor by a compact FSM, while still satisfying the Scheimpflug condition. In Section 2 the system design and the geometrical relations for image reconstruction are presented. The system hardware, controller design and scan trajectories are described in Section 3. The measurement results are discussed in Section 4, while Section 5 concludes the paper. 2. SYSTEM DESIGN AND IMAGE RECONSTRUCTION 2.1 System Design A laser line sensor (type: LLT 2810-25, Micro-Epsilon GmbH, Germany) with a measurement range of 25 mm and a resolution of 10 µm is selected as the starting point for the system design. From the sensor only the lens set, the detector and the evaluation unit are used. The surface of the sample is illuminated by a laser beam, which is generated from a dot laser module. To change the position of the laser spot on the sample, the orientation of the laser beam is manipulated by means of an FSM. As discussed in Section 1, a sharp projection of the scattered laser spot on the sample onto the detector is necessary, to correctly determine the distance between sensor and sample. For point or line triangulation sensors this can be realized by aligning the object, lens and image plane according to the Scheimpflug condition. For a three dimensional measurement system, however, the position and orientation of the object plane changes during the scanning motion, such that it is difficult to fulfil this imaging condition. By placing the mirror surface of the FSM scanner on the intersection line of the lens and image plane the condition can be satisfied at each measurement point [Schlarp et al. (2019)], since the object plane rotates around the intersection line. For the used laser line sensor, 827

the intersection line is too close to the circuit board of the evaluation unit, such that the FSM surface cannot be positioned directly on the actual intersection line. By inserting an additional static mirror between the FSM and the sample, as depicted in Fig. 2, the optical path between the static mirror and the laser source can be folded around the surface of the static mirror, such that the FSM is optically placed on the intersection line. Therefore, the distance dF SM between the FSM and static mirror has to be equal to the distance between the static mirror and the intersection line. This distance together with the angular range of the FSM also determines the required aperture size for the static mirror.

ylens

actual dFSM intersection line laser

z

detector y

dFSM

x

zlens

yz‘



lens static mirror

zs fast steering mirror

folded optical intersection line zmeas

sample

Fig. 2. Schematic setup of the scanning triangulation system with characteristic dimensions. The position of the laser spot on the sample can be manipulated by the FSM. Through the static mirror, the FSM is optically positioned on the intersection line. To manipulate the illumination path a novel high performance compact FSM is used, which is described in detail in [Csencsics et al. (2018)]. The achievable range times bandwidth product of this hybrid reluctance actuated system is significantly higher as compared to state of the art voice coil actuated FSMs and the system dimensions are as small as 32 x 30 mm. The orientation of the FSM ϕ and the static mirror is 45◦ with respect to the xz-plane, to enable good alignment of the system components. The outer diameter of the compact FSM is 32 mm, such that the distance dF SM is selected to 20 mm. At this distance a static mirror (type: PF05-03-P01, Thorlabs Inc., USA) with an aperture size of 12.7 mm is sufficient to redirect the laser beam to the sample over the entire scan range. 2.2 Image Reconstruction The measured quantities consist of ∆ϕ, ∆ϑ, which are the angular position of the FSM around the x-, yz  -axis and zmeas , which is the reconstructed distance from the distance measured on the detector of the laser line sensor.

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with ∆ϕ and ∆ϑ the angular position of the FSM around the x- and yz  -axis, respectively. The measurement range zs of the laser line sensor is between 106 mm and 131 mm. Since the actuation range of the compact FSM is ±3◦ , the maximum achievable scan range is 19.5 mm and 27.5 mm in x- and y-direction, respectively. The maximum lateral resolution of the scanning system is determined by the laser spot diameter on the sample. The used laser spot size on the sample is 60 µm in the center of the measurement range and expands to 250 µm towards the edges of the measurement range, due to divergence of the Gaussian beam. The resolution in the z-direction is determined by the used laser line sensor to 10 µm. 3. SYSTEM HARDWARE AND SCAN TRAJECTORIES

To design tailored feedback controllers for the FSM, a model of each system axis of the FSM is necessary. To derive this model the system dynamics of the two system axis are measured with a system analyzer (type: 3562A, Hewlett-Packard, USA). The current through the coils serve as the system inputs, while the angular positions of the mirror are the system outputs. Fig. 4 depicts the measured frequency response of the tip (solid red) and tilt axis (solid magenta). Due to manufacturing tolerances the resonance frequency of the tilt axis is higher (415 Hz) as compared to the tip axis (315 Hz), such that separate models for each system axis are derived. Beyond the resonance frequency an increasing phase lag as well as a slope of -50 dB is observable for both system axes. This fractional order slope can be explained by eddy currents in the flux conducting parts of the actuator, which can be modelled by a lag-lead term [Csencsics et al. (2018)]. At about 2 kHz the noise floor (∼ -60 dB) of the system is reached. 20 0 -20 -40 -60 -80 100

Tip measurement Tilt measurement 10

Tip model Tilt model

1

Crosstalk Tip actuated Crosstalk Tilt actuated 2

103

104

102

103

104

10

0 -100 -200 -300 -400 -500 100

101

Frequency [Hz]

3.1 Experimental setup Fig. 3 depicts the experimental setup of the scanning system. In order to align the various components according to the system design, the laser source is mounted on a post assembly and the remaining components are mounted on manual linear stages.

stage

303

3.2 Identification

Magnitude [dB]

As can be observed in Fig. 2, this reconstructed distance zmeas is acquired in the xz-plane. To reconstruct the surface profile of the sample from the measured quantities, geometrical relations need to be determined. With the similarity theorems for triangles the distance zs between sensor and sample in the z-direction and the reconstructed distance zmeas can be linked in the following form zs − zlens zmeas − zlens = , (2) ylens ylens − ys in which ys is the position of the laser spot on the sample in the y-direction, and ylens and zlens are the position of the lens in the y- and z-direction, respectively. By rearranging this equation and with the use of trigonometric functions the surface profile which is described by xs , ys and zs can be calculated by zmeas · ylens (3a) zs = ylens + (zmeas − zlens ) · tan(2∆ϕ) (3b) xs =zs · tan(2∆ϑ) · cos(ϕ + ∆ϕ) ys =zs · tan(2∆ϕ), (3c)

Phase [°]

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Fig. 4. Measured and modelled frequency response of the tip and tilt axis. The resonance frequencies of the tip and tilt axis are at 315 Hz and 415 Hz, respectively. The measured crosstalks between the two axes are 16 dB lower then the single axis response. Fig. 4 also shows the magnitude response of the crosstalk frequency responses (dashed dotted green and orange) between the two system axes. Since the magnitudes are about 16 dB lower as compared to the single axis transfer function (TF) over the relevant part of the frequency spectrum, each system axis can be controlled by a singleinput-single-output (SISO) controller. The dynamics of each system axis can be modelled by

stage

eddy current

   s + ω1 d P (s) = K · 2 · · es·T   , (4) s + 2ζ0 ω0 s + ω02 s + ω2    time delay ω02

sample

mass spring damper

Fig. 3. Experimental setup of the optical scanning system and long time exposure of a low resolution raster scan trajectory. 828

with parameters according to Table 1 and DC gains of KT ip = 0.1663 and KT ilt = 0.0935 of the tip and tilt axis, respectively. A time delay of Td = 100µs is used to model the sensor system. The modelled TFs of the tip (dotted blue) and tilt axis (dashed cyan) are also shown in Fig. 4.

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Table 1. Coefficients of the modelled FSM system axes. Axis Tip Tilt Tip and Tilt Tip and Tilt

Index 0 0 1 2

ωIndex [rad/s] 1.98e3 2.61e3 6.28e4 1.26e4

with the gain V = 1.374e7 and the coefficients according to Table 2 for the tip axis and V = 1.376e7 and the parameters according to Table 3 for the tilt axis.

ζIndex 0.033 0.0187 -

Table 2. Coefficients of the controller for the tip axis. Index ωazIndex [rad/s] ωapIndex [rad/s] ζbzIndex ωbzIndex [rad/s] ζbpIndex ωbpIndex [rad/s]

3.3 Feedback Control

r



e

w1 C

w2

WU u

P

n 

p

Fig. 5. Block diagram of the extended model for the derivation of a feedback controller for one system axis. The weighting functions WS and WU for the sensitivity function and input sensitivity function are used to shape the controller C. In order to guarantee a sufficient phase margin, the open loop crossover frequency is selected to 700 Hz. To enforce a good tracking within the selected bandwidth the requirements on the sensitivity function is formulated by the weighting function s + zws WS (s) = 0.1 · , (5) s + pws with the crossover frequency zws = 2π · 700 Hz and pws = 2π·0.01 Hz. The weighting function WS has a tamed inverse high pass behaviour, such that a good tracking at low frequencies is achieved [Csencsics et al. (2017)]. In order to reduce the control effort at high frequencies the weighting function WU of the input sensitivity function is selected to s + zwu , (6) WU (s) = 0.0707 · s + pwu with zwu = 2π ·10 kHz and pwu = 2π ·100 MHz. This leads to a low pass behaviour of the resulting system at higher frequencies. With the selected weighting functions and the model of the two system axis, described in Section 3.2, the feedback controller of both axis can be derived to 3 2   2 s + ωazi s2 + 2ζbzi ωbzi s + ωbz i C(s) = V ·

i=1

4 

i=1

s + ωapi

·

i=1

2 

, (7)

2

s + 2ζbpi ωbpi s +

2 ωbp i

i=1

829

80

Magnitude [dB]

WS

2 1.26e5 6.3e4 1 1.26e5 0.56 4.68e5

3 6.28e8 4.82e5 -

4 9.49e6 -

The resulting TF of the controller (dotted green) of the tip axis is shown in Fig. 6. For low frequencies a high gain can be observed, such that a zero steady-state error is achieved. For a high phase margin at the selected crossover frequency, the phase of the controller increases between 100 Hz and 1 kHz. The measured open loop frequency response (dashed red) of the tip axis with the implemented controller is also depicted in Fig. 6. The crossover frequency of the system is 642 Hz. At this frequency a phase margin of 40◦ can be observed, the gain margin of the system is 10 dB. At around 315 Hz a peak in the magnitude response is observable, which matches the resonance frequency of the tip axis. The control effort at this frequency is only slightly reduced by the controller, to ensure a stable system behaviour even if slight parameter changes occur. Controller

Open loop

Closed loop

60 40 20 0 -20 100

101

102

103

102

103

50

Phase [°]

Based on the identified system dynamics feedback controllers are designed for the tip and tilt axis using an H∞ -approach [Schitter et al. (2004); Kwakernaak (1993)]. The controllers are derived by minimizing the H-norm of the used extended model of a single axis. Fig. 5 depicts this model, which consists out of the controller C, the identified system dynamic P and the weighting functions WS and WU for the sensitivity function and input sensitivity function, respectively. Furthermore, the reference mirror position r, the sensed position p, the resulting error e, the control effort u and the measurement noise n are observable in the model.

1 1.26e4 0.033 0.15 1.98e3 0.87 2.39e4

0 -50 -100 -150 100

101

Frequency [Hz]

Fig. 6. Measured controller TF (dotted green), loop gain (dashed red) and complementary sensitivity function (solid blue) of the tip axis. The crossover frequency of the open loop system is 642 Hz, with a phase margin of 40◦ . Fig. 6 also depicts the measured complementary sensitivity function (solid blue) of the system. Due to the low magnitude of the loop gain at around 300 Hz, the magnitude and phase of the complementary sensitivity function slightly decrease around this frequency. By selecting a higher crossover frequency, the magnitude of the loop gain could be increased, such that this decline could be avoided. Due to the high time delay of the sensor system (100 µs), the crossover frequency can not be increased, without impairing the phase margin. The achieved -3 dB bandwidth of the tip axis is 1.4 kHz, the maximum peaking of 2.9 dB

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is reached at 400 Hz. For the tilt axis the same -3 dB bandwidth was achieved, with a slightly higher peaking (3.42 dB). Table 3. Coefficients of the controller for the tilt axis. Index ωazIndex [rad/s] ωapIndex [rad/s] ζbzIndex ωbzIndex [rad/s] ζbpIndex ωbpIndex [rad/s]

1 1.26e4 0.032 0.2 2.61e3 0.88 2.39e4

2 1.26e5 6.3e4 1 1.26e5 0.56 4.63e5

3 6.28e8 4.79e5 -

4 9.53e6 -

Appropriate scan patterns are required to scan the area of interest on the sample. Raster trajectories are applied in various applications, like scanning electron microscopes [Goldstein et al. (2017)], atomic force microscopes [Schitter and Stemmer (2004)] and imaging systems [Ito et al. (2018)]. A raster trajectory is generated by applying a slow triangular signal to one system axis and a fast triangular signal to the other axis. The resulting scan trajectory has a uniform scan speed and spatial resolution [Hedding (1990)], as shown in Fig. 7(a). Reference

Angle  [deg]

2

Angle  [deg]

Reference

Measurement

1

0

5

Time [s] Reference

Angle  [deg]

-1

-2

-3 -3

-2.8

-2.6

-2.4

Angle  [deg]

(a)

-2.2

-2

Measurement

3 2 1 0 -1 -2 -3

0

10

Measurement

3 2 1 0 -1 -2 -3 0

0.5

be operated with the maximum actuation range of ±3◦ and a triangular signal up until 200 Hz, a framerate of 2 frames per second at a resolution of 100 x 100 pixels would be possible. The actuation range of both axes of the FSM can be selected, such that large area scans as well as high resolution sectional scans can be performed. Large area scans and high resolution scans can also be combined to automatically detect features on the sample and rescan them with a higher resolution [Schlarp et al. (2018a)]. 4. VALIDATION OF THE MEASUREMENT RESULTS

3.4 Scan Trajectory

3

305

1

Time [s]

To validate the performance of the scanning system the hollow cylinder shaped feature on a Duplo brick (type: Duplo Brick 2 x 4, Lego, Billund, Denmark), which is shown in Fig. 8(a), was measured. Reference measurements of this object were performed in previous experiments with a mechanical scanning system [Schlarp et al. (2018c)], such that the measurement results of the proposed system can be validated. Fig. 8(b) depicts the measured surface profile, which features a similar shape to the in Fig. 8(a) shown sample. Furthermore, the height and thickness of the hollow cylinder appears to be constant. An incorrect value at x = 5 mm and y = 0 mm can be obtained in the surface profile, which is caused by multiple reflections at the edge of the cylinder. This type of artefact can be handled by inserting a threshold, which determines the valid height of the sample. Along the y-axis the edges of the cylinder do not appear as steeply as along the xaxis. This is caused by shading effects in the optical path of the laser sensor (see Fig. 2), such that certain areas on the sample can not be obtained. To reconstruct the surface profile, the missing measurement points are linear interpolated, which leads to the decreased slope along the y-axis. The height of the hollow cylinder was determined with the reference measurement to 4.663 mm [Schlarp et al. (2018c)]. This dimension was determined with the optical scanning system to 4.577 mm with a standard deviation of 87.7 µm, which matches the result of the reference measurement.

(b)

Fig. 7. Raster trajectory. (a) demonstrates the dual axis operation. A raster trajectory with an amplitude of 3◦ and a frequency of 0.05 Hz for the slow and 10 Hz for fast triangular signal is tracked. (b) depicts the tracking over the time for both axis. For the optical scanning system an image with 100 x 100 pixels is desired. Since the sample rate of the laser line sensor is 1 kHz, the scan speed of the fast triangular reference signal is selected to 10 Hz. For the slow triangular reference signal only the rising half of the trajectory is used to scan the sample (see Fig. 7(b)), such that the frequency needs to be 200 times smaller as compared to the fast triangular signal. With the chosen frequencies of 100 Hz and 0.05 Hz, a framerate of 0.1 frames per second can be achieved. Fig. 7(a) demonstrates the dual axis operation, with the selected frequencies and an amplitude of 3◦ . The rms error is 35m◦ and 2.7m◦ for the fast and slow triangular signal, respectively. As can be observed, the framerate is strongly determined by the sample rate of the applied laser line sensor. Since the compact FSM can 830

y x

(a) Sample

(b) Measurement result

Fig. 8. Measurement result. (a) shows the sample and selected area of interest. (b) depicts the measured and reconstructed surface profile. In summary, the feasibility of an optical scanning system, which maintains the Scheimpflug condition even tough only the illumination path of the sensor is scanned with a compact high performance hybrid reluctance actuated fast steering mirror is demonstrated.

2019 IFAC MECHATRONICS 306 Vienna, Austria, Sept. 4-6, 2019

Johannes Schlarp et al. / IFAC PapersOnLine 52-15 (2019) 301–306

5. CONCLUSION In this paper the design, control and a first measurement result of a scanning laser triangulation sensor, which maintains the imaging condition are shown. To satisfy the Scheimpflug condition at each measurement point, the FSM is placed on the intersection line of the lens and image plane. The optical path between FSM and sample is folded by a static mirror, such that the FSM can be mounted elsewhere and is still optically positioned on the intersection line. With the the geometrical relations, which are determined from the system design, the surface of the sample can be reconstructed from the measured data. To scan the area of interest raster trajectories are employed, since this scan patterns are commonly applied in imaging systems. To follow the scan trajectory, feedback controllers are designed using the H∞ -approach. With the applied novel high performance compact FSM a closed loop bandwidth of 1.4 kHz is achieved. The measurement results show, that the calculated height of the rotational scan matches with the results of a classical mechanical scanning system. Therefore, it can be concluded that it is possible to manipulate only illumination path with a compact FSM and still satisfy the imaging condition. ACKNOWLEDGEMENTS The financial support by the Christian Doppler Research Association, the Austrian Federal Ministry for Digital and Economic Affairs, and the National Foundation for Research, Technology and Development, as well as MICROEPSILON MESSTECHNIK GmbH & Co. KG and ATENSOR Engineering and Technology Systems GmbH is gratefully acknowledged. REFERENCES Blais, F., Rioux, M., and Beraldin, J.A. (1988). Practical considerations for a design of a high precision 3-d laser scanner system. Optomechanical and electro-optical design of industrial systems, 959, 225–247. Brosed, F.J., Aguilar, J.J., Guilloma, D., and Santolaria, J. (2010). 3d geometrical inspection of complex geometry parts using a novel laser triangulation sensor and a robot. Sensors, 11(1), 90–110. Csencsics, E., Schlarp, J., and Schitter, G. (2017). Bandwidth extension of hybrid-reluctance-force-based tip/tilt system by reduction of eddy currents. In Proceedings of the 2017 IEEE International Conference on Advanced Intelligent Mechatronics (AIM2017), 1167–1172. IEEE. Csencsics, E., Schlarp, J., Schopf, T., and Schitter, G. (2018). Compact high performance hybrid reluctance actuated fast steering mirror system. IFAC Mechatronics. Submitted. Donges, A. and Noll, R. (2015). Laser measurement technology. Springer, Atlanta. Goldstein, J.I., Newbury, D.E., Michael, J.R., Ritchie, N.W., Scott, J.H.J., and Joy, D.C. (2017). Scanning electron microscopy and X-ray microanalysis. Springer. Hedding, L.R. (1990). Fast steering mirror design and performance for stabilization and single axis scanning. In Acquisition, Tracking, and Pointing IV, volume 1304, 14. International Society for Optics and Photonics. 831

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