Frequency Scanned Interferometry for ILC Tracker Alignment
PProceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 Frequency Scanned Interferometry for ILC Tracker Alignment
Hai-Jun Yang , Tianxiang Chen ∗ , Keith Riles Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA ∗ Department of Physics, University of Science and Technology of China, Hefei, China
In this paper, we report high-precision absolute distance and vibration measurements performed with frequencyscanned interferometry. Absolute distance was determined by counting the interference fringes produced whilescanning the laser frequency. High-finesse Fabry-Perot interferometers were used to determine frequency changesduring scanning. A dual-laser scanning technique was used to cancel drift errors to improve the absolute distancemeasurement precision. A new dual-channel FSI demonstration system is also presented which is an interimstage toward practical application of multi-channel distance measurement. Under realistic conditions, a precisionof 0.3 microns was achieved for an absolute distance of 0.57 meters. A possible optical alignment system for asilicon tracker is also presented.
1. Introduction
The motivation for this project is to design a novel optical system for quasi-real time alignment of trackerdetector elements used in High Energy Physics (HEP) experiments. A.F. Fox-Murphy et.al. from OxfordUniversity reported their design of a frequency scanned interferometer (FSI) for precise alignment of the ATLASInner Detector [1–3]. Given the demonstrated need for improvements in detector performance, we plan to designand prototype an enhanced FSI system to be used for the alignment of tracker elements in the next generationof electron-positron Linear Collider detectors. Current plans for future detectors require a spatial resolution forsignals from a tracker detector, such as a silicon microstrip or silicon drift detector, to be approximately 7-10 µm [4]. To achieve this required spatial resolution, the measurement precision of absolute distance changes oftracker elements in one dimension should be on the order of 1 µm . Simultaneous measurements from hundredsof interferometers will be used to determine the 3-dimensional positions of the tracker elements.In this paper, we describe ongoing R&D in frequency scanned interferometry (FSI) to be applied to align-ment monitoring of a detector’s charged particle tracking system, in addition to its beam pipe and final-focusquadrupole magnets.The University of Michigan group has constructed several demonstration FSIs with the laser light transportedby air or single-mode optical fiber, using single-fiber and dual-laser scanning techniques, and dual-laser withdual-channel for initial feasibility studies. Absolute distance was determined by counting the interference fringesproduced while scanning the laser frequency. The main goal of the demonstration systems was to determine thepotential accuracy of absolute distance measurements that could be achieved under both controlled and realisticconditions. Secondary goals included estimating the effects of vibrations and studying error sources crucialto the absolute distance accuracy. Two multiple-distance-measurement analysis techniques were developedto improve distance precision and to extract the amplitude and frequency of vibrations. Under laboratoryconditions, a measurement precision of ∼
50 nm was achieved for absolute distances ranging from 0.1 metersto 0.7 meters by using the first multiple-distance-measurement technique. The second analysis technique hasthe capability to measure vibration frequencies ranging from 0.1 Hz to 100 Hz with amplitude as small as a fewnanometers, without a priori knowledge[5]. The multiple-distance-measurement analysis techniques are wellsuited for reducing vibration effects and uncertainties from fringe & frequency determination, but do not handlewell the drift errors, such as from thermal effects.We describe a dual-laser system intended to reduce the drift errors and show some results under realistic con-ditions. The dual-channel FSI is used to make sanity checks of the displacement of the detector simultaneously.Dual lasers with oppositely scanned frequency directions permit cancellation of many systematic errors, makingthe alignment robust against vibrations and environmental disturbances.We also report on progress using a dual-channel dual-laser FSI with prototype. Under realistic environmentalconditions, a precision of about 0.2-0.3 microns was achieved for a distance of about 57 cm for the prototype.
2. Principles
The intensity I of any two-beam interferometer can be expressed as I = I + I + 2 √ I I cos( φ − φ ), where I and I are the intensities of the two combined beams, and φ and φ are the phases. Assuming the optical a r X i v : . [ phy s i c s . i n s - d e t ] S e p Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 path lengths of the two beams are D and D , the phase difference is Φ = φ − φ = 2 π | D − D | ( ν/c ), where ν is the optical frequency of the light, and c is the speed of light.For a fixed path interferometer, as the frequency of the laser is continuously scanned, the optical beamswill constructively and destructively interfere, causing “fringes”. The number of fringes ∆ N is ∆ N = D ∆ ν/c ,where D is the optical path difference between the two beams, and ∆ ν is the scanned frequency range. Theoptical path difference (OPD for absolute distance between beamsplitter and retroreflector) can be determinedby counting interference fringes while scanning the laser frequency. Tunable LaserIsolatorBSFabry Perot InterferometerFiber CouplerFiber BS RetroreflectorStageReturn Optical FiberFemtowatt Photoreceiver
Figure 1: Schematic of an optical fiber FSI system.
If small vibration and drift errors (cid:15) ( t ) occur during the laser scanning, then Φ( t ) = 2 π × ( D true + (cid:15) ( t )) × ν ( t ) /c ,∆ N = [Φ( t ) − Φ( t / π = D true ∆ ν/c + [ (cid:15) ( t ) ν ( t ) /c − (cid:15) ( t ν ( t /c ], Assuming ν ( t ) ∼ ν ( t
0) = ν , Ω = ν/ ∆ ν ,∆ (cid:15) = (cid:15) ( t ) − (cid:15) ( t D measured = ∆ N/ (∆ ν/c ) = D true + ∆ (cid:15) × Ω . (1)
3. Demonstration System of FSI
A schematic of the FSI system with a pair of optical fibers is shown in Figure 1 The light source is a NewFocus Velocity 6308 tunable laser (665.1 nm < λ < > mK are used to monitor temperature. The apparatus is supported on a damped Newport optical table.In order to reduce air flow and temperature fluctuations, a transparent plastic box was constructed on top ofthe optical table. PVC pipes were installed to shield the volume of air surrounding the laser beam. Inside thePVC pipes, the typical standard deviation of 20 temperature measurements was about 0 . mK . Temperaturefluctuations were suppressed by a factor of approximately 100 by employing the plastic box and PVC pipes.Detectors for HEP experiments must usually be operated remotely for safety reasons because of intensiveradiation, high voltage or strong magnetic fields. In addition, precise tracking elements are typically surroundedby other detector components, making access difficult. For practical HEP application of FSI, optical fibers forlight delivery and return are therefore necessary.The beam intensity coupled into the return optical fiber is very weak, requiring ultra-sensitive photodetectorsfor detection. Considering the limited laser beam intensity used here and the need to split into many beamsto serve a set of interferometers, it is vital to increase the geometrical efficiency. To this end, a collimator isattached to the optical fiber, the density of the outgoing beam from the optical fiber is increased significantly.The return beams are received by another optical fiber and amplified by a Si femtowatt photoreceiver with again of 2 × V /A .
4. Multiple-Distance-Measurement Techniques
For a FSI system, drifts and vibrations occurring along the optical path during the scan will be magnified by afactor of Ω = ν/ ∆ ν , where ν is the average optical frequency of the laser beam and ∆ ν is the scanned frequency roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 ∼
67. Small vibrations and drift errors that have negligible effects formany optical applications may have a significant impact on a FSI system. A single-frequency vibration may beexpressed as x vib ( t ) = a vib cos(2 πf vib t + φ vib ), where a vib , f vib and φ vib are the amplitude, frequency and phaseof the vibration, respectively. If t is the start time of the scan, Eq. 2 can be re-written as∆ N = L ∆ ν/c + 2[ x vib ( t ) ν ( t ) − x vib ( t ) ν ( t )] /c (2)If we approximate ν ( t ) ∼ ν ( t ) = ν , the measured optical path difference L meas may be expressed as L meas = L true − a vib Ω sin[ πf vib ( t − t )] × sin[ πf vib ( t + t ) + φ vib ] (3)where L true is the true optical path difference in the absence of vibrations. If the path-averaged refractiveindex of ambient air ¯ n g is known, the measured distance is R meas = L meas / (2¯ n g ).If the measurement window size ( t − t ) is fixed and the window used to measure a set of R meas is sequentiallyshifted, the effects of the vibration will be evident. We use a set of distance measurements in one scan bysuccessively shifting the fixed-length measurement window one F-P peak forward each time. The arithmeticaverage of all measured R meas values in one scan is taken to be the measured distance of the scan (althoughmore sophisticated fitting methods can be used to extract the central value). For a large number of distancemeasurements N meas , the vibration effects can be greatly suppressed. Of course, statistical uncertainties fromfringe and frequency determination, dominant in our current system, can also be reduced with multiple scans.Averaging multiple measurements in one scan, however, provides similar precision improvement to averagingdistance measurements from independent scans, and is faster, more efficient, and less susceptible to systematicerrors from drift. In this way, we can improve the distance accuracy dramatically if there are no significant drifterrors during one scan, caused, for example, by temperature variation. This multiple-distance-measurementtechnique is called ’slip measurement window with fixed size’, shown in Figure 2. However, there is a trade offin that the thermal drift error is increased with the increase of N meas because of the larger magnification factorΩ for a smaller measurement window size. slip measurement window with fixed sizeslip measurement window with fixed start point...... // Figure 2: The schematic of two multiple-distance-measurement techniques. The interference fringes from the femtowattphotoreceiver and the scanning frequency peaks from the Fabry-Perot interferometer(F-P) for the optical fiber FSI systemrecorded simultaneously by DAQ card are shown in black and red, respectively. The free spectral range(FSR) of twoadjacent F-P peaks (1.5 GHz) provides a calibration of the scanned frequency range.
In order to extract the amplitude and frequency of the vibration, another multiple-distance-measurementtechnique called ’slip measurement window with fixed start point’ is used, as shown in Figure 2. In Eq. 3, if t isfixed, the measurement window size is enlarged one F-P peak for each shift, an oscillation of a set of measured R meas values indicates the amplitude and frequency of vibration. This technique is not suitable for distancemeasurement because there always exists an initial bias term, from t , which cannot be determined accuratelyin our current system. Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011
5. Absolute Distance and Vibration Measurement
The typical measurement residual versus the distance measurement number in one scan using the abovetechnique is shown in Figure 3(a), where the scanning rate was 0.5 nm/s and the sampling rate was 125 kS/s.Measured distances minus their average value for 10 sequential scans are plotted versus number of measurements( N meas ) per scan in Figure 3(b). The standard deviations (RMS) of distance measurements for 10 sequentialscans are plotted versus number of measurements ( N meas ) per scan in Figure 3(c). It can be seen that thedistance errors decrease with an increase of N meas . The RMS of measured distances for 10 sequential scans is1.6 µm if there is only one distance measurement per scan ( N meas = 1). If N meas = 1200 and the average valueof 1200 distance measurements in each scan is considered as the final measured distance of the scan, the RMSof the final measured distances for 10 scans is 41 nm for the distance of 449828.965 µm , the relative distancemeasurement precision is 91 ppb. -505 200 400 600 800 1000 1200Measurement Number in one Scan M ea s . R e s i du a l ( m m ) (a) -1-0.500.51 0 200 400 600 800 1000 1200 L meas = 449828.965 m m No. of Measurements / Scan M ea s . R e s i du a l ( m m ) (b) -2 -1 No. of Measurements / Scan R M S ( m m ) (c) M a gn i f i ca ti on F ac t o r (d) -5-2.502.55 250 500 750 1000 1250 1500 1750 2000 (e) -0.02500.0250.05 250 500 750 1000 1250 1500 1750 2000 Number of Measurement M ea s u r e m e n t R e s i du a l ( m m ) (f) Figure 3: Distance measurement residual spreads versus number of distance measurement N meas (a) for one typical scan,(b) for 10 sequential scans, (c) is the standard deviation of distance measurements for 10 sequential scans versus N meas .The frequency and amplitude of the controlled vibration source are 1 Hz and 9.5 nanometers, (d) Magnification factorversus number of distance measurements, (e) Distance measurement residual versus number of distance measurements,(f) Corrected measurement residual versus number of distance measurements. The standard deviation (RMS) of measured distances for 10 sequential scans is approximately 1.5 µm if thereis only one distance measurement per scan for closed box data. By using the multiple-distance-measurementtechnique, the distance measurement precisions for various closed box data with distances ranging from 10cm to 70 cm collected are improved significantly; precisions of approximately 50 nanometers are demonstratedunder laboratory conditions, as shown in Table 1. All measured precisions listed in Table I are the RMS’s ofmeasured distances for 10 sequential scans. Two FSI demonstration systems, ’air FSI’ and ’optical fiber FSI’,were constructed for extensive tests of multiple-distance-measurement technique, ’air FSI’ means FSI with thelaser beam transported entirely in the ambient atmosphere, ’optical fiber FSI’ represents FSI with the laserbeam delivered to the interferometer and received back by single-mode optical fibers.Based on our studies, the slow fluctuations are reduced to a negligible level by using the plastic box and PVCpipes to suppress temperature fluctuations. The dominant error comes from the uncertainties of the interferencefringes number determination; the fringes uncertainties are uncorrelated for multiple distance measurements.In this case, averaging multiple distance measurements in one scan provides a similar precision improvement toaveraging distance measurements from multiple independent scans. But, for open box data, the slow fluctuationsare dominant, on the order of few microns in our laboratory. The measurement precisions for single andmultiple distance open-box measurements are comparable, which indicates that the slow fluctuations cannot beadequately suppressed by using the multiple-distance-measurement technique. Improvement using a dual-lasersystem will be discussed in the next section. roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 Distance Precision( µm ) Scanning Rate FSI System(cm) open box closed box (nm/s) (Optical Fiber or Air)10.385107 1.1 0.019 2.0 Optical Fiber FSI10.385105 1.0 0.035 0.5 Optical Fiber FSI20.555075 - 0.036, 0.032 0.8 Optical Fiber FSI20.555071 - 0.045, 0.028 0.4 Optical Fiber FSI41.025870 4.4 0.056, 0.053 0.4 Optical Fiber FSI44.982897 - 0.041 0.5 Optical Fiber FSI61.405952 - 0.051 0.25 Optical Fiber FSI65.557072 3.9, 4.7 - 0.5 Air FSI70.645160 - 0.030, 0.034, 0.047 0.5 Air FSITable I: Distance measurement precisions for various setups using the multiple-distance-measurement technique. In order to test the vibration measurement technique, a piezoelectric transducer (PZT) was employed toproduce vibrations of the retroreflector. For instance, the frequency of the controlled vibration source was setto 1 . ± .
01 Hz with amplitude 9 . ± . f vib = 1 . ± .
002 Hz, A vib = 9 . ± .
6. Dual-Laser FSI System
A dual-laser FSI system was built in order to reduce drift error and slow fluctuations occuring during thelaser scan. Two lasers are operated simultaneously; the two laser beams are coupled into one optical fiberbut temporally isolated by using two choppers. The principle of the dual-laser technique[2] is shown in thefollowing. For the first laser, the measured distance D = D true + Ω × ∆ (cid:15) , and ∆ (cid:15) is drift error during thelaser scanning. For the second laser, the measured distance D = D true + Ω × ∆ (cid:15) . Since the two laser beamstravel the same optical path during the same period, the drift errors ∆ (cid:15) and ∆ (cid:15) should be very comparable.Under this assumption, the true distance can be extracted using the formula D true = ( D − ρ × D ) / (1 − ρ ),where, ρ = Ω / Ω , the ratio of magnification factors from two lasers. If two identical lasers scan the same rangein opposite directions simultaneously, then ρ (cid:39) − .
0, and D true can be written as, D true = ( D − ρ × D ) / (1 − ρ ) (cid:39) ( D + D ) / . I +∆ I and J +∆ J , where I and J are integers, ∆ I and ∆ J are fraction of fringes; then the number oftrue fringes can be determined by minimizing the quantity | N correction +( J +∆ J ) − ( I +∆ I ) − N expected − average | ,where N correction is an integer used to correct the fringe number in the chopper off slot, N expected − average is theexpected average number of fringes, based on a full laser scanning sample.Under realistic conditions with large thermal fluctuations, air flow (large drift errors), 10 sequential dual-laserscans data samples each with open box, with a fan on and then off, were collected. The two lasers were scannedoppositely in frequency over the same band with scanning speed of 0.4 nm/s, the scanning time is 25 secondsfor one full scan. The measured precision is found to be about ∼ Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 -15-10-5051015 0 5 10 15 20 25 30
Number of Scans D i s t a n ce M ea s u r e m e n t R e s i du a l ( u m ) Laser 1(dots) Laser 2(boxes)Dual-Laser Cancellation(stars)
Figure 4: The top figure shows interference fringes and Fabry-Perot peaks from dual-laser scanning, the bottom plotrepresents distance measurement residual with and without dual-laser cancellation. box data with the fan on shown in the bottom plot of Figure 4. Detailed information can be found in anotherpublication [6].
7. Dual-laser with dual-channel FSI System
Simultaneous multi-channel distance measurements are required for practical application of an FSI system toILC tracker alignment. To this end, we built dual-channel FSI as shown in Figure 5. The laser beam is coupledinto a single mode optical fiber splitter which split incoming beam into two outgoing beams for two point-to-point FSI distance measurements. The two retroreflectors are mounted on same tunable stage and changepositions simultaneously, allowing cross check of the displacement of the retroreflectors (detector). The resultsfor both FSI channels using dual-laser scanning technique are listed in Table II, where the measured point-to-point distance is about 57 centermeters, and the tuning stage changes the positions of two retroreflectors by20 ± roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 Figure 5: The demonstration FSI system with dual-laser and dual-channel.Distance Dual-LaserChange ( µm ) Channel 1 Channel 2d2-d1 20.746 ± ± ± ± ± ± ± ± consistent at each position change, the displacement measurement precision is about 0 . − .
8. A Possible Silicon Tracker Alignment System
One possible silicon tracker alignment system is shown in Figure 6 for a generic tracker. The top left plotshows lines of sight for alignment in the R-Z plane of the tracker barrel, the top right plot for alignment in X-Yplane of the tracker barrel, the bottom plot for alignment in the tracker forward region. Red lines/dots show thepoint-to-point distances need to be measured using FSIs. There are 752 point-to-point distance measurementsin total for the alignment system. More studies are needed to optimize the distance measurements grid.
Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011
Alignment of ILC Silicon Tracker Detector -150-100-50050100150-200 -150 -100 -50 0 50 100 150 200
Z (cm) R ( c m ) Alignment of ILC Silicon Tracker Detector -150-100-50050100150 -150 -100 -50 0 50 100 150
X (cm) Y ( c m ) Alignment of ILC Silicon Tracker Detector -150-100-50050100150 0 20 40 60 80 100 120 140 160 180 200
Z (cm) R ( c m ) Figure 6: A Possible SiLC Tracker Alignment System.
Acknowledgments
This work is supported by the National Science Foundation and the Department of Energy of the UnitedStates.
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