Proceedings of IBIC2012, Tsukuba, Japan

MOPA13

REAL-TIME CALCULATION OF SCALE FACTORS OF X-RAY BEAM
POSITION MONITORS DURING USER OPERATION
C. Bloomer, G. Rehm, Diamond Light Source, Oxfordshire, UK
Abstract
Circular polarisation, horizontal response

A−B −C +D
A+B +C +D(Δ/Σ)y =A+B −C −D
A+B +C +D

where A,B,C,D are the four XBPM blade signal currents.
There are several limitations to both of these calibration
methods. Both require dedicated beamline time, during
which the beamline is not able to accommodate users: ifstepper motor movements are utilised then users may see−0.5

XBPM Δ/Σ

−2−10120Circular polarisation, vertical response

XBPM Δ/Σ

0.5

24mm gap
32mm gap
40mm gap

0.5

−0.5

000.5(mrad)−0.5−2−1012

Linear horizontal polarisation, horizontal response
24mm gap
32mm gap
40mm gap

0.5Power distribution
24mm gap

0−0.5

−0.5

−2−1012

Linear horizontal polarisation, vertical response

XBPM Δ/Σ

0.500.524mm gap
32mm gap
40mm gap−0.5000.5(mrad)−0.5−2−101
Stepper motor position (mm)2Figure 1: XBPM response to stepper motor movements forthe I06 beamline at Diamond. The simulated power distribution of circular and linear horizontal polarised light are
shown on the right to give an indication of the different
photon distributions. Each gap and phase requires a different scale factor.
X-ray beam shadowing as the XBPM moves across thebeam; if electron beam bumps are used then the changing X-ray beam position and angle causes changes to themeasured intensity and photon energy at the sample-point.
A second limitation is that a scale factor must be measured for each ID setting that a beamline could use, as different ID gaps produce different spatial distributions of radiation and thus require different scale factors. Ellipticallypolarising undulators, such as APPLE II devices, also require a different scale factor value for each different polarisation, as seen in Fig. 1. It is possible to create a look-up
table for each individual ID setting, but populating such atable is a time consuming process. Typically at Diamond,a single XBPM stepper motor scan in one axis would takeISBN 978-3-95450-119-9
Beam Position Monitor System

1c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○(Δ/Σ)x =Power distribution
24mm gap

0−0.5

INTRODUCTION
Diamond Light Source utilizes two photoemission X-ray
Beam Position Monitors (XBPMs) on most front ends inorder to monitor and improve the stability of the photon beam. XBPMs for Insertion Device (ID) beamlines
are mounted on stepper motors with micron-precision encoders, and traditionally the XBPMs are calibrated by using known stepper motor offsets to emulate real X-ray
beam movements. Alternatively, controlled electron beam
bumps through the ID straight can also be used to calibrate
the XBPMs [1, 2]. A scale factor is calculated by comparing the measured response from the four XBPM blades to
the known magnitude of the controlled movements. Thisgives a scale factor measured for a selection of ID gaps,
which is saved into an EPICS database. During user operation the scale factor database is interpolated to give a factor
for the current ID gap and used to convert the dimensionless position given by the XBPM signal into a position inmm. The dimensionless response of the XBPM, Δ/Σ, isdefined as follows:

24mm gap
32mm gap
40mm gap

0.5

XBPM Δ/Σ

Photoemission based X-ray Beam Position Monitors(XBPMs) are widely used at 3rd generation light sources toboth monitor and stabilise the photon beam to sub-micron
precision. Traditionally, finding the geometric scale factors
requires either systematic stepper motor movements of theXBPM or well controlled electron beam displacements tomeasure the response of the XBPM. For each Insertion Device gap it is required to repeat this in order to build up acomplete set of scale factors covering all possible operating
conditions. Elliptically Polarising Undulators further complicate matters by having multiple operating modes which
would require multi dimensional lookup tables. Presented
in this paper is a method for retrieving the geometric scale
factors of an XBPM in real time by making use of the intrinsic small random movements of the electron beam andfinding the correlation in synchronous measurements from
Electron BPMs and XBPMs at kHz sample rates.

MOPA13Proceedings of IBIC2012, Tsukuba, Japansome minutes, and would be performed for 10 different ID
gaps. Performing such a scan for two axes, horizontal andvertical, and for three different polarisations for an APPLEII device would take two hours of dedicated beamline time.
On top of this, a typical scale factor is linear only on asmall range, typically ±100μm. Beyond this, a new scaling
factor needs to be produced or non-linear correction needs
to be used.
Previous efforts to calculate the XBPM scale factors automatically using self-learning and artificial intelligence
methods have still relied on performing physical stepper
motor movements, and generating scale factor tables for arange of gaps [3, 4]. Presented in this paper is a method for
acquiring the XBPM scale factor, K, in real-time by making use of the intrinsic electron beam movements, and fastelectronics that are capable of recording the Electron Beam
Position Monitor (EBPM) and XBPM measurements synchronously.

c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○SYSTEM CONFIGURATION
A Fast Acquisition (FA) communications network has
been developed at Diamond [5] to capture and distribute
position data from EBPMs and XBPMs at an update rateof 10kHz. This stream allows for a real-time comparisonof the electron beam trajectory through the ID straight asmeasured on the EBPMs, and the photon beam position at
12.25m from the ID, as measured on an XBPM.
Using the FA network the last 10s of data from the BPMs
is pulled into a rolling buffer. The data is then low-passfiltered in order to remove high frequency (kHz) noise. The
projected X-ray beam position, Px , at XBPM-01 can becalculated from the EBPMs as follows:
Px = (Pe2 − Pe1 )The SVD is a factorisation of the form:
M = U SV T
where M is an m × 2 matrix. The two columns containthe measured XBPM response and projected EBPM data,
and m is the length of the buffer used. U and V are unitarymatricies of size m × m and 2 × 2 respectively. S is a 2 × 2
diagonal matrix whose elements are the singular values ofthe original matrix.
The scale factor between the XBPM response and theEBPM projections is found by taking the ratio of the firsttwo elements of V T , the rotational component of the SVD:
K=V T (2, 1)
V T (1, 1)

Because the residual movements of the electron beam
are so small, the resulting scale factor computed from theSVD can be noisy. A longer buffer of data can be usedin order to reduce the noise. However, a longer buffer requires more computing power to calculate the SVD, andalso brings a slower response after a change to the system(such as an ID gap or polarisation change). With our system, the noise on a 10s buffer is an acceptable compromise
between computing time, stability, and system response.

dx
Pe1 + Pe2+de2

where Pe1 and Pe2 are the upstream and downstream
EBPM beam positions respectively, dx is the distance fromthe ID to XBPM-01 (12.25m), and de is the separation between the two EBPMs (5.76m), as shown in Fig. 2.

Figure 2: Schematic of the EBPM and XBPM locations fora typical ID straight at Diamond.

Figure 3: Block diagram of the on-line calibration system.
Figure 4 shows the correlation between the projected
measurement and the XBPM measurement. Once the calculated scale factor has been applied the standard deviation of the residual error between the two measurements is
0.81μm horizontally, and 0.61μm vertically. If the calculations are still noisy, then further averaging is performed. Arolling average of the scale factor from the last 60 seconds
generally provides very stable results.

The two sets of data (measured XBPM response andprojected EBPM data) are stored in a matrix for analysis.
Calculating the Singular Value Decomposition (SVD) of
this matrix to find the major axis between the two sets ofdata then returns the required information: the scale factor
between the XBPM response and the EBPM projections(Fig. 4).

ISBN 978-3-95450-119-92Beam Position Monitor System

Proceedings of IBIC2012, Tsukuba, Japan
Horizontal correlation

0.02
0.01
0−0.01−0.02−0.03−0.02 −0.01
00.01
XBPM Δ/Σ

0.02

that this is down to simple geometry: the electron beam
is around 10 times larger horizontally than vertically, leading to the horizontal position measurement on the EBPMs
being less sensitive, and thus containing more noise. Compounding this, the XBPM blades are located 25% closer
together horizontally than they are vertically, also resulting
in slightly reduced sensitivity to horizontal motion.

Vertical correlation
0.03

Scale factor = 1.56
EBPM projection to 12.25m (mm)

EBPM projection to 12.25m (mm)0.03

Scale factor = 0.84

0.02
0.01
0−0.01−0.02

Comparison of On−line calibration andstepper motor calibration−0.03−0.02 −0.01
00.01
XBPM Δ/Σ

0.02

21.8

Horizontal beam motion

0−0.01−0.02

1.6

XBPM−01
EBPM proj.
Scale Factor, K

00.002 0.004 0.006 0.008

0.010.012 0.014 0.016 0.018

1.4
1.2
10.8

0.02

0.6

Vertical beam motion

On−line K, X
on−line K, Y
Stepper motor K, X
Stepper motor K, Y

XBPM−01
EBPM proj.

0.01

0.4
0.2

06

6.5

77.5
ID Gap (mm)88.5

9−0.01−0.02

00.002 0.004 0.006 0.008

0.01 0.012 0.014 0.016 0.018
Time (s)0.02Figure 4: Beam position measurements from the I19 IDstraight. The geometric projection of the EBPM measurements to a distance of 12.25 m is in excellent agreementwith the XBPM measurements. The scale factor shown
here is calculated from the SVD of the correlation. The
photon beam size at the XBPM is σx = 296 μm, σy = 51 μm(calculated from electron beam divergence).

Figure 5: Calibration results during a scan of the I18 ID.
An averaging time of 60 seconds is used for the on-line
calibration.
Horizontal calibration
1s SVD buffer10s SVD buffer
10s SVD, rolling average
Stepper motor

2.05
2Scale factor, K

Beam position (mm)

0.02

1.95
1.9
1.85
1.8
1.75

FIRST RESULTS

15:15

15:20

15:25
15:30
Time (hours:mins)

15:35

15:40

Vertical calibration
1s SVD buffer
10s SVD buffer
10s SVD, rolling average
Stepper motor

1.3
1.25
Scale factor, K

The initial results show that the system can indeed provide an on-line scale factor measurement, over a range of
ID gaps (Fig. 5). However, there are some discrepancies
between the on-line measurement and the stepper motor
measurement, particularly in the vertical axis. The on-line
calibration shown in Fig. 5 has been averaged over a long
period of time to reduce the effects of random variations,and the stepper motor calibrations were calculated from
±10μm movements.
More work is required to understand these differences,
but this method could conceivably make a good replacement for the large, multi-dimensional look-up tables thatare required in order to fully utilise the XBPM measurement for every possible ID gap and polarisation.
Calculating the scale factor over a long period of timeshows that there significantly more variation in the horizontal measurement than the vertical (Fig. 6). The exact reasonsfor this are not fully understood, but one could hypothesize

1.7
1.65

1.2
1.15
1.1
1.05
1

15:15

15:20

15:25
15:30
Time (hours:mins)

15:35

15:40

Figure 6: The calculated scale factor over a 20 minute period, for a constant gap on the I18 beamline. There is aclear discrepancy between the on-line measurement and thestepper motor measurement in the vertical axis.

ISBN 978-3-95450-119-9
Beam Position Monitor System

3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Beam position (mm)

0.02
0.01

MOPA13

c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○MOPA13

Proceedings of IBIC2012, Tsukuba, Japan

CONCLUSIONSREFERENCES

This method of utilising the residual movements of theelectron beam shows promise, but the small size and random nature of the movements is the limiting factor. Thesemovements are of 10% of beamsize horizontally and∼10% of beamsize vertically, however they are of sufficiently high frequency to be negligible to the beamline users. One could consider deliberately introducing aknown modulation onto the electron beam at >200Hz that
could be detected by the XBPMs, but this introduces therisk of disturbing the beam unnecessarily. Further work isrequired to optimise the system in order to reduce the fluctuation seen in the calculated scale factor.
The final limitation on the system is that the calculation
relies on the accuracy of the EBPM measurements. Whilst
this has been simulated to a high degree of precision [6] andexperimentally verified using LOCO [7], the EBPMs experience the same non-linearity as the XBPMs. Over time it
is possible that we may drift from the physical centre of theEBPMs, which may introduce errors into the results. It ispossible that this is the cause of the discrepancy between
the vertical stepper motor results and the on-line measurement. Fortunately, the on-line calibration method presented
here can always be verified by using the XBPM steppermotors.
Currently the system runs as a MatLab script, and will
shortly be ported to a more robust system suitable for longterm deployment.

[1] O Singh and G Decker. Operational experience with Xray beam position monitors at the Advanced Photon Source.
In Proceedings of the 2001 Particle Accelerator Conference,
volume 1, pages 539–543. Ieee, 2001.
[2] E Van Garderen, J Krempaský, M Böge, J Chrin, V Schlott,T Schmidt, and A Streun. Characterisation of the Systematic
Effects of the Insertion Devices with Photon Beam Position
Monitors. Proceedings of DIPAC, pages 126–128, 2007.
[3] D Shu and T Kuzay. Smart x-ray beam position monitor system for the Advanced Photon Source. Review of Scientific
Instruments, 67(9):3367, 1996.
[4] D Shu, H Ding, J Barraza, T M Kuzay, D Haeffner, and M Ramanathan. Smart X-ray beam position monitor system using artificial-intelligence methods for the Advanced Photon
Source insertion-device beamlines. Journal of synchrotron
radiation, 5(Pt 3):632–5, May 1998.
[5] M G Abbott, G Rehm, and I S Uzun. A New Fast Data Loggerand Viewer at Diamond: The FA Archiver. Proceedings ofICALEPCS, pages 1244–1247, 2011.
[6] A Olmos, F Pérez, and G Rehm. MatLab Code for BPM Button Geometry Computation. Proceedings of DIPAC, pages
186–188, 2007.
[7] J Safranek, G Portmann, A Terebilo, and C Steier. MatLabBased LOCO. Proceedings of the 2002 Particle Accelerator
Conference, pages 1184–1186, 2002.

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4Beam Position Monitor System