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A NOVEL BPM MECHANICAL CENTER CALIBRATION METHODBASED ON LASER RANGING
Xuhui Tang1, Yanfeng Sui1, Jun He, Yaoyao Du, Jianshe Cao, Junhui Yue†
Institute of High Energy Physics, Chinese Academy of Science, Beijing, China1also at University of Chinese Academy of Science, Beijing, China
Abstract
Determining the mechanical center of the beam position
monitor (BPM) has been a difficulty for BPM calibration.
To solve this problem, a method of positioning the BPM
mechanical center based on laser ranging is proposed. Thismethod uses high-precision antenna support as the core
locating datum, and high-precision laser ranging sensor(LRS) as the detection tool. By detecting the distancesfrom the LRSs to the antenna support and the distancesfrom the LRSs to the BPM, the mechanical center of theBPM can be indirectly determined. The theoretical systemerror of this method is within 20 μm, and the experimental
results show that the measurement repeatability is 15 μm,
This method has low cost and fast speed, which can be used
for large-scale calibration.

INTRODUCTION
The BPM system, as the eyes of the particle accelerator,
plays an important role in the stability of the beam orbit.
About 600 BPMs are produced during the construction ofHigh Energy Photon Source (HEPS) project [1]. Due toprocessing errors, the mechanical center and electricalcenter of BPM do not coincide. Therefore, each BPM isdemanded to calibrate before use [2]. For the button-type
BPM with 45-degree rotation, as shown in Fig. 1, therelationship between position coordinates and electrodesignal amplitudes is defined as Eq. (1) [3].

where 𝐾 , 𝐾 are the BPM sensitivity coefficients, 𝑋,𝑌
are the difference between the BPM electrical centerand mechanical center. The process of determining 𝐾 , 𝐾 ,𝑋, and 𝑌
is called BPM calibration. A BPM
automatic calibration system is shown in Fig. 2 and it iscomposed of an RF signal source, antenna (Goubau line),precision motion stages and their controller, BPM
electronics, and the industrial personal computer [4, 5].
The Goubau line emits transverse electromagnetic (TEM)
waves with the excitation of the RF signal source, so as tosimulate the electromagnetic field of the charged particle
beam in the accelerator to enable BPM calibration [5]. The
BPM is driven by the precision motion stages to move inhorizontal and vertical directions. The industrial computer
saves the real BPM position data recorded by the controller
and the calculated BPM position data from the BPM
electronics. Then, the sensitivity coefficients and offsets
are analyzed by the software algorithm.
.

Figure 2: Schematic of BPM automatic calibration system.
In general, it is relatively easy to ascertain the BPM
electrical center, as long as the operator observes the fourchannels of BPM electronics and makes them equal byadjusting the BPM motion stage. To achieve this goal, it isnecessary to ensure that the four channels of BPM
electronics and the coaxial cables are calibrated. However,finding the mechanical center is extremely difficult, so it ishard to determine 𝑋and 𝑌.
Figure 1: A HEPS BPM and its define of electrode andbeam coordinate system.
𝑉 +𝑉 −𝑉 −𝑉+𝑋
𝑉 +𝑉 +𝑉 +𝑉
𝑉 +𝑉 −𝑉 −𝑉
𝑦=𝐾+𝑌
𝑉 +𝑉 +𝑉 +𝑉

𝑥=𝐾=𝐾 𝑈+𝑋=𝐾 𝑉+𝑌(1)

A NEW APPROACH TO DETERMINING
BPM MECHANICAL CENTER
The main difficulties in calibrating the mechanicalcenter are as follows: firstly, it is not easy to ensure that theantenna is parallel to the axis of BPM; Secondly, it isalmost impossible to directly measure the distance between

MOP0268202 Beam Position Monitors

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the antenna and the edge of the BPM vacuum chamber;
Finally, the high accuracy requirement (tens ofmicrometers) poses great challenges for manualadjustment. In order to solve the problems above, a highprecision antenna positioning support was designed, and ahigh-performance laser ranging sensor (span 30±4 mm,resolution 0.5 μm) was introduced as the detection tool forthe system self-inspection and seeking BPM mechanicalcenter. The schematic diagram of the positioning system isshown in Fig. 3, where the uppercase letters XYZ represent
the geodetic coordinate system (GCS) and lowercase
letters xy represent the BPM coordinate system. Figure 4
shows the distances that need to be measured to determine
the BPM mechanical center, where 𝐻 and 𝐿 are thedimensions of BPM, 𝐻 are the dimensions of the antenna
support, 𝑟 is the radius of the antenna, 𝑋 and 𝑌 are thedistances from the LRSs to the antenna support, and 𝑋and Y
are the distances from the LRSs to BPM. Whenthe antenna is located in the BPM mechanical center, thefollowing relationship is satisfied:
𝐻+ +𝑟(2)𝑌 +𝐻 =𝑌2𝐿
𝑋 =𝑋
+ +𝑟2
Transfer Eq. (2) to Eq. (3). When the position of BPM,and 𝑌, have been adjusted to meet
namely 𝑋Eq. (3), it can be considered that the mechanical center ofBPM has been found.
𝐻(3)𝑌 _ =𝑌 +𝐻 − −𝑟2𝐿
𝑋 _ =𝑋 − −𝑟2
In Eq. (3), the right side of the equals sign is theparameters of the positioning system. Moreover, only 𝑌and 𝑋 are measured values, the rest are all constants. Aslong as the system state is unchanged, 𝑋 _ and 𝑌 _are two constants. When the antenna is in the electricalcenter of BPM, let the distance measured by the two laser
sensors be denoted by 𝑋 _ and 𝑌 _ , then the offset
between the electrical center and the mechanical center canbe calculated as= −(𝑌 _ − 𝑌 _ )(4)
𝑋𝑌=𝑋 _ −𝑋 _The specific calibration operating steps are shown inTable 1.
In Table 1, step 1 is a system self-test, which only needs
to be performed once as long as the system state remainsunchanged. Step 2 is to make the antenna parallel to thesystem, and steps 3-4 ensure that the BPM is parallel to thesystem. Steps 5 and 6 are optional operations. If calibratingfrom the mechanical center, proceed to step 5. If only
measuring offset, perform step 6.

ERROR ANALYSISThe processing errors of the antenna support and BPM
is the main source of system errors. Now assume that thesize errors of the support and BPM are ∆𝐻 and ∆𝐻, so themeasured value 𝑌 in Eq. (3) will turn into 𝑌 + ∆𝐻 , andFigure 3: BPM machine center calibration method basedon laser ranging.

Figure 4: The distances that need to be measured todetermine BPM mechanical center.
𝑌 _ will become 𝑌 _ + ∆𝐻. Then, the offset in theY direction is 𝑋′=𝑋+ ∆𝐻 − ∆𝐻 . Similarly,=𝑌+ ∆𝐿 − ∆𝐹, where ∆𝐿 is the size error of𝑌′
the BPM in the X direction, and ∆𝐹 is the geometry errorof the support’s positioning plane. The error model isshown in Fig. 5.
Considering the worst-case scenario, when the error
direction of the antenna support is opposite to the BPM, thetotal systematic errors are the sum of absolute values:∆𝑋∆𝑌= |∆𝐻 | + |∆𝐻|
= |∆𝐿| + |∆𝐹|

(5)
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ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3IBIC2023, Saskatoon, Canada
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1

Move the LRSs in the Z-direction from the leftmost tothe rightmost of the antenna support, and observe
whether the data of the two LRSs change

2
3
4

5

6

Operation Purposes

Install BPM. Let the antenna through the BPM vacuum
chamber and press it on the positioning planes of theantenna support.
Move the LRSs in the Z direction, scan the top and sides
planes (shown in Fig. 4) of the BPM, and observe
whether the readings of the two LRSs change.
Hold the LRSs at the middle position of the antenna
support, move BPM along the Y-axis, and observe
whether the reading of the No. 2 LRS changes
Adjust the position of BPM so that the distances between
BPM and LRSs are equal to 𝑋 _ and 𝑌 _ , whichmeans that the antenna is in the BPM mechanical centerat this time.
Adjust BPM and let the antenna reach its electricalcenter, read the two LRSs data 𝑋 _ and 𝑌 _ , andcalculate offsets according to Eq. (4).

Figure 5: Schematic diagram of system error.
Since the machining error of both antenna and BPM iswithin 10 μm , the maximum system error is less than
20 μm.
The random error of this method includes themeasurement resolution (0.5 µm) of the LRSs, thedisplacement accuracy (1 μm ) of the motion stage, theinfluence of temperature drift or ground vibration, and theinstallation repetitive error of the BPM. Among them, thefirst three are small enough so as to be ignored, while theBPM installation errors will affect the electrical centerparameters 𝑋 _ , 𝑌 _ , and the mechanical centerparameters 𝑋 , 𝑌 . which means that installation errors arethe main source of random errors.

Ensure that the movement direction of theLRSs is parallel to the two positioning planes(shown in Fig. 4) of the antenna support. Then,calculate 𝑋 _ and 𝑌 _ based on Eq. (3).
Ensure that the antenna between the two pillarsof the support is parallel to the two positioningplanes.
Ensure that the axis of the BPM is parallel tothe antenna (Eliminating the rotational errors
around X-axis and Y-axis)
Ensure that BPM is placed vertically(Eliminating the rotational error around Z-axis)
Align the antenna with the BPM mechanicalcenter, open the automatic calibration softwareand start the calibration program.
Only measure the electro-mechanical offset

Installation errors resulting in imperfect parallel within
the system that causes rotation errors in in the X, Y, and Z
planes of the BPM coordinate system. Theoretically, if
steps 3-4 in Table 1 are strictly executed, all installation
errors will be eliminated, but the calibration efficiency will
be seriously reduced in actual engineering. Therefore, inorder to improve calibration efficiency, the BPM
installation errors were analyzed without performing steps
3-4, and the results are shown in Table 2. The error
generated by rotation around the Z-axis is shown in Fig. 6.
Hence, excluding the errors that can be software
eliminated, the measured random errors can be expressedas Eq. (6):∆𝑌= ∆𝑋 _ + ∆𝑋 _ + ∆𝑋 _ + ∆𝑋 (6)∆𝑋= ∆𝑌 _ + ∆𝑌 _ + ∆𝑌 _ + ∆𝑌
Assuming that 𝜃 = 0.1°, 𝑙 = 4 mm, 𝑙 = 50 mm, and𝐻 = 210 mm , the error value ∆𝑋 = 7 μm and∆𝑌 = 87 μm will be obtained. Thus, due to the large 𝑙 ,slight rotation of the Z axis will cause a large ∆𝑌 , whichshould be avoided as much as possible. In order toeliminate the installation rotation error, it is necessary toinstall BPM with a fixed torque wrench.

EXPERIMENT AND DISCUSSION
The physical experimental platform designed according
to Fig. 3 is shown in Fig. 7. To improve the calibration
efficiency, the two LRSs and precision motion stages arecontrolled by a computer program. The parameters of thetested BPM are 𝐻 = 210 and 𝐿 = 12. Support parameter
𝐻 = 182 and the diameter of the antenna 𝑟 = 0.105. Bycompleting step 1 in Table 1, we can get 𝑋 = 5.820 ,𝑌 = 1.780 , 𝑋 _ = −0.287 , and 𝑌 _ = −0.328 .
The unit of all above data is mm. Then, install a BPM andMOP026
8402 Beam Position Monitors

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adjust its position until the antenna is located at theelectrical center, and measure 𝑋 _ and 𝑌 _ . Repeat
the experiment 5 times in three different ways and observe
the repeatability accuracy. The experimental data is shownin Table 3.
Table 3 shows that changing only the antenna or BPM
results in small random errors, and the repeatability
accuracy is within 10 μm . If both of them are changed
simultaneously, the repetition precision is approximately
15 μm . The more objects that are changed, the more
uncertainties are introduced and the greater themeasurement error is obtained. In practical engineering,each calibration requires manual operation of the BPM andantenna at the same time, so the third row in Table 3 is themost realistic. On the basis of three-sigma rule, the rangeof measurement results is mostly within ±30 μm.

(NE01G74Y2), and the National Natural Science
Foundation of China (11805221).

Figure 6: The error model for BPM rotation around Z-axis.

CONCLUSION
In order to quickly, low-cost, and high-precision
measure the BPM electro-mechanical offset, a new method
using precision antenna support and laser ranging sensor isproposed. The system’s mechanical components aredesigned, and an automatic measurement program wasdeveloped. The resolution and maximum absolute error ofthis method are 15 μm and 20 μm, respectively. Improving
the machining accuracy and surface finish of the antenna
support, and designing a more reliable antenna pressing
mechanism can further improve the calibration accuracy.

ACKNOWLEDGEMENT
This work was funded by the Foundation of YouthInnovation Promotion Association, CAS (Y202005), andthe Major achievements cultivation project of major
scientific and technological infrastructure, CAS

Figure 7: The experimental platform.
Table 3: The Experimental Data (unit: μm)
Measurement operation
Repeat installation of the BPM
without changing the status of theantenna
Repeat installation of the antenna
without changing the BPM status
Repeat the installation of theantenna and BPM simultaneously

𝛔𝐱_𝐨𝐟𝐟𝐬𝐞𝐭

𝛔𝐲_𝐨𝐟𝐟𝐬𝐞𝐭

3.3

10.2

8.1

2.4

15.4

12.2

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Table 2: BPM Installation Errors Analysis
Error
SourceEffect on Measurement

Rotationaround Xaxis∆𝑋 _ is difficult to evaluate.
∆𝑌 _ is difficult to evaluate.
∆𝑌 ≈ 𝑙 𝜃 , 𝑙 is the distance from the laser spot to theX-Y plane. 𝜃 is the rotational error.

Rotationaround Yaxis∆𝑋 _ is difficult to evaluate.
∆𝑌 _ is difficult to evaluate.
∆𝑋 ≈ 𝑙 𝜃 , 𝑙 is the distance from the laser spot to theX-Y plane. 𝜃 is the rotational error.

Rotationaround Zaxis∆𝑋 _ is difficult to evaluate.
∆𝑌 _ is difficult to evaluate.
∆𝑌 ≈ 𝑙 𝜃 − 𝐻𝜃 /2, 𝑙 is the distance from the laser
spot to the Y-Z plane. 𝜃 is the rotational error.
∆𝑋 ≈ 𝑙 𝜃 , 𝑙 is the distance from the laser spot to theX-Z plane.

Elimination Method
Hardware: Tighten the BPM mounting
screws using a fixed torque wrench
Software: The LRS1 scans along the Z-axis
and the error ∆𝑌 can be eliminated byaveraging the measured 𝑌 at multiplepositions.
Hardware: Tighten the BPM mounting
screws using a fixed torque wrench
Software: The LRS2 scans along the Z-axis
and the error ∆𝑋 can be eliminated byaveraging the measured 𝑋 at multiple
positions.
Hardware: Tighten the BPM mounting
screws using a fixed torque wrench
No feasible software elimination method

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[3] J.Y. Chen, C.H. Chen, M.S. Chiu, et al., “A fast gain
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[4] X.H. Tang, J. He, J.H. Yue, et al., “Development of anautomatic calibration system for beam positionmonitor”. Nucl. Tech., vol. 45, p. 020102, 2022.
[5] J. He, Y.F. Sui, Y. Li, et al. “Design and optimizationof a Goubau line for calibration of BPMs for particleaccelerators”, Nucl. Instrum. Methods Phys. Res.,
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