Tilt angle measurement with a Gaussian-shaped laser beam tracking Martin Sarbort Simon Re rucha Petr Jedli cka Josef Lazar Ond rej C p

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Tilt angle measurement with a Gaussian-shaped laser beam
tracking
Martin ˇ
Sarbort, ˇ
Simon ˇ
Reˇrucha, Petr Jedliˇcka, Josef Lazar, Ondˇrej ˇ
C´ıp
Institute of Scientific Instruments, AS CR (ISI) , Kr´alovopolsk´a 147, 612 64 Brno, Czech
Republic
ABSTRACT
We have addressed the challenge to carry out the angular tilt stabilization of a laser guiding mirror which is
intended to route a laser beam with a high energy density. Such an application requires good angular accuracy
as well as large operating range, long term stability and absolute positioning. We have designed an instrument
for such a high precision angular tilt measurement based on a triangulation method where a laser beam with
Gaussian profile is reflected off the stabilized mirror and detected by an image sensor. As the angular deflection
of the mirror causes a change of the beam spot position, the principal task is to measure the position on the image
chip surface. We have employed a numerical analysis of the Gaussian intensity pattern which uses the nonlinear
regression algorithm. The feasibility and performance of the method were tested by numeric modeling as well as
experimentally. The experimental results indicate that the assembled instrument achieves a measurement error
of 0.13 microradian in the range ±0.65 degrees over the period of one hour. This corresponds to the dynamic
range of 1:170 000.
Keywords: optical alignment, tilt angle measurement, laser beam tracking, metrology
DOI: 10.1117/12.2052880
Note: This is a preprint rendition of a conference paper M. Sarbort et al, Tilt angle measurement with a
Gaussian-shaped laser beam tracking, Proc. SPIE, vol. 9132, pp. 91321E, 2014.
1. INTRODUCTION
One of the most challenging scientific projects currently ongoing in Europe is Extreme Light Infrastructure
(ELI) which is part of a European plan to build a new generation of large research facilities. The first research
center ELI Beamlines is located in the Czech Republic. It aims to develop an internationally unique laser device
that will provide platform for research and application projects involving the interaction of light with matter
at intensity which is about ten times higher than the currently achievable values. ELI will provide ultra-short
laser pulses of a few femtoseconds (10-15 fs) duration and give performance up to 10 PW. These extraordinary
characteristics predispose ELI to bring new techniques for medical image-display and diagnostics, radiotherapy,
tools for new materials developing and testing, latest in X-ray optics, etc.
The initial research program involves development and construction of the laser device itself, which represents
a major challenge due to extreme scientific and technical demands. To attain high focused intensities intended
for ELI it is necessary to utilize optical compressors and amplifiers that consist of many optical elements enclosed
in vacuum chambers and interconnected by vacuum pipes through which the laser beam is routed. Given the size
of these devices the path length of the laser beam reaches hundreds of meters. Therefore, an extremely precise
positioning of involved optical elements becomes an important issue.
In this paper we present a method to measure the angular tilt of the laser guiding mirrors designed for ELI
laser with desired angular accuracy of 1 microradian, operating range ±4◦, long term stability and absolute
positioning in two axes. Our approach is based on a triangulation method where a laser beam profile is reflected
off the stabilized mirror and detected by an image sensor. Since the angular deflection of the mirror causes a
change of the beam spot position, the principal task is to measure the position on the image chip surface. For
Further author information: please send correspondence to e-mail address martins@isibrno.cz (M. Sarbort)
arXiv:2210.13224v1 [physics.ins-det] 18 Oct 2022
this purpose we have employed a numerical analysis of the Gaussian intensity pattern which uses the nonlinear
regression algorithm. The performance of the method was tested numerically and verified experimentally with
satisfactory results that exceed the required accuracy.
The rest of the paper is organized as follows: Section 2 specifies the requirements imposed on the measurement
system, describes the proposed method and estimates its performance by means of numerical testing. Section 3
presents experimental verification of our method. Section 4 holds the discussion and Section 5 concludes the
paper.
LASER
CCD/CMOS
Collimating
lens Mirror
±4°
±8°
Figure 1: Principle of triangulation method.
2. METHODS
The requirements imposed on the tilt angle measurement system are given by high angular resolution of 1 mi-
croradian, large operating range ±4◦, long term stability in hours and absolute positioning in two perpendicular
axes. The key problem was neither the high accuracy nor the large measurement range alone, but the combina-
tion of both these requirements together with demand for two-dimensional measurements. The target dynamic
range is 1:150 000.
The preliminary considerations selected three possible approaches to the tilt angle measurement – a triangu-
lation method with laser beam tracking,1, 2 an autocollimator-based method3, 4 and an interferometric method
based on differential measurements in two parallel laser beams.5, 6 The main disadvantage of the autocollimator
is a limited dynamic range, the main problem of interferometric methods is the impossibility of absolute mea-
surement. Considering these drawbacks we selected the triangulation as the preferred measurement approach.
The principle of triangulation method is shown in Figure 1. It utilizes a laser beam emerging from the
source that is sequentially reflected off a mirror and detected by an image sensor. The angular deflection of the
mirror is determined from the measured deflection of the laser spot position on an image sensor and the given
geometrical configuration of the measurement system. Considering the measurement distance of 1 meter, the
desired angular accuracy of 1 microradian corresponds to the laser spot detection with resolution of 1 micrometer.
To achieve such a high accuracy it was necessary to choose proper hardware components of the measurement
system (especially an image sensor) and to develop extremely precise numerical method for detection of the laser
spot position.
Among the available laser sources we preferred the helium-neon lasers that are relatively cheap and robust
devices providing an output beam with a Gaussian intensity profile of excellent quality. As the most suitable
image sensors we selected the full-frame CCD/CMOS chips that are characterized by high spatial resolution
(pixel size about 5 µm), relatively large size (28 ×35 mm), standard bit depth (8-12 bits) and high sample rates
(hundreds of frames per second).
The laser beam tracking on an image sensor lies in a numerical analysis of the detected intensity pattern
by means of non-linear regression. The key idea is that an expected intensity pattern spanning multiple pixels
allows for detection of its position with resolution better than the size of a single pixel. The simplest case is to
detect a single laser spot with the Gaussian intensity profile given in the Cartesian coordinates by
I(X, Y ) = I0exp "−2(X−X0)2+ (Y−Y0)2
w2
0#,(1)
摘要：

TiltanglemeasurementwithaGaussian-shapedlaserbeamtrackingMartinSarbort,SimonRerucha,PetrJedlicka,JosefLazar,OndrejCpInstituteofScienti cInstruments,ASCR(ISI),Kralovopolska147,61264Brno,CzechRepublicABSTRACTWehaveaddressedthechallengetocarryouttheangulartiltstabilizationofalaserguidingmirr...

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