High Power Laser Science and Engineering, (2020), Vol. 8, e28, 5 pages.
doi:
10.1017/hpl.2020.29
RESEARCH ARTICLE
Decoupling of the position and angular errors
in laser pointing with a neural network method
Lei Xia
1,2
, Yuanzhang Hu
1
, Wenyu Chen
1
, and Xiaoguang Li
1
1
Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
2
Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province,
College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
(Received 12 February 2020; revised 31 May 2020; accepted 1 July 2020)
Abstract
In laser-pointing-related applications, when only the centroid of a laser spot is considered, then the position and angular
errors of the laser beam are often coupled together. In this study, the decoupling of the position and angular errors is
achieved from one single spot image by utilizing a neural network technique. In particular, the successful application of
the neural network technique relies on novel experimental procedures, including using an appropriate small-focal-length
lens and tilting the detector, to physically enlarge the contrast of different spots. This technique, with the corresponding
new system design, may prove to be instructive in the future design of laser-pointing-related systems.
Keywords: artificial neural networks; laser pointing; pointing errors
1. Introduction
Accurate laser pointing is crucial for many applications
such as free-space communication
[
1]
, fusion ignition
[2]
, high-
power lasers
[
3]
and robot manipulators
[4]
. The position and
angular errors of a laser beam should therefore be accu-
rately measured and synchronously adjusted. In measure-
ments based on the centroidal position of a laser spot
[
5–7]
the two errors are often coupled together, which means
that they cannot be determined with one single measure-
ment. The pure angular error in many applications can
actually be obtained with the detector located on the in-
focus plane. In this case, however, the position error of the
laser is totally sacrificed. For applications requiring both the
position and angular errors, such as fine optical systems
[
8]
,
laser resonator alignment
[
9]
, laser beam drift control
[10]
and
lithography
[
11, 12]
, the common decoupling method for these
two errors involves making two measurements, wit h one
measurement on the in-focus plane and the other on the
out-of-focus plane. It can be implemented by repositioning
detectors at different locations
[9]
, or splitting the beam into
two paths
[
10–14]
. Since these methods only utilize informa-
tion regarding spot centroids, long-focal-length lenses are
Correspondence to: X. Li, Institute for Advanced Study, Shenzhen
University, Shenzhen 518060, China. Email: xgli@szu.edu.cn
required to improve the sensitivity of the spot centroid dis-
placement. Optical measurement systems using these meth-
ods inevitably involve complex structures and a reduction in
system reliability.
The artificial neural network technique can establish the
connection between the input and the output of systems by
learning from datasets, and has been used in many fields
for function approximation and pattern recognition
[
15, 16]
. In
particular, t his technique has already been used in many
different optical systems. In adaptive optics systems, neural
networks have been applied to derive the distorted wavefront
from a simultaneous pair of in-focus and out-of-focus images
of a reference star
[
17–19]
. Breitling et al. have used neural
networks to predict the angular deviation of a pulse laser
from the final four sample positions
[
20]
. Guo et al. have
utilized neural networks to reconstruct the wavefront of
human eyes from the spot displacements from a Hartman–
Shack sensor
[
21]
. Abbasi et al. have adopted neural networks
to obtain the position vector of a Gaussian beam for vibration
analysis from four quad cell power distributions
[
22]
. Yu et al.
have employed neural networks to obtain the tilt, decenter
and defocus of a laser diode fast-axis collimator from four
parameters from the measured field distribution
[
23]
.
In this study, a neural network is applied to extract full
information from the intensity distribution of a laser spot,
and the position and angular errors of a laser beam can be
© The Author(s) 2020. Published by Cambridge University Press in association with Chinese Laser Press. This is an Open Access article, distributed under
the terms of the Creative Commons Attribution licence (
http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and
reproduction in any medium, provided the original work is properly cited.
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