Laser beam cleanup using improved model-based
wavefront sensorless adaptive optics
Bing Dong (董 冰)* and Rui Wang (王 瑞)
School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China
*Corresponding author: bdong@bit.edu.cn
Received October 21, 2015; accepted January 8, 2016; posted online February 26, 2016
An improved model-based wavefront sensorless adaptive optics algorithm is proposed for laser beam cleanup.
Deformable mirror (DM) eigenmodes are used to replace traditional Lukosz modes in order to avoid DM fitting
errors. The traditional method is based on a sophisticated calibration process and solving linear equations. In our
method, coefficients of DM eigenmodes are estimated by adding bidirectional modal biases into the system and
then solving parabolic equations. The calibration process is omitted in our method, which makes it more feasible.
From simulation and experimental results, the corrective accuracy of the improved method is higher than the
traditional one.
OCIS codes: 140.3300, 220.1080.
doi: 10.3788/COL201614.031406.
High beam quality is required in most laser-related appli-
cations. Adaptive optics (AO) has been proven as an ef-
fective way to improve the beam quality
[1]
. In traditional
AO, a dedicated wavefront sensor is generally used to
measure the wavefront aberration and a conjugated
deformable mirror (DM) is driven to make compensation
accordingly. However, the performance of traditional AO
can be affected by non-common path error and scintilla-
tion. In recent years, wavefront sensorless AO (WSAO)
based on model-free algorithms like hill climbing, and ge-
netic and stochastic parallel gradient descent (SPGD), are
used to improve the beam quality
[2–4]
. However, the con-
vergence speed of model-free algorithms highly depends
on the control channel number and the achievement of
a global optimum is not always guaranteed. Model-based
WSAO provides a more efficient way to correct wavefront
aberrations
[5–8]
. In model-based WSAO, wavefront aberra -
tion is estimated from the deterministic relationship
between Zernike or Lukosz mode coefficients and a well-
chosen metric function. The convergence speed of model-
based WSAO is much faster than model-free WSAO. Only
two or three correction cycles are needed by model-based
WSAO, in contrast with several hundreds of iterations
typically needed by model-free algorithms.
Although it has been successfully demonstrated in prin-
ciple, model-based WSAO has drawbacks in practice. In
this Letter, a traditional model-based WSAO algorithm
is briefly reviewed first, then an improved algorithm is
proposed to enhance robustness and accuracy. The supe-
riority of our algorithm is demonstrated both by simula-
tion and experiment.
Phase aberration can be expressed by a linear combina-
tion of Lukosz modes
[6]
,
φ ¼
X
N
i¼4
a
i
L
i
¼ a · L; (1)
where a
i
is the Lukosz mode coefficient, L
i
is the Lukosz
mode except piston and tip/tilt, and a and L are the
corresponding vectors.
Unlike Zernike modes, the orthogonality of Lukosz
modes is described as
Z
2π
0
Z
1
0
∇L
j
· ∇L
j
0
rdrdθ ¼ πδ
jj
0
; (2)
where ∇ is the gradient operator and δ
jj
0
is the Kronecker
delta.
In the geometrical optics regime, the mean-square
radius of the far-field spot is proportional to an integral
over the pupil area as
[7]
hρ
2
i ∝
ZZ
P
j∇φj
2
dA: (3)
From Eqs. (
1) and (2), the integral can be rewritten as
ZZ
P
j∇φj
2
dA ¼ π
X
N
i¼4
a
2
i
: (4)
From Eqs. (
3) and (4), the mean-square spot radius hρ
2
i
is dependent on the modulus square of the Lukosz
coefficients,
hρ
2
i¼μjaj
2
; (5)
where μ is a constant related to optical system parameters.
The metric function J with maximum value 1 is
defined as
J ¼
Z
ρ
Z
θ
I ðρ; θÞð1 − ρ
2
∕R
2
Þρdρdθ ¼ 1 −
μ
R
2
jaj
2
; (6)
where I ðρ; θ Þ is the normalized intensity distribution at
the focal-plane detector and R is the detector radius.
COL 14(3), 031406(2016) CHINESE OPTICS LETTERS March 10, 2016
1671-7694/2016/031406(4) 031406-1 © 2016 Chinese Optics Letters