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Computational Test bench and Flow Chart for Wavefront Sensors
Úrsula V. Abecassis1,2, Davies W. de Lima Monteiro3, Luciana P. Salles3,
Rafaela Stanigher3, Euller Borges3
1
Department of Electronics and Telecommunications,
Instituto Federal do Amazonas – IFAM, Brazil.
2
Graduate Program in Electrical Engineering PPGEE- Federal University of Minas Gerais - Av.
Antônio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil.
3
Department of Electrical Engineering
Federal University of Minas Gerais – Av. Antônio Carlos 6627, 31270-901, Belo Horizonte,
MG, Brazil.
ABSTRACT
The wavefront reconstruction diagram has come to supply the need in literature of an ampler
vision over the many methods and optronic devices used for the reconstruction of wavefronts
and to show the existing interactions between those. A computational platform has been
developed using the diagram’s orientation for the taking of decision over the best technique
and the photo sensible and electronic structures to be implemented. This work will be directed
to an ophthalmological application in the development of an instrument of help for the
diagnosis of optical aberrations of the human eye.
KEY WORDS: Computational test bench, Flow Chart, wavefront sensors and ophthalmology.
INTRODUCTION
Adaptive Optics is a multidisciplinary topic with a growing number of applications, from
ophthalmology to astronomy, each with their respective requirements. There are, to date,
many methods, algorithms, components and devices that can be combined in a vast variety of
ways for a wavefront-sensor design in Adaptive Optics. There is also an increasing number of
didactic books, scientific papers and websites that assist one through the meanders of
wavefront sensing, control and actuation. Nevertheless, they often tackle a specific subject or
are organized in a sequential structure of general topics, short of displaying in a
straightforward fashion how elements can be chosen to work together. Most groups indeed
have the knowledge to make suitable decisions, but for a newcomer, the realm of available
options is often fuzzy, from device to system level. In this context, we have envisioned a chart
that will be useful to aid the visualization of possible choices and how they relate to each
other.
We will focus on wavefront sensing and propose a method to display the available options,
from wavefront generation to error analysis, aiming to assist in decision making and in
organizing a Test bench for simulation and optimization of a device or sensing system. This is
based on a flow chart branching downwards and laterally, linking together only structurally
feasible options. This detector sub-block of an Adaptive Optics system alone features such
numerous pathways that we limit ourselves to detail just a few of the possible tracks to
Optical Modelling and Design III, edited by Frank Wyrowski, John T. Sheridan, Jani Tervo,
Youri Meuret, Proc. of SPIE Vol. 9131, 91312A · © 2014 SPIE
CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2051643
Proc. of SPIE Vol. 9131 91312A-1
illustrate how one can couple simulation codes and tools to design a system and preview its
performance. The chart is flexible enough to accommodate new developments on devices and
codes. As the chart is communally extended to actuation and control, and its branches are
cooperatively populated with simulation models, a more complete mapping of possible
systems will result. We will present simulation results that include the effect of several
components, including the sampling plane, photodetectors and electronic circuitry on
wavefront reconstruction.
2. FLOW CHART FOR WAVEFRONT SENSORS
The flow chart is a tool that allows a broad and organized overview of the existing
techniques and structures in the setting of adaptive optics, which composes the wavefront
sensors. Noting that in the complexity of this scenario the organization of the flow chart is a
didactic form for presentation.
The flow chart for wavefront sensors methodology will be described in general by a block
diagram. Each block of the diagram represents a section in the wavefront sensing process,
which is in [1]. Figure 2.1 shows the steps in a simplified manner.
At the first section, are declared and initialized all functions and global variables, which
could be used in the calculations process of the wavefront sensor. The use and choice of the
parameters of this section depends on the technology involved in the process.
At the second section, happens the generation, detection and visualisation of the
wavefront. The visualisation of the input wavefront is fundamental in this step, because is with
those datas that the sensor will be able to describe the wavefront that will be reconstructed
and treated. The input wavefront may have aberrations from atmospheric disturbances,
aberrations of the human eye, or other specific application . Depending on the method
chosen, modal [2] or zonal [3] with there are several characteristics techniques for detecting of
wavefronts.
At sampling plan, the input wavefront can be sampled, for exemple, through Castro lenses
[4], optical aperture with Liquid Crystal Display (LCD) [5], or a microlens array [6], which has
the function of providing information on the local inclination of the wavefront input. In other
words, it is at this stage that will be sampled parts of the wave front entrance in the shape of
light spots, regarding the same to the next step.
The 4th section, receives through the sampling plan, points of light that can be projected on
cameras like Charge-Coupled Devices (CCD) or Complementary Metal-Oxide-Semiconductor
(CMOS) [7], or even in the surface of the optical position sensitive detectors (PSDs) [8]. With
treatment of light spots captured by the focal plane, is possible to obtain local information
from the aberrated wavefront and estimate its topology.
The 5th section refers to the reconstruction of the aberrated wavefront through the
information from the local deviations of the light spots from the sampling process and from
the sensor and processes the data (sections 3 and 4). With this information and knowing the
Proc. of SPIE Vol. 9131 91312A-2
distance between the sampling plans and detection, is determined the best representation in
terms of Zernike polynomials describing the wavefront measurement.
In this step, you can choose how the wavefront will be reconstructed. The wavefront can be
reconstructed without or with the use of electronic modules. These modules consist of
electronic circuits that actually shape the system in practice. Electronics modules of 5th section
refers to optoelectronic models, electronic circuits and conversion of electronic signals.
In the last stage of the diagram, 6th section, is calculated the Root Mean Square (RMS)
reconstruction error, between the output wavefront (reconstructed), and the input wavefront
(original). The reconstruction error will measure the accuracy of the reconstructed wavefront
relative to the original one. With those numbers will be possible to analyze and find solutions
to minimize noise from the sensor itself or electronic modules involved.
i
1- Inicial
Parameters
4- Sensor and
Data
processing
2-Wavefront
3- Sampling
Plan
1
5- Wavefront
reconstruction
6- Calculation
of the
Reconstruction
error
I
Figure 2.1 - Block diagram of the wavefront sensor flow chart in a simplified manner.
3. Computational Test bench
The flow chart shows an overview of the organizational structure of wavefront sensor. This
computational test bench is a software developed to simulate one of the many ways that one
could elect to reconstruct wavefronts. This Test bench models a wavefront sensor enabling
design it and optimize it to suit various applications. Seeking to evaluate different structures
and techniques that make up a wavefront sensor without the necessity of fabricate it, that is,
select and analyze structures attached to the sensor or aggregates electronics modules. This
tool also help in analyzing the efficiency of a new structure of a wavefront sensor.
Proc. of SPIE Vol. 9131 91312A-3
The computational test bench was designed, adapting a code in C language, originally
developed in Delft - Netherlands by Gleb Vdovin and Davies W. de Lima Monteiro [9] and
modified by Luciana P. Salles [10] and Otávio G. Oliveira [11]. The initial structure of the
computational Test bench was constructed using the Hartmann-Shack technique of wavefront
sensor. Arrows in the Flow Chart in [1]. indicate the path followed on the test bench. The
computational test bench structures will be explained below.
Among the parameters that can boot the platform are: the wavelength of operation, the
number of terms of Zernike polynomials, the number of microlenses in the microlens array,
variables used to initialize the electronic modules when the algorithm requests them. In the
phase of generating and detecting the wavefront, the input wavefront (aberrated wavefront) is
constructed from prior knowledge of the amplitude of the Zernike coefficients [12] as specific
statistics per application, in the case of this work are for ophthalmological applications [13].
The usage of Hartmann-Shack was done due to the fact that it presents a compact
configuration that is robust to vibrations, because their components are generally secured
together, has low cost, has a quick wavefront reconstruction since it uses relatively simple
mathematical models to find the coefficients that describe the topology of a wavefront with
modal method [9-11].
Finally, there is the calculus of the reconstruction error (RMS) between the output
wavefront
( , ) and the input wavefront
( , ) that is given by:
=
∑ (
( , )−
−1
( , ))
,(3.1)
where
is the total number of grid points used to coordinates in which, the wavefront
( , ) values are calculated for each point ( , )
function is described.
( , ) and
using equations (3.3) and (3.2) respectively.
( , )=∑
( , )(3.2)
( , )=∑
( , )(3.3)
4) METHODOLOGY AND SIMULATION RESULTS
4.1 Methodology
The conventional aberrations such as defocus, astigmatism, coma and spherical aberration,
correlate with a subset of Zernike polynomials, and some of these are of interest for analysis.
The unit of measurement of wavefronts used in this work is the micrometer (µm).
Wavefronts used in this work are obtained through statistical models of ocular aberrations
based on [13]. Where it registered the normal ranges and mean values of the Zernike
coefficients for average pupil diameter of 5.7 mm. 109 people participated in the experiment
were normal and measures the aberrations of the right and left eyes. These distributions of
aberrations were described in 20 Zernike terms, and the terms piston and x and y inclinations
were not considered.
Proc. of SPIE Vol. 9131 91312A-4
To evaluate the results of simulations of the reconstruction error RMS platform will be
chosen three paths of the flow chart, serving as an initial validation for the same. The
established pathways can be seen in [1], through the paths indicated by the two arrows of
colors pink and red, except for three exceptions in the way indicated by the red arrow, the
intensity profile of the spot and the type of position-sensitive detectors (quad-cell)[8]. At first,
simulation was used for the spot intensity profile of the circular type and the quad-cell with
circular perimeter geometry and sensitivity homogeneous. The parameters and devices used
for the simulation results were the same for analyze the effects of the reconstruction error in
each selected path on the test bench. The other path is the same path followed by the pink
arrow, with the difference of using the response quad-cell without linearization, approaching
the data with a sigmoidal function with a known Boltzmann function.
The computational test bench has 6 stages: Parameter initial wavefront, sampling plan,
sensor and treatment of sensor data, reconstruction of the wavefront and calculation of the
reconstruction error. Following will be presented how the test bench was organized for the
simulations. All the parameters and values of the test bench simulations were adjusted by
observing the ophtalmology requirements, it is mentioned as an example the wavelength of
operation and maximum power of the laser incident on the eyeball is approximately 1.78 mW.
1) All the parameters and values of the test bench simulations were adjusted by observing
the ophthalmic requirements.
2) The input wavefronts used in this work were the average values of the Zernike
coefficients, recorded by Porter [13]. The numbers of the terms of Zernike polynomials
used for reconstruction of the wavefront is 20 terms.
3) In the sampling plan were used microlenses static and contiguous. The array of
microlenses was the regular square type and a circular sinc2 intensity profile. The
simulations were performed with 16, 36, 64 and 100 microlenses.
4) In this step we used the optical sensor position sensitive (PSD) of type quad-cell (QC)
with circular perimeter geometry and sensitivity homogeneous.
5) The wavefronts were reconstructed considering with and without electronics modules.
Emphasizing that the devices used in electronics module are DIMOS technology models
and this system does not include the influence of noise.
6) Evaluating and comparing the reconstruction error (RMS) in the three selected paths in
the platform will be adopted the following procedure:
a) The first path (arrow pink without linearization) will go through a stage of sampling
with reconstruction without electronics modules and step over the position of the
optical sensor type QC considering sigmoidal function approximation.
b) The second path (pink arrow) traverses the stage of sampling with reconstruction
without electronics modules and step over the position of the optical sensor type
QC considering a linear function approximation of its response.
c) The third path (red arrow with the three exceptions discussed above) traverses the
sampling reconstruction with electronic modules and optical position sensor type
QC considering a linear function approximation of its response.
Proc. of SPIE Vol. 9131 91312A-5
4.2 Simulation Results
Analyzing Figure 4.1, the RMS reconstruction error using the electronic modules is much
higher compared to reconstructions without them. This proves that there really is a significant
difference in physically implementing electronic in a wavefront sensor simulation. One can
extract important information about parameters optimization and the behavior of various
types of electronic structures without necessarily installing them in an optical or electronic
device. Besides, one can also test and verify new structures in order to improve the
performance of a specific wavefront, e.g. with human eye’s aberrations.
The amplitudes of the average values of the Zernike coefficients of the wavefront vary from
0.0009 μm to 0.2181 μm, being considered low in amplitude compared with the error that
suppliers use to ensure good optical structures, which is λ/10 = 0.0634 μm for red laser. For
the reconstruction of this wavefront were despised the terms tilt and defocus. The term tilt
was discarded because it is not an actual aberration; and the term defocus usually has way too
high of an amplitude, and can be optically corrected to prioritize the resolution of other terms.
These smaller amplitudes of the Zernike coefficients of the wavefront impact in the quad-cell
response. The response of quad-cell depends on the intensity profile and the size of the spot.
When a spot type sinc2 travels over the surface of a circular homogeneous quad-cell, the
response of quad-cell is a nonlinear behavior. This response of the quad-cell can be
approximated by a sigmoidal function [10].
Another approach used in this work is called the linear approximation. This approach is made
in a certain range around the center of the quad-cell response curve, aiming also to
approximate the response of the QC in relation to the position of the spot on the sensor. With
these considerations, when the wavefront aberration is constituted by large amplitudes the
spot focus will be at the ends of the QC, and therefore sigmoid approximation will result in a
smaller error. However, when the amplitudes are smaller, the spot focus will be closer to the
center of the QC, where linear approximation is privileged. That can be observed in Figure 4.1.
Another important aspect to be analyzed in Figure 4.1 is that the greater the number of
microlenses, the largest the reconstruction error. Simply by the fact that the greater the
number of sampling points, the more trustworthy will be the reconstruction.
Proc. of SPIE Vol. 9131 91312A-6
á
)rter's Coefficientt without tilt and ciefocus
for Z =20
V
0 0` `-0 ó-
°°- °- óiaqwnN
sua\oniW 4o
0
SMANI
°N°o`e
pazAI2waoN
Wa'tla013.2,
o
aberrations using 20 Zernike terms.
t
Figure 4.1 - Waveefront for the average vaalues of the ocular
Show
wing the RMSS error for th
he three routes followed
d through thee platform and the number of
micro
olenses used
d in the recon
nstruction sim
mulation.
Following, will be shown in Figure 4.2
4 the wavvefront reco
onstructed w
with and wiithout
electronic modulees through paths
p
stated earlier in Figgure 4.1.
Ob
bserving Figu
ure 4.2, theere may seeem that there is not much
m
difference between the
reference wavefrront and reconstructed one. But in
n any waveffront reconsstruction pro
ocess,
theree is the intro
oduction of error,
e
which
h means therre exists what we call a residue bettween
the reference and the reconsstructed wavvefronts. That can be seeen in Figuree 4.3 which shows
s
the reesidual figures.
An
nalyzing the residuals in Figure 4.3, we
w note thatt in the reco
onstruction w
without electronic
modu
ules, their amplitudes
a
a lower when
are
w
compaared to the ones in thee figure witth the
recon
nstruction with
w electron
nic modules, confirming again that the
t reconstrruction errorr with
the use
u of electtronics increeases. This kind
k
of analysis providees more cleearly this tyype of
inform
mation when compared to the analyysis that can
n be done through the reesults from Figure
F
4.2.
The results presented by the wavefro
ont reconstrruction confiirms that th
he computing test
bench is "workin
ng". Getting reconstructted wavefronts so closee to the refeerence wave
efront
motivvates the en
nhancementt this platfo
orm for the specific purrpose of evaluating diffferent
techn
niques and sttructures thaat are part of the contextt of wavefront sensing.
Proc. of SPIE Vol. 9131 91312A-7
Slpnoldal Response
Robroneo
oa
loon
AIM
u,+
ANC
41
0
Linear. Response
Linoar. Rosponso wnh Ebctromcs
o wo
PM
en
eaw
Figure 4.2-Mean values of Porter ocular aberrations reconstructed with 100 microlenses
showing the wavefronts: a) reference b) without electronics modules using QC sigmoidal
response c) without electronics modules using QC response linearized and d) with electronics
modules using QC with linearized response.
Uneer. Residual without Electronics
Linear. Residual with Electronics
4 MO
Figure 4.3 - Residual wavefront between the reference WF and WF reconstructed using QC
with linearized response. a) Without electronics module and b) with the electronic module.
CONCLUSION
The proposed work focuses studies in the area of adaptive optics, more precisely in the
wavefront sensor. Here was shown a flow chart and a computational tool which have great
applicability in adaptive optics, concentrating on ophthalmologic application , and presented
preliminary results in order to explain the whole scenario of a computational test bench that
aims to evaluate different techniques and structures of a wavefront sensor.
Proc. of SPIE Vol. 9131 91312A-8
Wavefronts were reconstructed using only the program written in C language, and the digital
simulation platform (Spice) which allows analysis of the electronic circuit behavior close to real
implementation of the circuitry. Modifications were made to improve the performance of the
platform. Among which is worth mentioning the automation of the wavefront reconstruction
steps. In addition to the modifications made during this step, investigation and improvement
of the computational platform must continue, now considering what was exposed in the
simulation results.
Acknowledgments
This work was supported by CAPES National Agency, the national agency for funding the
National Council for Scientific Research (CNPq) and the funding agencies of the State
Foundation for Research Support of the State of Amazonas (FAPEAM) and Minas Gerais
(FAPEMIG) and the Graduate program in Electrical Engineering (PPGEE).
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