HYBRID ALGORITHM TO OPTIMIZE THE OPTICAL QUALITY OF SCLERAL LENSES

DANIEL F. FILGUEIRAS, ANA L. S. BRAGA, RODNEY R. SALDANHA, LUCIANA P. SALLES

Departamento de Engenharia Elétrica, Universidade Federal de Minas Gerais

Av. Antônio Carlos, 6627, Pampulha, 31270-010, Belo Horizonte, MG, Brazil E-mails: danielff@ufmg.br,analuizasb@ufmg.br,rodney@cpdee.ufmg.br,

luciana@cpdee.ufmg.br

Abstract Scleral lens is a large contact lens that cover part of scleral region of human eye. They are constructed from

two surfaces (anterior and posterior). In the design and production process of these lenses, optical imperfections

(aberrations) can be inserted, among other factors, due to the fact of peripheral light rays incident on the lens are refracted more than the paraxial rays. In this case, instead of a well defined focal point, the lens presents a spread point (blur) in the

focal plane, and it produces a spherical aberration on the image. Spherical aberrations are optical effects that impair the

optical quality of the lens and therefore decrease the image quality. This paper presents a hybrid algorithm to optimize the optical quality of scleral lens using a lower processing time than the one obtained using only genetic algorithm. The hybrid

algorithm combines the genetic algorithm and the Quasi-Newton Broyden, Fletcher, Goldfarb and Shanno (BFGS) method.

This optimization generates an optimal conic constant, which is added to the lens anterior curvature calculated to ensure

higher optical quality to the product by correcting its spherical aberration.

Keywords Genetic Algorithm, BFGS, Scleral Contact Lens, Raytrace software, MTF, Optical Aberration, Conic

Constant.

Resumo Lentes esclerais são lentes de contato maiores que cobrem parte de região da esclera do olho humano. Elas são

construídas a partir de duas superfícies (anterior e posterior). No projeto e processo produtivo destas lentes, imperfeições

(aberrações) ópticas podem ser inseridas devido, dentre outros fatores, ao fato dos raios de luz incidentes na periferia das lentes serem mais refratados do que os raios que incidem próximo ao eixo óptico. Nesse caso, ao invés de um ponto focal

bem definido, a lente apresenta um ponto focal espalhado (borrado) no plano focal, produzindo uma aberração esférica na

imagem formada. Aberrações esféricas são efeitos ópticos que prejudicam a qualidade óptica das lentes e, portanto, diminuem a qualidade da imagem. Este trabalho apresenta um algoritmo híbrido para otimizar a qualidade óptica de lentes

de contato esclerais usando um tempo de processamento menor que o obtido usando somente o algoritmo genético. O

algoritmo híbrido proposto é construído pela associação de um algoritmo genético ao método Quase-Newton de Broyden, Fletcher, Goldfarb e Shanno (BFGS). Esta otimização gera uma constante cônica ótima que, quando acrescentada à

curvatura anterior esférica calculada para a lente, garante maior qualidade óptica para o produto através da correção das

suas aberrações esféricas.

Palavras-chave Algoritmo Genético, BFGS, Lente de Contato Escleral, Raytrace software, MTF, Aberração Óptica, Constante Cônica.

1 Introduction

Scleral lenses are large-diameter rigid gas

permeable lenses. They can range from 13.6 mm to

over 20 mm in diameter (Figure 1). They are called

“scleral” lenses because they completely cover the

cornea and extend onto the sclera, the white part of

the eye. Technological advances in the discovery of

materials with high oxygen transmissibility and

sophisticated designs made possible the widespread

use of large-diameter lenses nowadays (Roach,

2012).

(a) (b)

Figure 1: (a) Scleral lens (right) in comparison to a conventional

soft lens. (b) Scleral lens in the eye. (Worp, 2012)

Indications to scleral lens have evolved in the

last years, starting from a lens to hardly irregular

corneas to a very large gamma of indications. The

correction of irregular cornea to restore the vision is

the main indication to scleral lens because it covers

the entire corneal surface with a regular curvature

(Figure 2). However, there are suggestions from

experts (Worp, 2010; Worp, 2012; Roach, 2012)

about scleral lens use in a wide range of corneal

irregularities, instead of using a conventional

corneal lens. This indication is based on the fact that

the cornea is one of the most sensitive parts of

human body, since it has exposed sensory nerves

and any mechanical stress, which can be induced by

corneal lens direct contact, causes discomfort to the

user. Unlike the cornea, the sclera has a very low

sensitivity, favoring scleral lens use. When well

fitted, it exempts any contact to the sensitive cornea

(Worp, 2010; Worp, 2012).

Patients, in general, when submitted to an

adaptation test with scleral lens, show positive

reception in relation to its comfort, which favors the

increasing popularity of this kind of lens on the

market (Worp, 2012).

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2508

Figure 2: Scleral lens basic design (Rosenthal, 2009).

Some lens is likely to fails and aberrations. One

of the most undesirable aberrations is spherical

aberration.

Spherical aberration is the focus blur caused by

a higher deviation of the peripheral rays in

comparison to the paraxial rays. This deviation

produces a blur instead of a point in the image plane

(Figure 3). Spherical aberration is more intense on

high power lens and can be reduced using aspheric

surfaces (Coral-Ghanen et al., 1999), which means

to add conics to the spherical radius. Then, the lens

gets into a conic form and improves its optical

quality.

Therefore, this work aims to develop a choice

method to the best conic constant that will be added

to lens spherical surface in the production process.

(a) (b)

Figure 3: (a) Lens with spherical aberration (b) Correction to spherical aberration.

2 Theoretical concepts

Concepts about lens design, prescription, optical

analysis and optimization are presented below to

provide a wider view of the proposed project.

2.1 Design aspects

In general, a simple scleral lens design may be

divided in optical zone, transitional zone and haptic

zone (Figure 4).

2.1.1 Optical Zone

The optical zone corresponds to the lens central

area and acts like an optical device. This region is

related to the lens desired power and can vary

according to the radius values of both conjugated

curvatures, the distance between them (central

thickness) and the refractive index of the material.

The anterior surface of the optical zone may be

produced in spherical or aspherical form. The

aspheric surfaces may reduce some intrinsic optical

aberration and they can be found in more

sophisticated designs of lens (Coral-Ghanen et al.,

1999). The posterior surface (concave face) should

be similar to the corneal curvature (Worp, 2010;

Rosenthal, 2009).

2.1.2 Transitional Zone

The transitional zone (Figure 4) corresponds to

the intermediary zone between the optical zone and

the haptic zone. This region must be changeable to

fit to different corneal curvatures that the patient

may present.

2.1.3 Haptic Zone

The haptic zone (Figure 4) is the lens region that

touches the sclera and provides the adequate support

to the system. Typically, the haptic zone is flat or it

is composed of a series of curves with radius from

13.5 mm to 15.4 mm, which normally fit to the

majority of the eyes (Worp, 2010).

Figure 4: Variation of Transitional Zones following the

Optical Zone (Rosenthal, 2009).

2.2 Scleral lens prescription

To recommend contact lens to a patient, the

ophthalmologists usually makes tests to define the

lens specifications that best fits to the cornea.

Corneal biometric parameters and the lens power to

correct refractive errors are measured (Coral-

Ghanen et al. 1999; Gemoules, 2008). These

informations are then sent to the lens maker, who

will calculate the three different zone parameters to

produce the lens. The optical zone, which is object

of this optimization work, is made up of two curves:

anterior and posterior (Figure 4). The posterior curve

represents the concave part and faces the eye,

therefore it is defined by the corneal dimensions of

the patient. The anterior radius of curvature, ra

(mm), is defined by: the desired lens power, diopter

(d), the central thickness, esp (mm), the refractive

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2509

index, idxr, and the posterior curve radius rp (mm),

through the following equation (Douthwaite, 1987):

𝑟𝑎 =(1+

(𝑒𝑠𝑝∗(𝑖𝑥𝑑𝑟−1))

(𝑖𝑥𝑑𝑟∗𝑟𝑝))

((𝑑𝑖𝑜𝑝

1000∗(𝑖𝑑𝑟𝑥−1))+(

1

𝑟𝑝))

. (1)

Defining the anterior radius of curvature, by the

equation 1, there is a spherical radius value. This

value is used to produce the lens with a blurred in

the image focus, called spherical aberration.

2.3 Lens optical analysis

The quality of the projected image on the focal

plane is obtained by determining the modulation

transfer function (MTF). MTF is the magnitude of

optical system response when sinusoids of different

spatial frequencies are put on its input (Boreman,

2001). In other words, MTF is one common figure

of merit to measure lens quality. The MTF reference

value related to the International Standard ISO

11979-2:1999(E) (ISO, 1999) shall be greater or

equal to 0.43 for an acceptable imaging quality of

the optical system of model eye.

Since the purpose of the work is focused on the

optimization of the lens and not the modeling of a

wavefront that propagates and interacts with each

surface composing the eye to reach the retina, we

used a Raytrace software for optical design that is

capable of performing all tests required to

characterize optical lens. With it, you can model the

human eye; and the variables of optical quality, as

the MTF, are calculated from the propagation of

light rays.

2.4 Optimization Algorithms

Optimizing is the process of making something

better. An engineer or scientist evokes a new idea

and the optimization obtains the best point in this

idea. Optimization consists in trying variations

about an initial concept and uses the obtained results

to improve the idea. Optimization is then the specific

mathematic tool to obtain the best solution (Haupt

and Haupt, 2004).

2.4.1 Genetic Algorithm

Genetic algorithms use concepts originating from

the principle of natural selection of species to

approach a wide range of optimization problems.

Basically, the genetic algorithm creates a population

of possible answers to the problem being treated and

submit it to the evolution process, constituted by the

following stages (Costa, 1999):

1. Evaluation: the fitness of individuals that are

randomly generated are evaluated.

2. Selection: the best individuals are selected to

reproduction. The probability of being

selected is proportional to the fitness.

3. Cross-over: the best individuals’

characteristics are recombined, generating

new solutions.

4. Mutation: the individuals from the

reproduction process have their

characteristics altered to add variety to the

population.

5. Actualization: the individuals created in this

generation are inserted in the population.

6. Termination: it is checked if the solution

meets the end condition. If positive, the

algorithm terminates and returns the answer.

If not, the process is repeated.

2.4.2 Quasi-Newton Algorithm - BFGS method

The quasi-Newton algorithms are algorithms for

nonlinear systems that in their method it need only

the gradient of the objective function available in

each iteration. By measuring changes in the gradient

between the iterations, it tries to build a model to the

objective function good enough to converge the

result (Lewis and Overton, 2013). Among Quasi-

Newton methods, Broyden, Fletcher, Goldfarb and

Shanno algorithm (BFGS) is considered the most

efficient and because of it the most popular (Skajaa,

2010).

Experiments have shown that the method has

strong properties of auto-correction, thus, if in some

interaction the matrix contains bad information of

curvature, it conducts to only a few actualizations to

correct these inaccuracies. Because of this reason,

BFGS method often has excellent working, and once

close to a minimum, normally reaches the

superlinear convergence rate (Skajaa, 2010).

3 Hybrid algorithm to optimize scleral lenses

3.1 Hybrid code purpose

The purpose of the hybrid algorithm model was to

utilize the genetic algorithm capability of spatial

search with the speed and precision of local search

of the deterministic BFGS method. In this proposal,

the genetic algorithm, which was limited to a few

number of iterations, was used in the beginning of

the program execution, to reduce the searching space

and find the direction of the top of the correct

answer. Starting in this point, the BFGS algorithm

will search the optimal result, with high

performance, precision and low cost.

3.2 Hybrid code structure

The algorithm has basically the following

structure:

1. Data acquisition from the

ophthalmologist (program inputs):

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2510

patient’s corneal height in relation to

iris (Sagittal height), corneal diameter,

lens power.

2. Calculus of posterior curve radius (rp)

and anterior curve radius (ra).

3. Establishment of communication with

the Raytrace software and loading the

calculated curves radius in the eye

model close to anatomical, biometric,

and optical realities from Liou and

Brennan (Liou and Brennan, 1997).

4. Start of the genetic algorithm through

the GA (Genetic Algorithm) in the

optimization toolbox of Matlab with a

limit of 12 conic constants random

values (initial population) in the

defined range of [-5 to 0] and number

of iterations limited to five. The

objective function inside of the

Raytrace software evaluates the conic

constant inserted in the optical system.

The return of this function is the MTF

fitness (lens optical quality).

5. At the end of five iterations, a conic

constant close to the ideal is given,

then the BFGS method is called to find

in a precise and fast way the conic

optimal value.

6. The algorithm returns the conic ideal

value to a specific lens, the MTF

theoretical value and the execution

time.

4 Simulation

The Raytrace software allows communication

with Matlab, therefore, it is possible to use the

optimization tools in Matlab’s toolbox, and “call”

the software only when analyzing the objective

function, understood as a “black box”. Therefore,

data like the anterior curvature, posterior curvature,

and conic value of the lens are given to Raytrace

software, which, in return, gives the MTF value.

The motivation to use optimization algorithms to

define the best conic constant, instead of only an

equation group, is the fact that it is very complex to

model analytically a light beam spreading through

eye structures.

The algorithm tests were performed to

analysis of the following situations:

- Analysis of lens optical quality with and

without optimization

Lens optical quality of a four diopter test

lens with the constant optimized through

the genetic and BFGS hybrid algorithm;

Lens optical quality of a four diopter test

lens considered as totally spherical

(without the optimization process);

- Analysis of optimizing algorithms performance

Analysis of pure BFGS algorithm

performance with five different values of

starting point within the search limit from -

5 to 0 to optimize a four diopter test lens;

Analysis of pure genetic algorithm

performance;

Analysis of the genetic and BFGS hybrid

algorithm to optimize a four diopter test

lens;

- Analysis of the hybrid algorithm proposed

considering a wide range of corneal curvatures:

Hybrid algorithm test with 13 lens of

different powers, considering the range of

corneal anterior curvature measures in

human eyes: 7.0 to 8.4 mm, presented by

Bo Tan (2009).

5 Results

5.1 Analysis with optimization

Firstly, it was performed the analysis of a lens

optimized with the hybrid process purposed in the

work. The rays focus at a single point, as shown in

Figure 5.

(a)

(b)

Figure 5: (a) Eye in focus refraction model. (b) Graph

representing the high optical quality of the tested lens.

The result was a conic constant value optimized

to -0.2749 (best result returned by the hybrid

algorithm), in which the program returned an MTF

value equal to 91.1621. This value is considered a

good result because it is very close to the theoretical

maximum and it allowed sharp view of the test

object, represented by a window, with high

distinctness (Figure 6).

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2511

Figure 6: Graph representation of an image seen using the optimized lens. (Image generated by the Raytrace software).

5.2 Analysis without optimization

Posteriorly a lens without optimization was

evaluated, namely, a lens with conic constant equal

to zero (spherical). The results are shown in Figure

7, in which the rays do not focus at a single point,

therefore the MTF also decreases, making clear the

effects of spherical aberration.

(a)

(b)

Figure 7: (a) Blurred eye refraction model. (b) Graph

representing the low optical quality of the tested lens.

With the conic constant equal to zero, the

algorithm returned an average of MTF values equal

to 18.9000, considered a low value (the top line

means the maximum value). Despite the blur, that

MTF value does not preclude the observer to

interpret the object using a spherical lens, (Figure 8).

5.3 Algorithm comparison

As a second part of this work, it was performed

the comparison of the following algorithms

prosecution: pure BFGS, pure genetic and finally the

genetic and BFGS hybrid algorithm.

5.3.1 Pure BFGS algorithm

To analyze the purposed problem with the pure

BFGS algorithm, it was performed tests with five

conic different initial values within the searching

limit from -5 to 0 and epsilon step size tolerance of

1e-10:

Table 1: Test with BFGS algorithm

Start

point

MTF Iteration Processing

time (s)

0 11.6988 0 4.949017

-1 11.4407 0 5.711302

-2 9.7003 7 24.670184

-3 7.3660 0 4.109644

-4 6.9591 0 27.804823

-5 6.8080 0 3.835138

According to Table 1, BFGS algorithm has low

processing time, but it has also premature

convergence in local maximum. Therefore, to have

a good BFGS performance, it is necessary to have a

start point close to global maximum.

5.3.2 Pure genetic algorithm

The following test is performed using pure

genetic algorithm. The inputs and outputs are

described in Table 2.

According to the results, the genetic algorithm

has good convergence, as shown in Figure 9. The

Fitness value, in MTF, is the response of the optical

system model for the various conic values in the

entrance of the objective function.

The pure genetic algorithm converging graph

shows that in the 30 iterations available, the

algorithm reaches the best fitness after the 23rd

iteration and generates satisfactory results, but it

needs high processing time (Table 2), 18 times

higher than the average of pure BFGS method.

Figure 8: Graph representation of an image seen using a spherical lens. (Image generated by the Raytrace software).

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2512

Table 2: Test with genetic algorithm

Inputs Outputs

Population 12 Conic -0.2749

Iterations 30 MTF 91.1621

Searching

limit

-5 to

0

Time (s) 326.7735

Crossover

fraction

0.8

Mutation

fraction

0.2

(a)

(b)

Figure 9: (a) Pure genetic algorithm convergence graph. (b)

Object image viewed with lens optimized by pure genetic algorithm.

At the figure 9 (a), the “Best fitness” means

that in each iteration of the genetic algorithm, it is

the best value of MTF found, the “Mean fitness”

is the mean of the value found.

5.3.3 Hybrid algorithm

In this stage, hybrid algorithm is analyzed

using genetic algorithm in the first stage, with a

limited iteration number, followed by BFGS. The

inputs and outputs are shown in the Table 3, and the

graph results in Figure 10: the genetic algorithm

converges to a conic value close to the optimal, and

the BFGS improves this value with few iterations.

It is possible to observe that the genetic

algorithm (Figure 10), with few iterations, reaches a

conic result of -0.3050 and 67.8181 for MTF (close

to global maximum). It can lead the BFGS algorithm

to find the optimal solution with five iterations. The

total execution time was 112.848 seconds, almost

three times better than pure genetic algorithm.

Table 3: Hybrid algorithm test

𝟏𝒔𝒕 stage (Genetic)

Inputs Outputs

Population 12 Conic -0.3050

Iterations 5 MTF 67.8181

Searching limit -5 to 0 Time(s) 72.9550

Crossover

fraction

0.8

Mutation

fraction

0.2

𝟐𝒏𝒅 stage (BFGS)

Inputs Outputs

Start point -0.305 Conic -0.2749

Tolerance

epsilon

1e-10 MTF 91.1621

Searching limit -5 to 0 Time(s) 39.8933

Iterations 6

Total execution time (s) 112.848

(a)

(b)

Figure 10: (a) Convergence graph of the genetic algorithm in the first stage. (b) Convergence graph of the BFGS algorithm.

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2513

5.4 Hybrid algorithm test to different values of

corneal biometry.

In the final test (Table 4), it was performed lens

optimization based on different corneal curvatures,

aiming to simulate maximum and minimum

variation present in human population, and then

verify the feasibility of the proposed method.

Table 4: Hybrid algorithm test to 13 different values of corneal

curvatures.

Cornea

(mm)

Power

(D)

Conic MTF Time (s)

7.00 -2.3764 -0.266 91.15 97.0516

7.15 -1.4789 -0.265 91.14 102.8150

7.30 -0.6153 -0.263 91.15 112.4616

7.35 -0.3347 -0.263 91.14 98.5801

7.40 -0.0576 -0.263 91.14 107.0267

7.47 0.3247 -0.262 91.16 109.0845

7.53 0.6471 -0.261 91.16 99.1091

7.60 1.0172 -0.260 91.16 105.0452

7.70 1.5353 -0.259 91.16 104.6501

7.85 2.2894 -0.258 91.16 105.8560

8.00 3.0172 -0.256 91.16 116.5243

8.15 3.7201 -0.254 91.16 105.3883

8.40 4.8397 -0.251 91.17 95.6065

The tests were performed using 13 different

values of corneal curvatures, from 7.0 mm to 8.4 mm

(Tan, 2009) and their respective powers.

According to the results, the hybrid algorithm

has good response in extreme corneal curvatures.

6 Conclusion

The genetic algorithm, through its global search

of solutions space, reached convergence in the best

global individual, but it had high processing cost.

The BFGS algorithm, in contrast with the first one,

was a fast algorithm; however this algorithm has a

premature convergence in the local maximum, and

then it needs an initial searching value close to the

best result. The hybrid algorithm, proposed in the

work, extracted the best of each method to reach the

ideal value. Using the global search of genetic

algorithm with few iterations (to keep the low

processing cost) the way to the solution was found.

Then, using the BFGS algorithm, the best conic

value was located.

Therefore, the hybrid algorithm proposed in the

work allows to reach the best conic constant in an

average three times lower than the pure genetic

algorithm. This advantage impacts the production

process in the time required to design the lens and

provides the best optical quality.

Nowadays, the use of optimized aspheric scleral

lenses is not common on the market and the use of

spherical lenses is wider. The simulation results of

this work showed that is possible to make high

optical quality scleral lenses to improve the human

vision.

Acknowledgements

This work was supported by FAPEMIG,

MEC/SESu/FNDE-PETEE-UFMG, “Programa

Institucional de Auxílio à Pesquisa de Doutores

Recém-Contratados” (PRPq/UFMG), and

Mediphacos Ltda. Special thanks to friends and

coworkers: Marcelo Duarte Camargos, Otavio

Gomes de Oliveira, Felipe Tayer Amaral, Luiz Melk

de Carvalho and Rodolfo Felipe de Oliveira Costa.

References

Boreman, G. D. (2001) Modulation Transfer

Function in Optical and Electro-Optical

Systems. SPIE Press, Bellingham, WA.

Coral-Ghanem, C., Stein, H.A. and Freeman, M.I.

(1999) Lentes de Contato; do básico ao

avançado. Joinville: Soluções e Informática. p

32.

Costa JR, I. (1999) Introdução aos algoritmos

genéticos. In VII ESCOLA DE

INFORMATICA DA SBC REGIONAL SUL.

Anais... [S.l.: s.n.].

Douthwaite, W.A. (1987) Contact lens optics. 1st ed.

London. p 219.

Gemoules, G. (2008) A novel method of fitting

scleral lenses using high resolution optical

coherence tomography. Eye Contact Lens.

2008 Mar;34(2):80-3. Haupt, R.L. and Haupt, S.E. (2004) Practical

Genetic Algorithms, Second Edition. John

Wiley & Sons, Inc.

International Standard, ISO (1999). Ophthalmic

implants – Intraocular lenses – Part 2: Optical

properties and test methods, ISO 11979-

2:1999(E).

Lewis, A. S and Overton, M. L (2013) Nonsmooth

optimization via quase-Newton methods. Math.

Program., 141 (1-2, Ser. A): 135-163.

Liou, H-L. and Brennan, N.A.(1997) Anatomically

accurate, finite model eye for optical modeling.

J. Opt. Soc. Am. A 14, p 1684-1695.

Roach, L. (2012) Special Needs, Special Lenses:

Update on Contacts. Eyenet Magazine -

January, 2012.

Rosenthal, P. (2009) Evolution of an Ocular Surface

Prosthesis -The development of an adaptive

design process may help revolutionize scleral

lens fitting. Available at

www.clspectrum.com/articleviewer.aspx?articl

eid=103704 [Access on 11/29/13].

Skajaa, A. (2010) Limited memory BFGS for

nonsmooth optimization. Master´s thesis. New

York University, Courant Institute of

Mathematical Sciences, 251 Mercer Street,

New York, NY 10012.

Tan, BO. (2009). "Optical Modeling of Schematic

Eyes and the Ophthalmic Applications." PhD

diss., University of Tennessee.

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2514

Worp, E.V.D. (2010) A Guide to Scleral Lens

Fitting (monograph online). Scleral Lens

Education Society. Available at:

http://commons.pacificu.edu/mono/4/. [Access

on 11/29/2013].

Worp, E.V.D. (2012) "Scleral Lens Case Report

Series: Beyond the Corneal Borders". Pacific

University. Books and Monographs. Book 5.

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

2515