Optical coherence tomography system … coherence tomography system optimization using simulated annealing algorithm ... the integration of Visual C++ and ... telescope increases the

Optical coherence tomography system optimization

using simulated annealing algorithm

MOHAMMAD-REZA NASIRI-AVANAKI1, S. A. HOJJATOLESLAMI

1, MARIA

PAUN2, SIMON TUOHY

2, ALEXANDER MEADWAY

2, GEORGE DOBRE

2 and

ADRIAN GH. PODOLEANU2

1. Research and Development Centre, School of Biosciences, University of Kent,

Canterbury, Kent, CT2 7PD, UNITED KINGDOM

2. Applied Optics Group (AOG), School of Physical Sciences,

University of Kent, Canterbury, CT2 7NH, UNITED KINGDOM

[email protected]

http://www.kent.ac.uk/physical-sciences/research/aog/

Abstract: - In this study optimized compensation of wavefront aberrations utilizing an electromagnetic

deformable mirror is presented. The mirror is controlled by PCI cards and sound card through simulated

annealing algorithm implemented by using the integration of Visual C++ and MATLAB in MATLAB

environment.

Key-Words: - optimization, simulated annealing algorithm, adaptive optics, Matlab

1 Introduction Optical coherence tomography (OCT) is an

advanced imaging tool, which produces high-

resolution three-dimensional (3D) images [1]. OCT

is a non-invasive imaging modality that applies non-

ionizing safe optical radiation [1]. OCT images are

constructed by measuring the magnitude of the

optical echoes at different transverse positions on

the sample [2]. The optical devices and the surface

of the sample deteriorates the wavefront and

produce aberrations. Wavefront aberrations reduce

the signal to noise ratio and consequently diminish

the contrast of the OCT images. In addition,

aberrations reduce the resolution of the imaging

system. The aberrations are different from sample to

sample, hence it is difficult to correct them by a

static technique. Adaptive optics (AO) has been

introduced to reduce the effect of the aberrations. It

becomes essential especially in the applications

demanding a higher image signal-to-noise ratio and

higher resolution.

An AO system is made up of a wave-front

sensor, such as a Shack-Hartmann, to measure the

wave-front error, a deformable mirror (DM), to

compensate the distortion, and a control loop

method, to find the optimized compensation.

Unfortunately such systems are expensive [3]. On

the other hand, although open-loop wavefront or

beam-shape control can in principle be achieved

using the knowledge of a deformable mirror’s

influence matrix, its nonlinear characteristics make

implementation of a wide range of pre-deformed

shapes problematic without the use of feedback

through a wavefront sensor or other forms of closed-

loop control system. Less expensive closed-loop

methods are required for correcting distortions, such

as the so-called blind optimization or sensor-less

approaches [4-7]. In blind optimization algorithms,

only a DM is required. Such algorithms operate in a

closed-loop iteratively to optimize a single

measurable variable by reducing the wavefront error

obtained by changing the mirror surface shape.

Simulated annealing (SA) introduced in 1982 by

Kirkpatrick et al. [9], is a technique for

combinatorial optimization problems, such as

minimizing multivariate functions [10-11] to

improve the solution to the so-called Travelling

Salesman Problem [12]. SA is favoured due to its

efficiency with less computational complexity since

all other known techniques for obtaining an

optimum solution which require an exponentially

increasing number of steps as the problems become

larger [10]. In comparison with iterative

improvement methods [9], which are captured

simply in local minima, SA improves the result by

occasionally searching in directions that lead to

worse solutions [13]. SA is however a heuristic

optimization technique which does not guarantee in

achieving the optimum value [10]. The concept of

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the optimization technique comes from a physical

process of heating to a temperature that permits

many atomic rearrangements, and then slowly

cooling a substance allowing it to come to thermal

equilibrium at each temperature until the material

freezes into an ordered crystalline structure or into a

structure with the lowest energy [14]. In the context

of adaptive-optical control, the simulated annealing

algorithm is well-suited to the task because of its

ability to independently optimize many variables at

once [15].

In this paper, we aim to utilize DM and we

propose an effective optimization technique to

provide a simple, compact and affordable adaptive

optic system to compensate aberrations introduced

by distorting optical elements in the optical

coherence tomography.

2 Materials and Methods

2.1 Optical Coherence tomography

system configuration As shown in Figure 1, light is launched from a super

luminescent diode (SLD) with the central

wavelength of λ = 830 nm and with nm17=∆λ .

The light is split by BS1 into the reference and

sample arms by the ratio of 55/45. In the sample

arm, the light is split by another beam splitter, BS2,

with the ratio of 70/30. To compensate for the loss

introduced by the beam splitters, one can increase

the power in the source.

Fig1. Schematic of the optical coherence tomography setup with adaptive optics. SLD: super luminescent laser diode, PD: photodiode,

M: microscope objective, Mirao52d: 52-actuator electromagnetic

deformable mirror, BS1,2: beam splitter, HM1,2: heat mirror, CM1-6: concave mirror, XY: transversal scanners, C: coupler, SIP: sound card

input port, PC: personal computer, EU: electronic unit

Light then goes through a telescope containing

two concave Gold coated mirrors, CM1 (f=20cm,

Ø50.8 mm) and CM2 (f=101.6cm, Ø50.8 mm), in

order to expand the beam diameter. The telescope

increases the beam diameter from 3 mm to 15 mm

so as to cover the whole aperture of the deformable

mirror. The light then is projected onto the

deformable mirror (DM). DM for this study is a

Mirao52d manufactured by Imagine which is an

electromagnetic deformable mirror with 52 actuators

[16]. Each actuator couples a miniature magnet with

a miniature coil attached to the deformable

membrane covered by a silver coated membrane. By

applying a voltage to the coils a magnetic field is

induced in the coils which can attract or repeal the

magnets attached to the membrane [16]. Therefore

by varying the coil voltage one can adjust the

magnetic force and control the local shape of the

mirror so as to correct the aberrations. Reflected

light from the mirror is projected into another

telescope containing two concave Gold coated

mirrors; CM3 (f=76 cm, Ø50.8 mm) and CM4 (f=10

cm, Ø50.8 mm). This is to reduce the beam size on

the deformable mirror to a size that would fit on the

aperture of the XY scanners. The scanners, provided

by Cambridge Technologies, produce the transversal

scans. Another telescope containing two concave

mirrors CM5 (f=20cm, Ø50.8 mm) and CM6

(f=60cm, Ø50.8 mm) have been used to increase

the beam diameter to 6 mm. A hot mirror, HM2 is

used to deflect the beam towards the object.

On the return path, the beam passes through BS2

and on to HM1. The reflected light then is coupled

into the optical fibre. The light in both arms are

joined in a coupler to produce the interference signal

and the resultant light is detected on a Nirvana

photodetector from Newport Corporation. The

electrical signal obtained from the photodetector is

coupled into the computer sound card input port

(SIP) (microphone port) for signal processing and

controlling the shape of the mirror. SIP allows the

photodetector signal to be recorded onto the personal

computer (PC) in real time.

2.2 Signal processing flow The system from a signal processing point of view

includes SLD, optical system excluding the mirror,

detector, SIP, MATLAB as the processing unit

centre, PCI card and the DM. Signal from the SIP is

gathered using MATLAB for data acquisition in real

time. The signal is processed in the optimization

algorithm. The output of the algorithm is a set of 52

values which are sent to the DM. The values are in

the range between -1 and +1 V in order to produce

50 micron summit or depression respectively on the

surface of the mirror, respectively. We send the 52

voltage values to an 8-bit PCI7200. The voltage

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signals are amplified in the digital electronics unit,

converted to analogue signal and applied to the

mirror’s actuators to produce a certain shape on the

mirror. When no voltage is applied to the actuators,

the reflecting membrane is an uncontrolled shape.

However in this study we assume that the shape of

the mirror with zero volt applied to all the actuators

is flat and applying the positive and negative

voltages results in the membrane going up and

down, respectively. With the variation of the surface

of the mirror one can compensate for all Zernike

modes up to order 4 and also part of Zernike modes

order 6.

As we intended to manage the input and output

signals in a single programming environment, we

converted the port controller code written in VC++

to MATLAB using mex file [17].

2. 3 Our optimization schedule In this study, the cost function is defined as the

difference between the new intensity and the highest

intensity detected up to that point, which we call

Current Maximum Intensity (CMI). The variables

are the 52 components of a vector sent to the

actuators. The vector controls the actuator voltages.

The flowchart of our SA-based algorithm designed

to find the best mirror shape is given in Figure 2.

Fig.2 Flowchart of our simulated annealing algorithm

We use an artificial parameter which we call the

“synthetic temperature” to determine how often the

system switches between local and global search.

The initial value of the synthetic temperature has to

be high enough to let the algorithm jump up to

anywhere in the variable space. We experimentally

considered the initial temperature (melt temperature)

to be 1000 and the final (frozen) temperature to be

10-12

. The algorithm starts by sending a random set

of 52 values as actuators’ voltages between -1 and

+1. A uniformly distributed pseudo-random function

is chosen to generate the random values [11]. The

maximum intensity is set to zero at the beginning.

From now on, the algorithm operates in its ordinary

optimization loop (OOL) while the temperature is

examined to see whether or not it is still less than the

frozen temperature. The shape of the mirror changes

according to the actuator voltages and this results in

a new value of the light intensity detected. If the

intensity is greater than the CMI value, it becomes

the new CMI and also the voltage vector is saved as

the best vector. At each temperature, the OOL is

continued until we reach the situation where in 10

successive iterations the rate of increase of the

intensity becomes less than a threshold value. We

defined an allowed variation at each iteration which

is constant for a determined number of iterations. As

shown in Figure 3-a, the threshold values decrease

by the equation ])4/[*25.02/()001.0()( ttTr += for each

iteration (temperature step decrease), where t is the

iteration step and Tr specifies the allowed variation

at each step. As a result, the thermal equilibrium

condition of the algorithm is obtained in a smaller

range of intensity variation.

(a)

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(b) Fig.3 (a) Threshold intensity decrease profile with iteration number. (b)

Temperature reduction profile during the simulated annealing process

based on successive temperature reductions given by T new = 0.9Told.

The cooling schedule as shown in Figure 3-b is

based on Tnew=0.9Told; in this study, the number of

cooling-down steps based on our choice of initial

and final temperatures is 328 steps. In the OOL in

each iteration, the value of actuators’ voltages are

updated around the best voltage by adding/reducing

a random value in the range of one tenth the

actuator’s voltage that is correspondence to the

CMI. In the OOL the Boltzmann probability

function is compared with a random value in the

interval 0 and 1. If the probability is greater than the

random value we let the algorithm jump to random

points in the variable space 5 times (this value was

obtained experimentally), by changing the voltage

vector in the range of [-1 +1], however

corresponding to the number of iterations, a

coefficient progressively lessened is multiplied to

this range. If the intensity at this stage is higher than

the CMI, it becomes the new CMI and the

corresponding voltage set is recorded and becomes

the best voltage set. After reaching the thermal

equilibrium in each temperature, the system

temperature is decreased. The process terminates

when the temperature becomes lower than the frozen

temperature. In the end, the optimal shape of the

mirror is determined by the best voltage obtained

from the algorithm which leads to producing the

highest obtainable intensity with the optical setup

which accordingly produces a better image quality.

3 Results and discussion The algorithm was tested on a 2.2 GHz Pentium IV

computer with 2.2 GB memory. The progression of

intensity along the simulated annealing algorithm

in finding the more appropriate shape of the mirror

with higher intensity is given in Figure 4.

Fig.4 Output intensity amplitude profile recorded from audio card

during 328 iterations (or 7405 number of voltage changes) in our

simulated annealing algorithm. The minimum and maximum intensities are specified on the graph with pink arrows. The green

starts show the improved intensity obtained from the ordinary

optimization loop (OOL) and the red starts show the improved intensity obtained from the Boltzmann optimization loop (BOL).

As shown in Figure 4, the output intensity of the

system is increased from 0.0024 mA to 0.0626 mA

which shows a 26-fold increase. We can not claim

that the algorithm is able to enhance the DOCI by

the order of 26 times for instance, but we can say

that if the optical system presents a static aberration,

the proposed algorithm is able to find an appropriate

shape of the mirror to correct and compensate for the

aberration such that the system achieves the highest

possible intensity and the highest image quality

accordingly.

As seen in Figure 4, consideration the

application of the Boltzmann probability condition

resulted in large variations of the intensity. In this

loop the algorithm looks for a better intensity value

throughout the variable space by changing the

voltage set values (randomly in the interval between

-1 and +1). The number of improved intensities

indicated by red stars in Figure 4 shows the

significance of the use of Boltzmann probability

scheme. As the algorithm reaches to the lower

temperature the probability condition is fulfilled

fewer times and the OOL operates without going

through the Boltzmann loop. We examined our

algorithm for a similar setup and different samples

to make sure that the algorithm works correctly.

The mirror is hexagonal and the actuators are

placed in the centre of square pixel. The shape of the

mirror with the numbering of the actuators are given

in Figure 5.

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Fig.5 Mirao52d mirror schematic. The numbers show the index of the

actuators.

We simulated the surface of the deformable

mirror simplistically for 12 sets of voltages by using

the actuator’s voltage value and an interpolation

technique. The surfaces display a shaded surface

based on a combination of ambient, diffuse, and

specular lighting models [11]. For datagrid we used

built-in Matlab function with v4 method [18]. The

surfaces are demonstrated in Figure 6. This

simulation performed on the voltage sets obtained

from the experiment that its results have been given

in Figure 4.

Fig.6 Surface curvature of the mirror demonstrated at 60o azimuthally

with 60o elevation which result the different value of Imax during our

simulated annealing algorithm. The z-axis in the graph indicates the voltage range applied on the mirror.

As seen, the surface of the mirror is changed

quite a lot during the optimization process. However

towards the end of the algorithm where the system

reaches to a very low energy the mirror surface is

just slightly changed.

In some SA applications, due to time limitations,

it is not possible to obtain the optimum answer in the

allocated time [19]. Further research is aimed at

investigating the optimum run time on our OCT

system, which will allow faster optimization.

4 Conclusion In summary, we have demonstrated an efficient

method for optimization of an optical coherence

tomography system using an electromagnetic

deformable mirror in conjunction with our simulated

annealing algorithm (Figure 2). We configured an

adaptive optics OCT setup (Figure 1) and examined

the optimization algorithm successfully. We used a

simple and inexpensive computer interface (audio

card for receiving and PCI7200 card for sending

signals) in single programming environment,

Matlab. We showed that the algorithm is quite

promising in finding the global maximum intensity

(Figure 4 and 6) and that is reproducible by running

it several times on different samples. We showed

that with this configuration, a compact, inexpensive

and simple optimization approach is achievable.

We conclude that while this technique is

unlikely to find the optimum solution, it can often

find a very good solution. We have plans to

investigate the use of this approach to remove the

effect of aberrations on the images obtained from

OCT. This will enable deeper exploration of

specimens.

References:

[1] E. A. S. D. Huang, C. P. Lin, J. S. Schuman, W.

G. Stinson, W. Chang, M. R. Hee, T. Flotte, K.

Gregory, C. A. Puliafito, and J. G. Fujimoto.,

"Optical coherence tomography," Science 254,

1178-1181 (1991)

[2] Podoleanu, A. G.: Optical Coherence

Tomography. Br. J. Radiol., 78 (2005) 976-988

[3] Plett, M. L., Barbier, P. R., Rush, D. W.:

Compact Adaptive Optical System Based on Blind

Optimization and a Micromachined Membrane

Deformable Mirror. Appl. Opt., 40 (2001) 327-330

[4] Booth, M.: Wave Front Sensor-Less Adaptive

Optics: A Model-Based Approach using Sphere

Packings. Optics Express, 14 (2006) 1339-1352

[5] Grisan, E., Frassetto, F., Da Deppo, V. et al.: No

Wavefront Sensor Adaptive Optics System for

Compensation of Primary Aberrations by Software

Analysis of a Point Source Image. 1. Methods. Appl.

Opt., 46 (2007) 6434-6441

[6] Zommer, S., & Ribak, E.: Adaptive Optics

almost without Wave Front Sensing, 2006

Conference on Visual Optics, Ed. W F Harris,

MATHEMATICAL METHODS AND APPLIED COMPUTING

ISSN: 1790-2769 673 ISBN: 978-960-474-124-3

Mopani Camp, Kruger National Park, South Africa,

August 5-10 (2006).

[7] Toledo-Suárez, C. D., Valenzuela-Rendón, M.,

Terashima-Marín, H. et al.: On the Relativity in the

Assessment of Blind Optimization Algorithms and

the Problem-Algorithm Coevolution. (2007) 1436-

1443

[8] Paterson, C., Munro, I., Dainty, J.: A Low Cost

Adaptive Optics System using a Membrane Mirror.

Optics Express, 6 (2000) 175-185

[9] Kirkpatric, S., Gelatt, C., Vecchi, M.:

Optimization by Simulated Annealing. Science, 220

(1983) 671-680

[10] Yang, P., Liu, Y., Yang, W. et al.: Adaptive

Mode Optimization of a Continuous-Wave Solid-

State Laser using an Intracavity Piezoelectric

Deformable Mirror. Opt. Commun., 278 (2007) 377-

381

[11] MathWorks, M.: The Language of Technical

Computing. At: http://www.mathworks.com, last

accessed April, (2009)

[12] Lawler, E. L., Rinnooy-Kan, A., Lenstra, J. K.

et al.: The traveling salesman problem: A guided

tour of combinatorial optimization. John Wiley &

Sons Inc (1985)

[13] Rutenbar, R.: Simulated Annealing

Algorithms: An Overview. IEEE Circuits Devices

Mag., 5 (1989) 19-26

[14] Fang, M.: Layout Optimization for Point-to-

Multi-Point Wireless Optical Networks Via

Simulated Annealing & Genetic Algorithm. Master

Project, University of Bridgeport, Fall, (2000)

[15] El-Agmy, R., Bulte, H., Greenaway, A. et al.:

Adaptive Beam Profile Control using a Simulated

Annealing Algorithm. Optics Express, 13 (2005)

6085-6091

[16] Gambra, E., Sawides, L., Dorronsoro, C. et al.:

Development, Calibration and Performance of an

Electromagnetic Mirror Based Adaptive Optics

System for Visual Optics. (2008) 322–328

[17] Carr, Roger. "Simulated Annealing." From

MathWorld-A Wolfram Web Resource, created by

Eric W. Weisstein.

http://mathworld.wolfram.com/SimulatedAnnealing.

html

[18] Sandwell,D.T.:Biharmonic Spline Interpolation

of GEOS-3 and SEASAT Altimeter Data. Geophys.

Res. Lett., 14 (1987) 139–142

[19] Rutenbar, R.: Simulated Annealing

Algorithms: An Overview. IEEE Circuits Devices

Mag., 5 (1989) 19-26

MATHEMATICAL METHODS AND APPLIED COMPUTING

ISSN: 1790-2769 674 ISBN: 978-960-474-124-3