Imaging through scattering medium by recording 3D “spatial-frequential” interferograms

Optics Communications 267 (2006) 310–317 www.elsevier.com/locate/optcom

Imaging through scattering medium by recording 3D ‘‘spatial-frequential’’ interferograms I. Verrier, M. Jacquot *, G. Brun, C. Veillas, K. Ben Houcine Laboratoire Traitement du Signal et Instrumentation, UMR CNRS 5516 Universite´ Jean Monnet Saint-Etienne, Baˆtiment F, 18 rue Benoıˆt Lauras, 42000 Saint-Etienne, France Received 29 August 2005; received in revised form 16 June 2006; accepted 19 June 2006

Abstract Speed acquisition for image formation process through scattering medium is a challenge in optical coherence tomography (OCT) approach. Besides time domain (TD), spectral Fourier domain (FD) is now widely studied. By using a swept laser source, we demonstrate that a particular time domain OCT method (optical SISAM correlator) can be simultaneously implemented in a single set-up with the corresponding Fourier domain OCT approach (spectral interferometry). Then, FD-OCT and TD-OCT signals are obtained by processing a 3D ‘‘spatial-frequential’’ interferences pattern. We show that these two numerical approaches can be complementary when imaging in scattering medium is achieved.  2006 Elsevier B.V. All rights reserved.

1. Introduction Among all the classical methods to restore a 3D image in medical and biological applications, optical methods are very competitive in terms of harmless feature and resolution. In scattering medium, the ballistic photons keep a determinist path and contribute to image formation. The scattered and back-scattered photons undergo multiple reflections and then decrease the image signal to noise ratio. To separate noise from useful signal, filtering systems like temporal or spatial gates are used [1]. An example of temporal filtering [2] consists in mixing the analyzed signal with a pump signal into a non-linear crystal in order to enhance the ballistic signal. An appropriate filtering process keeps only the amplified signal. An example of spatial filtering is the confocal principle [3]. A pinhole is set at the focal of the imaging lens in order to stop main of the scattered light.

*

Corresponding author. Tel.: +33 477915817; fax: +33 477915781. E-mail address: [email protected] (M. Jacquot).

0030-4018/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.06.063

The optical coherence tomography (OCT) is one of the most popular temporal filtering techniques [4–7]. In this interferometric method, the interferences occur only when the optical paths difference between the two waves remains smaller than the coherence length of the source. With a low coherence length source, interferences stand only for a specific position of the object corresponding to a given position of the reference mirror. Light scattered by the other planes of the medium is then filtered by selection of the optical path. In order to explore the medium, modulation of the reference arm path is achieved by a movable mirror. OCT leads then to interferometric sensitivity with adjustable dynamics according to mirror range displacement. Besides the time domain OCT (TD-OCT) method, similar approaches based on Fourier domain OCT (FD-OCT) are being studied more, recently [6–10]. The FD-OCT differs from the TD-OCT by setting a spectrometer at the interferometer output or by the use of a swept laser source. Spectral analysis and inverse temporal Fourier transform of the interferogram avoid the mirror displacement. Then the resolution is increased and real time signal recording becomes possible. On the other hand, FD-OCT suffers from the numerical Fourier transform procedure of the

I. Verrier et al. / Optics Communications 267 (2006) 310–317

channeled spectrum in order to extract the correlation between the reference and measured beams. Indeed, the Fourier transform leads to artifacts on the final result (crosstalk between intercorrelation and autocorrelation signals). Our work is based on the TD-OCT [11,12] principle with a particular optical correlator [13–15] named Interferential Spectrometer by Selection of the Amplitude of Modulation (SISAM). The correlation signal can be directly displayed in real time on the detector without optical path modulation. The set-up arrangement allows also scanning only one transversal direction. Measurements can be performed in a reflection or in a transmission way. Up to now, images are directly extracted from the SISAM correlation signal or they are improved by a filtering procedure of the continuous background [14]. As the optical source is a tunable dye laser, spatial interferograms are recorded for each optical frequency of the accessible bandwidth. Then the spectral information is extracted from the recorded interferograms by the FD-OCT approach leading to complementary object depth information. This paper discusses the opportunity to detect simultaneously, with a single set-up, FD-OCT and TD-OCT signals by tuning the wavelength of a dye laser. After a description of the set-up, the numerical procedures are explained and some results are presented for a basic object. We show that the FD-OCT approach is sometimes more suitable to extract z-depth information in scattering medium than the SISAM procedure. Finally, the advantages and drawbacks of the two approaches are presented. 2. Interferograms recording and numerical procedures The same experimental set-up (Fig. 1) allows a 3D object reconstruction by means of two different numerical procedures. The two possible ways to extract data from the interferometric signal are explained in the following sections. 2.1. 3D interferograms recording The set-up is a Mach-Zehnder interferometer with a tunable dye laser source. The wavelength bandwidth is

Dk = 20 nm centered at k0 = 650 nm. The wavelength tuning synthesizes a broadband source whose round trip coherence length is given [6] by lc ¼

2 ln 2 k20 ¼ 9 lm: p Dk

At the interferometer output, the reference and measurement fields are combined by the particular SISAM correlator, which includes one diffraction grating in each arm, a beam splitter and an imaging lens [15]. The interferometric signal undergoes a different phase delay for each frequency m because of the spectral dependence of the wave vectors diffracted by each grating of the SISAM [13–16]. A 2D 8 bits CCD camera with 768 · 576 square pixels of 8.3 lm is used to record interferograms. For each spectral component m and along the transverse coordinates ~ r ¼ ðx; yÞ, the 2D-spatial interferogram intensity Ið~ r; mÞ is recorded by a wavelength scanning procedure: 2

Mirrors

Probe medium

Delay line BeamGrating splitter

Imaging system

Beamsplitter

where c is the light speed in vacuum, hp is the diffraction angle for the flat tint and h(m) is the diffraction angle for the m frequency. ~ ¼ 2 cosðhp h0 Þ and Q ¼ 2 sinðhp  h0 Þ  Q~ are opto-geoQ m0 K cosðh0 Þ c metrical parameters appearing when a first order development is realized on the phase term. h0 is the diffraction angle for the central frequency m0 and K the grating period. Then, the phase difference depends on the spatial coordinate x at each frequency m. Fig. 2 shows a simulated interferences patterns sequence accessible with our set-up. The frequency scanning proce-

y

x=x0

y=y0

y

.

Lens

z

ν

Spatial interferences (x,y)

Grating

Fig. 1. Experimental set-up.

ð1Þ

where eR ð~ r; mÞ and eM ð~ r; mÞ are the optical fields complex amplitudes corresponding to the reference and to the measurement arms. f(x)* denotes complex-conjugation and R½f ðxÞ the real part of the function f(x). The phase difference D~ k ~ r introduced by the correlator for each spectral component m is given by [13–16] m ~ þ QmÞx; D~ k ~ r ¼ 4p sinðhp  hðmÞÞ x  2pðQ ð2Þ c

x

Mirror

Source

2

Ið~ r; mÞ ¼ jeR ð~ r; mÞj þ jeM ð~ r; mÞj h i þ 2R eR ð~ r; mÞ  eM ð~ r; mÞ  expðiD~ k ~ rÞ ;

Spectral interferences (x,ν) Beamsplitter

311

CCD

Spectral interferences (y,ν)

x

Fig. 2. Simulation of 3D ‘‘spatial-frequential’’ interferograms sequence.

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Fig. 4. Intercorrelation function extracted from the channeled spectrum.

Fig. 3. Intercorrelation function extracted directly from the SISAM signal.

dure gives therefore a 3D ‘‘spatial-frequential’’ interferences pattern in the (x, y, m) referential. As it can be noticed, two sets of 2D spectral interferences patterns are available: one in the (x, m) plane (Fig. 3) and the other in the (y, m) plane (Fig. 4). A previous letter [16] dealt with results obtained from a post-processing method directly applied to the SISAM signal leading to a TD-OCT line. However, another approach for data processing consists in using information in the frequency space leading to FD-OCT signal. 2.2. Numerical procedures The filtering procedure of the optical continuous background presented in a previous letter [14] is achieved before performing the two following numerical treatments. The first procedure [16], named filtered SISAM treatment, is summarized in Fig. 3. This numerical treatment consists in summing pixel by pixel the spatial interferograms over all the frequencies and over the whole field of the CCD camera. It permits to build up a correlation line signal for each line y of the interferograms sequence. Consequently, spectral information is transformed – because of the sum over m – into spatial information depending on the transverse coordinate x and linked to the temporal response (or z-depth) introduced by the object thickness. The resulting synthesized signal is the same as the one

obtained directly with a broadband source. Then, this procedure leads to a typical 2D (y, z) TD-OCT signal. y-coordinate corresponds to a transverse line image of the studied object and a scan along x-axis is necessary to build-up the 3D image. The second numerical procedure, named spectral interferometry treatment, consists in analyzing the 2D spectral interferences pattern in the (x, m) or (y, m) plane corresponding to a synthesized channeled spectrum. A numerical inverse temporal Fourier transform is achieved leading to an intercorrelation function whose peak is localized at a time s linked to the object depth. An example for the case of the (y, m) plane is given in Fig. 4 and this numerical procedure is iterated for each value of x. Then, the temporal response intensity I 0 ð~ r; sÞ is deduced from Eqs. (1) and (2): h i I 0 ð~ r; sÞ ¼ FT 1 eM ð~ r; mÞeR ð~ r; mÞ expðjD~ k ~ rÞ m

~  EM ð~ r; tÞ  ER ð~ r; tÞ  dðt þ QxÞ expðj2pQxÞ; s

s

ð3Þ

where d is the Dirac distribution. I 0 ð~ r; sÞ is then defined along three coordinates: (x, y, s) where s leads to the z-depth object information and (x, y) corresponds to the transverse 2D image in a whole field configuration. This signal is typical of FD-OCT approach. The important difference comes from the phase term D~ k ~ r introduced by the optical correlator [15]. We will see in the following sections that this phase term can be filtered out in the whole-field configuration and is useful when a line-field imaging of the object is achieved. Indeed, if we consider the resulting 3D ‘‘spatial-frequential’’ interferences pattern, we access

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plates of thickness e = 150 lm, of refractive index n = 1.5 and separated by a gap h = 150 lm. The scattering medium is an aqueous solution (refractive index n0 = 1.33) of different latex beads (diameter B = 0.105 lm) concentrations from 0 to 1.67% corresponding to a minimum mean free path mfp = 0.7 mm or to a maximum scattering coefficient ls = 1.43 mm1. For a better efficiency of the 3D object reconstruction, two arrangements are then achieved.

to a set of phase shifted spectral interferograms (and then to a set of temporally translated intercorrelation peaks) of the same object line along each x-coordinate (Eq. (3)). The spectral interferometry treatment becomes a complementary approach in order to extract z-depth information from the well-chosen coordinate x of the spectral interferogram giving the intercorrelation peaks with the best visibility. This treatment takes place when the intercorrelation peaks obtained by the SISAM treatment are blurred by illumination artifacts, as explained in a previous article [16]. It can be noticed that, the z-depth information contained in the intercorrelation function obtained by the SISAM procedure is encoded as function of the transverse coordinate x, whereas the intercorrelation function I 0 ð~ r; sÞ obtained by the spectral interferometry method (Eq. (3)) is directly expressed as a function of time. Unlike the first numerical procedure, the second one gives access to a real 3D image without scans because of the whole information for each coordinate (x, y, s).

3.1. Whole-field imaging system An afocal system, constituted of two similar spherical lenses (fs = 80 mm), performs the whole-field image onto the grating plane (Fig. 5) and is imaged afterwards onto the CCD by the SISAM lens. To prove the ability of the set-up and numerical treatment to extract the 3D information, measurements on the object (Fig. 6a) are realized in air without scattering medium. The filtered SISAM signal (Fig. 6b) exhibits four brighter vertical areas corresponding to the correlation peaks. The gaps in between these peaks are linked to different paths through the object. The filtered SISAM treatment permits to enhance the contrast and to measure the delay d introduced by the plates. However, the spatial horizontal information x cannot be distinguished from the temporal s (or z-depth) information.

3. Results To validate the two post-processing methods, a simple object is set into the measurement arm at the center of a 8 mm depth cell, which also contains scattering medium or air. The object is constituted of two microscope cover

Beam-splitter fs fs fs

Spherical lens Spherical lens

Object plane

fs Beam from the reference at λ Spherical lens

Grating

CCD Beam-splitter Beams from the object and reference at λp (flat tint) Beam from the object at λ

y x

z Fig. 5. Set-up for whole-field imaging for two wavelengths kp (flat tint) and k.

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Gap (h)

e 3 2

y

1 1’

x

a

y ( µm)

Cover-plates

b y( m) -800 -600 -400 -200 0 200 400 600 800 1000

-600 -400 -200 0 200 400 ( m) 2h 2e -1000 -800 -600 1 -400 2 3 -200 0 200 400 1’ 600 800 1000 -2000 -1500-1000 -500 0 500 1000 15002000 t (fs)

-600 -400 -200 0 2h

200 400

( m)

2

3

1’ x=-306µm -1000

0 t (fs)

1000

-600 -400 -200 0 y( m) -800 -600 -400 -200 0 200 400 600 800 1000

2e

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c

z

2000

1

2

200 400

( m)

3 2e

2h

1’ x=-990µm -2000

-1000

0 t (fs)

1000

2000

Fig. 6. Results with imaging set-up of Fig. 5 for the object in air: (a) object, (b) filtered SISAM treatment, and (c) spectral interferometry treatment for x = 306 lm and x = 990 lm.

On the contrary, the spectral interferometry processing allocates to each pixel of the camera – and then to each point of the object – a set of delays characterizing the object in z-depth. Fig. 6c gives an example of the restored delays for two different x spatial coordinates. In this figure, intercorrelation peaks are spaced out the expected round trip through the object (2h, 2e), but they do not appear at the same temporal coordinates. This temporal shift (or z-depth shift) is due to the phase difference (Eq. (2)) introduced by the optical correlator. In order to restore a 3D object, a preliminary standard numerical procedure consists in filtering out this phase term in each 2D spatial interferogram Ið~ r; mÞ recorded at each frequency m (Eq. (1)). This procedure is performed at the same time as the continuous background filtering procedure [14]. Indeed, a 2D spatial Fourier transform of Ið~ r; mÞ allows to suppress D~ k ~ r by centering the peak obtained in the inverse-space and inverse spatial Fourier restores Ið~ r; mÞ without the phase

term modulation. This well-known procedure is of great interest because the temporal shift is removed without calibration stage. Fig. 7 illustrates the 3D object reconstruction by spectral interferometry treatment applied to the whole x-coordinates range. 3.2. Line imaging optical system The line-imaging configuration achieves the image of a vertical line of the object onto the grating plane by the means of a cylindrical lens (fc = 12.7 mm) and an afocal system of spherical lenses (fs = 80 mm) (Fig. 8). The SISAM lens images the grating plane on the CCD camera. Surrounding medium is an aqueous solution of different latex beads concentrations. With the filtered SISAM treatment (Fig. 9b), the correlation peaks contrast decreases progressively as latex beads concentration increases (0.74% and 1.67% corresponding

I. Verrier et al. / Optics Communications 267 (2006) 310–317

315

z

3

z

3 2 2

1’

1’

1

1

x

y

x

y

Fig. 7. 3D object build-up by spectral interferometry treatment for the imaging set-up of Fig. 5.

Object line

Cylindrical lens Spherical lens

fc

Spherical lens fs

fs fs

Grating fs

Beam from the reference at λ Spherical lens CCD

Beam-splitter Beams from the object and reference at λ p (flat tint) Beam from the object at λ

y

x

z Fig. 8. Set-up for vertical line imaging for two wavelengths kp (flat tint) and k.

respectively to mfp = 1.4 mm and mfp = 0.7 mm). Moreover, the intercorrelation peaks visibility on the left side of the two images is poor because they stand at the beam edge, due to laser beam spatial distribution and artifacts [16]. For the two solution concentrations (0.74% and 1.67%), the same object and the same imaging system, the FD processing method allows a better correlation peaks visibility than the one obtained with the filtered SISAM procedure

(Fig. 9). Indeed, the image of one object line is displayed by the optical correlator as a set of phase shifted spectral interferograms (Eq. (3)). The numerical procedure explained in Fig. 4 is performed for each column x along y-coordinate. Then, a set of temporally translated intercorrelation peaks of the same object line is computed by the spectral interferometry treatment. The peaks visibility of each restored image varies because the illumination of each CCD camera column depends on the laser beam spatial distribution [16]. Among

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e 1

e

2

3

Cover-plates 4

y Gap (h) x

a -600 -400 -200 0 1

-1000

200 400 2

3

δ (µm)

-600 -400 -200 0

4

y (µm)

y (µm)

200 400 2

3

δ (µm) 4

-500

0 500

0 500

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2ne 0,74% -2000 -1000

b -2000

-1000 1

-1000

2h 0 t (fs)

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2 3

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2ne

1,67%

δ (µm)

4

-2000

2h

2ne

-2000 -1000

0 t (fs)

-1000 1

0 2 3

2ne 1000

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δ (µm)

4

-1000

-500

-500 y (µm)

y (µm)

1

-1000

-500

0 500 2h 2ne 2ne

1000

c

z

0,74% -6000

-2000

2000 t (fs)

0 500

1000

2h 2ne 2ne 1,67% -6000

-2000

2000 t (fs)

Fig. 9. Results with imaging set-up of Fig. 8 for the object in 0.74% and 1.67% latex beads concentrations: (a) object, (b) filtered SISAM treatment, and (c) spectral interferometry treatment.

this set of images, only the image exhibiting intercorrelation peaks with the best S/N ratio is kept, and we do not consider the others. Figs. 9b and c show that the intercorrelation peaks are restored with a higher contrast when the spectral interferometry treatment is performed along the well-chosen pixel column x = x0. For the two imaging arrangements, the measured optical paths differences d lead to the same thickness of the two plates: e = 150 lm in agreement with the values given by the constructor and to the gap value: h = 150 lm according to the space between the cover plates. 4. Discussion The tunable laser source permits to record 2D spatial interferograms at each frequency m that are improved by filtering out the continuous background with a standard Fourier transform approach [14]. However, in both treatments, the limits of the experiment do depend not only on the scattering medium but also on the opto-geometrical parameters of the set-up.

For the line imaging, the x and y transverse resolutions are the same for both treatments but differ from each other due to the cylindrical lens used to shape the beam into a vertical y line. The resolution along x direction depends on the cylindrical lens (fc = 12.7 mm corresponding to 3 lm spot size) but the ultimate resolution is given by the scan process and is then 5 lm. Otherwise, the y transverse resolution is fixed by the spherical lenses (fs = 80 mm) and is equal to 13 lm. For the whole-field image formation, the two treatments are unlike. Indeed, the SISAM signal mixes the temporal s and the spatial x variables whereas spectral interferometry keeps separate information between the spatial x and temporal s-coordinates. For spectral interferometry, the transverse (x, y) resolution is 13 lm because of the spherical lenses (fs = 80 mm). For SISAM signal, the y resolution keeps the same value (13 lm), whereas no resolution can be defined along x-coordinate. For these two imaging arrangements, the two treatments also differ because the z-depth dynamics and the sampling intervals are different. For the SISAM treatment, the

I. Verrier et al. / Optics Communications 267 (2006) 310–317

dynamics (Dz)1 = 700 lm along the axial z direction (depth) is half the optical path difference dynamics (Dd)1. The dynamics (Dz)1 is fixed by the beam diameter at the SISAM correlator output and is limited by the CCD chip size along x-axis. The z-depth sampling interval of the SISAM treatment is fixed by the CCD pixel size and is 1 given by ðdzÞ1 ¼ ðDzÞ  1 lm (768 is the number of pixels 768 on x direction). For the spectral interferometry treatment, the dynamics (Dz)2 = 2 mm along the axial z direction is fixed by the tuning wavelength process (sampling interval dk = 0.1 nm). The z-depth sampling interval is given by ðdzÞ2 ¼  ðDzÞ2 ¼ 10 lm N ¼ Dk ¼ 200 . dk N In order to estimate the limits of our methods, the sampling intervals (dz)1 and (dz)2 of the two treatments have to be compared with the round trip coherence length (lc = 9 lm) of the low-time coherence synthesized light source. Considering that the scattering medium (refractive index n0 = 1.33) induces weak dispersion for the experimental wavelength bandwidth, the ultimate z-depth resolution [6] reaches nlc0 providing that (dz)1 and (dz)2 fulfill the sampling condition: (dz)1, ðdzÞ2 < nlc0 ¼ 7 lm. This condition is satisfied for the SISAM treatment whereas in the spectral interferometry treatment, the sampling interval limits the z-depth resolution to (dz)2 = 10 lm. In the case of a whole field imaging system, the filtered SISAM treatment is not suitable because of the mixed (x and s) information, whereas the spectral interferometry treatment gives access directly to a 3D image. In the case of a line field imaging system, both SISAM and spectral interferometry numerical procedure become complementary in order to restore the intercorrelation peaks with the best visibility. Indeed, the optical correlator arrangement offers the possibility with a tunable laser source to record a sequence of phase shifted spectral interferograms from a single object line without mechanical scanning procedure, which is impossible with a classical spectral interferometry set-up. The final intercorrelation peaks are then extracted from the 2D spectral interferogram exhibiting the best S/N ratio. 5. Conclusion In this work, the ability of the set-up to image transparent objects through scattering medium is pointed out. The experimental scattering limits reach 1.67% of latex beads in water corresponding to a mean free path of 0.7 mm or to a scattering coefficient ls of 1.43 mm1. Whole-field and linefield imaging systems with several scattering medium concentrations and two numerical treatments are tested. We demonstrated that, in a line field imaging configuration,

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the optical correlator permits the acquisition of a set of phase shifted spectral interferograms of same object line without mechanical scanning procedure in order to extract z-depth information with the best S/N ratio. This treatment is complementary to the SISAM treatment. In both cases the signal is directly detected but the use of the tunable laser source remains the main limit of the set-up for real time (yz) imaging. That is why we explore a promising way by using another source based on a supercontinuum generation in microstructured optical fibre. Our first results concern spectral interferometry for profilometric applications [17]. This broadband source will be used in our SISAM correlator in order to perform in real time, a (yz) image reconstruction of the object slice. A simultaneous temporal and spectral exploration of the object with a broadband source will be accessible in a similar approach than with a tunable laser source, by using the second output available from the last beam splitter of the set-up (Fig. 1). This modified configuration implies the use of two different optical arrangements and two CCD synchronized cameras. By this way, the two outputs of the optical correlator record simultaneously a spectral interferogram and a SISAM intercorrelation signal. References [1] C. Dunsby, P. French, J. Phys. D: Appl. Phys. 36 (2003) 207. [2] G. Le Tolguenec, F. Devaux, E. Lantz, Opt. Lett. 24 (1999) 1047. [3] R. Juskaitis, T. Wilson, M.A.A. Neil, M. Kozubek, Nature (London) 383 (6603) (1996) 804. [4] B.E. Bouma, G.J. Tearney, Handbook of Optical Coherence Tomography, Marcel Dekker, New York, 2002. [5] J.M. Schmitt, IEEE J. Select. Topics Quant. Electr. 5 (1999) 1205. [6] A.F. Fercher, W. Drexler, C.K. Hitzenberger, T. Lasser, Reports on Progress in Physics 66 (2003) 239. [7] A. Dubois, A.C. Boccara, M. Lebec, Opt. Lett. 24 (1999) 309. [8] A.F. Fercher, C.K. Hitzenberger, G. Kamp, S.Y. El-Zaiat, Opt. Commun. 117 (1995) 43. [9] R. Leitgeb, C.K. Hitzenberger, A.F. Fercher, Opt. Exp. 11 (2003) 889. [10] R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C.K. Hitzenberger, M. Sticker, A.F. Fercher, Opt. Lett. 25 (2000) 820. [11] I. Zeylikovitch, R.R. Alfano, Opt. Commun. 135 (1997) 217. [12] Y. Yasuno, M. Nakama, Y. Sutoh, M. Itoh, M. Mori, T. Yatagai, Opt. Commun. 186 (2000) 51. [13] G. Brun, K. Ben Houcine, D. Reolon, M. Jacquot, I. Verrier, C. Veillas, in: L. Mazuray, P.J. Rogers, R. Wartmann (Eds.), Opt. Des. Eng., Proc. SPIE 5249 (2004) 526. [14] K. Ben Houcine, G. Brun, I. Verrier, C. Veillas, Opt. Lett. 26 (2001) 1969. [15] G. Brun, I. Verrier, D. Troadec, C. Veillas, J.P. Goure, Opt. Commun. 168 (1999) 261. [16] K. Ben Houcine, M. Jacquot, I. Verrier, G. Brun, C. Veillas, Opt. Lett. 29 (2004) 2908. [17] D. Reolon, M. Jacquot, I. Verrier, G. Brun, C. Veillas, Opt. Express 14 (2006) 128.