Eric Lacot
email: eric.lacot@ujf-grenoble.fr

Olivier Jacquin

Olivier Hugon

Huguesguillet De Chatellus

Control of the differential interference contrast in reinjected bimode laser

We have demonstrated both theoretically and experimentally that it is possible to control (i.e. to enhance or to cancel) the contrast of the interference pattern appearing in the intensity images obtained with a Laser Optical Feedback Imaging (LOFI) setup using a bimode laser. The laser is composed of two coupled orthogonally polarized states which interact (i.e. interfere) through the cross saturation laser dynamics. The contrast control is made by choosing the frequency-shift (i.e. the beating frequency) between the feedback electric fields and the intracavity electric fields. We show that the interference contrast of the output power modulation of the laser total intensity is independent from the frequency-shift and is always maximal. On the other hand, the interference contrast of each polarization state is frequency dependent. The maximal contrast is obtained when the frequency shift is equal to one of the resonance frequencies of the bimode dynamics, and is very low (and almost cancels) for an intermediate frequency located at the intersection of the two resonance curves.

Introduction

With the optical setups based on the detection of ballistic photons (which have not experienced a scattering event), while we are able to obtain high optical resolution (µm), the accessible depth is quickly limited (mm) by the small number of remaining photons. For example, optical setups like Optical Coherence Tomography (OCT) [START_REF] Fercher | Ophthalmic laser interferometry[END_REF][START_REF] Dubois | Full-field OCT[END_REF] or confocal microscopy [START_REF] Minsky | Memoir on inventing the confocal scanning microscope[END_REF], belong to this family. To improve the in-depth resolution, the challenge is therefore to increase the sensitivity of such methods, but not at the price of expensive equipment and of complex optical alignment. To overcome this problem, one solution is to use the laser optical feedback. Indeed, since the pioneer work of K. Otsuka on self-mixing modulation effects in class-B laser [START_REF] Otsuka | Effects of external perturbations on LiNdP4012 Lasers[END_REF], the sensitivity of laser dynamics to frequencyshifted optical feedback has been used in autodyne interferometry and metrology [START_REF] Otsuka | Self-Mixing Thin-Slice Solids-State Laser Metrology[END_REF], for example in self-mixing laser Doppler velocimetry [START_REF] Otsuka | Highly sensitive measurement of Doppler-shift with a microchip solid-state laser[END_REF][START_REF] Okamoto | Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser[END_REF][START_REF] Kawai | Ultrahigh-Sensitivity Self-Mixing Laser Doppler Velocimetry with Laser-Diode-Pumped Microchip LiNdP4O12 Lasers[END_REF][START_REF] Suddo | Determination of velocity of self-mobile phytoplankton using a self thin-slice solidstate laser[END_REF], vibrometry [START_REF] Otsuka | Real-time nanometer vibration measurement with self-mixing microchip solid-state laser[END_REF][START_REF] Muzet | Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures[END_REF][START_REF] Lacot | Phase-sensitive laser detection by frequencyshifted optical feedback[END_REF], near field microscopy [START_REF] Gilles | Near-field amplitude and phase measurements using heterodyne optical feedback on solidstate lasers[END_REF][START_REF] Blaize | Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry[END_REF] and laser optical feedback imaging (LOFI) experiments [START_REF] Lacot | Laser optical feedback tomography[END_REF][START_REF] Witomski | Synthetic aperture laser optical feedback imaging using galvanometric scanning[END_REF][START_REF] Hugon | Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser[END_REF][START_REF] Hugon | Coherent microscopy by laser optical feedback imaging (LOFI) technique[END_REF][START_REF] Glastre | Demonstration of a plenoptic microscope based on laser optical feedback imaging[END_REF][START_REF] Glastre | Deep and optically resolved imaging through scattering media by space reversed propagation[END_REF]. Compared to conventional optical heterodyne detection, frequencyshifted optical feedback shows an intensity modulation contrast higher by several orders of magnitude and the maximum of the modulation is obtained when the shift frequency is resonant with the laser relaxation oscillation frequency [START_REF] Lacot | Coherent laser detection by frequency-shifted optical feedback[END_REF]. In this condition, an optical feedback level as low as -170 dB (i.e. 10 17 times weaker than the intracavity power) has been detected [START_REF] Okamoto | Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser[END_REF]. In previous papers [START_REF] Lacot | Comparative study of autodyne and heterodyne laser interferometry for imaging[END_REF][START_REF] Jacquin | Experimental comparison of autodyne and heterodyne laser interferometry using an Nd:YVO4 microchip laser[END_REF], we have demonstrated that in LOFI interferometry, the main advantage of the resonant gain (defined by the ratio between the cavity damping rate and the populationinversion damping rate of the laser) is to raise the laser quantum noise over the detector noise in a relatively large frequency range around to the laser relaxation frequency, leading to a shot noise limited signal to noise ratio (SNR). For high-speed imaging, the signal acquisition time must be decreased, leading to a reduction of the SNR of our LOFI setup. To overcome this problem, the laser output power could be increased, but this often leads to a multimode behavior of the laser and more particularly to a coupled dynamical behavior (principally due to spatial hole burning) in a microchip solid-state laser. Due to the multimode behavior of the laser, the LOFI image, obtained from the measurement of the modulation amplitude of the laser intensity, can exhibit interference pattern. More specifically, in our bimode microchip laser which runs on two orthogonal states of polarization, interferences come from the interaction (i.e the superposition) of the intensity modulation of the two laser polarization states, via the cross coupling laser dynamics [START_REF] Otsuka | Laser-diode-pumped thin-slice c-cut Nd:GdVO4 multimode laser with coherent vector fields[END_REF][START_REF] Zhang | Phase difference in a modulated signals of two orthogonally polarized outputs of a Nd:YAG microchip laser with anisotropic optical feedback[END_REF][START_REF] Bielawski | Antiphase dynamics and polarization effects in the Nd-doped fiber laser[END_REF][START_REF] Lacot | Nonlinear mode coupling in a microchip laser[END_REF]. The main objective of this paper is to show how the cross coupling dynamics of a bimode laser can be used to control (enhance or cancel) the contrast of the interference patterns in LOFI amplitude images. To our knowledge, this paper is also the first demonstration of a LOFI setup working with a bimode laser. This paper is organized as follows. Firstly, after a basic description of our LOFI setup working with a bimode laser, we give the model describing our laser working with two orthogonal states of polarization coupled trough the cross saturation laser dynamics. In our model, each polarization is submitted to a specific frequencyshifted optical feedback. From this model, the analytical expression of the LOFI signal, (i.e. the amplitude and phase of the beating) is obtained. Then the theoretical contrast of the interference pattern, induced by the cross saturation laser dynamics and due to the phase difference between the two reinjected polarization states (and therefore by the phase difference between the two intensity modulations) is determined for each polarization state and also for the total intensity of the laser. Then, the frequency-shift which allows canceling the interference contrast is determined. Finally, the analytical predictions are confirmed by numerical simulations and by the acquisition of images in different experimental conditions.

LOFI with a bimode laser A. LOFI Setup

A schematic diagram of the LOFI experimental setup is shown in Fig. 1. The laser is a diode pumped Nd:YAG microchip laser. The maximum available pump power is 380 mW at 810 nm, the threshold pump power of a laser is 75mW and the total output power of the microchip laser is 80 mW with a central wavelength of 1064 nm. The laser cavity is a plane-parallel cavity which is stabilized by the thermal lens induced by the Gaussian pump beam. The two dielectric mirrors are directly coated on the laser material (full cavity). The input dichroic mirror allows to transmit the pump power and to totally reflect the infrared laser wavelength. On the other side, the dichroic output mirror allows to totally reflect the pump power (to increase the pump power absorption and therefore the laser efficiency) and only partially reflects (95%) the laser wavelength. The microchip cavity is relatively short . This ensures a high damping rate of the cavity and therefore a good sensitivity to optical feedback. Due to small birefringence induced by a small mechanical pressure on the laser crystal, the optical spectrum of the laser is composed of two wavelengths corresponding to orthogonal polarization states (indexed 0 and 90 in the following) [START_REF] Otsuka | Laser-diode-pumped thin-slice c-cut Nd:GdVO4 multimode laser with coherent vector fields[END_REF][START_REF] Zhang | Phase difference in a modulated signals of two orthogonally polarized outputs of a Nd:YAG microchip laser with anisotropic optical feedback[END_REF][START_REF] Bielawski | Antiphase dynamics and polarization effects in the Nd-doped fiber laser[END_REF][START_REF] Lacot | Nonlinear mode coupling in a microchip laser[END_REF] The laser beam is sent on the target through a frequency shifter (acousto-optic device). A part of the light diffracted and/or scattered by the target is then reinjected inside the laser cavity after a second pass through the frequency shifter. Therefore, the optical frequencies of the reinjected light are shifted by e F . This frequency can be adjusted and is typically of the order of the laser relaxation frequencies which are in the megahertz range for our microchip laser. ) takes into account the target albedo, the numerical aperture of the collection optics, the frequency shifters efficiencies, the transmission of all optical components and the overlap of the retro-diffused field with the Gaussian cavity beam (confocal feature).

The coherent interaction (beating) between the lasing electric fields and the frequency-shifted reinjected fields leads to a modulation of the laser output power at e F . For the detection purpose, the laser output beam is split into two beams. The first one is used to record the dynamics of each polarization state through a Wollaston prism, while the second one is used to record the dynamics of the total intensity of the laser. The voltage delivered by the photodiodes are finally analyzed by a numerical oscilloscope which allows Fast Fourier Transform (FFT) calculations, and processed by a lock-in amplifier which gives the LOFI signal (i.e. the amplitude and the phase of the retro-diffused electric field) at the demodulation frequency At this point, one can already notice that compared to a conventional heterodyne interferometer, the LOFI setup shown here does not require complex alignment. Indeed, the LOFI interferometer is even always self-aligned because the laser simultaneously fulfills the functions of the source (i.e. photons-emitter) and of the photodetector (i.e. photons-receptor).

B. LOFI Modeling

In the case of a weak frequency shifted optical feedback reinjected into a bimode laser (

1 i R 
) and of a short round trip time delay ( 1 ee F   ), the dynamical behavior of the bimode laser can be described by the following set of differential equations [START_REF] Lacot | Laser optical feedback tomography[END_REF][START_REF] Lacot | Coherent laser detection by frequency-shifted optical feedback[END_REF][START_REF] Bielawski | Antiphase dynamics and polarization effects in the Nd-doped fiber laser[END_REF][START_REF] Lacot | Nonlinear mode coupling in a microchip laser[END_REF][START_REF] Thévenin | Phase and intensity dynamics of a two-frequency laser submitted to resonant frequency-shifted feedback[END_REF]:

    0 0 0 0 0 0 0 0 cos c c e I dI BI N I R I t dt Lt         (1a)     0 0 1 0 0 0 90 pN dN N N BN I I L t dt         (
I L t dt R I t          (1c)     90 90 1 90 90 90 0 pN dN N N gBN I I L t dt         ( 1d
)
where is the pumping rate and B is related to the Einstein coefficient (i.e. the laser cross section), where g describes the cross section ratio of the two polarization states. In the present paper, the case of a bimode laser with a symmetrical gain ( 1 g  ) will be studied both analytically and numerically, while the case of the asymmetrical gain ( 1 g  ) will only be processed numerically. This choice has been made in order to avoid heavy (but straightforward) analytical calculations which are not necessary for the physical interpretation of our experimental results. Indeed, the laser that has been used in the experimental section is a bimode laser with a very slightly asymmetrical gain ( 1 g  ).

For a symmetrical gain ( 1 g  ), the steady-state of Eqs. ( 1) is simply given by:

0, 90, c s s s N N N B     (2a)   0, 90, 1 1 1 s s sat s I I I A I       ( 2b
)
where

p s N A N
 is the normalized pumping parameter and

1 sat I B  
is linked to the saturation intensity of the laser transition.

The two orthogonal polarization states of the laser have therefore the same intensity, making it possible to obtain interferences (between the two laser intensity modulations induced by the optical feedback) with a maximum contrast (i.e. a high visibility).

To determine the small modulation of the laser intensity induced by the optical feedback, the set of Eqs.( 1) are linearized around the steady state given by Eqs. ( 2):

    ,, i s i I t I I t      (3a)     ,, i s i N t N N t      (3b) with   , is I t I    ,   , is N t N   
and where

0 90 2 22 e m d          
is the phase difference between the two feedback modulations induced by the phase difference between the two reinjected electric fields. Then a Fourier transformation allows to convert the differential equations into linear algebraic equations [START_REF] Lacot | Coherent laser detection by frequency-shifted optical feedback[END_REF][START_REF] Kolobov | Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources[END_REF]

I i A i R i i A R I i A i A                                               , ( 4a
)       2 2 2 1 90 90 1 0 90 2 2 2 2 , 1 , 1 exp exp , c s e R e e R e R e e R e e I i A i R i A R i I i A i A                                                       , ( 4b
) with   2 ,1 1 Rc A      ,   22 ,, 1
1 RR         and 22 ,, 2 2 RR R      .
At this point, one can notice that the cross coupling parameter can be simply extracted from the knowledge (i.e. from the experimental measurements) of the two angular eigenfrequencies of the laser dynamics. The cross coupling parameter is given by the following relation:

                0 90 1 90 22 , 1 0 90 22 , 1 90 , , , = , exp exp
I i A i iA R i R iA Gi                                                    0 90 exp R i R        (5a)                 0
I i A i iA R i R iA Gi R i R                                                   (5b)
One can observe that   More particularly, Eq. (5a) shows that the modulation of the total laser intensity is therefore an eigenmode of the laser dynamics. At this point, one can also notice that, in our particular case (g1), the intermediate angular frequency previously defined by

    RR GG     .
C. Theoretical interference contrast When  is scanned over two pi, one can determine the interference contrast due to the interaction (i.e. the superposition) of the intensity modulation of the two laser polarization states, via the cross-coupling laser dynamics. More precisely, from the power spectra

  2 , ie I    
, the interference contrast is determined by using :

          22
                 (6)
with 0 i  , 90 i 
for the orthogonal polarization states and i tot 

for the total intensity.

From Eqs. ( 4) and ( 5), one easily obtains:

              22
Eqs. [START_REF] Okamoto | Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser[END_REF], show that the interference contrast of the total intensity is independent of the frequency-shift ( e  ), while the interference contrasts of both polarization states are frequency dependent.

At this point, one can notice that when we detect only one polarization state, the interference interaction between the two feedback modulations comes from the coupling by the laser dynamics ( 0   ). Indeed Eq. (7a) gives

  0(90) 0 e C when 0   .
To study the dynamical effects of the laser dynamics on the interference contrast, we focus the discussion on the particular case where the amount of optical feedback in each polarization state is approximatively the same   0 90

RR 

and therefore has no impact on the reduction of the interference contrast (i.e. the fringes visibility).

Under this condition and for a class-B laser  

1 R A   
, Eqs. [START_REF] Okamoto | Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser[END_REF] give:

    0 90 2 2 0.7 1 eR C           (8a)     , 0 90 1 R C   (8b)     3 1 0 90 2 10 1 R R A C            (8c)     , 0 90 1 R C   (8d)     2 0 90 2 21 R eR e C             (8e) 1 tot C  (8f)
For both polarization states, Eqs. [START_REF] Kawai | Ultrahigh-Sensitivity Self-Mixing Laser Doppler Velocimetry with Laser-Diode-Pumped Microchip LiNdP4O12 Lasers[END_REF] show that the interference contrast is high at low frequency and is maximal if we detect the feedback interaction (i.e. the beating) at the resonance angular frequencies ( In agreement with Eq. (8f), one can observe on Fig. 2(b) that the interference fringe pattern of the total intensity is independent of the frequency shift and that the visibility of the fringes (i.e. the contrast) is always the same. When detecting the polarization states separately, Fig. 2(a) shows that the interference fringe contrasts are maximal at 4) and ( 5) give:

  1 0 90 , R cs R A R I IR            (9a)   1 90 0 , R cs R A R I IR            (9b)       1 0 90 0 90 ,0 , 0 , 0 R cs tot R A R RR I I R R II                     (9c)   1 0 90 0 90 ,0 R cs tot R A R R R I I R R                (

Cancellation of the interference fringes

A. Numerical simulations Fig. 3 shows numerical results obtained by using a RungeKutta method to solve (without any approximation) the differential equations ( 1). This numerical simulation is made with a frequency shift equal to the intermediate frequency ( For the LOFI signal, one can observe that the beating frequency appears on the total intensity [see Fig. 3(c)] and also on the vertical polarization state [see Fig. 3(a)] despite the fact that there is no feedback on this state ( 90 0 R  ). In agreement with Eqs. (9b) and (9c), one can also observe that the two peaks have the same amplitude. On the other hand, one can observe on Fig. 3(b) that no modulation appears at the beating frequency in the horizontal state ( 0 i  ) despite the fact that feedback is only on this mode (

0 0 R  ).
As already mentioned, this counter-intuitive result is induced by the coupling between the dynamical behaviors of the two polarization states. This result is in agreement with Eq. (9a). In our numerical simulation, the Langevin forces allow to stimulate the noise of the laser dynamics at all frequencies and one can observe that the two polarization states resonate for both frequencies F  [see Fig. 3(c)]. On Fig. 3(a), one can also observe that the intermediate frequency which is a very particular frequency for the laser dynamical behavior corresponds to the frequency where the two resonance curves intersect each other. Fig. 4 shows the variation of the laser output power modulation when the phase difference between the two modes (  ) is changed over 4 . This numerical simulation is made with a frequency shift once again equals to the intermediate frequency

, , 2 R R F      and , , 2 R R F      [see Figs.
( 22 ,¨,2 RR eR FF FF   
) and this time with an isotropic target ( 0 90

RR 

). The laser quantum noise is also taken into account in this numerical simulation.

In Fig 4(a), the numerical simulation is made for a bimode laser with a symmetrical gain ( 1 g  ). The numerical results can therefore be directly compared with the analytical results given previously. Indeed, in agreement with Eqs (9), Fig. 4(a) shows that the modulation amplitude of both polarization state is independent from the phase difference  . At the intermediate frequency, the LOFI signal for each polarization is therefore insensitive to the interference interaction between them. On the other hand, the LOFI signal of the total intensity is strongly dependent on the phase difference  . One can, also observe on this figure that the sum of the LOFI signal of the two polarizations corresponds the maximum value of the LOFI signal of the total intensity (no energy loss).

In Fig. 4(b), the numerical simulation is made for a bimode laser with an asymmetrical gain ( 1 g  ). This condition is closer to real experimental situation. Due to the asymmetry, Fig. 4(b) shows a little modulation of the amplitude of both polarization states. Nevertheless, one can observe that the corresponding contrast remains very low as compared to the contrast of the total intensity fringes. In the Fig. 4(b), one can also observe that the interference fringes of the two polarizations have a phase shift of  . Indeed, the bright fringes of 0 I   correspond to the dark fringes of 90 I   and vice versa. As a consequence, the sum of the LOFI signal of the two polarizations is nearly constant and therefore is independent from the phase difference  (i.e. independent from the interference condition).

The corresponding value once again equals the maximum value (bright fringes) of the LOFI signal of the total intensity [31]. Firstly, one can observe on the four graphs of the right column, a global bell shape due the confocal filtering of the LOFI microscope, induced by the overlap of the retro-diffused field with the Gaussian cavity beam. Above the global shape, one can also observe that the interference contrast depends on the frequency shift (i.e. modulation frequency). In agreement with Fig. 2(a), one can observe that the interference contrast is high in the vicinity of the resonance frequencies [Figs 5(a Therefore by choosing the frequency shift (i.e. the beating frequency) between the feedback electric field and the intracavity electric field, we are able to control and also to cancel the interference pattern appearing in the LOFI images. This control is induced by the cross coupling of the laser dynamics between the two orthogonal polarizations of our bimode laser.

Conclusion

We have demonstrated both theoretically and experimentally that it is possible to control (i.e. to enhance or to cancel) the contrast of the interference pattern appearing in the intensity images obtained with a Laser Optical Feedback Imaging (LOFI) setup using a bimode laser.

Firstly, after a basic description of our LOFI setup working with a bimode laser, we have given the model describing our laser running on two coupled polarization states and submitted to frequencyshifted optical feedbacks. From this model, the analytical expression of the LOFI signal is obtained in the case of a bimode laser with a symmetrical gain ( 1 g  ). Then, the theoretical contrast of the interference pattern (induced by a phase difference  between the two reinjected polarizations) is determined for each polarization state and also for the total intensity of the laser. These results show that the contrast can be controlled by choosing the frequency-shift (i.e. the beating frequency) between the feedback electric field and the intracavity electric field. This control is possible due to the cross coupling dynamics between the two polarizations (i.e. 0   ). We show that the interference contrast of the output power modulation of the laser total intensity is independent from the frequency-shift and is always maximal. On the other hand, the interference contrast for each polarization is frequency dependent. The maximal contrast is obtained when the frequency shift is equal to the resonance frequencies of the bimode dynamics ( predictions are confirmed by a numerical simulation of the laser dynamics. These simulations show that each polarization state exhibits two resonance frequencies while the total intensity, which is an eingenmode of the laser dynamics, exhibits only the highest relaxation frequency. The numerical simulation also confirm that by working at the intermediate frequency and by detecting both polarizations separately, one can obtain a LOFI signal of the same value (no loss of energy) than the total intensity, but without the interference fringe pattern (i.e. without the dependence with  ).

Finally all the predictions are confirmed by the acquisitions of LOFI images where the contrast of the interference fringe pattern can be controlled (enhanced or cancelled) by adjusting the value of the frequency shift and by choosing the detected polarization states.

From this work, one can suppose that the same mode-dependent modulation property is expected in general multimode solid-state lasers besides dual-polarization lasers [START_REF] Otsuka | Alternate time scale in multimode laser[END_REF].

  output power of the microchip bimode laser is approximately equally divided between the two orthogonal polarization states. This ratio can be controlled by adjusting the orientation of the linear polarization of the pump.

  LOFI images are obtained pixel by pixel (i.e. point by point, line after line) by a full 2D galvanometric scanning.

Fig. 1 (

 1 Fig. 1 (Color online) Schematic diagram of the LOFI setup using a bimode laser. BS: Beam Splitter, WP: Wollaston Prism, PDs: Photodiodes. The bimode laser in a Nd:YAG microchip laser with two orthogonal polarization states which are cross-coupled by the saturation of laser gain. The image is obtained pixel by pixel by using a 2D galvanometric scanning.

N 1 

 1 are respectively the laser intensity (photon unit) and the population inversion of the polarization state 0 i  and 90 i  , which are coupled through the cross-saturation parameter  In Eqs.[START_REF] Fercher | Ophthalmic laser interferometry[END_REF], each cosine function expresses the coherent interaction (i.e. the beating at the angular frequency: lasing and the optical feedback electric field. Regarding the noise, the laser quantum fluctuations are described by the Langevin noise functions have a zero mean value and a white noise type correlation function[START_REF] Kolobov | Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources[END_REF][START_REF] Khanin | Principles of laser dynamics[END_REF]. In Eqs .[START_REF] Fercher | Ophthalmic laser interferometry[END_REF], is the decay rate of the population inversion,

  By summing and subtracting Eqs. (4), one obtains:

  amplitudes of the eigenmodes of the coupledlaser dynamics, with their respective angular eigenfrequencies (i.e. resonance angular frequencies) given by ,

  , corresponds to the angular frequency for which the two resonance curves, defined by the eigenmodes, intersect each other and therefore have the same modulus:

  Fig. 2 shows the normalized amplitude of the laser output power modulation versus the frequency shift ( 2 ee F

Fig. 2 .

 2 Fig. 2. (Color online) Normalized amplitude of the laser output power modulation (in a logarithmic false color scale) versus the normalized angular frequency: eR  and the phase difference  . For each angular frequency: ( e  ), the amplitude of the modulation is normalized to the brightest interference condition according to  . a) Laser horizontal polarization:

  vanishes (i.e. have no dependence with the target distance) when working at the intermediate angular frequency eR    or when working far away from the resonance zone eR    . At this point one can also notice the phase shift of between the interference pattern at , . Between the two possibilities which allow canceling the interference effect between the intensity modulations of the two polarization states, the first solution [Eq. (8c)] is the best. Indeed, the LOFI SNR is shot noise limited only in the vicinity of the resonance frequencies of the laser [22, 23]. Working at this particular angular frequency: ( eR    ), and coming back to the more general situation where 0 R is not necessary equal to 90 R , Eqs. (

C

  9d)In agreement with Eq.(8c) (i.e.     Eqs. (9a) and(9b) show that the amplitude of the modulation of both polarization states is independent of the phase difference  . At the intermediate frequency, the LOFI signal for each polarization state is therefore insensitive to the interference condition between the two polarization states. More surprisingly (because less intuitive), Eq. (9a), shows that the LOFI signal of the horizontal polarization ( 0 I   ) is only induced by the feedback in the vertical polarization ( 90 0 R  ) and vice versa for Eq. (9b). On the other hand and in agreement with Eq. (8a) (  ), Eqs. (9c) and (9d) show that the value of the LOFI signal of the total intensity is strongly dependent on the phase difference  and can disappear for destructive interference condition [see Eq. (9d)]. One can also observe that for constructive interference ( 0   ), the amplitude of the LOFI signal of the total intensity is the sum of the LOFI signal of the two orthogonal states [see Eq. (9c)]. Therefore, by working at the intermediate frequency and by detecting both modes separately instead of directly detecting the total intensity, one can Nomalized angular frequency: Ω e /Ω R signal of the same value (no loss of energy), but without the interference fringe pattern (i.e. without the dependence of  ).

R

   ). To describe realistic experimental conditions, the laser quantum noise is taken into account in this numerical simulation by programming the Langevin forces.

Fig. 3 (R

 3 Fig. 3 (Color online) Numerical simulation: square modulus of the Fast Fourier Transform (FFT) of the temporal evolution the bimode laser dynamics, versus the dimensionless frequency

  3(a) and 3(b)] while the total intensity, which is an eigenmode of our bimode system, only resonate at the frequency , R

Fig. 4 (

 4 Fig. 4 (Color online) Numerical simulation: amplitude of the laser output power modulation, at the intermediate frequency eR FF  , versus the phase difference between the two polarization states. Laser parameters: 2.5 A , 5 1 10

eFF

  ) induced by the frequency shifted feedback, and also the two resonance frequencies (  ) stimulated by the laser quantum noise. For different values of e F , the right column shows the variation of the LOFI signal (i.e. the amplitude of the modulation of the laser intensity at the modulation frequency e F ) when the detected target is moved over a few millimeters on either side of a mean distance of 2.5 e dm  .

  ) and 5(c)] and is minimum (and roughly equal to zero) when working at the intermediate frequency [Fig.5(b)] or far away from the resonance zone [Fig.5(d)]. In agreement with Fig.2(a), one can also observe on the right column that the fringes are shifted when we detect the interference fringes on either side of the intermediate frequency R F . Indeed, the minima of Fig. 5(a) and 5(c) are not obtained for the same position of the target.

Fig. 6

 6 Fig.6shows LOFI images of a slightly tilted target located at a mean distance of 2.5 e dm  away from the laser. The target is a small part of a car registration plate. The interference fringes are induced both by a small tilt of the registration plate (of the order of 5°) and by the spherical scanning of the laser beam induced by the galvanometric mirrors (see Fig.1).The left column shows that the interference fringe pattern is independent from the frequency shift (i.e. of the beating frequency) when we detect the amplitude of the modulation of the total intensity of the bimode laser. On the other hand, when we detect only one mode (the horizontal one in this case), one can observe on the right column that the interference contrast depends on the frequency shift.In agreement with the results of Fig.5, one can observe that the interference contrast is high in the vicinity of the resonance frequencies [Figs. 6(a) and 6(c)] and is minimum (and roughly equal to zero) when we work at the intermediate frequency [Fig. 6(b)] or far away from the resonance zone [Fig. 6(d)]. In agreement with Fig. 2(a), one can also observe on the right column that the fringes are shifted when we look at the interference pattern detected on either side of the intermediate frequency R F . Indeed, the bright fringes of Fig. 6(a) correspond to the dark fringes of Fig. 6(c) and vice versa.Therefore by choosing the frequency shift (i.e. the beating frequency) between the feedback electric field and the intracavity electric field, we are able to control and also to cancel the interference pattern appearing in the LOFI images. This control is induced by the cross coupling of the laser dynamics between the two orthogonal polarizations of our bimode laser.

  is very low (and almost cancels) for an intermediate frequency located at the intersection of the to cancel the interference contrast is to use a beating frequency very far away from the resonance range of the laser dynamics. But this last solution gives a lower SNR for the LOFI images. Then, the theoretical

Fig. 5 :FFig. 6 :

 56 Fig. 5: Experimental feedback signals for a target located at a mean distance of 2.5 e dm  away from the laser. Left column: power spectrum of


W Glastre

O Hugon

O Jacquin

H Guillet De Chatellus

E Lacot
email: eric.lacot@ujf-grenoble.fr

Plenoptic microscope based on Laser Optical Feedback Imaging (LOFI)

We present an overview of the performances of a plenoptic microscope which combines the high sensitivity of a laser optical feedback imaging set-up, the high resolution of optical synthetic aperture and a shot noise limited signal to noise ratio by using acoustic photon tagging. By using an adapted phase filtering, this microscope allows phase drift correction and numerical aberration compensation (defocusing, coma, astigmatism …). This new kind of microscope seems to be well adapted to make deep imaging through scattering and heterogeneous media.

I.

INTRODUCTION

Making fast 3D images with a good in-depth resolution through both heterogeneous and turbid media have always been a major issue. The problem is double with scattering media: firstly the scattering medium generally attenuates strongly the signal, which decreases the signal to noise ratio (SNR) and secondly the wavefront is highly perturbed, which degrades the point spread function (PSF) of the imaging system and therefore the resolution. Several ways to overcome these problems have been proposed; two main methods aiming at keeping a good optical resolution are actively developed. The first one uses pre-compensation of the wavefront before propagation, to improve the resolution [START_REF] Popoff | MeasuringtheTransmissionMatrixinOptics:AnApproachto theStudyandControlofLightPropagationinDisorderedMedia[END_REF]. The second one only uses ballistic photons to make images [START_REF] Dubois | Full-filedOCT[END_REF][START_REF] Lacot | Coherent laser detection by frequency-shifted optical feedback[END_REF]. Our laser optical feedback imaging (LOFI) setup [START_REF] Lacot | Coherent laser detection by frequency-shifted optical feedback[END_REF], based on optical self-mixing inside the laser cavity, belong to this second family. LOFI has the advantage of providing a self-aligned and very sensitive optical system limited by shot noise [START_REF] Otsuka | Self-Mixing Thin-Slice Solid-State Laser Metrology[END_REF][START_REF] Jacquin | Experimental comparison of autodyne and heterodyne laser interferometry using Nd:YVO4 microchip laser[END_REF].

In this paper, after a brief reminder of what LOFI is, we present our plenoptic microscope which combines LOFI (based on the ballistic photons detection), synthetic aperture (SA) [START_REF] Glastre | Limitation of synthetic aperture laser optical feedback imaging[END_REF][START_REF] Glastre | Deep and optically resolved imaging through scattering media by space-reversed propagation[END_REF] and acoustic photon tagging (APT) [START_REF] Glastre | Deep and optically resolved imaging through scattering media by space-reversed propagation[END_REF][START_REF] Jacquin | Acousto-optic laser optical feedback imaging[END_REF]. This new kind of microscope demonstrates the possibility of making deep imaging through scattering and heterogeneous media at the shot noise level [START_REF] Glastre | Demonstration of a plenoptic microscope based on Laser Optical Feedback Imaging[END_REF].

II. SYNTHETIC APERTURE LOFI

A. Experimental setup

Fig. 1 shows a description of the LOFI experimental setup. The laser is a microchip laser emitting a power of tens mWatλ = 1064 nm. This laser has a relaxation frequency F R in the megahertz range. On its first pass, the laser beam is frequency shifted by a frequency F e /2 where F e is close to the relaxation frequency of the laser (F R ≈ F e ), and then sent to the bidimensional target by means of two rotating mirrors. The beam diffracted and/or scattered by the target is then reinjected inside the laser cavity after a second pass in the galvanometric scanner and the frequency shifter. The total frequency shift undergone by the photons reinjected in the laser cavity is therefore F e which results in triggering relaxation oscillations of the microlaser and in amplifying the sensitivity of the device to the reinjected photons. A small fraction of the output beam of the microchip laser is sent to a photodiode. The delivered voltage is analyzed by a lock-in amplifier at the demodulation frequency F e , which gives the LOFI signal (i.e. the amplitude and the phase of the electric field of the reinjected light). Experimentally, the LOFI images (amplitude and phase) are obtained pixel by pixel (i.e. point by point, line after line) by a full 2D galvanometric scanning. In the case of SA LOFI, the target is located at a distance L from the focal plane of the objective. The image is therefore obtained with a defocused beam. The raw complex image h R (x,y) must be numerically filtered to realize post focusing with the advantages to obtain images beyond the working distance of the lens [START_REF] Glastre | Limitation of synthetic aperture laser optical feedback imaging[END_REF][START_REF] Glastre | Deep and optically resolved imaging through scattering media by space-reversed propagation[END_REF]. In order to increase the image contrast an acoustic transducer can be used to tag (i.e. to shift the laser beam frequency by an additional amount F a ) the specific photons which have reached the immersed target

B. SA Refocusing

When a punctual target is scanned with the defocused beam, one obtains the blurred PSF [START_REF] Glastre | Limitation of synthetic aperture laser optical feedback imaging[END_REF][START_REF] Glastre | Deep and optically resolved imaging through scattering media by space-reversed propagation[END_REF]:

     2 2 2 2 2 2 E R ) L 2 y x 2 j exp( ) r L y x exp( F G ) y , x , L ( h                  
where G(F E ) is the LOFI gain [START_REF] Lacot | Coherent laser detection by frequency-shifted optical feedback[END_REF][START_REF] Jacquin | Experimental comparison of autodyne and heterodyne laser interferometry using Nd:YVO4 microchip laser[END_REF] at the frequency F e and where r is the laser beam waist in the image focal plane of the objective.

By taking the 2D Fourier transform of this expression, one obtains:

   ) 2 ) ( L j exp( ) r 2 exp( ) , , L ( H 2 2 2 2 2 R                
where  and  are the spatial frequency coordinates along x and y directions. The right-term of (2) shows the defocus which corresponds to the quadratic phase dependence. To numerically refocus raw images, this phase has to be cancelled by multiplying the signal in Fourier space by the phase filter:

                 2 ) ( L j exp ) , , L ( H 2 2 filt filt filt

 

This filter corresponds to the free space retro-propagation transfer function over a distance L filt /2 (the factor 2 is due to the round trip configuration of LOFI). After an adapted filtering (L filt =L) and inverse Fourier transform in the spatial domain, one has the following final synthetically refocused signal:

                      2 2 2 filt R 1 SA 2 r y x exp ) , , L ( H ) , , L ( H TF ) y , x ( h   In this expression TF -1
is the inverse Fourier transform. One can observe that after numerical refocusing, the resolution is equal to r/2 (and not r, due to the round trip configuration of LOFI ), whatever the initial defocus L, is [START_REF] Glastre | Limitation of synthetic aperture laser optical feedback imaging[END_REF][START_REF] Glastre | Deep and optically resolved imaging through scattering media by space-reversed propagation[END_REF]. This property can also be used to obtain in a single 2D scan a pseudo 3D image (image of non-plane surface) [START_REF] Glastre | Demonstration of a plenoptic microscope based on Laser Optical Feedback Imaging[END_REF].

Figure 2 shows, an example of a numerical refocusing for a plane target composed of small silica beads of 30-40 m diameter located behind a  shape hole with both a width and a height of the order of 1 mm.

C. Acoustic Photon Tagging

As shown on Fig. 3, there is a drawback to SA concerning the photometric balance. By comparison with the classical LOFI imaging (focalized case), the SA signal power is decreased by a ratio r 2 /S SA (ratio between the surface of the laser beam in the image plane of the objective and in the plane of the target) [START_REF] Glastre | Deep and optically resolved imaging through scattering media by space-reversed propagation[END_REF]. So we have a signal loss proportional to L 2 and we can quickly be limited by optical parasitic reflections (see background on Fig. 3a and3b) which are above the shot noise limit (the LOFI ultimate limit) [START_REF] Lacot | Coherent laser detection by frequency-shifted optical feedback[END_REF][START_REF] Jacquin | Experimental comparison of autodyne and heterodyne laser interferometry using Nd:YVO4 microchip laser[END_REF].

In order to eliminate parasitic signal from unwanted reflections, we can use APT which eliminates by filtering the contribution of parasitic reflections and offers real shot noise sensitivity giving access to a greater depth (L). One needs to tag photons just before the target [START_REF] Glastre | Deep and optically resolved imaging through scattering media by space-reversed propagation[END_REF][START_REF] Jacquin | Acousto-optic laser optical feedback imaging[END_REF]. This tagging is obtained with an acoustic transducer which focuses an acoustic wave in the image plane of the objective (see Fig. 1). This acoustic wave produces a sinusoidal modulation of the pressure (amplitude ~MPa) at the frequency F A /2= 2.25 MHz.

In order to consider only tagged photons for the detection, the signal can be demodulated (with the lock-in amplifier) at the frequency F e -F A instead of previous F e . With the complete setup of Fig. 1, we made an image of a target composed of small silica beads of 30-40 m diameter located behind a circular hole of 1 mm diameter. This target was placed in a rectangular glass tank filled with diluted milk acting as the scattering medium. Without APT we have F e = 4.4 MHz and with APT, we have F A = 4.5 MHz and F e =8.9 MHz. As a result, in both cases (with or without APT), the total round-trip frequency shift is equal to 4.4 MHz. By comparing Figs. 3a and 3b with Figs. 3c and3d we clearly see an improvement with the reduction of the background and therefore an increase of the image contrast (i.e of the image SNR). In both cases the optical resolution is recovered after numerical refocussing.

D. Phase drift compensation

During the LOFI image acquisition, made point by point, line after line, a slow phase drift can occurs, which degrades the final synthetic image (i.e. the refocused image). This drift is mainly due the variations of optical path between the laser and the target due to slight variations of the refractive index of the air (because of temperature or pressure changes). In typical experiment conditions (i.e. without any particular isolation), the phase drift is about 1 radian/minute in our lab, and principally affect the slow direction of the scan. Because our total acquisition time is about 1 minute, we see that this phase noise (which acts like an optical aberration) is very important (of the order of ) and needs to be corrected before SA processing. To do so, we propose a simple and efficient solution which consists in taking two raw images. The first one with a quick scan along the horizontal direction and therefore with a phase drift principally along the vertical direction and a second image by inverting the slow and fast acquisition directions. By combining these two images (i.e. by subtracting the two phase images), we can numerically determine the phase drift in any direction (horizontal or vertical) and we can finally recover a corrected"raw"acquisition [START_REF] Glastre | Limitation of synthetic aperture laser optical feedback imaging[END_REF]. By applying SA filtering, one can finally obtain a quasi-perfect synthetic image. Fig. 5a shows the amplitude of the raw image, when the vertical direction (i.e. Y) is the slow direction of acqusition. Fig. 5b, shows the amplitude of the corresponding synthetic aperture image. This last image clearly shows, that, the slow phase drift causes vertical aberrations and that the synthetic image is blurred in the Y direction. By using the second acqusition (not shown here), we can determined the phase drift (see Fig. 5c) by eliminating vertical phase difference between the two images . Finally, when SA operation is applied to the corrected raw image, we get Fig. 5d, showing that our blur (i.e. aberration) correction method is efficient.

III. PLENOPTIC LOFI

Aberration compensation is also an important concern for imaging through heterogeneous biological media [START_REF] Levoy | Recording and controlling the 4D lightfieldinamicroscopeusingmicrolensarrays[END_REF]. To correct aberrations, one possible solution consists in the introduction of adaptive optics resulting in an aberration-free laser spot in the target plane. Spatial light modulators or deformable mirrors can be used in this way [START_REF] Zawadzki | Ultrahigh-resolution optical coherence tomography with monochromatic and chromatic aberration correction[END_REF][START_REF] Facomprez | Accuracy of correction in modal sensorless adaptive optics[END_REF]. Another way to handle that problem is to use a plenoptic detector (i.e. a detector recording simultaneously the position and the direction of propagation of the photons), where the compensation is made by a numerical post-processing of the acquired raw images.

The LOFI setup, which allows to record the feedback electric field (i.e. the amplitude and the wave front of the complex electric field), is therefore a plenoptic imaging setup [START_REF] Glastre | Demonstration of a plenoptic microscope based on Laser Optical Feedback Imaging[END_REF]. To demonstrate aberration compensation in a SA LOFI setup, we can first consider the simplified situation of a constant aberration in the image field (i.e. we assume that the raw PSF does not depend on the field. Under this assumption, one obtains in the Fourier space the following transfer function:

 ) , ( ) , , ( ) , , ( '       aber R R H L H L H   
In this expression H aber (,) is the plane waves dephasing term responsible for the aberrations. In order to both refocus and correct aberrations, the filter function is turned into:

 ) , ( ) , , ( ) , , ( 1 '
        aber filt filt H L H L H  
To illustrate the capabilities of the LOFI technique for aberration correction, spherical silica beads of 30-40 m diameter are imaged by the LOFI setup depicted on Fig. 1. The advantage of this object is that a single bead acts as a punctual reflector (Dirac) located at its centre. The raw PSF is then directly accessible. Contrary to the paraxial lens usually used, an objective introducing large aberrations is now placed in the setup. This objective is a simple plano-convex spherical lens which is voluntarily tilted to induce important asymmetrical aberrations relatively to the optical axis (astigmatism and coma). From raw image, the defocus is first removed which leads to Fig. 6a where only remain higher order aberrations. Then astigmatism and coma are removed leading to Fig. 6b. This final image can be compared to Fig. 6d where the image has been obtained with an aberration-free objective.

To finish, on Fig. 6c, |h SA (L,x,y)*h aber (L,x,y)| is represented with h aber the inverse Fourier transform of H aber . This illustrates the astigmatism and coma that are compensated and thus which were initially present in the objective. By comparing Figs. 6a and6b, an important improvement in the image quality can be observed, which confirms the interest of our numerical aberration compensation technique. However by comparing Figs. 6b and6d, it is also possible to see that these corrections are not totally perfect and needs to be improved.

IV. CONCLUSIONS AND PERSPECTIVES

In this paper, an overview of the properties of a plenoptic microscope based on LOFI technique is made. This plenoptic microscope combines the high resolution of optical synthetic aperture and the high sensitivity of a self-mixing heterodyne technique called LOFI. This association enables to overcome the limitation of the accessible depth due to the objective working distance by numerical refocusing. This plenoptic microscope has also been coupled with APT to reach shot noise sensitivity. Other interesting properties of the plenoptic microscopes, such as numerical aberration compensation by using an adapted filtering and numerical removing of an unwanted phase drift have also been demonstrated. All these properties are possible at the price of a slow point by point galvanometric scanning and of the degradation of photometric performanceswhenthetargetisnotintheobjective'simaging focal plane. In the future, we plan to extend this work by implementing a correction of local aberrations beyond local defocus. Such an improvement will enable aberrations-free images through both scattering and heterogeneous media, which paves the way to biological sample imaging.

LFig. 1 .

 1 Fig. 1. Schematic diagram of Synthetic Aperture LOFI setup with acoustic PD, photodiode; BS, beam splitter; Fe and FA round-trip frequency shifts respectively induced by acousto-optic modulators and acoustic transducer; × frequency mixer. The target is located at a distance L from the focal plane of the objective (Obj) .

Fig. 2 .

 2 Fig. 2. Example of numerical refocusing. a) Raw image, b) Refocussing image with a filter mismatch (L=Lfilt-L= 4 cm), c) Filter mismatch (L= 2 cm), d) Adapted filter (L= 0 cm).

Fig. 3 .

 3 Fig. 3. Effect of Synthetic Aperture operation on the raw acquisition equivalent setup. L is the raw defocus, r the beam waist and  the numerical aperture. OD = log(SSA/r 2 ) is the equivalent Optical Density and SSA the surface of the laser beam after a propagation over a distance L.

Fig. 4 .

 4 Fig. 4. Comparison of LOFI images, with and without APT. a) and b), images without APT; c) and d), images with APT; a) and c), raw images; b) and d) images after SA processing.

Fig. 5 .

 5 Fig. 5. Correction of the effects of the phase drifts occuring during the raw acquisition. a) Raw image; b) Synthetic image without phase drift correction; c) Phase drift experimentally determined; d) Synthetic image with phase drift correction. One can see that the blur in the Y direction has disappeared.

Fig. 6 .

 6 Fig. 6. Example of partial abberation compensation of the plenoptic LOFI microscope. Image a) is obtained after numerical refocusing and b) with both refocusing and numerical aberration compensation. c) is the PSF used for filtering which shows the aberrations which are compensated. d) Perfect refocused image obtained with an abberation-free objective (this last figure obtained with an aberration-free objective has not be acquired on the same zone of the field: this explains why no correlations on the placement of the beads can be observed).


Keywords: H, 5, 2 [Information Systems]: User Interfaces-Input devices and strategies

We present the design of a 6-DOF tangible controller for 3D spatial data selection. Such selection is a primary and fundamental task in scientific visualization: it is performed prior to many other interactions. Many datasets are defined in 3D space, yet selection is often performed based on 2D input. While 2D selection may be efficient for datasets with explicit shapes, it is less efficient for data without such objects. We address this issue by combining 2D tactile with 3D tangible input to perform 3D selection in volumetric datasets.

INTRODUCTION

Many visualization systems rely on exploratory data visualization and analysis [START_REF] Tukey | Exploratory data analysis[END_REF] that allows domain experts to explore unknown dataset to discover specific regions of interest. An essential aspect of exploratory analysis is the selection of these specific regions of interest [START_REF] Wills | Selection: 524,288 ways to say "this is interesting[END_REF] that need to be more carefully examined to reveal their interesting patterns, properties or internal structures. While 2D selection on a 2D dataset can be easily performed with a mouse, 3D datasets require the specification of 3D volumes for selecting the intended data subset. Existing techniques are based on picking or ray-casting [START_REF] Argelaguet | A survey of 3D object selection techniques for virtual environments[END_REF] and are effective for selecting explicit shapes. Many scientific datasets such as particle clouds or medical scans, however, lack these explicit shapes and thus require other selection approaches in which the selection is achieved by specifying a selection volume. Our goal with this work is to facilitate such 3D selection using a position-aware tablet. We make use of Google's Project Tango tablet 1 as it supports both tactile input and tangible manipulations with its position-aware mechanism. We use the tactile input to adjust parameters and draw a 2D selection shape, and the position-aware mechanism to extend the 2D area into a 3D volume selection. Our approach thus extends existing automatic, interactive, and contextaware selection techniques with explicit adjustments of the selection volume in a tangibly spatial manner.

CONTEXT AND RELATED WORK

Several techniques have been developed in the past for making selections in 2D datasets. Picking-clicking on the target-is one of them and is often used for exploration of scatterplots or other 2D charts. It is a serial technique that is time-consuming when applied to multiple points-infeasible for the selection of 3D subsets within volumetric data. An alternative is the use of brushing: the user drags a pre-defined shape with the mouse to specify a region of interest in 2D. This approach facilitates the selection of multiple points in parallel with a single and efficient action [START_REF] Lucas | Design and evaluation of 3D multiple object selection techniques[END_REF]. A second alternative is the lasso technique-the user draws a shape or indicates its endpoints to perform a selection-which has been extensively used in operating systems. These two techniques have proven their efficiency for 2D datasets due to the match between input and data space dimensionality. 3D selection, however, requires the user to provide an additional depth information to create a selection volume and, in contrast to 2D environments, the 3D space is not fully visible (i. e., occlusion) and accessible for interaction. The lasso technique is the foundation on which we build our prototype implementation. Ulinski et al. [START_REF] Ulinski | Two handed selection techniques for volumetric data[END_REF] proposed to use two hands to manipulate a cuboidal selection volume. However, cuboidal selection might include undesired parts of the dataset due to the shape of the selection. Other approaches rely on the context or the inherent structure or properties of the data have also been investigated. For instance, Yu et al. [START_REF] Yu | Efficient structureaware selection techniques for 3D point cloud visualizations with 2DOF input[END_REF][START_REF] Yu | CAST: Effective and efficient user interaction for context-aware selection in 3D particle clouds[END_REF] propose to base their selection on a 2D lasso which is then refined and extended into a 3D selection by taking into account the density of particles in 3D point cloud dataset as well as the drawn shape. While Yu et al. rely on an automatic approach for the 3D extension, our approach emphasizes an interactive and tangible user control. Lucas and Bowman [START_REF] Lucas | Design and evaluation of 3D multiple object selection techniques[END_REF] use a physically tracked tablet on which a lasso is drawn, which is then extended into a 3D selection shape automatically. We build on the latter: we extend the selection area manually-with user input-instead of automatically creating it. We achieve this through the manipulation of a position-aware device, inspired by, e. g., Konieczny et al.'s [START_REF] Konieczny | A handheld flexible display system[END_REF] work.

The main idea of our approach is to show the data on the tablet, selecting a good view, and making a selection by creating a selection shape with tactile input and extending it to 3D with tangible interaction. Thus a user can start by making view adjustments to the data projection on the tablet-either by tangible or tactile interaction. After a good view is found, the user can initiate the Tangible Brush. It works similar to 2D brushing, only that a tangible interaction is used to move the brush shape in 3D space. We thus start by creating a selection shape using tactile input (see Fig. 1(a)). 2Next, the tangible motion of the tablet is used to move the 2D selection shape in 3D space to specify the selection volume. For this tangible interaction we can either make use of only the motion perpendicular to the tablet's orientation or its full 6 DOF motion. In contrast to 2D brushing, however, we not only actively select data items touched by the brush but use its motion to derive a 3D selection volume as shown in Fig. 1(b) and(c). This approach has the advantage that we can support both particle-based and volumetric data. Moreover, we can also make selections in large datasets for which only a well-chosen sample can be shown on the tablet.

This overall approach can be repeated several times to extend or adjust the selection volume, potentially with a re-adjustment of the view in-between the selection interactions. This iterative selection process can be achieved by a user by simply creating a new selection brush using tactile input, and then using the tangible interaction to complete the selection volume. For example, one may start with a larger brush to select the main part of a dense region in the data, and then create a smaller brush to add fine details (see Fig. 1(c)).

Our setup that combines the mobile tablet with a larger but static display supports this iterative creation of the selection (Fig. 2): The vertical display does not only show a second (potentially more detailed) copy of the data (on the left) but also a representation of the selection volume (on the right) which may be otherwise difficult to see in, for example, volumetric datasets. Together with the tablet, this setup thus combines the flexibility of tactile and tangible input for navigation and selection with the larger screen real estate and more computational power of the separate vertical display/workstation.

To facilitate and demonstrate the use of both input modalities, we implemented the prototypical interface shown in Fig. 2. Menus on top allow users to load different datasets and change general visualization settings. User-contolled mode switching between selection and data manipulation is achieved through an explicit button. To provide a better control over the tangible interaction, clutching is achieved by the pressing or releasing of this button-which is located right under the left thumb of users. We provide users with an additional toggle button that constrains the tangible interaction to motions perpendicular to the tablet or enables full 6 DOF motions. Finally, we provide users with a slider to adjust the control gain of tangible manipulations.

REALIZATION

A crucial point of our approach was to use position-aware devices to avoid expensive and tracking systems that are difficult to maintain and often dismissed by users. We thus decided to use the Tango device: a 7" tablet with a touch-sensitive screen, augmented with tracking capabilities and built-in sensors. We combine it with a vertical display (55", 3840 × 2160 pixels) to provide multiple synchronized views as shown in Fig. 2.

Communication between the devices uses the UDP protocol and we send absolute transformation matrices to ensure that packet loss does not negatively impact the display/tablet synchronization. We process datasets with the VTK library. 3 We render them with OpengGL ES 2.0 on the tablet and OpenGL 3.0 on the large display.

CONCLUSION AND FUTURE WORK

Our 3D selection technique relies on both tactile and tangible modalities, facilitated by Google's position-aware Tango tablet. It allows researchers to explore their 3D datasets using both tangible and tactile interaction paradigms, and combine the exploration with a hybrid selection technique. The advantages of this selection technique are that selections can now be made and adjusted though physical motions in 3D space, reinforcing the 3D spatial character of the data.

Future work includes adding the possibility to draw different selection shapes. We wish to implement additional Boolean operations to support intersections and subtractions as well. Furthermore, we would like to compare Tangible Brush against other selection techniques used in scientific visualization as well as explore how it can be combined with such existing techniques. Ultimately, we wish to integrate Tangible Brush into our already existing platform for the visualization of fluid dynamic datasets and explore how it can be integrated with existing tactile, tangible, and hybrid interaction paradigms for 3D data exploration. After this integration we are also planning to observe experts using our Tangible Brush selection to understand how it can support their data analysis workflow.

Figure 1 :

 1 Figure 1: Tangible Brush technique: Fig. 1(a) creation of selection are with tactile input; Fig. 1(b) the area is extended to a volume with tangible input; Fig. 1(c) users can check their selection and manipulate it.

Figure 2 :

 2 Figure 2: The overall data exploration setup including the interface on the position-aware tablet.

The current implementation uses rectangular shapes, but we are working on extending these to support arbitrary lasso-like input.

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