Acousto-optic imaging with photorefractive holography 

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Parallel speckle processing

As I showed in the previous section, the amount of light modulation due to ultrasound is small. In order to increase the SNR of the detection, it is necessary to accumulate the measured modulation over a high number of speckle grains. Because of the random wave-front of scattered light, the phase of this modulation is random from one grain to another so that it incoherently adds over large area single detectors. In order to overcome this difficulty, the first techniques that were used were camera-based techniques able to sample speckle patterns in order to parallel process each grain one by one.
The first use of a camera for detecting tagged photons in acousto-optic imaging was reported by S. Lévêque et al. in [81]. In this paper, the authors suggest to use parallel speckle detection thanks to a 105 pixels CCD camera in order to process as many speckle grains through a lock-in approach. Because the camera exposure time is very long compared to the period of the ultrasonic modulation, they suggested to use a synchronous light excitation instead of a conventional synchronous detection. This technique was later used in other papers such as [82]. Progresses in CMOS technologies allowed recent development of smart-sensors arrays with a lock-in detection associated with each pixel in order to real-time demodulate all speckle grains in parallel [83, 84]. The ultrasound modulation is extracted from the interference between scattered light and a reference tuned on the untagged photons frequency. The beating component is analogically demodulated pixel by pixel and only the AC-component is encoded thus reducing the amount of transferred data. It allows single-shot acousto-optic signal recording whereas synchronous excitation needed at least four images. Until recently, the main limitation of such an approach was the limited number of pixels (24×24 pixels in [83], 64×64 in [84]). In 2016, Liu et al. used a commercial lock-in camera with a lot more pixels (300 × 300) and showed promising results inside decorrelating objects [85].
These previous approaches aim at directly measuring the modulation depth in each speckle grain. In case an analog lock-in detection in each pixel is not available, previous examples showed that the exposure time of cameras is often too long to properly measure the ultrasound modulation so that it is necessary to perform synchronous excitation. Because such approaches are not convenient, other techniques were developed that take advantage of this “drawback” in order to deduce the amount of modulated light. The principle of these techniques is the same as speckle contrast imaging techniques described in chapter 1. Because exposure times of cameras are often longer than the ultrasonic period, the presence of ultrasound induces a blurring of the speckle image. By quantifying this amount of blurring through the measurement of the speckle contrast (see section 1.3.2), it is possible to recover the modulation depth. The first proof of concept was performed by J. Li et al. [86] and a theoretical framework can be found in [87]. The major issue of this approach is that the exposure time of the camera must be shorter than the speckle decorrelation time so that the measured decorrelation is only due to ultrasound. Recently, S.
Resink et al. showed that such a detection scheme may be coupled with nanosecond pulses in order to couple acousto-optic and photoacoustic imaging or solve this speckle decorrelation issue [88]. Because nanosecond pulses are used, there is no speckle decorrelation due to tissue moving at this time-scale. The measured speckle decorrelation is then only due to ultrasound. S. Resink and W. Steenbergen showed that acquiring two frames corresponding to two nanosecond pulses emitted at two different ultrasound phases allows recovering the modulation [89–91].

Wave-front adaptive holography

A way of overcoming the imaging speed issue of cameras is to use detection schemes based on high surface single-detectors. Because the bandwidth of such detectors is typically of several MHz, it is possible to time-resolve ultrasound propagation with a temporal resolution under 1 μs.
– corresponding to a spatial sampling under 1.5 mm. However, as I explained above, speckle patterns lead to the measured AC-modulation increasing as the square root of the number of integrated speckle grains whereas the DC-level increases as the number of speckle grains. It thus results in SNR that is limited to the SNR of a single speckle grain. In order to increase this ratio, people developed holographic techniques that allow adapting the scattered and reference wavefronts.
The principle is as follows. The interference pattern between the scattered and reference light is recorded in a holographic medium. The interference is given by: |ES (r′, t) + ER (r′, t) |2 = E2 0 + E2R + ES (r′, t) E∗ R (r′, t) + E∗ S (r′, t) ER (r′, t) (2.39) “Recording” means that the light irradiance slightly modifies one of the physical properties of the material so that the transmission T (x, y) becomes spatially inhomogeneous and proportional to the interference pattern. This inhomogeneous transmission thus creates a grating on which light can diffract.

Of acousto-optic imaging and resolution

I previously presented several possible techniques that were used to filter and count tagged photons. In section 2.3.2, it appeared that photons are tagged over the entire volume occupied by ultrasound, the shape of which will then naturally define the resolution of the technique. One thus explored a lot of different ultrasound sequences in order to obtain different resolutions and levels of acoustooptic signal. In this section I suggest to study a few examples of typical acousto-optic sequences and their corresponding resolution.
First proofs of concepts were performed using single-element focused transducers and continuous wave [64, 82] and suffered from very poor longitudinal resolution (in the ultrasound propagation direction ux). If the lateral and elevational resolution (along uy and uz) of such an approach is approximately the lateral size of the focus (a few Λ), the longitudinal resolution is the entire scattering medium depth. A means of recovering the resolution consists in using a tomographic approach by rotating the emitting transducer around the sample [109].

Fusion of conventional ultrasound and acousto-optics

In order to properly understand how acousto-optic imaging and conventional ultrasound can be coupled, I will first give a quick overview of how conventional ultrasound works. Conventional ultrasound scans are based on multi-element transducer arrays of several tens or hundreds of small piezoelectric transducers (64, 192, 256 or 512 elements for instance). Transducer arrays can have different shapes (1D or 2D, linear or curved…) depending on the application. In this manuscript, I use linear arrays with rectangular 0.2 × 0.4 mm2 elements with a pitch of 0.2 mm1, see figure 3.1(a). Each transducer can be electronically driven independently from the others with a variable delay. Because of Huygens-Fresnel principle, these delay lines define the shape of the ultrasound wave under the probe. For instance, pulsing all elements at the same time generates a plane wave propagating vertically under the probe, whereas applying a linear delay generates a plane wave propagating with a tilted angle.

Photorefractive detection of tagged photons

In this section I will further detail the detection of tagged photons through photorefractive holography. Because it was already studied in several previous PhDs [66, 111, 118] and articles [79,97,98,110], a lot of calculations will not be detailed here and were moved in appendix A. I will only recall the main results here.
The main goal of the photorefractive detection is to have the scattered and reference beams coherently interfere all over the surface of a single detector. The interest of such crystals is that they can adapt the two wave-fronts through a phenomenon so-called Two-Wave Mixing (TWM). In order to introduce TWM, it is important to first explain the photorefractive effect. Once TWM is detailed, I will show how it can be used for tagged photons detection.


The photorefractive effect

The photorefractive effect is known since the mid 60’s and was first considered as an unwanted effect. Its use as a tool for imaging vibrations was suggested at the end of the 90’s. For instance, P. Delaye et al. [119] used photorefractive Fe:InP crystals under a DC-electric field around 1.06 μm in order to measure vibrations of rough surfaces. Acousto-optic imaging then widely benefited from these works so that a lot of theoretical derivations were inspired by the developments of this field. The photorefrective effect occurs in materials that are both photoconductive and electrooptic. Several materials present a photorefractive effect such as polymers [99] or light valves [100]1. In the following, I will focus on photorefractive crystals. Typical photorefractive materials are crystals or oxides with a forbidden band, for instance:
• ferroelectric crystals such as lithium niobate (LiNbO3), barium titanate (BaTiO3) or SPS (Sn2P2S6, tin thiohypodiphosphate),
• sillenites such as BSO (Bismuth Silicon Oxide, Bi12SiO20), BTO (Bismuth Titanate, Bi12TiO20) or BGO (Bismuth Germanate, Bi12GeO20),
• semi-conductors such as gallium arsenide (GaAs), cadmium telluride (CdTe) or indium phosphide (InP).

Table of contents :

I Optical imaging of thick biological tissues 
1 Optical properties of biological tissues 
1.1 Optical contrast in medical imaging
1.2 Light-tissues interactions
1.2.1 Absorption
1.2.2 Scattering
1.2.3 The case of biological samples
1.3 Light propagation in scattering samples
1.3.1 The propagation regimes
1.3.2 Of multiply scattered electric field
1.4 Optical imaging of scattering samples
1.4.1 Ballistic and single-scattered light
1.4.2 Working with multiply scattered light
1.5 Summary on optical imaging of scattering media
2 Acousto-optic imaging 
2.1 Introduction to acousto-optics
2.1.1 From acousto-optic effect to imaging
2.1.2 Applications of the technique
2.2 Light/ultrasound mixing in multiply scattering media
2.2.1 Modulation of the scatterers position
2.2.2 Modulation of the refractive index
2.2.3 Modulation of the optical path
2.3 The modulated light
2.3.1 Expression of the modulated electromagnetic field
2.3.2 Coherent acousto-optic modulation
2.4 Tagged photons filtering
2.4.1 Challenges of filtering modulated light
2.4.2 Parallel speckle processing
2.4.3 Wave-front adaptive holography
2.4.4 Spectral filtering
2.4.5 Summary on filtering techniques
2.5 Of acousto-optic imaging and resolution
2.6 Conclusion on acousto-optic imaging
II Acousto-optic imaging with photorefractive holography 
3 Bimodal acousto-optic/ultrasound imaging 
3.1 Fusion of conventional ultrasound and acousto-optics
3.2 Photorefractive detection of tagged photons
3.2.1 The photorefractive effect
3.2.2 Two-wave mixing process
3.2.3 Detecting tagged photons
3.2.4 Application to acousto-optic imaging
3.3 Bimodal imaging of ex vivo liver tumours
3.3.1 Uveal melanoma
3.3.2 Results on liver biopsies
3.3.3 A discussion about acousto-optic imaging and uveal melanoma
3.4 What next for bimodal imaging?
3.4.1 Quantitative imaging
3.4.2 Functional brain imaging
3.4.3 Sketches of in vivo imaging
3.5 Bimodal imaging limitations
III Acousto-optic imaging thanks to ultrasonic plane waves 
4 Introduction to acousto-optic imaging with ultrasonic plane waves 
4.1 Of low imaging rate in acousto-optic imaging
4.2 Tomography and multi-waves imaging
4.3 Acousto-optic signal with an ultrasonic plane wave
4.3.1 From focused acousto-optic imaging to tomography
4.3.2 Problem inversion and image reconstruction
4.4 Theoretical study of the acousto-optic signal
4.4.1 Analytical inversion
4.4.2 Point-spread function and limited angular range
4.4.3 Approximate expression of the PSF
4.5 Influence of angular exploration
4.5.1 Behaviour of the inductive terms
4.5.2 Study of the 2D PSF
4.5.3 Resolution as a function of the angular range
4.6 Intermediary conclusion
5 Ultrafast acousto-optic imaging with ultrasonic plane waves 
5.1 Reconstruction method
5.2 Study of a single inclusion
5.2.1 Experimental setup
5.2.2 Focused ultrasound reference image
5.2.3 Improvement of imaging speed
5.2.4 Further considerations on plane waves images
5.3 Influence of absorbers
5.3.1 Robustness to ultrasound artefacts
5.3.2 Towards more complex objects
5.4 Two probes imaging
5.5 Prospects for acousto-optic imaging with plane waves
IV Acousto-optic imaging with spectral holeburning 
6 Basic principle of spectral holeburning 
6.1 Spectral filtering techniques for tagged photons
6.2 Choice of Tm3+:YAG crystals
6.2.1 Tm3+ ions in a YAG matrix
6.2.2 Linewidth broadening
6.2.3 Characterization of the linewidths
6.3 Principle of spectral holeburning
6.3.1 General idea
6.3.2 Simple model for spectral holeburning
6.3.3 Acousto-optic imaging with spectral holeburning
6.4 Characterization of a hole
6.4.1 Study of a hole
6.4.2 Influence of the burning beam
6.5 Laser stabilization
6.5.1 Of laser stabilization necessity
6.5.2 Shape of a hole
6.5.3 Influence of the burning power
6.6 Experimental limitations of spectral holeburning
7 Acousto-optic imaging using spectral holeburning under a magnetic field 
7.1 Tm3+:YAG under a magnetic field
7.2 Spectral holeburning under a magnetic field
7.2.1 General principle
7.2.2 Simple model for spectral holeburning under a magnetic field
7.2.3 Towards acousto-optic imaging
7.3 Quantification of hole properties
7.3.1 Hole and anti-holes
7.3.2 Influence of the burning power
7.4 Transposition to tagged photons
7.4.1 Acousto-optic imaging setup
7.4.2 Of burning beam shape and absorption
7.5 A proof of concept
7.5.1 Acousto-optic signal
7.5.2 Behaviour of the acousto-optic signal
7.5.3 Towards scattering media
7.6 Conclusions and prospects
Conclusions and prospects
A The photorefractive effect 
A.1 The band transport model
A.1.1 Principle
12 Table of contents
A.1.2 The space-charge field
A.1.3 Photoinduced variation of the refractive index
A.2 Two-wave mixing
A.2.1 Photorefractive gain
A.2.2 Transmission of time-modulated signals
A.3 Detection of acousto-optic signals
A.3.1 Small diffraction efficiency
A.3.2 Accurate solution
B The Radon transform 
B.1 Radon transform and backprojection
B.2 Analytical inversion of the Radon transform
B.2.1 The projection-slice theorem
B.2.2 The filtered backprojection
C Of the inductive relationship of chapter 4 
D Calculation of the delay in plane waves imaging 
D.1 The emitted delay line
D.2 Time-of-flight calculation
E Simple model for spectral holeburning 
E.1 About the different parameters
E.2 Population equations and steady state
E.2.1 Population equations
E.2.2 Derivation of the absorption coefficient
E.2.3 Effect of linewidth broadening
E.3 Holeburning process in steady state
E.3.1 Reminder about holeburning process
E.3.2 Absorption of the probing beam
E.3.3 Dynamics of hole erasure
F Simple model for spectral holeburning under a magnetic field 
F.1 Model of the atomic levels
F.1.1 General model
F.1.2 Main assumptions
F.2 Population equations and steady state
F.2.1 Steady-state solution
F.2.2 Population difference
F.2.3 The homogeneous linewidth
F.2.4 Comparison with the no-magnetic-field case
F.2.5 Dynamics of hole erasure
G Scientific contributions 
H Résumé (FR) 
H.1 À la recherche du contraste optique dans les milieux biologiques
H.1.1 Imagerie optique des tissus biologiques
H.1.2 Des milieux fortement diffusants à l’imagerie acousto-optique
H.2 Vers l’imagerie acousto-optique clinique ?
H.2.1 Détection des photons marqués et résolution
H.2.2 Imagerie bi-modale couplant acousto-optique et échographie
H.2.3 Preuve de concept
H.3 Imagerie ultra-rapide par ondes planes ultrasonores
H.3.1 Principe de l’imagerie acousto-optique en ondes planes
H.3.2 Simulation de la fonction d’étalement du point (PSF)
H.3.3 Preuve de concept expérimentale
H.3.4 Perspectives pour les ondes planes
H.4 Imagerie acousto-optique par creusement spectral
H.4.1 Réalisations de filtres ultrafins par holeburning spectral dans des cristaux de Tm3+ :YAG
H.4.2 Holeburning spectral sous champ magnétique
H.5 Conclusion et perspectives


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