Frequency-swept ultrasound-modulated optical tomography in biological tissue by use of parallel detection

Coaxial interferometry for camera-based ultrasound-modulated optical tomography with paired illumination

Ultrasound-modulated optical tomography (UOT), which combines the advantages of both light and ultrasound, is a promising imaging modality for deep-tissue high-resolution imaging. Among existing implementations, camera-based UOT gains huge advances in modulation depth through parallel detection. However, limited by the long exposure time and the slow framerate of modern cameras, the measurement of UOT signals always requires holographic methods with additional reference beams. This requirement increases system complexity and is susceptible to environmental disturbances. To overcome this challenge, we develop coaxial interferometry for camera-based UOT in this work. Such a coaxial scheme is enabled by employing paired illumination with slightly different optical frequencies. To measure the UOT signal, the conventional phase-stepping method in holography can be directly transplanted into coaxial interferometry. Specifically, we performed both numerical investigations and experimental validations for camera-based UOT under the proposed coaxial scheme. One-dimensional imaging for an absorptive target buried inside a scattering medium was demonstrated. With coaxial interferometry, this work presents an effective way to reduce system complexity and cope with environmental disturbances for camera-based UOT.

Towards non-contact photoacoustic imaging [review]

Photoacoustic imaging (PAI) takes advantage of both optical and ultrasound imaging properties to visualize optical absorption with high resolution and contrast. Photoacoustic microscopy (PAM) is usually categorized with all-optical microscopy techniques such as optical coherence tomography or confocal microscopes. Despite offering high sensitivity, novel imaging contrast, and high resolution, PAM is not generally an all-optical imaging method unlike the other microscopy techniques. One of the significant limitations of photoacoustic microscopes arises from their need to be in physical contact with the sample through a coupling media. This physical contact, coupling, or immersion of the sample is undesirable or impractical for many clinical and pre-clinical applications. This also limits the flexibility of photoacoustic techniques to be integrated with other all-optical imaging microscopes for providing complementary imaging contrast. To overcome these limitations, several non-contact photoacoustic signal detection approaches have been proposed. This paper presents a brief overview of current non-contact photoacoustic detection techniques with an emphasis on all-optical detection methods and their associated physical mechanisms.

Coherent acousto-optic tomography with diffuse light

We propose a method to reconstruct the optical properties of a highly scattering medium from acousto-optic measurements. The method is based on solving an inverse problem with internal data for a system of diffusion equations.

Enhanced tagging of light utilizing acoustic radiation force with speckle pattern analysis

In optical imaging, the depth and resolution are limited due to scattering. Unlike light, scattering of ultrasound (US) waves in tissue is negligible. Hybrid imaging methods such as US-modulated optical tomography (UOT) use the advantages of both modalities. UOT tags light by inducing phase change caused by modulating the local index of refraction of the medium. The challenge in UOT is detecting the small signal. The displacement induced by the acoustic radiation force (ARF) is another US effect that can be utilized to tag the light. It induces greater phase change, resulting in a stronger signal. Moreover, the absorbed acoustic energy generates heat, resulting in change in the index of refraction and a strong phase change. The speckle pattern is governed by the phase of the interfering scattered waves; hence, speckle pattern analysis can obtain information about displacement and temperature changes. We have presented a model to simulate the insonation processes. Simulation results based on fixed-particle Monte Carlo and experimental results show that the signal acquired by utilizing ARF is stronger compared to UOT. The introduced mean irradiance change (MIC) signal reveals both thermal and mechanical effects of the focused US beam in different timescales. Simulation results suggest that variation in the MIC signal can be used to generate a displacement image of the medium.

Selection of the tagged photons by off axis heterodyne holography in ultrasound-modulated optical tomography

Ultrasound-modulated optical tomography (UOT) is a technique that images optical contrast deep inside scattering media. Heterodyne holography is a promising tool that is able to detect UOT-tagged photons with high efficiency. In this work, we describe theoretically the detection of the tagged photon in heterodyne holography-based UOT, show how to filter the untagged photon, and discuss the effect of shot noise. The discussion also considers speckle decorrelation. We show that optimal detection sensitivity can be reached, if the frame exposure time of the camera used to perform the holographic detection is on the order of the decorrelation time.

Acousto-optic effect in random media

We consider the acousto-optic effect in a random medium. We derive the radiative transport equations that describe the propagation of multiply scattered light in a medium whose dielectric permittivity is modulated by an acoustic wave. Using this result, we present an analysis of the sensitivity of an acousto-optic measurement to the presence of a small absorbing inhomogeneity.

Lock-in camera based heterodyne holography for ultrasound-modulated optical tomography inside dynamic scattering media

Ultrasound-modulated optical tomography (UOT) images optical contrast deep inside scattering media. Heterodyne holography based UOT is a promising technique that uses a camera for parallel speckle detection. In previous works, the speed of data acquisition was limited by the low frame rates of conventional cameras. In addition, when the signal-to-background ratio was low, these cameras wasted most of their bits representing an informationless background, resulting in extremely low efficiencies in the use of bits. Here, using a lock-in camera, we increase the bit efficiency and reduce the data transfer load by digitizing only the signal after rejecting the background. Moreover, compared with the conventional four-frame based amplitude measurement method, our single-frame method is more immune to speckle decorrelation. Using lock-in camera based UOT with an integration time of 286 μs, we imaged an absorptive object buried inside a dynamic scattering medium exhibiting a speckle correlation time ([Formula: see text]) as short as 26 μs. Since our method can tolerate speckle decorrelation faster than that found in living biological tissue ([Formula: see text] ∼ 100-1000 μs), it is promising for in vivo deep tissue non-invasive imaging.

Frequency-swept time-reversed ultrasonically encoded optical focusing

A technique to rapidly scan an optical focus inside a turbid medium is attractive for various biomedical applications. Time-reversed ultrasonically encoded (TRUE) optical focusing has previously demonstrated light focusing into a turbid medium, using both analog and digital devices. Although the digital implementation can generate a focus with high energy, it has been time consuming to scan the TRUE focus inside a sample. Here, by sweeping the frequencies of both ultrasound and light, we demonstrate a multiplex recording of ultrasonically encoded wavefronts, accelerating the generation of multiple TRUE foci. Using this technique, we obtained a 2-D image of a fluorescent target centered inside a turbid sample having a thickness of 2.4 transport mean free paths.

State-of-the art of acousto-optic sensing and imaging of turbid media

Acousto-optic (AO) is an emerging hybrid technique for measuring optical contrast in turbid media using coherent light and ultrasound (US). A turbid object is illuminated with a coherent light source leading to speckle formation in the remitted light. With the use of US, a small volume is selected,which is commonly referred to as the "tagging" volume. This volume acts as a source of modulated light, where modulation might involve phase and intensity change. The tagging volume is created by focusing ultrasound for good lateral resolution; the axial resolution is accomplished by making either the US frequency, amplitude, or phase time-dependent. Typical resolutions are in the order of 1 mm. We will concentrate on the progress in the field since 2003. Different schemes will be discussed to detect the modulated photons based on speckle detection, heterodyne detection, photorefractive crystal (PRC) assisted detection, and spectral hole burning (SHB) as well as Fabry-Perot interferometers. The SHB and Fabry-Perot interferometer techniques are insensitive to speckle decorrelation and therefore suitable for in vivo imaging. However, heterodyne and PRC methods also have potential for in vivo measurements. Besides measuring optical properties such as scattering and absorption, AO can be applied in fluorescence and elastography applications.

Effects of modulation phase of ultrasound-modulated light on the ultrasound-modulated optical image in turbid media

In this paper, our investigations suggest that the modulation phase of ultrasound-modulated light escaping from the different locations in the ultrasonic field is different. In turbid media, the modulation phase causes the ultrasound-modulated light intensity collected outside the media to fluctuate. However, the ultrasound-modulated optical technology uses the ultrasound-modulated light signals to image. Consequently, the modulation phase affects the quality of ultrasound-modulated optical imaging.

Application of a maximum likelihood algorithm to ultrasound modulated optical tomography

In pulsed ultrasound modulated optical tomography (USMOT), an ultrasound (US) pulse performs as a scanning probe within the sample as it propagates, modulating the scattered light spatially distributed along its propagation axis. Detecting and processing the modulated signal can provide a 1-dimensional image along the US axis. A simple model is developed wherein the detected signal is modelled as a convolution of the US pulse and the properties (ultrasonic/optical) of the medium along the US axis. Based upon this model, a maximum likelihood (ML) method for image reconstruction is established. For the first time to our knowledge, the ML technique for an USMOT signal is investigated both theoretically and experimentally. The ML method inverts the data to retrieve the spatially varying properties of the sample along the US axis, and a signal proportional to the optical properties can be acquired. Simulated results show that the ML method can serve as a useful reconstruction tool for a pulsed USMOT signal even when the signal-to-noise ratio (SNR) is close to unity. Experimental data using 5 cm thick tissue phantoms (scattering coefficient μ(s) = 6.5 cm(-1), anisotropy factor g=0.93) demonstrate that the axial resolution is 160 μm and the lateral resolution is 600 μm using a 10 MHz transducer.

Ultrasound-mediated optical tomography: a review of current methods

Ultrasound-mediated optical tomography (UOT) is a hybrid technique that is able to combine the high penetration depth and high spatial resolution of ultrasound imaging to overcome the limits imposed by optical scattering for deep tissue optical sensing and imaging. It has been proposed as a method to detect blood concentrations, oxygenation and metabolism at depth in tissue for the detection of vascularized tumours or the presence of absorbing or scattering contrast agents. In this paper, the basic principles of the method are outlined and methods for simulating the UOT signal are described. The main detection methods are then summarized with a discussion of the advantages and disadvantages of each. The recent focus on increasing the weak UOT signal through the use of the acoustic radiation force is explained, together with a summary of our results showing sensitivity to the mechanical shear stiffness and optical absorption properties of tissue-mimicking phantoms.

Theoretical study of acousto-optical coherence tomography using random phase jumps on ultrasound and light

Acousto-optical coherence tomography (AOCT) is a variant of acousto-optic imaging (also called ultrasonic modulation imaging) that makes it possible to get the z resolution with acoustic and optic continuous wave beams. We describe here theoretically the AOCT effect, and we show that the acousto-optic "tagged photons" remain coherent if they are generated within a specific z region of the sample. We quantify the z selectivity for both the "tagged photon" field and for the Lesaffre et al. [Opt. Express 17, 18211 (2009)] photorefractive signal.

Inverse scattering and acousto-optic imaging

We propose a tomographic method to reconstruct the optical properties of a highly scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes use of the principle of interior control of boundary measurements by an external wave field.

Acousto-optical coherence tomography using random phase jumps on ultrasound and light

Imaging objects embedded within highly scattering media by coupling light and ultrasounds (US) is a challenging approach. In deed, US enable direct access to the spatial localization, though resolution can be poor along their axis (cm). Up to now, several configurations have been studied, giving a millimetric axial resolution by applying to the US a microsecond pulse regime, as is the case with conventional echography. We introduce a new approach called Acousto-Optical Coherence Tomography (AOCT), enabling us to get a millimetric resolution with continuous US and light beams by applying random phase jumps on US and light. An experimental demonstration is performed with a self-adaptive holographic setup containing a photorefractive GaAs bulk crystal and a single large area photodetector.

Modeling of nonphase mechanisms in ultrasonic modulation of light propagation

While phase variation due to ultrasonic modulation of coherent light has been extensively studied in acousto-optical imaging, fewer groups have studied nonphase mechanisms of ultrasonic modulation, which may be important in exploring ultrasonic modulation of incoherent light for imaging. We have developed a versatile Monte Carlo based method that can model not only phase variation due to refractive index changes and scatterer displacement in tissue or tissue-like phantoms, but also amplitude and exit location variations due to the changes in optical properties and refractive index under ultrasonic modulation, in which the exit location variation has not, to the best of our knowledge, been modeled previously. Our results show that the modulation depth due to the exit location variation is three orders of magnitude higher than that due to amplitude variation, but two to three orders of magnitude lower than that due to phase variation for monochromatic light. Furthermore it is found that the modulation depth in reflectance due to the exit location variation is larger than that in transmittance for small source-detector separations.

Correlation transfer equation for multiply scattered light modulated by an ultrasonic pulse

We develop a temporal correlation transfer equation (CTE) and a Monte Carlo algorithm (MC) for multiply scattered light modulated by an ultrasonic pulse propagating in an optically scattering medium, where the ultrasound field can be nonuniform and the medium can have spatially heterogeneous distribution of optical parameters. The CTE and MC can be used to obtain the time-varying specific intensity and the spatial distribution of the time-dependent power spectral density, respectively, of ultrasound-modulated light. We expect the CTE and MC to be applicable for estimation of contrast and resolution in a wide spectrum of conditions in ultrasound-modulated optical tomography of soft biological tissues.

Correlation transfer equation for ultrasound-modulated multiply scattered light

In this paper, we develop a temporal correlation transfer equation (CTE) for ultrasound-modulated multiply scattered light. The equation can be used to obtain the time-varying specific intensity of light produced by a nonuniform ultrasound field in optically scattering media that have a heterogeneous distribution of optical parameters. We also develop a Monte Carlo algorithm that can provide the spatial distribution of the optical power spectrum in optically scattering media with focused ultrasound fields, and heterogeneous distributions of optically scattering and absorbing objects. Derivation of the CTE is based on the ladder diagram approximation of the Bethe-Salpeter equation that assumes moderate ultrasound pressures. We expect the CTE to be applicable to a wide spectrum of conditions in the ultrasound-modulated optical tomography of soft biological tissues.

Intense acoustic bursts as a signal-enhancement mechanism in ultrasound-modulated optical tomography

Biophotonic imaging with ultrasound-modulated optical tomography (UOT) promises ultrasonically resolved imaging in biological tissues. A key challenge in this imaging technique is a low signal-to-noise ratio (SNR). We show significant UOT signal enhancement by using intense time-gated acoustic bursts. A CCD camera captured the speckle pattern from a laser-illuminated tissue phantom. Differences in speckle contrast were observed when ultrasonic bursts were applied, compared with when no ultrasound was applied. When CCD triggering was synchronized with burst initiation, acoustic-radiation-force-induced displacements were detected. To avoid mechanical contrast in UOT images, the CCD camera acquisition was delayed several milliseconds until transient effects of acoustic radiation force attenuated to a satisfactory level. The SNR of our system was sufficiently high to provide an image pixel per acoustic burst without signal averaging. Because of the substantially improved SNR, the use of intense acoustic bursts is a promising signal enhancement strategy for UOT.

Correlation transfer and diffusion of ultrasound-modulated multiply scattered light

We develop a temporal correlation transfer equation (CTE) and a temporal correlation diffusion equation (CDE) for ultrasound-modulated multiply scattered light. These equations can be applied to an optically scattering medium with embedded optically scattering and absorbing objects to calculate the power spectrum of light modulated by a nonuniform ultrasound field. We present an analytical solution based on the CDE and Monte Carlo simulation results for light modulated by a cylinder of ultrasound in an optically scattering slab. We further validate with experimental measurements the numerical calculations for an actual ultrasound field. The CTE and CDE are valid for moderate ultrasound pressures and on a length scale comparable with the optical transport mean-free path. These equations should be applicable to a wide spectrum of conditions for ultrasound-modulated optical tomography of soft biological tissues.

Modulation of multiply scattered coherent light by ultrasonic pulses: an analytical model

We present an analytical solution for the acousto-optical modulation of multiply scattered light in a medium irradiated with a train of ultrasound pulses. Previous theory is extended to cases where the ultrasound-induced optical phase increments between the different scattering events are strongly correlated, and it is shown that the approximate similarity relation still holds. The relation between the ultrasound induced motions of the background fluid and the optical scatterers is generalized, and it is shown that correlation exists between the optical phase increments that are due to the scatterer movement and the optical phase increments that are due to the modulation of the optical index of refraction. Finally, it is shown that compared with the spectrum of ultrasound pulses, the power spectral density of acousto-optically modulated light is strongly attenuated at the higher ultrasound frequencies.

Imaging in diffuse media with pulsed-ultrasound-modulated light and the photorefractive effect

Acousto-optic imaging in diffuse media is a dual wave-sensing technique in which an acoustic field interacts with multiply scattered laser light. The acoustic field causes a phase modulation in the optical field emanating from the interaction region, and this phase-modulated optical field carries with it information about the local optomechanical properties of the media. We report on the use of a pulsed ultrasound transducer to modulate the optical field and the use of a photorefractive-crystal-based interferometry system to detect ultrasound-modulated light. The use of short pulses of focused ultrasound allows for a one-dimensional acousto-optic image to be obtained along the transducer axis from a single, time-averaged acousto-optic signal. The axial and lateral resolutions of the system are controlled by the spatial pulse length and width of the ultrasound beam, respectively. In addition, scanning the ultrasound transducer in one dimension yields two-dimensional images of optical inhomogeneities buried in turbid media.

Pulsed acousto-optic imaging in dynamic scattering media with heterodyne parallel speckle detection

We present a new detection scheme for acousto-optic tomography based on pulsed-wave ultrasound and illumination combined with heterodyne parallel speckle detection. This setup can perform tomographies inside several-centimeter-thick scattering samples. Test experiments confirm the suitability of this method for performing tomographies inside various types of optically scattering media, including liquids.

High-resolution ultrasound-modulated optical tomography in biological tissues

We present a novel implementation of high-resolution ultrasound-modulated optical tomography that, based on optical contrast, can image several millimeters deep into soft biological tissues. A long-cavity confocal Fabry-Perot interferometer, which provides a large etendue and a short response time, was used to detect the ultrasound-modulated coherent light that traversed the scattering biological tissue. Using 15-MHz ultrasound, we imaged with high-contrast light-absorbing structures placed >3 mm below the surface of chicken breast tissue. The resolution along the axial and the lateral directions with respect to the ultrasound propagation direction was better than 70 and 120 microm, respectively. The resolution can be scaled down further by use of higher ultrasound frequencies. This technology is complementary to other imaging technologies, such as confocal microscopy and optical-coherence tomography, and has the potential for broad biomedical applications.

Signal dependence and noise source in ultrasound-modulated optical tomography

A Monte Carlo modeling technique was used to simulate ultrasound-modulated optical tomography in inhomogeneous scattering media. The contributions from two different modulation mechanisms were included in the simulation. Results indicate that ultrasound-modulated optical signals are much more sensitive to small embedded objects than unmodulated intensity signals. The differences between embedded absorption and scattering objects in the ultrasound-modulated optical signals were compared. The effects of neighboring inhomogeneity and background optical properties on the ultrasound-modulated optical signals were also studied. We analyzed the signal-to-noise ratio in the experiment and found that the major noise source is the speckle noise caused by small particle movement within the biological tissue sample. We studied this effect by incorporating a Brownian motion factor in the simulation.

Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging

We propose a new detection method for ultrasound-modulated optical tomography that allows us to perform parallel speckle detection with optimum shot-noise sensitivity, using a CCD camera. Moreover, we show that making use of a spatial filter system allows us to fully filter out speckle decorrelation noise. This method is confirmed by a test experiment.

Transmission- and side-detection configurations in ultrasound-modulated optical tomography of thick biological tissues

Ultrasound-modulated optical tomography of thick biological tissues was studied based on speckle-contrast detection. Speckle decorrelation was investigated with biological tissue samples of various thicknesses. Images of optically absorbing objects buried in biological tissue samples with thicknesses up to 50 mm were obtained in a transmission-detection configuration. The image contrast was more than 30%, and the spatial resolution was approximately 2 mm. In addition, a side-detection scheme along with two specific configurations were examined, and the advantages were demonstrated. Experimental results implied feasibility of applying the ultrasound-modulation technique to characterize optical properties in inhomogeneous biological tissues.

High-contrast fast Fourier transform acousto-optical tomography of phantom tissues with a frequency-chirp modulation of the ultrasound

We report new results on acousto-optical tomography in phantom tissues using a frequency chirp modulation and a CCD camera. This technique allows quick recording of three-dimensional images of the optical contrast with a two-dimensional scan of the ultrasound source in a plane perpendicular to the ultrasonic path. The entire optical contrast along the ultrasonic path is concurrently obtained from the capture of a film sequence at a rate of 200 Hz. This technique reduces the acquisition time, and it enhances the axial resolution and thus the contrast, which are usually poor owing to the large volume of interaction of the ultrasound perturbation.

Ultrasound-modulated optical tomography of biological tissue by use of contrast of laser speckles

Ultrasound-modulated optical tomography based on the measurement of laser-speckle contrast was investigated. An ultrasonic beam was focused into a biological-tissue sample to modulate the laser light passing through the ultrasonic column inside the tissue. The contrast of the speckle pattern formed by the transmitted light was found to depend on the ultrasonic modulation and could be used for imaging. Variation in the speckle contrast reflected optical inhomogeneity in the tissue. With this technique, two-dimensional images of biological-tissue samples of as much as 25 mm thick were successfully obtained with a low-power laser. The technique was experimentally compared with speckle-contrast-based, purely optical imaging and with parallel-detection imaging techniques, and the advantages over each were demonstrated.

Ultrasonic modulation of multiply scattered coherent light: an analytical model for anisotropically scattering media

In this work, we have calculated analytically the temporal autocorrelation function of the electrical field component of multiply scattered coherent light transmitted through an anisotropically scattering media irradiated with a plane ultrasonic wave. The accuracy of the analytical solution is verified with an independent Monte Carlo simulation for different values of the ultrasonic and optical parameters. The analytical model shows that an approximate similarity relation exists; if the reduced scattering coefficient is unchanged regardless of the mean cosine of the scattering angle, the autocorrelation function remains approximately the same.

Autocorrelation of scattered laser light for ultrasound-modulated optical tomography in dense turbid media

Based on measurement of the intensity autocorrelation function, a new method to determine the modulation depth of scattered laser light modulated by an ultrasonic wave in turbid media was applied to ultrasound-modulated optical tomography. Good signal-to-noise ratios and high sensitivities were demonstrated. Images of double optically absorbing objects buried in a highly optically scattering gel sample were obtained. The contrast was more than 10%, and the spatial resolution was approximately 2 mm.

Nonlinear effects in acousto-optic imaging

Acousto-optic (AO) imaging is a promising technique that is able to reveal optical properties in the millimeter range inside scattering media by tagging the photon paths with an ultrasonic beam. To increase both the contrast and the resolution of the AO images, we have explored the possibility of using the nonlinear response of the speckle modulation. Variation of the second-harmonic signal as the square of the ultrasonic amplitude has been found, and strong reduction of the tagged zone size has been demonstrated.

Analysis of the picosecond magneto-optical phenomena in scattering media of biological interest

The behaviour of a magneto-optically active biological-like medium under picosecond optical excitation is analysed. The new technique is based on the fact that photons trapped in multiple scattering events inside the magneto-optical medium leave the medium with larger induced rotation angles, as they travel longer distances. Two- and three-dimensional displacements of the photons in the medium are separately analysed. The dependence of this effect on the applied magnetic field strength, the value of the magneto-optical constant of the medium and the standard deviation of the statistical distribution of the photons scattered inside the turbid medium are studied. The best values for the magnetic field and optical parameters of the biological medium are proposed for the experimental observation of the picosecond magneto-optical phenomena in scattering media of biological origin. We also make some prospective studies to evaluate the potential application of the magneto-optical effect as a tool for optical tissue biopsy. Values for the optimum magnetic field intensities and for the expected experimental sensitivity in diverse conditions are reported.

Methods for parallel-detection-based ultrasound-modulated optical tomography

The research reported here focuses on ultrasound-modulated optical tomography based on parallel speckle detection. Four methods were investigated for signal acquisition and analysis, in which laser speckle statistics was applied. The methods were compared with the previously used four-phase method in the imaging of all-biological-tissue samples, in which the buried objects were also biological tissues. The image quality obtained with these methods was comparable with that obtained with the four-phase method; in addition, these methods have advantages in reducing acquisition time and improving the signal-to-noise ratio.

Mechanisms of ultrasonic modulation of multiply scattered coherent light: a Monte Carlo model

A Monte Carlo model of the ultrasonic modulation of multiply scattered coherent light in scattering media is provided. The model is based on two mechanisms: the ultrasonic modulation of the index of refraction, which causes a modulation of the optical path lengths between consecutive scattering events, and the ultrasonic modulation of the displacements of scatterers, which causes a modulation of optical path lengths with each scattering event. Multiply scattered light accumulates modulated optical path lengths along its path. Consequently, the intensity of the speckles that are formed by the multiply scattered light is modulated. The contribution from the index of refraction is comparable with the contribution from displacement when the acoustic-wave vector is less than a critical fraction of the transport mean free path and becomes increasingly greater than the contribution from displacement beyond this critical point. This Monte Carlo model agrees well with an independent analytical model for isotropically scattering media. Both mechanisms are coherent phenomena, requiring the use of a coherent light source.

Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model

An analytic model of the ultrasonic modulation of multiply scattered coherent light in scattering media is developed based on two mechanisms: the ultrasonic modulation of the index of refraction and the ultrasonic modulation of the displacements of Rayleigh scatterers. In water solutions, for example, the first mechanism is slightly less important than the second mechanism when the scattering mean free path is less than a critical fraction (0.0890) of the acoustic wavelength, and it becomes increasingly more important beyond this point. This model agrees well with an independent Monte Carlo model.