What is the acousto optics introduction?

The Acousto-optic (AO) Effect is a phenomenon that occurs when light (optics) interacts with sound (acoustic) waves in a material. This effect was first discovered by Brillouin in and it involves sound waves that cause diffraction of light. The AO effect has been widely studied and applied in various fields, including telecommunications, spectroscopy, and laser technology.

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The acousto-optic effect arises from the photo-elasticity of the medium. Photoelasticity is a property of certain transparent materials to exhibit changes in optical properties when subjected to mechanical stress. A sound wave can alter the refractive index of the medium, creating a grating with varying refractive indices.

Working of AO Effect

Figure 1: Working of Acousto-optic modulator

The acousto-optic effect is the working principle of an acousto-optic modulator. It works by using a piezoelectric transducer that is attached to a photo-elastic medium to introduce a sound wave into a material. 

When an electric field is applied to the transducer, a sound wave is created that propagates through the material and causes periodic variations in the refractive index of the material. When a light beam is introduced into the material, it interacts with the sound wave. The refractive index variations caused by the sound wave lead to diffraction or scattering of the light beam. This diffraction is similar to that of Bragg diffraction. Figure 1 shows the schematic of an acousto-optic modulator.

The amount of light diffracted or scattered depends on the frequency and amplitude of the sound wave, as well as the properties of the material. The diffraction angle can be controlled by adjusting the frequency and amplitude of the sound wave. 

Condition for Diffraction

The diffraction of acousto-optic modulator is similar to Bragg diffraction as it operates under Bragg condition. That is, if the incident light is at Bragg angle, the obtained diffraction pattern satisfies the following condition:

Where Λ is the wavelength of the sound, θ is the diffraction angle, m=...,&#;2,&#;1,0,+1,+2,.. is the integer representing the order of diffraction, and n is the refractive index of the material.

Applications

The acousto-optic effect is used in fiber-optic communication systems to control the direction and amplitude of light beams. This allows for the modulation and switching of light signals, enabling high-speed data transmission.

It is used in spectroscopy to analyze the properties of materials by measuring the scattering or diffraction of light waves. This allows for the identification and characterization of different materials based on their optical properties.

This effect is used in laser technology to control the direction and intensity of laser beams. It helps in the creation of complex laser patterns and the manipulation of laser beams for various applications.

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The AO effect also has applications in heterodyning techniques, acousto-optic momentum matching, guided wave effects, and Bragg diffraction imaging.

On the other hand, US modulation of light can be explained by mixing two waves, US and optical waves. When interacting with light, US generates sidebands in scattered light that are shifted by multiple US frequencies. In practice, only the first two sidebands containing a number of photons or power spectra (+1 order of sidebands) are detected and processed [ 10 , 17 ]. In contrast to untagged photons that are not shifted in optical frequency when measured, tagged photons usually exhibit one US frequency shift, and their number is very low in comparison to the background of untagged photons, because deep tissues have a large diffuse volume, but very little US focus. Therefore, very efficient filtering techniques are necessary to remove as many untagged photons as possible before detection, or very sensitive detection techniques must be applied to detect very weak modulations.

In coherent light illumination, the relative influence of the first two mechanisms, ultrasonic&#;induced displacement of scatterers and ultrasonic&#;modulated index of refraction, depend on properties of the medium and the used waves. The relative influence of these two mechanisms is changed by the scattering coefficient and the wavelengths of the US and the probing light. The strength of both mechanisms is comparably high, but the ultrasonic&#;modulated index of refraction becomes dominant when the acoustic wavelength becomes larger than a critical fraction of the mean free path of the photons [ 14 , 15 ]. It is worth mentioning that the modulation depth is closely related to the intensity of the speckle patterns produced by US&#;induced variation of the optical phase of a coherent light. In studying biological tissues in vivo, the speckle decorrelation time is usually shorter than 1 ms [ 16 ] due to scatterers&#; irregular (non&#;modulated) movements in the microfluidic system of living tissues. Hence, differing from tissue phantom studies, in vivo detection techniques must be fast enough to avoid speckle decorrelation.

Several mechanisms can cause tagging of light in a medium [ 3 , 10 , 14 ]. The first is the displacement or oscillation of scatterers by US waves; scatterers oscillating at US amplitudes cause a variation in the optical path, resulting in phase variations in light. The mechanism can only be valid when the mean free path is far greater than the acoustic wavelength [ 10 ]. The second mechanism describes phase variation caused by a refractive index change between scattering events. It is worth mentioning that refraction of light occurs between two scattering events due to changes in the index of refraction. Because of this mechanism, optical path lengths, and therefore phases, are modulated. This, in turn, modulates the intensity of the resulting speckle pattern [ 14 ]. Lastly, the third mechanism is caused by variation in density and consequent changes in the optical properties of the medium due to US perturbation, including changes in the absorption coefficient, scattering coefficient, and index of refraction. According to previous studies, the first two mechanisms need a coherent light source, whereas the third mechanism is an incoherent phenomenon, in which the US modulated signal is very weak, so the third mechanism can be ignored in the case of a coherent light source.

A biological tissue is a high scattering multilayer medium with heterogeneous physical properties [ 3 , 4 , 10 , 12 ]. Applying a US field to a tissue will change its optical properties in time and space, making light propagation in it more complicated. As the transmitted light is detected, a speckle pattern forms owing to interference of different phase differences. illustrates what happens when light frequency is modulated or &#;tagged&#; as it passes through the US focus region. As a result of this modulation, the speckle pattern is blurry and varies due to time&#;varying US, and the detected speckle spectrum contains n orders of sidebands. Additionally, the tagged signal is small compared to untagged light [ 3 , 13 ].

2.2. Theoretical Modeling and Computational Simulation

A solid basis for the AO effect theory is provided by an electromagnetic wave propagation model in a material medium. In a general case, such a model is based on Maxwell equations for a dielectric whose permittivity is modulated by acoustic wave propagation [18]. In addition, phenomenological theories can be employed for multiplying scattered light using the radiative transport equation (RTE) or diffusion approximation (DA) to the RTE [19,20]. The theory of diffraction of light by an US wave was first proposed by Brillouin [21] in and then proved experimentally by Debye and Sears [22] as well as Lucas and Biquard in . Raman and Nath proposed an analytical model of the AO effect&#;also called Raman&#;Nath diffraction&#;in a homogeneous non&#;absorbing and non&#;scattering medium [23]. A numerical simulation of time&#;reversed ultrasonically encoded optical focusing (TRUE) was developed by Jang et al. [24] to explore the penetration depth limit of TRUE optical focusing, considering the limitations of incident light fluence and TRUE&#;s recording time. They used diffusion approximation with a zero&#;boundary condition for light propagation into a US&#;focused region in deep tissue. US frequency&#;shifted light was determined using Raman&#;Nath theory, and the intensity of frequency&#;shifted light propagating back to the tissue surface was determined to calculate detection shot noise. In addition, they determined the relationship between shot noise and focus contrast (peak&#;to&#;background ratio, PBR) and came up with a practical depth limit of between 30 and 100 mm. It is worth mentioning that most of their assumptions and parameters are not reasonable in practical applications. Walther et al. [10] proposed a simple theoretical model based on the diffusion equation to evaluate the imaging depth of two interesting non&#;invasive imaging techniques, AO and PA. This model calculated absorption contrast levels, where a drop of one percent in blood oxygenation resulted in a decrease of 0.37 percent in the absorption coefficient (at the wavelength of 880 nm). For both techniques, limiting noise sources were identified, and assumptions were considered to evaluate general optical performance versus depth. It was found that the absorption contrast, and hence the oxygenation contrast that could be distinguished, was three orders of magnitude greater for AOI than for PAI at a depth of a few centimeters. They showed analytically that AOT with rare&#;earth&#;ion crystals as spectral hole&#;burning filters could be considered a deep non&#;invasive imaging technique superior to PA.

By utilizing the Monte Carlo (MC) simulation, light modulation in tissues can be precisely examined to gain an insight into the tagging mechanism. Wang [15] originally developed the acousto&#;optic Monte Carlo (AO&#;MC) model for homogeneous media to simulate US tagging of photons. AO&#;MC models were later developed for inhomogeneous and multiply scattered light [25]. Wang&#;s MC model has been the basis for several simulation&#;based studies, since the model can be used for simulating photon propagation and determining light&#;s phase change under continuous US perturbation in a non&#;absorbing homogeneous isotropic medium. The model was further extended to include a graphics processing unit (GPU) and a method to acquire the speckle pattern [26]. Additionally, the model was further refined for inhomogeneous media with designated US regions [27]. Gunther et al. [5] used MC simulations to analyze the contrast&#;to&#;noise ratio of AO tomography with slow light filters against possible imaging depths. They also studied the model&#;s ability to combine spectral hole burning (SHB) with AOI systems. To understand how much contrast can be achieved within a biological medium, they calculated the contrast&#;to&#;noise ratio (CNR) of both reflectance (for different source&#;detector distances) and transmittance configurations.

Huang et al. [17] have conducted MC simulation studies to gain a deeper understanding of the interaction between US and light and the quantification of tagging efficiency. They used the MC method to simulate the interaction between the two coherent modulation mechanisms to determine overall tagging efficiency. They showed that by considering the higher orders of modulation in the measurements, a higher degree of tagging efficiency could be achieved. They proposed a theoretical approach for obtaining tagging efficiency as the power of all frequency&#;shifted light over the power of light passing through the US region, which is more a robust and appropriate method. This knowledge is essential for estimating a system&#;s signal&#;to&#;noise ratio (SNR) and for improving detection methods to enhance SNR in US&#;assisted optical imaging techniques. They showed that the two US modulation mechanisms, particle displacement and refractive index change, counteract each other in scattering media. In addition, they quantified tagging efficiency versus US pressure and frequency via simulations and experiments. Their results indicate that tagging efficiency increases as US pressure increases. In contrast, a higher US frequency leads to lower amounts of tagging efficiency [17]. shows their results.

Gunther et al. [28] developed a MC model using the CUDAMCML code, a MC model of steady&#;state light transport in multi&#;layered tissues based on NVIDIA&#;s Compute Unified Device Architecture (CUDA), to study the contrast&#;to&#;noise ratio (CNR) of AO tomography in biological tissue. Their results showed that when the imaging depth reaches ~5 cm in reflection mode or ~12 cm in transmission mode setups, the CNR exceeds 1.

Bocoum [29] et al. developed a new structured AO tomography method, which allows a partial recovery of resolution. For image reconstruction, they presented a generalized Fourier slice theorem and a generalized filtered back&#;projection formalism. Field&#;II open&#;source software was used to simulate the propagation of US pulses using software operation based on the far&#;field calculation method detailed in [30].

Hill et al. [31] presented a rigorous description for modelling the interaction between US and light for US pulses in nonlinear media under pressures ranging up to the medical safety limit. Their model simulations agree well with measurements conducted with fully characterized US pulses. Furthermore, their results demonstrate that movements of acoustically induced scatterers can be ignored during AOI modelling. This modelling approach is based on re&#;implementing, iterating, and finally showing that, under certain limitations, the work performed by Huang et al. [17] is practical for describing the tagging process in high&#;pressure US. They finally presented and validated a simulation package [32] for interaction between arbitrary optical and acoustic fields in scattering media.

Hsieh et al. [33] combined MC eXtreme (MCX) simulation software and intralipid&#;phantom experiments to investigate the use of a HIFU&#;induced heating tunnel to reduce photon scattering and enhance the delivery efficiency of light within biological tissues. They assessed the correlation between heating tunnel size, temperature change, and the fluence of light. Their results indicate that the delivery of light energy increases with rising temperature, reaching a maximum when the size of the tunnel slightly exceeds the width of the laser beam.

The angular spectrum method is a frequency domain numerical simulation technique applied to compute the propagation of US beams [34]. For practical details about the implementation of the angular spectrum method, please refer to [35]. Using this method, Adam et al. [36] developed a numerical model to calculate the acoustic field generated by the HIFU source. A finite&#;difference time&#;domain solution to Pennes&#; bioheat equation was used to model the temperature field resulting from US absorption. An optical dose model based on measurements of tissue properties was used to calculate changes in tissue optical properties. This simulated acoustic field and the resulting effects on tissue properties were used to calculate phase modulations imparted on the optical field. Modeling of light propagation in the optical field was performed using an open&#;source GPU&#;accelerated MC algorithm that accounted for light&#;acoustic interactions and the detection of AO signals.

A Finite Element (FE)&#;based simulation method can also be used to solve AO effects. One of the first FE&#;based acousto&#;optic 3D simulation models, which also included a comparison with the MC method, was presented by Wang et al. in [37]. Their FE based&#;simulation results were close to those obtained with MC&#;based simulations, while requiring a more reasonable computational time. COMSOL Multiphysics is an FE application that incorporates light propagation, PA signal generation, and sound wave propagation in soft tissues. It provides the add&#;on modules &#;Wave Optics Module&#; and &#;Acoustics Module&#;, which can be combined to study these phenomena with 3D modelling [38]. Using COMSOL Multiphysics, Song et al. [39] simulated light propagation in biological tissue in a range of US fields, using the photon transfer equation and the &#;Coefficient form PDE&#; interface in the software. They also discussed the relationship between US&#;modulated scattering light and biological tissue optical properties. Acousto&#;optic signals exhibit exponential decay with an increase in the medium&#;s absorption and scattering coefficients, because the medium&#;s absorption coefficient influences the acousto&#;optic signal more than its scattering coefficient. Ling et al. [40] used COMSOL Multiphysics to investigate the relationship between the acoustic radiation force (ARF) and different types of acoustic pulses and waveforms to obtain optimum patterns for US excitation and pressure fields. Using their simulation results, they also conducted experiments on the enhancement effect of US generated ARF on diffuse correlation spectroscopy (DCS) data and blood flow measurements. It turns out that FE methods are faster and more flexible than MC, and they can measure photon density everywhere as well as boundary fluxes. However, they cannot deduce the history of individual photons [41].

Other alternatives for FE&#;based commercial simulation software are open&#;source Gmsh [42] and GetDP [43], which are often combined under the name ONELAB [44]. ONELAB is a FEM solver, which uses Gmsh for creating a FEM mesh, and GetDP for solving generic partial differential equations (PDEs) with the FEM method. Advantages of using Gmsh include its ability to create user&#;defined meshes, while also having standard interfaces with other commonly used mesh and computer&#;aided design (CAD) software such as STEP, IGES, and STL. Fadden et al. [45] used ONELAB for photo&#; and RF&#;acoustic computed tomography. To solve optical, electromagnetic, and acoustic propagation problems, ONELAB uses solutions to the optical diffusion equation, Maxwell&#;s equations in the frequency domain, and wave equation in the time domain. As shown by tests on a homogeneous phantom and an approximate breast phantom, ONELAB is an effective tool for both photo&#; and RF&#;acoustic simulations. It provides invaluable support for developing new reconstruction algorithms. Giuseppe et al. [46] studied US combined with DOT to increase imaging resolution for accurate lesion detection. They employed a self&#;generated breast 3D model, k&#;wave tool for US simulation, and machine learning for lesion classification. Eventually, the lesions were classified in the accuracy of 75%.

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