What Does Gray Levels in Continuous Wave Doppler Mean

Doppler Effect

The Doppler effect, described in 1842 by Christian Andreas Doppler, is the change or shift in the frequency or wavelength of a wave due to relative movement between a sound source or scatterer and the receiver.

From: Encyclopedia of the Neurological Sciences , 2003

Early optical diagnosis of pressure ulcers

I. Schelkanova , ... A. Douplik , in Biophotonics for Medical Applications, 2015

13.2.1.1 Laser Doppler perfusion monitoring and imaging

Doppler effect occurs when a scattering particle is nonstationary in the presence of an incident wave. The incident wave's frequency is modified according to the direction of motion of the particle.

Biological tissues are comprised of multiple stationary as well as mobile (mainly blood cells) scattering particles. Coherent light from a laser, when directed into tissues, exhibits a Doppler shift in frequency when encountering moving particles. As a result, the backscattered signal from the tissues can be decomposed into flux, cell concentration, and cell velocity (Humeau et al., 2007; Leahy et al., 2007). Two common methods are employed for laser Doppler perfusion monitoring: one where a fiber-optic probe (transmitting and receiving fibers) is kept in contact with skin (Figure 13.5) and the other where scanning (X–Y) mirrors or beam splitters are used to transmit light to the skin and direct the received light to the photodetector to form an image (Leahy et al., 2007). Interrogation depth of 1   mm can be usually achieved (Fredriksson et al., 2009) by this method where most of the capillaries and dermal vessels are situated and flow velocities ranging from 0.01 to 0.1   mm/s can be determined (Ferguson-Pell, 2005).

Figure 13.5. A fiber-optic-based laser Doppler flowmeter placed on skin. The blue lines emanating from the fiber indicate laser illumination and the red indicate Doppler shifted light.

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Local Anesthetics

Suzuko Suzuki , ... Kai Kuck , in Pharmacology and Physiology for Anesthesia (Second Edition), 2019

Doppler Ultrasound

The Doppler effect has important applications in ultrasound imaging and can be used to determine blood flow velocity and direction. The real-world example of sound heard by a stationary observer when a moving train blares its whistle is often used as an example of the Doppler effect. The sound of a passing train whistle is higher in pitch if the train is advancing toward a stationary observer and lower in pitch if moving away. Similarly, the pitch (frequency) of an ultrasound wave is shifted higher or lower as the sound is reflected off a moving anatomic target, usually erythrocytes or heart valve leaflets (Fig. P4.3). The greater the velocity (v) of the target, the greater the Doppler frequency shift:

$\mathrm{v}=({\mathrm{c}}_{\text{Ultrasound}}\times \Delta \mathrm{f})/(2\times {\mathrm{f}}_{\text{Ultrasound}}\times \cos \theta )$

where

c_Ultrasound is the speed of ultrasound in the tissue

Δf is the Doppler shift in frequency

f_Ultrasound is the original frequency of the ultrasound

θ is the incident angle of the ultrasound beam with respect to the moving object

Blood flow can be calculated from velocity by combining it with the cross-sectional area and an assumption of the velocity profile is made. Also, the Bernoulli equation allows an estimation of the pressure gradient (Δp) across the heart valve:

$\Delta \mathrm{p}=4{\mathrm{v}}^2$

Important uses of Doppler ultrasound in anesthesiology include TEE, TTE, vascular flow (patency, direction, flow rate, velocity), measurements of cardiac function (output, rate, ejection fraction, regurgitation, and so on), and vascular access (location and discrimination between arteries and veins).

Since many ultrasound systems use color (red, blue, or shades of these colors) to indicate blood flow within the lumen of a vascular structure, the clinician must be aware of how the transducer is oriented with respect to the target blood vessel for two reasons. The direction of blood flow is relative, so that if the transducer is rotated by 180 degrees and reapplied in the same location, what was first colored red as arterial flow would now be colored blue as venous, and vice versa. Second, the most effective estimation of flow is achieved when the transducer is held at a shallow angle relative to the vessel being scanned. Holding the transducer orthogonally over the blood vessel results in loss of a Doppler shifted signal and could lead to an incorrect diagnosis of little or no flow when, in fact, flow is present.

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Ultrasound, Carotid

R.S. Marshall , in Encyclopedia of the Neurological Sciences (Second Edition), 2014

Doppler Principle

The Doppler effect, described in 1842 by Christian Andreas Doppler, is the change or shift in the frequency or wavelength of a wave due to relative movement between an emitting or reflected sound source and the receiver. This change in frequency is called Doppler frequency shift (DFS), which equals the difference between the transmitted and the received frequencies. When using ultrasound to study blood flow in the carotid and vertebral arteries, the Doppler principle is applied to reflected (or scattered) sound waves from moving red blood cells to determine the speed and direction (velocity) of flow in the vessels. The DFS (MHz) depends on the speed of blood flow ( ν, m/s), angle between the sound beam and the direction of blood flow (angle of insonation, θ), transmitted frequency (f(t), MHz), and speed of sound in the soft tissue (C, m/s):

$\mathrm{DFS}=(2\times \upsilon \times f(t)\times \cos \theta )/C$

The direction of flow can be determined by determining whether the DFS is positive (flow toward the transducer) or negative (flow away from the transducer). According to the Doppler equation, the ideal Doppler angle of insonation is 0° (when the sound beam is parallel to the direction of flow). When the angle of insonation approaches 90° (right angle to the direction of flow), DFS decreases and approaches 0°. In a clinical study, the angle of insonation may change depending on in situ anatomy.

There are two broad categories of Doppler transducers: transducers that continuously transmit and receive (continuous-wave (CW) Doppler) and those that intermittently emit and receive a series of short pulses of sound (pulsed-wave (PW) Doppler). The CW Doppler provides a sensitive evaluation of any moving target in the path of the sound beam and can accurately identify extremely high flow velocities. However, CW Doppler is not able to localize the specific depth of the reflector or scatterer at which the signal originated, and it often includes detection of the signals from undesired vascular structures such as veins and small arteries. The PW Doppler transducers transmit discrete, brief pulses of sound and wait for any scattered signals to return before emitting the next pulse. By varying the timing of sampling, the PW Doppler can choose the specific depth of sampling (specific sample volume) and localize the depth of signal origination. Most modern carotid duplex ultrasound instruments use PW Doppler transducers.

Red blood cells move at a variety of speeds and directions within the vessel so that there are a variety of different DFS values (spectrum) from any sample volume within a vessel. Characteristics of the spectral waveform are determined by flow dynamics at the point of sampling, but they are also affected by hemodynamic factors proximal and distal to the point of sampling. Thus, the spectral pattern can infer disease distally or proximally to the site of insonation. The velocity spectrum can be analyzed using the specific parameters including flow direction, peak systolic flow velocity (V _s), and end diastolic flow velocity (V _d), as well as the characteristics of the velocity spectrum, such as the width or spread of the band or envelope of velocities, shape of the margin of the envelope, or a variety of derived indexes such as the mean flow velocity, acceleration time (systolic flow acceleration or systolic acceleration slope), and pulsatility and resistivity indices.

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Evaluating the mechanical properties of biomaterials

M. Capurro , F. Barberis , in Biomaterials for Bone Regeneration, 2014

Doppler effect imaging

The Doppler effect is the phenomenon whereby a monochromatic wave reflected by a moving target undergoes a frequency shift which is proportional to the target velocity, namely ω  = ω_o (1   − v   · n /c), where v is the target velocity, c is the wave velocity and n is the unit vector in the direction of the reflected ray. If the target velocity is due to a vibration with frequency ω*, the effect results in a frequency modulation of the reflected carrier wave. Using this principle, a map of tissue deformations can be reconstructed.

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Advanced Imaging Technologies

Pearse A. Keane , ... SriniVas R. Sadda , in Retina (Fifth Edition), 2013

Basic principles

The Doppler effect, first described in the 19th century by the Austrian physicist Christian Doppler, is the change in frequency of a wave as it is reflected off a moving object: if the reflecting object is moving away from the observer/transducer, the frequency of the reflected waves is lower than that of the waves emitted, and vice versa. As the frequency shift is dependent on the velocity of the moving object, this effect can be used to measure the velocity of blood flowing in the eye. ³⁷ Importantly, the Doppler effect is also dependent on the angle between the axis of the wave and the axis of movement of the object. Therefore, if the observer/transducer is not parallel to the axis of the moving object calculations must be performed using a Doppler angle correction formula:

$V=\Delta FC/2F_0\cos \alpha$

where V is the velocity of the moving object, ΔF is the Doppler (frequency) shift, C is the velocity of the wave in the medium, F ₀ is the frequency of the wave source, and cosα is the Doppler angle. Of note, accurate measurement of the Doppler angle is a significant obstacle to the noninvasive assessment of ocular blood flow. Furthermore, as the Doppler angle increases between 60° and 90°, velocities calculations are subject to significant errors (cosine 90° is equal to zero).

Utilization of the Doppler effect in ocular imaging systems allows calculation of ocular blood flow velocities. ³⁷ Reductions in blood flow velocity may occur as a result of vascular degenerative changes in diseases such as diabetic retinopathy, or as a result of vascular occlusion in diseases such as central retinal vein occlusion (CRVO). However, changes in retinal blood flow velocity may also occur as a result of either constriction or dilatation of vessels during normal physiological autoregulation (according to Bernoulli's principle, constriction of a blood vessel causes a conversion of pressure into kinetic energy, thereby increasing the velocity of the blood, but decreasing its pressure). Therefore, measurements of the absolute quantities of "blood flow" may represent a more clinically relevant parameter.

Blood flow (Q) is the volume of blood passing through a vessel in a given time, and is determined by the velocity of the blood (V) multiplied by the cross-sectional area of the blood vessel through which it passes (πr² ). ³⁸ Consequently, if blood flow velocity can be measured using the Doppler effect, and the diameter of the blood vessel can also be measured, then absolute values for blood flow may be determined. Measurements of retinal vascular diameter can be acquired from fundus images obtained with standard optical imaging techniques (e.g., fundus photography). ^39,40 However, in order to measure retinal vascular diameters in real units of length, the magnification of the image induced by the eye, as well as the magnification of the camera, must be known (failure to account for such magnification will result in significant errors).

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Imaging with ultrasound

Penelope Allisy-Roberts OBE FIPEM FInstP , Jerry Williams MSc FIPEM , in Farr's Physics for Medical Imaging (Second Edition), 2008

Doppler effect

The Doppler effect is familiar to those who have heard a siren sounding on an emergency vehicle as it passes by. When incident sound waves I of frequency f are reflected at right angles by a moving interface that is approaching the transducer, the waves are compressed (Fig. 9.22). The wavelength is reduced, and (the velocity being constant) the frequency f of the reflected wave R is increased. With a receding reflector, the frequency is reduced.

The change of frequency is proportional to the velocity of the interface:

$\frac{\text{change\hspace{0.17em}of\hspace{0.17em}frequency}}{\text{original\hspace{0.17em}frequency}}=2\times \frac{\text{velocity\hspace{0.17em}of\hspace{0.17em}the\hspace{0.17em}interface}}{\text{velocity\hspace{0.17em}of\hspace{0.17em}sound}}.$

The higher the transducer frequency or the faster the interface moves, the greater the Doppler frequency shift. For example, if the velocity of the interface v = 30 cm s⁻¹, and the frequency of the transducer f = 10 MHz, because the velocity of sound c = 1540 m s⁻¹ then the change of frequency f — f − f′ 4 kHz. The Doppler frequency (f — f′) is comparatively small and equivalent to an audio frequency, i.e. in the range 0–10 kHz.

The above example refers to motion in the direction of the sound; motion at right angles to the transducer shows no Doppler effect, and that at an angle θ has a reduced effect:

(f — f′)/f = 2(ν/c) cos θ.

(For the meaning of θ, sometimes called the angle of insonation, see Fig. 9.23.) The maximum Doppler shift is obtained when θ = 0, whereas in imaging the strongest echoes occur when θ = 90º.

The change of frequency is measured and shows how fast the reflector is moving towards or away from the transducer. It is also possible to detect electronically whether the frequency increases or decreases, and this shows the direction of movement.

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Pelvic Imaging in Reproductive Endocrinology

Dominique de Ziegler , ... Charles Chapron , in Yen & Jaffe's Reproductive Endocrinology (Seventh Edition), 2014

Principles and Applications

The Doppler effect (named after the German physicist, Christian Doppler) refers to the phenomenon whereby an apparent change in frequency is perceived when relative motion exists between the wave source (in our case, the reflected ultrasounds) and the receiver. Yet, the emitted frequency (here, the ultrasounds refected to the receiver) does not change. The frequency change is only perceived by the receiver, as the source-receiver distance changes due to movement. If ultrasounds are emitted (or reflected) from a source that moves toward the receiver, an increase in frequency will be perceived. The reverse will be perceived if the ultrasound source moves away from the receiver. In both cases, the perceived frequency change (i.e., the intensity of Doppler effect) is proportional to the speed of displacement of the target on which ultrasounds are reflected.

The primary application of the Doppler effect has been for analyzing the movement of blood particles on which ultrasounds are reflected for studying blood flow. Depending on the methodological approach used, Doppler-based analyses may (1) look at individual vessels or; (2) measure perfusion in a whole tissue area. The former approach assessing flow in specific vessels (i.e., the uterine artery) rely on the pulsed-Doppler technique. This consists of sending sound signals at timed intervals in a defined volume or sampling gate, and studying the perceived frequency changes of the return signal or Doppler waveform.

Doppler-based blood flow analyses stem from advances in cardiology, which established the methodological foundation for all Doppler analyses performed today. ¹²⁸ Pulse Doppler (Fig. 35.10) involves first physically locating the vessel to be studied in order to properly position the Doppler sampling gate. This can be done using a duplex system, which provides concomitant gray scale or color Doppler imaging for vessel identification (see later in the chapter). Once the emitting signal is targeted at the designated vessel, blood flow and resistance are calculated by analyzing the frequency changes perceived or Doppler waveform. The intensity of the Doppler effect reflects the speed of displacement of the blood particles toward or away from the probe, which emits and receives the return signal. An exact computation of blood flow and resistance implies, however, that the angle between the ultrasound wave and the great axis of the vessel is known. This is needed for determining the true displacement speed of the blood-borne particles. This calculation is, unfortunately, impossible in gynecological organs because uterine and ovarian vessels are far too tortuous.

The pulsed-Doppler technology in gynecology must, therefore, rely on approximations for assessing the Doppler signal, as an accurate determination of blood flow and resistance are impossible. ^9,10,129,130 Practically, the impedance to flow, a reflection of vascular resistance, is assessed by descriptive analysis of how the Doppler flow wave is modulated through the systolic and diastolic phases of the cardiac cycle. This permits semiquantitative measurements of systolic and diastolic signal ratios, or Doppler indices. The most common of these indices are the resistance indices (RI) and pulsatility indices (PI). RI (values from 0 to 1) and PI (values from 0 upward) are directly related to vascular resistance, with higher values corresponding to lower flow.

The alternate approach for Doppler analysis uses more complex real-time assessment of the Doppler effect directly on the return ultrasound signal serving gray scale imaging. This approach applies color-coding to voxels that are subjected to Doppler effect, while the rest of the voxels serve for gray scale imaging. The end result or color Doppler function and its variant angle-independent power Doppler, provide direct imaging (or mapping) of vascular flow overlying gray-scale ultrasound images. Color and power Doppler, therefore, offer a novel way for assessing vascularity in a given organ or territory. Color and power Doppler also permit global assessment of vascularization in a given area by direct computer-based visual analysis of colored voxels present over the total number of voxels, or power Doppler angiography (PDA). ⁸⁷ Unlike PI and RI, PDA values are directly related to local flow, with higher values indicating higher flow. Various systems have been developed for filtering nonspecific color Doppler signals or "flash" artifacts that are triggered by displacements of the targeted tissue as a result of bowel or respiration-linked movements.

More recently, computer-assisted power Doppler assessments have been coupled with 3D volume reconstruction (3D-PDA) for automated operator-independent measurement of vascularity in a precisely defined volume. ¹³¹ (Fig. 35.11A and B). This approach offers improved reproducibility, because measurements are conducted in an anatomically and electronically defined territory, such as the endometrium or ovary. ¹² 3D-PDA is measured in the volume of interest previously defined using VOCAL. ¹² The results of 3D-PDA are displayed on a histogram from which three indices, the vascular (VI), flow (FI), and vascular/flow indices (VFI), are derived. VI (%) represents the proportion of lighted voxels over all voxels, thus reflecting the degree of vascularity of the studied volume. FI (0-100) represents the mean power Doppler intensity of the lighted voxels, a parameter meant to reflect the vascularization flow rate. VFI (0-100) is a product of the two indices VI and FI (Fig. 35.12).

The Doppler function of ultrasound makes it possible to extend the diagnostic usefulness of gray-scale imaging. Doppler data have been used for two main purposes: (1) refining cancer detection by identifying or excluding suspicious vascularitiy in relation with gray-scale findings (i.e., an ovarian cyst); (2) assessing the effects of hormones (endogenous or exogenous) on blood flow in an attempt to identify markers of endometrial receptivity.

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Diagnostic Procedures

Armin Schneider , Hubertus Feussner , in Biomedical Engineering in Gastrointestinal Surgery, 2017

5.4.4 Doppler Imaging

The Doppler-effect enables US to be used to detect motion. US Doppler systems display the Doppler frequency shift produced by moving objects in an US beam (Fig. 5.22). Commonly, it is used to measure the velocity of the blood flow but also in detecting the velocity of structure movements, such as the heartbeat.

Figure 5.22. (A, B) Principle of Doppler sonography.

Modified by Dr. A. Schneider.

There are three main types of Doppler systems: continuous wave, pulsed wave, and power Doppler. They differ in transducer design and operating features, signal processing procedures, and in the types of information provided. Additionally, there are two main display modes used in Doppler systems: Spectral Doppler measurements display the spectrum of flow velocities graphically on the y-axis and time on the x-axis. In color Doppler mode, velocities are measured in points within a B-mode plane and represented by a color-coded image that is coregistered with a B-mode scan. Power Doppler imaging (PDI) is a technique for evaluating the vascular system. It uses special processing to display the amplitude or strength of the Doppler signal, rather than velocity and directional information as in conventional color Doppler. This allows a much greater sensitivity in detecting small vessels and slow-moving blood. Currently, PDI is being used in conjunction with color Doppler, but it has proven valuable in many applications. This approach makes an image very similar to an X-ray angiogram, which is easy to interpret. In addition, it avoids the aliasing problem of conventional color Doppler [40].

In general, Doppler US is used in any application that may need to evaluate the blood flow. In this manner, it is possible to find blood clots and blocked or narrowed blood vessels in almost any part of the body (Fig. 5.23).

Figure 5.23. (A) Normal blood flow of the kidney; (B) complete interruption of blood inflow into the kidney due to thrombosis.

All: Courtesy: Dr. E. Matevossian, Klinikum rechts der Isar.

In visceral medicine, it is of outstanding importance to assess the blood flow in the hepatic artery and portal vein (e.g., in case of portal hypertension or after kidney transplantation).

A continuous wave Doppler (CW Doppler) continuously generates and receives US waves. A CW Doppler uses two transducers. One transducer continuously transmits and one transducer continuously receives signals.

In contrast to CW Doppler systems, PW Doppler Systems use a single transducer for transmission and reception. Pulsed wave (PW) Doppler systems transmit short pulses of US into the tissue. The pulse travels for a given time until it is reflected back. It then returns to the transducer over the same time interval, but at a shifted frequency. A timing mechanism controls the range gating that samples the returning Doppler shift data from a given region. Only Doppler shift data from inside that area is displayed. The transducer alternates transmission and reception of US. Doppler signals can be acquired from a known depth. Today, pulsed Doppler systems for spectral Doppler measurements are typically used in combination with US B-mode imaging, which is known as duplex US. Duplex scanners use arrays of elements to produce both the B-mode image and the Doppler spectrum. This facilitates accurate anatomical location of the blood flow under investigation.

An advantage of CW Doppler systems is their capability for measuring movements with high velocity, which is needed in applications like cardiography, where high blood flow rates occur. A CW Doppler cannot provide range resolution because it is unable to separate Doppler signals that arise from different points along the transmitted US beam. If two blood vessels intersect the US beam, it will not be possible to separate velocities at the different points along the beam, so it cannot be used to produce color flow images.

One main advantage of pulsed Doppler is its ability to provide Doppler shift data selected from a small segment along the US beam, referred to as the "sample volume." The location of the sample volume can be controlled by the operator.

Recent Developments and Current Research

There are recent developments in measuring blood flow via low-peak frequency-modulated continuous wave (FMCW) and stepped frequency-modulated continuous waves (step-FMCW) US Doppler systems. Low-peak FMCW uses a new demodulation technique: the Doppler signals are demodulated with a reference FMCW signal to adjust delay times so that they are equal to propagation times between the transmitter and the receiver. Doppler signals can be obtained from a selected position, as with a sample volume in PW Doppler systems [49].

Step-FMCW leads to a high SNR and a high range resolution compared to traditional pulse-echo signals. In step-FMCW ultrasonic ranging, the phase and magnitude differences at stepped frequencies are used to sample the frequency domain. Step-FMCW features lower peak power, wider dynamic range, lower noise figure, and simpler electronics in comparison to pulse-echo systems [50].

Technologies using the Doppler-effect with pulsed US waves are widely matured. Recent developments are not based on developments of the CW Doppler technology but mostly on combinations of Doppler visualizations with other modifications of US, like elastography.

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ISCHEMIC STROKE: MECHANISMS, EVALUATION, AND TREATMENT

Bernardo Liberato , John W. Krakauer , in Neurology and Clinical Neuroscience, 2007

Duplex Doppler and Transcranial Doppler Imaging

The Doppler effect is noted through detection of flow velocity of a moving object, determined by the time between insonation and reflection of ultrasound waves through a given medium. In the case of duplex Doppler study, anatomical imaging is determined through the B-mode gray scale whereas Doppler shift values are determined through the reflection of the ultrasound waves by the moving red blood cells in the extracranial and intracranial vessels. When the intracranial vasculature is studied, both technologies can be used, but the use of Doppler studies, without the anatomical definition provided by the B-mode gray scale, is the most widely available.

Duplex study of the extracranial circulation is most useful in the determination of the degree of stenosis of the ICA (Fig. 42-9). This determination is crucial because of the difference in the approach to patients with a recent ischemic stroke related to an ipsilateral ICA stenosis (see later discussion). Analysis of the ECVAs also provides valuable information in patients with posterior circulation strokes.

When duplex Doppler imaging is compared with the "gold standard" for anatomical definition (digital subtraction angiog raphy), the sensitivity and specificity for hemodynamically significant (>70% diameter narrowing) extracranial ICA stenosis varies between 85% to 90% and 75% to 80%, respectively. ⁴⁴ On the basis of these numbers, the best approach is to combine duplex Doppler study with another noninvasive imaging modality, such as MRA, because both tests, when concordant, have been shown to accurately predict significant extracranial ICA stenosis in more than 90% of the cases. ^{45, 46} Nonconcordance most often occurs because ultrasonography and MRA can differ in the degree of stenosis they reveal, with a tendency for MRA to overcall degree of stenosis. Another concern is whether noninvasive techniques can reliably differentiate high-grade stenosis from occlusion, a critical factor in surgical decision making. For example, Doppler imaging might demonstrate total ICA occlusion, whereas, in fact, a string sign is present; conversely, an ascending pharyngeal artery or muscular branch may be mistaken for residual flow through an occluded ICA. In such a situation, conventional angiography, CTA, or gadolinium-enhanced MRA should be considered.

Transcranial Doppler (TCD) imaging is used to determine the blood flow velocities of the large and medium-sized intracranial arteries, and indirectly, estimate flow. The approaches used when TCD imaging is performed can be the transtemporal approach (ACA, MCA, and PCA), the transforaminal approach (vertebrobasilar system), and the transorbital approach (ophthalmic vessels and carotid siphons). Flow velocities can help identify a focal stenosis, proximal occlusion with decreased distal flow, or complete occlusion of one of the three cerebral arteries. TCD imaging is particularly helpful in cases of stenosis of the intracranial arteries, such as those in atherosclerotic or inflammatory vasculopathies, and is a test of proven utility in helping determine the need for exchange transfusion in patients with sickle cell disease.

TCD imaging is a valuable tool in the assessment of the intracranial consequences of cervical carotid or vertebral stenosis. Specifically, TCD imaging can detect blunted waveforms and recruitment of collateral pathways (e.g., cross-filling from the anterior communicating artery) (Fig. 42-10). TCD imaging can also provide information on adequacy of collateral flow through the use of vasodilatory challenges such as carbon dioxide inhalation (see later discussion). Also, TCD imaging can be used to monitor the MCAs for evidence of intermittent embolization from a proximal arterial or cardiac (PFO, atrial fibrillation) source (Fig. 42-11).

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Zeeman and Stark Methods in Spectroscopy, Instrumentation

Ichita Endo , Masataka Linuma , in Encyclopedia of Spectroscopy and Spectrometry (Third Edition), 2017

Atomic Beam Spectroscopy

The Doppler effect broadens absorption or emission lines from atoms in the gas phase at thermal equilibrium. Assume that an atom at rest is excited by a photon with wave vector k and de-excited to emit light with angular frequency ω ₀. If the atom is moving at a velocity v the angular frequency of the emitted light is shifted to a value ω′ ₀ according to the formula,

[1] ${\omega }_0^{\prime }={\omega }_0-\mathit{k}\cdot v$

At thermal equilibrium, the velocities of atoms in the gas phase obey a Maxwellian distribution. This results in the broadened intensity profile around ω₀ as approximately represented by a Gaussian form,

[2] $I\left(\omega \right)=I_{0}exp[-{\left(\frac{c(\omega -{\omega }_0)}{{\omega }_0{v}_{\text{th}}}\right)}^2]$

where m/c is the velocity of light and v _th=(2k _B T/m _a)^1/2 is the most-probable velocity of atoms with mass m _a, temperature T and Boltzmann constant k _B. The Doppler width defined by the full width at half maximum of the Gaussian profile is

[3] $\text{Δ}{\omega }_{\text{D}}=2\sqrt{ln2}\frac{{\omega }_0{v}_{\text{th}}}{c}=\left(\frac{{\omega }_0}{c}\right)\sqrt{\frac{k_{\text{B}}Tln2}{m_{\text{a}}}}$

A case is considered where the atoms are effusing into a vacuum chamber, as shown in Figure 1, from an orifice of an oven filled with vapour at a temperature T. Let the atomic beam travel along the z-axis, while the laser beam is parallel to the x-axis. One can reduce the Doppler broadening by limiting the beam divergence with a slit with a small aperture 2d in the x direction at a distance b from the orifice. This makes the beam divergence in the x-z plane smaller than θ₀ =arctan d/b and the Doppler broadening is reduced to Δω′_D=Δω_D sin θ₀ .

Figure 1. Schematic illustration of an atomic beam technique to reduce Doppler broadening. Atomic vapour effuses from a small orifice of an oven. The angular divergence of atoms in the beam is limited to θ ₀=tan⁻¹ b/d by a slit whose aperture is 2d placed at a distance b from the orifice.

An example of laser spectrometers for Zeeman and Stark spectroscopy using a collimated atomic beam is shown schematically in Figure 2. It consists of a continuous-wave (CW) tunable dye laser system, a frequency calibration system a vacuum chamber with a fluorescence detector and a data acquisition system. The interaction point of the atomic beam with the laser is inside the vacuum chamber.

Figure 2. Typical setup for a laser spectrometer based on the atomic beam method. The apparatus is composed of a continuous-wave (CW) tunable laser system, a laser frequency calibration system, a vacuum chamber and a data acquisition system. The fluorescence light from the excited I₂ molecules in a cell and the excited atoms in the vacuum chamber, and the transmitted light from a Fabry–Perot interferometer (FPl) are detected simultaneously with three photomultiplier tubes (PMTs). The signals are transformed to digital pulses event-by-event and introduced to the inputs of a multi-channel scaler (MCS).

A magnified view around the interaction point is illustrated in Figure 3. The oven made of molybdenum is attached to an end plate of the vacuum chamber in which the pressure is kept to approximately 10⁻⁶  torr. The oven is heated by a tungsten filament wound around it to eject a gas jet from the orifice with a diameter of 0.8   mm. The temperature can be increased to approximately 1000   K and is monitored with a Pt–Rh thermocouple. The atomic beam is collimated by the slit and led to the interaction point, where the two electrodes made of BK7 glass plates coated with ITO (InSnO₂) on one side are installed to apply the electric field E. The magnetic field B in parallel with the atomic beam is applied by a set of Helmholtz coils. The fluorescence from the atoms is detected with a photomultiplier tube (PMT) which is cooled to reduce thermal noise. To increase the collection efficiency of the emitted photons, a spherical mirror is installed on the opposite side of the PMT.

Figure 3. Magnified view around the interaction point of the atomic beam with the laser beam. The oven made of molybdenum is heated by a tungsten filament wound around it to eject a gas jet from the orifice with a diameter of 0.8   mm. The atomic beam is collimated with the slit to a diameter of approximately 4   mm at the interaction point, where the two electrodes for applying the electric field and a pair of Helmholtz coils to produce the magnetic field are installed. The photomultiplier tube (PMT) for detecting the fluorescence light from the atoms and a spherical mirror to collect light are shown.

Linearly polarized light from a laser is introduced to the inside of the vacuum chamber as shown in Figure 2. The CW dye laser is capable of continuously changing its frequency with time, sweeping over a certain frequency range. The laser polarization is adjusted with a half-wave plate when necessary. The signal from the PMT is fed to one of the inputs of a multi-channel scaler (MCS) where the number of counts in each time interval, corresponding to a small frequency segment, is recorded.

The spectra from molecular iodine, ¹²⁷I₂, together with the transmitted light through a Fabry–Perot interferometer (FPI), are recorded synchronously with the fluorescence from the excited atoms to give frequency marks separated by the free spectral range (FSR) of the FPI.

In Figure 4 a set of raw data obtained in Zeeman spectroscopy of Sm at B=167.38×10⁻⁴  T is shown as an example. The uppermost part corresponds to the Zeeman spectra for samarium atoms with the natural isotopic abundance (¹⁴⁴Sm: 3.1%,¹⁴⁷Sm: 15.0%, ¹⁴⁸Sm: 11.3%, ¹⁴⁹Sm: 13.8%, ¹⁵⁰Sm: 7.4%, ¹⁵²Sm: 26.7%, ¹⁵⁴Sm: 22.7%) in the transition from the level of E=0.184   68   eV (J=3) to the one of E=2.076   5   eV (J=3), where J is the electronic total angular momentum. The spectrum of ¹²⁷I₂ and that of the transmitted light from the FPI is shown in the middle and the lowest parts, respectively. After calibration on the horizontal axis and assignment of each peak, the spectra shown in Figure 5 are obtained for which the Zeeman splitting is completely resolved. Combining the spectra measured with different magnetic field strengths, the g-factor can be determined for either the upper or lower level if one of them has been known in advance.

Figure 4. Typical set of raw data for Zeeman spectrum of samarium atoms with the natural isotopic abundance under the magnetic field of 167.38×10⁻⁴  T. The number of counts of detected photons per 20   ms is plotted against the MCS channels corresponding to the elapsed time from the starting point of the frequency sweep of the laser. The top part corresponds to the Zeeman spectrum in the transition from the level of E=0.184   68   eV(J=3) to the one of E=2.076   5   eV(J=3). In the middle and the bottom, the spectrum of ¹²⁷I₂ and the spectrum of the transmitted light from the FPI are shown, respectively.

Figure 5. Zeeman spectra after calibration on the horizontal axis and peak assignments. The top part of the spectrum is the same as the one shown in Figure 4. Magnified spectra of just the area of the peaks for the ¹⁵²Sm atoms are shown in the middle and the lower parts, in which the magnetic field is 0   T and 167.38×10⁻⁴  T, respectively. The label above each peak is to indicate the relevant change in the magnetic quantum number, m, to the one with m′, associated with the optical transition.

The Stark spectrum for the same transition at E=26.04   kV   cm⁻¹ is shown in Figure 6. Here again, the splitting is clearly seen thanks to the Doppler-free technique applied here.

Figure 6. Stark spectra obtained by the analogous method to the one used for Figure 5. The transitions are the same as in Figure 5. The electric field of 26.04   kV   cm⁻¹ is applied. The middle and lower graphs correspond to the spectra for the ¹⁵²Sm atoms under the electric field of 0   kV   cm⁻¹ and 26.04   kV   cm⁻¹, respectively.

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