Doppler transverse

Beam Spectroscopy. Both specificity and sensitivity can be gready enhanced by suppressing coUisional and Doppler broadening. This is accompHshed in supersonic atomic and molecular beams (296) by probing the beam transversely to its direction of dow in a near-coUisionless regime. 

Now let us study Fig. 12 again and seek the direction (l) in which the traveler should experience zero Doppler shift. She should not look backward because in that direction there is a redshift. Nor should she look directly sideways because even then there is a redshift, the relativistic transverse redshift. As forward is the blueshift, she should look slightly forward. The way to find the zero Doppler shift for incoming light (a) is as follows ... 

Figure 15. Visualization of the Doppler shift d caused by a combination of radial velocity Vr and transverse velocity Vt- From this diagram, we see that large redshifts (d is positive) can be caused even when there is a large velocity toward the observer (Vr is negative) if combined with a sufficiently large transverse velocity.

When the transverse velocity is zero, Fig. 15 shows that the Doppler shift (d) increases (redshift) with increasing radial velocity to the right, away from the observer. The Doppler shift is negative (blueshift) when the radial velocity is negative, to the left, toward the observer. When the radial velocity is zero, even the Doppler shift is zero. 

However, when the transverse velocity differs from zero, everything becomes more complicated. Let us, for instance, study a Doppler shift of 0.5, which could be caused by a radial velocity of 0.38c. This could just as well have been caused by zero radial velocity combined with a transverse velocity of some 0.75c. It could even be caused by a radial velocity of 0.62c combined with the same transverse velocity of 0.75c. In the latter case, a motion toward the observer, which should result in a blueshift, results in a redshift when combined with a sufficiently large transverse velocity. 

The Doppler shift, of which the transverse redshift is a special case... 

In the case of the 1S-3S transition in hydrogen and for an estimated velocity of v=3km/s, the shift is Av =l4A kHz. We can t measure the velocity distribution by observing the Doppler broadened 1S-2P transition at 121 nm with a colinear laser beam, because the production of Lyman-a radiation is very difficult. In 1991 a method to compensate or at least to measure this effect was proposed by F. Biraben [7]. The basic idea is to apply a transverse magnetic field B in the atom-laser interaction region. This field has two effects ... 

To reduce sensitivity to the Doppler shift further the experiment can be carried out using a transverse geometry on a fast beam, or on a slow beam, or... 

Fig. 6.2a,b. Ischemic colitis in an 82-year-old patient, a Transverse view of the sigmoid colon shows thickening of the colon, with wall stratification and discrete mural flow detected with color Doppler sonography. The pericolic fat tissue is slightly infiltrated, b A CT scan of the pelvis of the same patient shows diffuse thickening of the sigmoid colon (SC)... 

Fig. 12.3a,b. Ileal tuberculosis, a Transverse sonogram of right lower quadrant abdomen shows diffuse mural thickening of the terminal ileum. The terminal ileum shows concentric thickening arrows). The thickness of the anterior and posterior walls is the same, b Transverse color Doppler sonogram of the terminal ileum shows numerous color signals... 

Color Doppler ultrasound (CDUS) is a noninvasive and cost-effective imaging modality. It is highly dependent on the operator and has limitations in obese patients and those with excessive bowel gas. Patients should be evaluated after 5-6 h fasting in supine and lateral position. The aorta is evaluated both transversally and longitudinally Leak is suspected when a reproducible color and Doppler signal inside the aneurysm is visualized. 

Example 4.4 AEth = 0.1 eV, eU = 10 keV Av = 3 x 10 Ano. This means that the Doppler width of the ions in the ion source has been decreased by acceleration cooling by a factor of 300 If the laser crosses the ion beam perpendicularly, the transverse velocity components for ions with n = 3 x 10 m/s at a collimation ratio e = 10 are = n, < 3 x 10 m/s. This would result in a residual Doppler width of An 3 GHz, which illustrates that for fast beams the longitudinal arrangement is superior to the transverse one. 

In Sect. 2.4 we saw that the first-order Doppler effect can be exactly canceled for a two-photon transition if the two photons hcoi = fuo2 have opposite wave vectors, i.e., k = —k2. A combination of Doppler-free two-photon absorption and the Ramsey method therefore avoids the phase dependence (p Vx) on the transverse velocity component. In the first interaction zone the molecular dipoles are excited with the transition amplitude a and precess with their eigenfrequency (jl> 2 = ( 2 — E )/h. If the two photons come from oppositely traveling waves with frequency u), the detuning... 

The a value depends on the flow velocity distribution. Variations in flow velocity will broaden the Doppler frequency spectrum and result in a large a value. Thus, the Doppler variance image can be an indicator of flow variations and can be used to study flow turbulences. In addition, standard deviation imaging can also be used to determine the transverse flow velocity [8]. 

High-resolution REMPI spectroscopy aims to resolve individual rotational transitions in addition to vibrational features. By employing supersonic molecular beam configurations (see Chapter 21 for a detailed description), two effects help in this task. First, the apparent rotational temperature can easily be lowered from standard room temperature ( 300 K) to just a few kelvin. This means that only very few rotational levels are populated, resulting in a normally sparse line spectrum. Second, the transverse velocity distribution, and consequently the Doppler width, is reduced to a level where fully resolved rotationally spectra can be obtained, if narrow-bandwidth lasers are used. Spectral resolution on the order of 100-500 MHz has been realized in typical (1 -h 1 ) REMPI experiments using a line-width-narrowed pulsed laser source to excite the intermediate energy level. 

A possible arrangement for saturation spectroscopy in a molecular beam is depicted in Fig. 9.18. The laser beam crosses the molecular beam perpendicularly and is reflected by the mirror Ml. The incident and the reflected beam can only be absorbed by the same molecules within the transverse velocity group = 0ibyA if the laser frequency (o = o)o y matches the molecular absorption frequency coo within the homogeneous linewidth y. When tuning the laser frequency col one observes narrow Lamb dips (Fig. 9.19) with a saturation-broadened width y at the center of broader profiles with a reduced Doppler-width cAcod, from the collimation ratio c 1 of the molecular beam (Sect. 9.1). 

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