Time-of-flight

The time of flight (TOF) describes the method used to measure the time that it takes for a particle, object or stream to reach a detector while traveling over a known distance. In time-of-flight mass spectrometry, ions are accelerated by an electrical field to the same kinetic energy with the velocity of the ion depending on the mass-to-charge ratio. Thus the time-of-flight can be used to determine the mass-to-charge ratio. The time-of-flight of electrons is used to measure their kinetic energy. In near infrared spectroscopy, the time-of-flight method is used to estimate the wavelength dependent optical pathlength. With an ultrasonic flow meter measurement, the principle is used to work out speed of signal propagation upstream and downstream of flow, in order to estimate total flow velocity. Optical time-of-flight sensors also exist, but depend on timing individual particles following the flow rather than using Doppler changes in the flow itself (as this would require generally high flow velocities and extremely narrow-band optical filters; see planar Doppler velocimetry). In kinematics, TOF is the duration in which a projectile is travelling through the air. Given the initial velocity $u$ of the particle, the downward (i.e. gravitational) acceleration $a$, and the projectile's angle of projection θ (measured relative to the horizontal), then a simple rearrangement of the SUVAT equation

$s\; =\; vt\; -\; begin\{matrix\}\; frac\{1\}\{2\}\; end\{matrix\}\; at^2$

results in this equation

$t=frac\; \{2u\; sin\; theta\}\; \{a\}$

for the time of flight of a projectile.

Time-of-flight mass spectrometry

Time-of-flight mass spectrometry (TOF-MS) is method of mass spectrometry in which ions are accelerated by an electric field of known strength. This acceleration results in an ion having the same kinetic energy as any other ion that has the same charge. The velocity of the ion depends on the mass-to-charge ratio. The time that it subsequently takes for the particle to reach a detector at a known distance is measured. This time will depend on the mass-to-charge ratio of the particle (heavier particles reach lower speeds). From this time and the known experimental parameters one can find the mass-to-charge ratio of the ion.

Ultrasonic flow meter and optical time-of-flight

An ultrasonic flow meter measures the velocity of a liquid or gas through a pipe using acoustic sensors. This has some advantages over other measurement techniques. The results are slightly affected by temperature, density or conductivity. Maintenance is inexpensive because there are no moving parts.

Ultrasonic flow meters come in three different types: transmission (contrapropagating transit time) flowmeters, reflection (Doppler) flowmeters, and open-channel flowmeters. Transit time flowmeters work by measuring the time difference between an ultrasonic pulse sent in the flow direction and an ultrasound pulse sent opposite the flow direction. Doppler flowmeters measure the doppler shift resulting in reflecting an ultrasonic beam off either small particles in the fluid, air bubbles in the fluid, or the flowing fluid's turbulence. Open channel flow measure upstream levels in front of flumes or weirs.

Optical time-of-flight sensors consist of two light beams projected into the fluid whose detection is either interrupted or instigated by the passage of small particles (which are assumed to be following the flow). This is not dissimilar from the optical beams used as safety devices in motorized garage doors or as triggers in alarm systems. The speed of the particles is calculated by knowing the spacing between the two beams. If there is only one detector, then the time difference can be measured via autocorrelation. If there are two detectors, one for each beam, then direction can also be known. Since the location of the beams is relatively easy to determine, the precision of the measurement depends primarily on how small the setup can be made. If the beams are too far apart, the flow could change substantially between them, thus the measurement becomes an average over that space. Moreover, multiple particles could reside between them at any given time, and this would corrupt the signal since the particles are indistinguishable. For such a sensor to provide valid data, it must be small relative to the scale of the flow and the seeding density. MOEMS approaches yield extremely small packages, making such sensors applicable in a variety of situations.

High-precision measurements in physics

Usually the tube is praised for simplicity, but for precision measurements of charged low energy particles the electric and the magnetic field in the flight tube has to be controlled within 10 mV and 1 nT respectively.

The work function homogeneity of the tube can be controlled by a Kelvin probe. The magnetic field can be measured by a fluxgate compass. High frequencies are passively shielded and damped by radar absorbent material. To generate arbitrary low frequencies field the screen is parted into plates (overlapping and connected by capicators) with bias voltage on each plate and a bias current on coil behind plate whose flux is closed by an outer core. In this way the tube can be configured to act as a weak achromatic quadrupole lens with an aperture with a grid and a delay line detector in the diffraction plane to do angle resolved measurements. Changing the field the angle of the field of view can be changed and a deflecting bias can be superimposed to scan through all angles.

When no delay line detector is used focusing the ions onto a detector can be accomplished through the use of two or three einzel lenses placed in the vacuum tube located between the ion source and the detector.

The sample should be immersed into the tube with holes and apertures for and against stray light to do magnetic experiments and to control the electrons from their start.

References