Transit time spread

The transit time between the absorption of a photon at the photocathode and the output pulse from the anode of a PMT varies from photon to photon. The effeet is called transit time spread , or TTS. There are three major TTS components in conventional PMTs and MCP PMTs - the emission at the photoeathode, the transfer of the photoelectron to the multiplieation system, and the multiplication process in the dynode system or mieroehannel plate. The total transit time jitter in a TCSPC system also contains jitter indueed by amplifier noise and amplitude jitter of the SER. 

The time constant of the photoeleetron emission at eonventional photoeathodes is small compared to the other TTS eomponents and usually does not notieeably contribute to the transit time spread. High effieiency semieonduetor photoeathodes of the GaAs, GaAsP and InGaAs type are an exception. These eathodes are mueh slower and can introduce a transit time spread on the order of 100 ps. 

The largest fraction of the total transit time spread results from the different trajectories of the photoelectrons on their way from the photocathode to the first dynode. The photoelectrons are emitted at random locations on the photocathode, with random start velocities and in random directions. Therefore, the time they need to reaeh the first dynode or the channel plate varies from electron to electron (see Fig. 6.12). 

Moreover, some of the photoelectrons may be reflected at the first dynode, return a few hundred ps or a few ns later, and release secondary electrons. These electrons cause a tail or secondary peaks in the transit time distribution. Another peak can appear before the main peak. This usually results from photoeleetron emission at the first dynode. Transit time distributions for a number of deteetors are shown under Sect. 6.4, page 242. 

Unfortunately the resulting transit time spread depends on the wavelength. With decreasing wavelength, i.e. increasing photon energy, the start veloeity and the velocity dispersion of the photoelectron increases, whieh eauses ehanges in the transit time distribution. 

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The present limitatkins in time resolution for the time-correlated photon counting technique are due to the time jitter in the detection electronics and the transit time spread in the photomultqjlier tube ( 500 ps). Mth future improvements in these components and using cw mode-locked lasers as an excitation source, deconvolution of fluorescence lifetimes to a few tens of picoseconds oidd be achieved. Alter-... 

The space-time pattern of Cerenkov wavefront can be reconstructed during off-line analysis fitting relation 9. The reconstructed muon direction will be affected by indetermination on PMTs position (due to underwater position monitoring) and on hit time (PMT transit time spread, detector timing calibration,...). 

Transit-Time Spread. In a photon counting detector, the transit time for the individual photons varies. The TTS is the distribution of the observed times of the output pulses for infinitely short input light pulses. 

Like all photon counting techniques, gated photon counting uses a fast, high-gain detector, which is usually a PMT or a single-photon avalanche photodiode. Due to the moderate time resolution of the gating technique, there are no special requirements to the transit time spread of the detector. However, the transit time distribution should be free of bumps, prepulses or afterpulses, and should remain stable up to a count rate of several tens of MHz. 

The effective resolution of a TCSPC experiment is characterised by its instrument response function (IRF). The IRF contains the pulse shape of the light source used, the temporal dispersion in the optical system, the transit time spread in the detector, and the timing jitter in the recording electronics. With ultrashort laser pulses, the IRF width at half-maximum for TCSPC is typically 25 to 60 ps for microchannel-plate (MCP) PMTs [4, 211, 547], and 150 to 250 ps for conventional short-time PMTs. The IRF width of inexpensive standard PMTs is normally... 

A number of typical detectors are described under Sect. 6.4, page 242. The main selection criteria are the transit-time spread and the spectral sensitivity. Together with the laser pulse shape, the transit-time spread determines the instrument response function (IRF). As a rule of thumb, lifetimes down to the FWHM of the IRF can be measured without noticeable loss in accuracy. For shorter lifetimes the accuracy degrades. However, single-exponential lifetimes down to 10% of the IRF width are well detectable. Medium speed detectors, such as the R5600 and R7400 miniature PMTs, yield an IRF width of 150 to 200 ps. The same speed is achieved by the photosensor modules bases on these PMTs (see Fig. 6.40, page 250). 

It should be noted that the IRF recorded in the cuvette is not identical with the laser pulse recorded directly. The horizontal path length of the laser in a 10-mm cuvette adds about 45 ps of transit-time spread to the IRF. If a large beam diameter is used, there are also path length differences for different depth in the cuvette. Moreover, reflection at the cuvette walls and scattering at the sample holder contributes to the IRF. However, these effects are essentially the same for IRF measurement by a dilute scattering solution and fluorescence measurement of a trans-... 

The results show that the full resolution of a fast TCSPC system cannot be exploited for measurements in the eommonly used 10 mm cuvettes. The optical transit-time spread can be reduced by recording only from a small spot in the cuvette. Another solution is a thin cuvette under front illumination. 

A cracial part of optical tomography instruments are the fibres or fibre bundles used to transmit the light to the sample and back to the detectors. The problem of the fibres is mainly pulse dispersion. The pulse dispersion in multimode fibres increases with the numerical aperture (NA) at which they are used. In particular, the detection fibre bundles, which have to be used at high NA, can introduce an amount of pulse dispersion larger than the transit time spread of the detectors [326, 443]. If the length of the bundles exceeds 1 or 2 meters, a tradeoff between time resolution and NA must often be made. 

Timing problems can be avoided by using PMTs with high-efficieney GaAsP photocathodes, such as the Hamamatsu H7422-40 module [214]. The modules have a stable and almost wavelength-independent transit time spread of about 300 ps duration (see Sect. 6.4.2 page 245). The quantum efficiency reaches 40% at... 

The Na source is placed between two identical samples. Two XP 2020 photomultipliers equipped with scintillators are attached directly to the two samples. The pulses from the photomultipliers are used as start and stop pulses for the TCSPC module. The pulses from PMT 2 are delayed by a few nanoseconds so that a stop pulse arrives after the corresponding start pulse. Eaeh y quantum generates a large number of photons in the scintillator. Therefore, the PMT pulses are multiphoton signals, and the time resolution can be better than the transit time spread of the PMTs. Moreover, the amplitudes of the photomultiplier pulses are proportional to the energy of the particle that caused the scintillation. Therefore the amplitudes can be used to distinguish between the 511 keV events of the positron decay and the 1.27 MeV events from the Na. The discriminator thresholds for start and stop are adjusted in a way that the stop channel sees all, the start channel only the larger Na events. The rate of the Na events is of the order of a few kHz or below. 

Currently manufaetured hybrid PMTs have gains of the order of 10,000. Therefore eleetronie noise from the matching resistor and from the preamplifier impairs the time resolution of single photon detection. The relatively large distance between the photoeathode and diode chip may also cause transit-time spread. In praetieal applieations, the extremely high operating voltage also causes problems. Currently hybrid PMTs are not routinely used for TCSPC experiments. 

The width of the transit time spread is proportional to the reciprocal square root of the voltage between the cathode and the first dynode. Increasing this voltage improves the IRF noticeably. It is, however, unknown how far the voltage can be increased without dielectric breakdown in the tube or the socket. 

The electronic time-resolution of current TCSPC modules is of the order of a few ps. The optical time resolution is therefore limited mainly by the transit-time spread of 25 ps in the currently available MCP PMTs. Possibly the transit-time spread can be reduced, e.g. by decreasing the channel width and the distance between the cathode and the channel plate. If faster detectors should require higher electronic time resolution, faster discriminators may be required. Discriminator chips of substantially increased speed have recently been introduced, so that TCSPC is likely to keep pace with future detector development. 

The electrons emitted by the photocathode are subsequently accelerated to 50 kV and focused on to a toroid-shaped anode. The anode is made of oxygen-free, high conductivity copper and is maintained at a high positive potential. The electron pulses interact with the copper anode forcing the emission of Cu-Ka x-ray photon pulses, which exit the vacuum chamber through a thin beryllium-foil window. A bend germanium crystal monochromator disperses and focuses the x-rays onto the sample. The duration of the x-ray pulses is measured by a Kentech x-ray streak camera fitted with a low density Csl photocathode. The pulse width of the x-rays at 50 kV anode-cathode potential difference is about 50 ps. This value is an upper limit for the width of the x-ray pulses because the transit time-spread of the streak camera has to be taken into consideration. A gold photocathode (100 A Au on 1000 A peiylene) is used to record the 266-nm excitation laser pulses. The intensity of the x-rays is 6.2 x 10 photons an r (per pulse), and is measured by means of a silicon diode array x-ray detector which has a known quantum efficiency of 0.79 for 8 kV photons. 

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