Time resolution

To be more specific, given a mother wavelet with its own time and frequency properties, the small values of scale coefficient a (high frequencies) lead to high time resolution (and poor frequency resolution). Correspondingly, high values of the scale coefficient (low frequencies lead to high frequency resolution (and poor time resolution), (see figure 10)... 

Q f)(t) wavelets in the time frequency plane, with the help of the Heisenberg ellipses. The axes of the ellipses are sized with respect to the RKfS value of the time resolution and frequency resolution. 

The evaluation of the deconvolution results show that time resolution is better or equal to 1 with the chosen processing time unit of 0.08 microseconds (respectively a rate of 12.5 MHz). First signals processed conservatively have been acquired with a samplerate of 12.5 MHz. A Fourier analysis shows that the signals spectras do not have energy above 2.0 MHz. This means that a sampling rate of 4.0 MHz would have done the job as well. Due to the time base of the ADC an experimental check with a sample rate of 5.25 MHz has been carried out successfully. 

At higher flow rates the dispersion of the tracer and the lower limit for time resolution of the concentration versus time distribution limits the accuracy to better than dt2%. 

More recently, studies employing STM have been able to address surface self-diffiision across a terrace [16, 17. 18 and 19], It is possible to image the same area on a surface as a fiinction of time, and watch the movement of individual atoms. These studies are limited only by the speed of the instrument. Note that the performance of STM instruments is constantly improving, and has now surpassed the 1 ps time resolution mark [20]. Not only has self-diflfiision of surface atoms been studied, but the diflfiision of vacancy defects on surfaces has also been observed with STM [18]. 

The final velocity of these two ions will be the same, but their final flight times will differ by the above turnaround time, This results in a broadening of the TOF distributions for each ion mass, and is anotiier limiting factor when considering the mass (time) resolution of the instrument. 

As a sununary it may be of interest to point out why TREPR spectroscopy and related methods remain important in the EPR regime, even though pulsed EPR methods are becoming more and more widespread. (1) For the case of an inliomogeneously broadened EPR line the time resolution of TREPR compares favourably with pulsed teclmiques. 

The low MW power levels conuuonly employed in TREPR spectroscopy do not require any precautions to avoid detector overload and, therefore, the fiill time development of the transient magnetization is obtained undiminished by any MW detection deadtime. (3) Standard CW EPR equipment can be used for TREPR requiring only moderate efforts to adapt the MW detection part of the spectrometer for the observation of the transient response to a pulsed light excitation with high time resolution. (4) TREPR spectroscopy proved to be a suitable teclmique for observing a variety of spin coherence phenomena, such as transient nutations [16], quantum beats [17] and nuclear modulations [18], that have been usefi.il to interpret EPR data on light-mduced spm-correlated radical pairs. 

In an extension of traditional CIDNP methods, Closs and co-workers developed time-resolved CIDNP (TR-CIDNP) m the late 1970s [24, 25 and 26]. The initial time-resolved experiments had a time resolution in the... 

Interpretable high-resolution structural infomiation (e.g. preservation of dimensions, or correlation of the stmctiiral detail with a physiologically or biochemically controlled state) is therefore obtained exclusively from samples in which life has been stopped very quickly and with a sufficiently high time resolution for the cellular dynamics [19]. Modem concepts for specimen preparation therefore try to avoid traditional, chemical... 

Frantz P, Agrait N and Salmeron M 1996 Use of capacitance to measure surface forces. 1. Measuring distance of separation with enhanced spacial and time resolution Langmuir 12 3289-94... 

The main cost of this enlianced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. Wlien the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is nnambiguous. When the pump and probe pulses temporally overlap in tlie sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feymuan diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to detenuine the various contributions to the sample response [125]. 

Walker G C, Maiti S, Cowen B R, Moser C C, Dutton P L and Hochstrasser R M 1994 Time resolution of electronic transitions of photosynthetic reaction centers in the infrared J. Phys. Chem. 

During the course of these studies the necessity arose to study ever-faster reactions in order to ascertain their elementary nature. It became clear that the mixing of reactants was a major limitation in the study of fast elementary reactions. Fast mixing had reached its high point with the development of the accelerated and stopped-flow teclmiques [4, 5], reaching effective time resolutions in the millisecond range. Faster reactions were then frequently called inuneasurably fast reactions [ ]. 

Many experimental methods may be distinguished by whether and how they achieve time resolution—directly or indirectly. Indirect methods avoid the requirement for fast detection methods, either by detemiining relative rates from product yields or by transfonuing from the time axis to another coordinate, for example the distance or flow rate in flow tubes. Direct methods include (laser-) flash photolysis [27], pulse radiolysis [28]... 

The time resolution of these methods is detennined by the time it takes to mitiate the reaction, for example the mixing time in flow tubes or the laser pulse width in flash photolysis, and by the time resolution of the detection. Relatively... 

One of the major limiting factors for the time resolution of flow-hibe experiments is the time required for mixing reactants and—to a lesser extent—the resolution of distance. With typical fast flow rates of more than 25 ms [42, 43] the time resolution lies between milliseconds and microseconds. 

More generally, the relaxation follows generalized first-order kinetics with several relaxation times i., as depicted schematically in figure B2.5.2 for the case of tliree well-separated time scales. The various relaxation times detemime the tiimmg points of the product concentration on a logaritlnnic time scale. These relaxation times are obtained from the eigenvalues of the appropriate rate coefficient matrix (chapter A3.41. The time resolution of J-jump relaxation teclmiques is often limited by the rate at which the system can be heated. With typical J-jumps of several Kelvin, the time resolution lies in the microsecond range. 

Figure B2.5.7 shows the absorption traces of the methyl radical absorption as a fiinction of tune. At the time resolution considered, the appearance of CFt is practically instantaneous. Subsequently, CFl disappears by recombination (equation B2.5.28). At temperatures below 1500 K, the equilibrium concentration of CFt is negligible compared witli (left-hand trace) the recombination is complete. At temperatures above 1500 K (right-hand trace) the equilibrium concentration of CFt is appreciable, and thus the teclmique allows the detennination of botli the equilibrium constant and the recombination rate [54, M]. This experiment resolved a famous controversy on the temperature dependence of the recombination rate of methyl radicals. Wliile standard RRKM theories [, ] predicted an increase of the high-pressure recombination rate coefficient /r (7) by a factor of 10-30 between 300 K and 1400 K, the statistical-adiabatic-chaunel model predicts a...

Direct time-dependent detection is limited by the response time of detectors, which depends on the frequency range, and the electronics used for data acquisition. In the most favourable cases, modem detector/oscilloscope combinations achieve a time resolution of up to 100 ps, but 1 ns is more typical. Again, this reaction has been of fiindamental theoretical interest for a long time [59, 60]. 

With the short pulses available from modem lasers, femtosecond time resolution has become possible [7, 71, 72 and 73], Producing accurate time delays between pump and probe pulses on this time scale represents a... 

Figure B2.5.11. Schematic set-up of laser-flash photolysis for detecting reaction products with uncertainty-limited energy and time resolution. The excitation CO2 laser pulse LP (broken line) enters the cell from the left, the tunable cw laser beam CW-L (frill line) from the right. A filter cell FZ protects the detector D, which detennines the time-dependent absorbance, from scattered CO2 laser light. The pyroelectric detector PY measures the energy of the CO2 laser pulse and the photon drag detector PD its temporal profile. A complete description can be found in [109].

He Y, Pochert J, Quack M, Ranz R and Seyfang G 1995 Dynamics of unimolecular reactions induced by monochromatic infrared radiation experiment and theory for C F XI—> C F X + I probed with hyperfine-, Doppler- and uncertainty limited time resolution of iodine atom infrared absorption J. Chem. Soc. Faraday Discuss. 102 275-300... 

Kummer S, Mais S and Basche T 1995 Measurement of optical dephasing of a single terrylene molecule with nanosecond time resolution J. Chem. Phys. 99 17 078-81... 

---