The optimum pulse shape

The tail of the pulse passing through the differentiator forces the output to fall below and then rise towards the baseline with a time constant equal to that of the feedback circuit in the preamplifier. This is then transmitted through the integrator to the output pulse. A second pulse following close behind the first may find itself in the 

Some high specification amplifiers have built-in facilities to help with pole-zero cancellation. For example, the ORTEC 672 Spectroscopy Amplifier provides automatic cancellation at the press of a button. Some amplifiers provide LED over/under indicators to assist with the adjustment. Nevertheless, because of the importance of this setting I would advocate that every gamma spectrometry laboratory should have ready access to an oscilloscope. With experience, a quick look at the pulses coming from the preamplifier or the amplifier can quickly reassure one that everything is normal, or lead one to a solution if it isn t. 

Note that the transistor reset preamplifier with its step pulse output has no need for PZ adjustment. If such a preamplifier is used, the pole-zero potentiometer should be adjusted to its fully anticlockwise position which corresponds to infinite time constant. Certain amplifiers provide a switch to disable the PZ cancellation. 

In this context, a high count rate would be when the duty cycle of the amplifier is more than 20 % and a low count rate when below 5 %. Duty cycle is the proportion of the time when the amplifier is busy and, assuming that the amplifier dead time is 6 times the shaping time constant, it can be estimated (as a percentage) as  

For example, an output count rate of 2800 pps with 3 p,s shaping would give a duty cycle of about 5 % while 17 000 pps with 2p.s shaping would give 20 %. 

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Step 3 To determine the optimum pulse shape the excitation profile should be calculated. The excitation profile can be simulated using either the Excitation Profile option of the Bloch module or as in Check it 5.2.2.1 a ID spectrum. The Bloch module can display both transverse magnetization components on the same graph while ID WIN-NMR can only show either the x- or the y-component (see Check it 5.2.2.1). 

Figure 19.1 Diagram showing the arrangement for closed-loop learning control. Following a femtosecond laser pulse, the products of the photochemical process are detected and compared with the user-defined objectives stored on the computer. A learning algorithm then calculates the modified electric fields required to shape the laser pulse and further optimize the yield of the desired product. Cycling through the loop many times gives the optimum pulse shape and best product yield. Adapted from Brixner et o/, Chem. Phys. Chem., 2003, 4 418, with permission of John Wiley Sons Ltd...

The peak rf amplitude required to achieve optimum excitation with a selective excitation pulse is given in comparison to the rf amplitude required to achieve an on-resonance 90° flip-angle with a selective rectangular pulse, the simplest conceivable shape. 

Fourier Transform-limited 100 fs, 800 nm, 1015 W cm 2 laser pulse and (b) the optimum result obtained by means of an 80-parameter unrestricted optimisation (dashed line) and a restricted 3-parameter optimisation (full line). The inset in (b) shows the evolution of the fitness value for the 80 parameter optimisation (full squares maximum fitness, open squares average fitness), (c) Autocorrelation trace of the optimal pulse corresponding to the 80 parameters optimisation. The pulse shapes consists of two pulses of 120 fs of equal amplitude separated by 500 fs. 

Finding the best shaped pulses (optimum field) to identify a compound can be a time consuming task given the almost infinite number of possibihties that a pulse-shaper provides. Using 100 pixels and only 100 phase values with 10 different amplitudes results in 10300 possible laser fields (pulse shapes). Such a staggering number of experiments... 

Different instrumental parameters affect the voltammetric response and especially the shape and resolution of the waves. The peak height was found to increase linearly with pulse amplitude between 20 and 80 mV. The value of 60 mV was chosen for this variable because with a larger value the wave becomes wider, decreasing the resolution. The height of the peak was also found to vary with the size of the drop, between 0.25 and 0.52 mm the latter value was chosen as the optimum value. The stirring speed during the accumulation was not... 

In the first scheme it is not necessary to use two different lasers if a femtosecond pulse with a broad spectral range is used for excitation. The different spectral components in the pulse give rise to many different excitation paths. In order to achieve optimum population in the excited state, the relative phases of these different spectral components have to be optimized. This can be realized by the pulse-shaping techniques discussed in Sect. 6.1.11 (Fig. 10.11). Here a plate of many liquid crystal pixels are placed in the laser beam, which changes the phases of the lightwave by orientation of the molecules where a feedback loop with a learning algorithm is used to maximize or minimize the wanted decay channel of the excited state [1402,1403]. 

It is important to emphasize that, in the above examples, knowledge of the PES was not required for the optimization process. The adaptive-control learning algorithm explores the available phase space and optimizes the evolution of the wave packet on the excited state PES without any prior knowledge of the surface. Thus, the intrinsic information about the excited-state dynamics of these polyatomic systems remains concealed in the detailed shape and phase of the optimized pulse. Inevitably, however, scientific curiosity, together with a desire to imder-stand how chemical reactions can be controlled, has led to pioneering studies that aim to identify the underlying rules and rationale that lead to a particular pulse shape or phase relationship that produces the optimum yield. 

Amplifier throughput is inversely proportional to the shaping time — the narrower the pulses, the more through the system per second. So, at any particular input rate there can be a trade-off between the throughput capability and resolution. If the optimum time constant is halved, then we expect twice as many counts to be processed before pile-up effects become a problem, at the cost of slight... 

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