Path length differences

Fig. 40.2. Interference of two beams with the same frequency (wavelength). The path-length difference between beams (a) and (b) is zero, between (a) and (c) X/2, between (a) and (d) A/5 (a+b), (a+c) and (a+d) are the amplitudes after recombination of the beams.

During an NFS experiment with a sample that contains more than one kind of scatterer (i.e., HS and LS isomer), the superposition of forward scattered waves could occur coherently or incoherently. Longitudinal scattering is always coherent, because there is no path-length difference for nuclei located along the X-ray beam. 

Since there are a large number of different experimental laser and detection systems that can be used for time-resolved resonance Raman experiments, we shall only focus our attention here on two common types of methods that are typically used to investigate chemical reactions. We shall first describe typical nanosecond TR spectroscopy instrumentation that can obtain spectra of intermediates from several nanoseconds to millisecond time scales by employing electronic control of the pnmp and probe laser systems to vary the time-delay between the pnmp and probe pnlses. We then describe typical ultrafast TR spectroscopy instrumentation that can be used to examine intermediates from the picosecond to several nanosecond time scales by controlling the optical path length difference between the pump and probe laser pulses. In some reaction systems, it is useful to utilize both types of laser systems to study the chemical reaction and intermediates of interest from the picosecond to the microsecond or millisecond time-scales. 

The subsequent thermal processes201 give rise to diffusion of the polycarbonate substrate into the dye layer, decomposition of the dye, and mechanical deformation of the film due to thermal contraction. Each of these processes can contribute to a reduction in the optical path length of the low-intensity readout beam. The optics within the detector are designed such that phase differences due to the optical path length differences cause the light intensity falling on the detector to be reduced when the beam passes over a recorded mark .196... 

The phase shift induced by the aberration function, can be understood geometrically in terms of the path length difference between a diffracted beam in an ideal lens and in a lens affected by aberrations. This path length difference is a function of the diffraction angle 0 Ag, which is the reason why it is more convenient to describe the imaging process in Fourier space. 

Question. Calculate the path-length differences which correspond to time intervals of 10-6, 10-7, 10-8, 10 9, 10 10, 10 n and 10 12 s between a photolysis and analytical flash. The velocity of light = 2.998 x 1010 cm s 1. Comment on the values. 

The previously discussed standardization methods require that calibration-transfer standards be measured on both instruments. There may be situations where transfer standards are not available, or where it is impractical to measure them on both instruments. In such cases, if the difference between the two instruments can be approximated by simple baseline offsets and path-length differences, preprocessing techniques such as baseline correction, first derivatives, or MSC can be used to remove one or more of these effects. In this approach, the desired preprocessing technique is applied to the calibration data from the primary instrument before the calibration model is developed. Prediction of samples from the primary or secondary instrument is accomplished simply by applying the identical preprocessing technique prior to prediction. See Section 5.9 for a brief overview of preprocessing methods and Chapter 4 for a more detailed discussion. A few methods are briefly discussed next. 

A diffraction beam is produced by constructive interference when the path-length difference between reflections from the motifs in any two parallel planes of motifs in a crystal lattice is equal to a whole number of wavelengths. The angle between the diffraction beam and the lattice planes (the angle of reflection) is equal to the angle between the incident X-ray beam and the lattice planes (the angle of incidence). These phenomena are quantified by the Bragg law (Cullity, 1956) ... 

Interferometry exploits the superposition of electromagnetic waves to measure some physical property that probes the original state of the waves. Interferometers typically have light beams that are split by beam splitters (BS) (at least one per interferometer), reflected off mirrors, and measured by either one or two detectors. The path length difference and/or the phase difference are measured. 

Pig. Schematic illustration olthe origin of the interference effects which occur between light scattered by two different segments. S1 and S2 in the same molecule. The path-length difference (IJS - in the... 

This represents the path-length difference with 0 as the glancing angle (see Section 5.2.3) allowed d, the distance between atoms, to be determined for the first time. The path to structure determination was open. 

The arrangement employed for the VPC experiment is described in Reference 4. A cw argon-ion laser at 488 nm was used in a standard DFWM geometry. The s-polarized output beam was first split by a beam-splitter to provide the pump and the probe beams. The transmitted beam from the beam-splitter was then divided into the two s-polarized pump beams each with a power of approximately 0.35 mW. The reflected beam from the beamsplitter was used as the probe beam, whose intensity was about 7% of the total intensity in both pump beams. The forward pump beam and the probe, which constituted writing beams, were overlapped at the sample. Their optical path length difference was much smaller than the laser coherence length, so that they were coherent at the sample. The backward pump beam was... 

Laue realized in 1912 that the path length differences PD, PD2, PD3 for waves diffracted by atoms separated by one crystal lattice translation must be an integral number of wavelengths for diffraction (i.e., reinforcement) to occur further, he showed that this condition must be true... 

Thus the total path length difference as a fraction of the wavelength X is... 

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