Sharp cutoff filters

The use of a sharp cutoff filter is recommended to avoid second-order interference from the Ne 335.5 nm line emitted by the lamp. 

Reactions can be initiated either by broadband flash photolysis or by laser flash photolysis. The former has the advantages of simplicity and lower cost, while the latter has the advantage of selective excitation. Selective excitation may be desirable to cleanly generate radicals of interest. However, some selectivity can be had from flashlamps when sharp cutoff filters are used, and it is sometimes possible to find photochemistry for generation of radicals of interest where selective excitation is not necessary. If laser sources are to be used, it may be necessary to have more than one laser available. 

Figure 3-7 Spectral characteristics of a sharp-cutoff filter (a) and a wide-bandpass filter (b). The narrow-bandpass filter (c) is obtained by combining filters a and b. The spectral bandwidth of filter c (distance n-m) is defined as the width in nanometers of the spectral transmittance curve at a point equal to one half of maximum transmittance.

Fig. 1.9. Possible spatial filters defining large-scale quantities with G = G1G2G3. The filter denoted by (a) is the volume-averaged box filter, the filter denoted by (b) is the Gaussian filter, and the filter denoted by (c) is the sharp cutoff filter. Note that the position vector, x, used by Leonard corresponds to r in this book. Reprinted from Leonard [97] with permission from Elsevier.

A Fourier transform of the filter shown in Fig. 1.9c is a spectrally sharp cutoff filter, a kind of box filter in k-space rather than r-space. The spectrally sharp top-hat filter, i.e., the filter normally used in spectral simulations, is in physical space defined by (e.g., [97] [106]) ... 

Sharp cutoff filters should be avoided in biopotential measurements where the bioelectric waveform shape is of interest Filtering can greatly distort waveforms where waveform frequencies are near the filter breakpoints. Phase and amplitude distoitions are more severe with higher-order sharp-cutoff filters. Filters such as the Elliptic and the Tchebyscheff exhibit drastic phase distortion that can seriously distort bioelectric waveforms. Worse still for biopotential measurements, these filters have a tendency to ring or overshoot in an oscillatory way with transient events. The result can be addition of features in the bioelectric waveform that are not really present in the raw signal, time delays of parts of the waveforms, and inversion of phase of the waveform peaks. Figure 17.34 shows that the sharp cutoff of a fifth-order elliptical filter applied to an ECG waveform produces a dramatically distorted waveform shape. 

Stray light measurements are made using a sharp cutoff filter. Examples of these filter materials include saturated solutions of such compounds as potassium ferromanganate or lithium carbonate. Other solutions exhibiting abrupt cutoff wavelengths include KBr, KCl, Nal, NaN03 solutions, and acetone. Refer to ASTM E 169-87, Practice for General Techniques of Ultraviolet-Visible Quantitative Analysis. ... 

Figure 3. Transient absorption spectrum of a 2 x 10 M solution i in butyronitrile at 100 ps following a 0.3 mJ, 0.5 ps, 600 nm laser flash. Filters that reject stray excitation light cut out the 580-620 nm wavelength region, while the sharp cutoff at 440 nm is due to the intense absorption of the porphyrin Soret band at 419 nm.

In this expression 1 is the cutoff frequency above which the data contain no information about o(x) that is, I( Q. We see that the sharpness criterion is a measure of the steepness of the solution o(x). The previous criterion, expression (40), is replaced with a sum of two terms. It includes both the mean-square-error criterion and sharpness. The filter is then sought that minimizes... 

The significance of the sharp spectral filter is apparent, it annihilates all Fourier modes of wave number ]A ] greater than the cutoff wave number, kc = -KI A, whereas it has no effect on the lower wave number modes. 

Fluorescence was measured with a Turner model 111 filter fluorometer. The excitation filter was a Corning 7-60 (365 nm primary wavelength). The emission filters were Wratten 65-A (495 nm primary wavelength) and 2-A (sharp-cutoff below 415 nm). A digital multimeter was connected to the recorder terminals of the fluorometer to provide digital readout. Fluorescence-quenching (FQ) titrations were performed in batches. Preliminary experiments indicated that quenching was independent of time (at least 26 hours) after 30 minutes. Equilibration times of 60 minutes were used. 

Consider the frequency domain again. The requirement for a sharp cutoff arises because we want to cut off as much noise as possible and the sharper the filter cutoff the closer it can be set to the spectral feature to be saved. It is clear that the filter cutoff needs to be only as sharp as the spectral feature. Therefore, a careful consideration of filter characteristics is most important for high resolution NMR, whereas the RC filter is tolerably good for very broad lines such as those in solids observed by normal NMR. But since the opportunity for some oversampling is much greater for high resolution NMR than in wideline NMR, the absolute necessity for an "ultrasharp" filter is not as great as it is supposed in either case. 

A box-filtered quantity is simply the volume average of this quantity over the box. It provides a sharp cutoff for values in the physical space that lies outside the box. In contrast, however, the cutoff of the wave numbers in the Fourier space is gradual. Further, the box filter is the only LES filter that satisfies the invariance property given in (19.23). Box filters have been used by Deardorff [12] in his pioneering LES investigations. 

The Fourier cutoff filter has the property of being able to provide a sharp cutoff of the wave lengths in Fourier space, but the cutoff in the physical space follows a hyperbolic decay. In this sense, the Fourier cutoff filter is the dual of the box filter (see Ref. [41]). Fourier cutoff filters are widely used in spectral methods (see Ref. [14]). 

The data without the filter reveal that the OBA is excited by virtually all the incident wavelengths. The dramatic error most adversely affects the calculation of UPF. Without correcting for the systematic error due to fluorescence, this fabric would seem to olfer a UPF of only 7. However, the true effect of the OBA absorption provides a UPF of 40, revealed when the UG-11 filter is utilized. Incidentally, the instrument fitted with the UG-11 filter did not produce useful data for wavelengths above 380 nm due to the filter s sharp cutoff in transmittance. 

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