Instrument spread function

The particle size analysis techniques outlined earlier show promise in the measurement of polydispersed particle suspensions. The asumption of Gaussian instrumental spreading function is valid except when the chromatograms of standard latices are appreciably skewed. Calc ll.ation of diameter averages indicate a fair degree of insensitivity to the value of the extinction coefficient. 

The variance of the instrumental spreading function, i.e. the spreading factor of monodispersed polymer in a SEC column was determined experimentally with narrow MWD polystyrene standard samples by the method of simultaneous calibration. The dependence of the spreading factor on the retention volume deduced from a simple theoretical approach may be expressed by a formula with four physically meaningful and experimentally determinable parameters. The formula fits the experimental data quite well and the conditions for the appearance of a maximum spreading factor are explicable. 

There have been a number of discussions about deconvolving beyond the Doppler limit (see Pliva et al, 1980) but we prefer to go back a step further and simply discuss deconvolving beyond removal of the instrumental spread function. Jansson discusses deconvolving inherent broadening in Section... 

Commonly the PSF is also known as the instrument spread function (ISF), the collection efficiency function (CEF) or the spatial detectivity function (SDF).The PSF is a convolution ofthe intensity profile of the excitation light with the volume from which fluorescence is collected (in the one-photon case) see [9] and Chapter 3, Section 3.2.2. 

Soares et al. [80] proposed a model using Stockmayer s distribution with additional help from a generic instrumental spreading function to account for the instrumental peak broadening in Crystaf. Again, although the model could fit the experimental profiles well, the parameters used in the spreading function were considered purely empirical. 

This technique assumes a Gaussian spreading function and thus does not take into account skewness or kurtosis resulting from instrumental considerations. It can, however, be modified to accommodate these corrections. The particle size averages reported here have been derived usino the technique as proposed by Husain, Vlachopoulos, and Hamielec 23). 

Another class of methods such as Maximum Entropy, Maximum Likelihood and Least Squares Estimation, do not attempt to undo damage which is already in the data. The data themselves remain untouched. Instead, information in the data is reconstructed by repeatedly taking revised trial data fx) (e.g. a spectrum or chromatogram), which are damaged as they would have been measured by the original instrument. This requires that the damaging process which causes the broadening of the measured peaks is known. Thus an estimate g(x) is calculated from a trial spectrum fx) which is convoluted with a supposedly known point-spread function h(x). The residuals e(x) = g(x) - g(x) are inspected and compared with the noise n(x). Criteria to evaluate these residuals are Maximum Entropy (see Section 40.7.2) and Maximum Likelihood (Section 40.7.1). 

Somljo Given the point spread function of the instrument how do you differentiate it from a large spark in another, slightly different focal plane ... 

The spreading factor C is the variance of the chromatograms of the monodisperse polymer species, i.e. of the instrumental spreading fimction G(V,Vr), If O g varies linearly vd.th the retention volume of the monodisperse polymer, then<0 > is numerically equal to the interpolated value 0 (v) of the function (T (Vr) for the polydisperse sample at its mean elution volume. 

If b and g are peaked functions (such as in a spectral line), the area under their convolution product is the product of their individual areas. Thus, if b represents instrumental spreading, the area under the spectral line is preserved through the convolution operation. In spectroscopy, we know this phenomenon as the invariance of the equivalent width of a spectral line when it is subjected to instrumental distortion. This property is again referred to in Section II.F of Chapter 2 and used in our discussion of a method to determine the instrument response function (Chapter 2, Section II.G). 

In Eq. (45), TM represents the true transmittance only if instrumental spreading is negligible. In previous sections, however, we learned that instrumental spreading may be described by the convolution product of the flux and the spectrometer response function, here called r(x), that incorporates all the instrumental spreading phenomena ... 

Brief reflection on the sampling theorem (Chapter 1, Section IV.C) with the aid of the Fourier transform directory (Chapter 1, Fig. 2) leads to the conclusion that the Rayleigh distance is precisely two times the Nyquist interval. We may therefore easily specify the sample density required to recover all the information in a spectrum obtained from a band-limiting instrument with a sine-squared spread function evenly spaced samples must be selected so that four data points would cover the interval between the first zeros on either side of the spread function s central maximum. In practice, it is often advantageous to place samples somewhat closer together. 

What meaning do these two-point resolution criteria have in describing the deconvolution process, that is, resolution before and after deconvolution Although width criteria may be applied to derive suitable before-after ratios, the Rayleigh criterion raises an interesting question. Because the diffraction pattern is an inherent property of the observing instrument, would it not be best to reserve this criterion to describe optical performance The effective spread function after deconvolution is not sine squared anyway. 

The difficulty of separation is highly dependent on peak spreading, as shown in Fig. 6.5. It is therefore critical to minimize the peak width as far as possible. This would be difficult for cell display methods if only single color fluorescent labeling were used, because the primary source of variability is biological. Flow cytometry instrumentation point spread functions generally contribute below 2 % to the overall coefficient of variance (CV = standard deviation/mean), but typical overall CVs for yeast display are approximately 50 - 100 % for the logarithmic fluorescence intensity. 

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). 

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