Dimension spectral

An ESRI system can be built with small modifications of commercial spectrometers by, for example, gradient coils fixed on the poles of the spectrometer magnet, regulated direct current (DC) power supplies, and required computer connections [40,53,55]. Gradients can be applied in the three spatial dimensions, and a spectral dimension can be added by the method of stepped gradients. The spectral dimension is important when the spatial variation of ESR line shapes (as a function of sample depth) is of interest this situation will be described below, in the ESRI studies of heterophasic polymers. In most systems, the software for image reconstruction in ESRI experiments must be developed in-house. 

A CCD array collects simultaneously the spectral data emanating from an array of spatial locations on the irradiated sample surface [20]. Thus, recorded is a three-dimensional data cube, with two coordinates representing the sample and one for the spectral dimension at each (x,y) point (cf. Figure 2). The spectral dimension in this case is only the intensity of a certain Raman band, used to identify the component of interest. This band should be unique for the component of interest of the sample and its intensity should be high enough in... 

In case of reaction course in the Euclidean spaces the value D is equal to the dimension of this space d and for fractal spaces D is accepted equal to spectral dimension ds [6], By plotting p i=( 1 -O) (where O is conversion degree) as a function of t in log-log coordinates the value D from the slope of these plots can be determined. It was found, that the mentioned plots fall apart on two linear parts at t<100 min with small slope and at PT00 min the slope essentially increases. In this case the value ds varies within the limits 0,069-3,06. Since the considered reactions are proceed in Euclidean space, that is pointed by a linearity of kinetic curves Q-t, this means, that the reesterefication reaction proceeds in specific medium with Euclidean dimension d, but with connectivity degree, characterized by spectral dimension ds, typical for fractal spaces [5],... 

The imaging data were collected over the spectral range of 1200-2400nm at lOnm increments using a Sapphire NIR-CI system (Spectral Dimensions, Inc., Olney, MD, USA). The size of FOV was 13 x 10mm, each pixel sampling an area of approximately 40 x 40 Um. 

With chemical imaging, a new type of data structure needs to be analyzed. Chemical imaging experiments yield a 3D X x Y x A, matrix or data cube, where X and Y are the spatial dimensions and A, the spectral dimension. One spectrum per pixel is recorded and selection of a wavelength will show an absorbance picture of the sample [10] (Figure 1). 

Method The sample contained starch, API, Avicel, crospovidone, and sodium lauryl sulfate. Sample and references were analyzed in triplicate by NIR imaging (Spectral Dimensions, 20 coadds, spectral range 1100-2450nm). Full image size was 320 x 256 pixels or 4.1 x 3.3 mm. The NIR images were interpreted, and sample raw materials mapped, using PLS classification with five loadings (based on the reference spectra for starch, API, Avicel, crospovidone, and sodium lauryl sulfate). 

From the scaling properties of G(x, t) one can derive that S = const(d, 0)T)ft/d with d = 2dj(2 + 9) the spectral dimension of the fractal. The growth of the cluster s sizes goes on until l L where L is the whole system s size. The further growth of clusters and accumulation of particles stop because the same quantity L is the characteristic scale of a pair of different particles created in the system according to [91] there is no accumulation effect when particles are created by pairs on fractals of the Sierpinski gasket type. 

In this section, we present the development of an automated protocol for prostate tissue histology [164] from infrared spectroscopic imaging data as an example of the techniques described (Fig. 8.11). The data is three dimensional with x-y—axes representing the image plane and the 2-axis representing the spectral dimension. After data acquisition, two important pre-processing steps, namely baseline correction and de-noising, are performed. Since the entire data set is derived from human tissue samples, the spectra have similar characteristics and, therefore, a manually chosen set of pre-defined wave number could be used as the reference points for baseline correction. It is... 

The imaging data were collected over the spectral range of 1200-2400 nm at 10-nm increments using a Sapphire NIR-CI system (Spectral Dimensions, Inc., Olney, MD, USA). The size of FOV was 13 x 10 mm, each pixel sampling an area of approximately 40 x 40 pm. The concentrations of the active ingredients as reported from the manufacturer s label are 37% acetaminophen, 37% aspirin, and 10% caffeine. The remainder of the tablet mass represents the excipient (binder, disintegrant, and lubricant) materials. Pure acetaminophen, aspirin, and caffeine samples are obtained in either tablet form or powder compact and are used to obtain reference spectra of pure components. 

Figure 8.8 A 58 mm x 46 mm NIR image of a Tempo top ply taken through a macroobjective on the MatrixNIR instrument (Spectral Dimensions). This image is a band integration map of the lotion absorption (1160-1260 nm) from a 4 scan, 24 frame data collection smoothed 13 points and offset corrected. The white box in the upper left shows the 5 mm x 5 mm size of images collected by the Perkin-Elmer Spotlight instrument (see Figs 8.6 and 8.7) for comparison.

Dr Kenneth S. Haber Spectral Dimensions Inc, 3416 Olandwood Court, Suite 210, Olney, MD 20832, USA... 

The definition of spectral dimension ds refers to the probability p(t) of a random walker returning to its origin after time t ... 

Finally, a stochastic viewpoint may be associated with the relation (2.8) since the spectral dimension also characterizes the number n (t) of distinct sites... 

---