Pixel width

In practice the pdf of the image is sampled using a CCD array with finite pixels. Using A to denote the pixel width and 5 to describe the offset from the origin to the first pixel the centroid can be computed from... 

The acquisition mode (detector pixel width, number of projections and scan time) was optimized for CSCT acquisition. Assuming a point source, in CT the spatial resolution is mainly given by the size of the detector pixels, whereas in CSCT it is given by the detector pixel size, the length of the collimator lamellae in front of the detector and the distance between the object and the detector. In the experiment presented here, the combined effects of detector and collimation resulted in an average spatial resolution of 8 mm. Therefore, only a low-resolution image can be expected from the reconstruction, and consequently a low number of projections is sufficient. 

Obviously, such a high-resolution monochromator requires active wavelength stabilization in order to avoid drift problems. This has been accomplished through an internal neon lamp, mounted on an adjustable stand in front of the intermediate slit between the pre- and echelle-monochromator, so that it can be moved into the beam automatically if necessary. The neon lamp emits many relatively narrow lines in the 580-720 nm range, and, in the absence of any pre-selection, these are separated by the echelle grating into various superimposed orders. This means that without pre-dispersion at least two neon lines for every grating position surely fall on the detector, and can be used for stabilization. The precision of this stabilization is only limited by the stepper motor for grating adjustment, and is better than one-tenth of a pixel width (see Welz et al. [10]). 

It should be noted that the actual spectral resolution is a fairly complex function of the slit width, pixel width, and spectrograph dispersion. The image of the entrance slit on the CCD may be wider or narrower than the pixel width... 

The procedures used to calibrate the Raman shift axis with neon lines can be fairly complex, due to subtleties introduced by the use of CCDs (5, 7-10). The image of the entrance slit usually covers more than one CCD pixel along the wavelength axis, and the Raman bandshape might be distributed over several pixels as well. So the observed Raman peak is a convolution of the slit function, the pixel width, and the line shape. These issues can become important when <1 cm accuracy is required or when comparing spectra from different insturements (7,9). 

An interesting development of the IPDA has recently been reported by Benjamin et al. (22). They use a high gain ( 10 ) MCP combination coupled with a rapid readout of the PDA to allow detection of individual photons. Centroiding of the photon pulse allows spatial resolutions less than the pixel width. Also, a P-46 phosphor is used for fast time response. This system may be quite useful for line profile measurements in the EUV, where low counting rates can be tolerated. 

C and in order to match as closely as possible the two spectral line shapes. With hydrostatic samples one can measure pressures with a precision of slightly better than 0.01 GPa. A l/4m spectrometer (1200 grooves/mm grating) and 750 bin CCD (11 pm pixel width) gave a dispersion of 2.3 x 10 A/bin. Micro FTIR spectra were taken on a Bruker Optics vector-33 FTIR spectrometer (4cm resolution). 

For best throughput, the core diameter of the optical fiber is chosen to be about a factor of 2 wider than the width of the entrance slit of the spectrograph. Pixel widths (15-... 

Figure 2 An atomic line spectrum showing typical line shapes for a system with slit width approximately twice the pixel width. 

Figure 7.4 Influence of a line shift on the transmittance signal (a) calculated Voigt profile (red line) and corresponding pixel response (black fine) (b) same profile shifted 10% of the pixel width to the right (c) resulting pixel-based quotient...

Third morphological treatment removal of artifacts [small objects less than 2 pixels (1.4 pixel width for a square object)]... 

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