Nonuniformity Correction

Nonuniformity correction (NUC). This can be done in the analog or digital domains. The NUC algorithms are described in Section 10.4.5. 

Figures of merit for detectors and SCAs were described in Chapters 1 and 3, and their testing is described in Chapter 10. Here we discuss some of that same material, but with an emphasis on ROICs. Discussion of calibration (nonuniformity correction) is referred to in Section 7.5.

Post Correction Nonuniformity. The PCNU is the standard deviation of the output after the nonuniformity correction process (see Section 10.4.4, PCNU). We are generally allowed to exclude some pixels from the standard deviation calculation - but any excluded pixels must be declared to be defective. That means that we have some latitude in the PCNU process - we may make PCNU better by excluding anomalous pixels - but at the cost of having more defective pixels. If the spec is very sfringent, we may need to devise an algorithm that finds the best compromise between PCNU and the number of defects. 

Spray characteristics of pressure nozzles depend on the pressure and nozzle-orifice size. Pressure affects not only the spray characteristics but also the capacity. If it is desired to reduce the amount of liquid sprayed by lowering the pressure, then the spray may become coarser. To correct this, a smaller orifice would be inserted, which might then require a higher pressure to produce the desired capacity, and a spray that would be finer than desired might result. Multiple nozzles tend to overcome this inflexible charac teristic of pressure atomization, although several nozzles on a diyer complicate the chamber design and air-flow pattern and risk collision of particles, resulting in nonuniformity of spray and particle size. 

To determine the average porosity of a homogeneous but nonuniform medium, the correct mean of the distribution of porosity must be evaluated. The porosities of natural and artificial media usually are normally distributed. The average porosity of a heterogeneous nonuniform medium is the volume-weighted average of the number average ... 

The average nonuniform permeability is spatially dependent. For a homogeneous but nonuniform medium, the average permeability is the correct mean (first moment) of the permeability distribution function. Permeability for a nonuniform medium is usually skewed. Most data for nonuniform permeability show permeability to be distributed log-normally. The correct average for a homogeneous, nonuniform permeability, assuming it is distributed log-normally, is the geometric mean, defined as ... 

For cases of nonuniform velocity distribution, Kays and London (1958) suggested using momentum correction and energy correction factors in the above equations. However, these factors are very difficult to evaluate, so the homogeneous model is used here. 

Weisman and Pei applied their approach to data from tubes with nonuniform axial heat flux. They found the predictive scheme to hold without the need for any nonuniform heat flux correction factor. The accuracy of their prediction was only slightly less than that of the W-3 correlation, Eq. (5-106), for the data they examined. 

However, further analysis of the behavior of the system in LC cells cast doubt on this interpretation. First, while intuitively attractive, the idea that relaxation of the polarization by formation of a helielectric structure of the type shown in Figure 8.20 would lower the free energy of the system is not correct. Also, in a thermodynamic helical LC phase the pitch is extremely uniform. The stripes in a cholesteric fingerprint texture are, for example, uniform in spacing, while the stripes in the B2 texture seem quite nonuniform in comparison. Finally, the helical SmAPF hypothesis predicts that the helical stripe texture should have a smaller birefringence than the uniform texture. Examination of the optics of the system show that in fact the stripe texture has the higher birefringence. 

In porous media the flow of water and the transport of solutes is complex and three-dimensional on all scales (Fig. 25.1). A one-dimensional description needs an empirical correction that takes account of the three-dimensional structure of the flow. Due to the different length and irregular shape of the individual pore channels, the flow time between two (macroscopically separated) locations varies from one channel to another. As discussed for rivers (Section 24.2), this causes dispersion, the so-called interpore dispersion. In addition, the nonuniform velocity distribution within individual channels is responsible for intrapore dispersion. Finally, molecular diffusion along the direction of the main flow also contributes to the longitudinal dispersion/ diffusion process. For simplicity, transversal diffusion (as discussed for rivers) is not considered here. The discussion is limited to the one-dimensional linear case for which simple calculations without sophisticated computer programs are possible. 

The cell diagrammed in Figure 29.20c has been used extensively by Kastening to study the reaction mechanisms and kinetics when a stable electro-chemically generated species is mixed with other reactants [38]. The calculations that were used to reduce the experimental data to kinetic parameters included the effects of flow rate, reaction mechanism, rate constant, and the dependence of the EPR spectrometer nonuniform sensitivity to the position of the radicals in the cavity. Unfortunately, the correction for the latter effect was introduced as the idealized cosine-squared function (solid line in Fig. 29.16) rather than the actual sensitivity variation that occurs with magnetic field modulation. It is important to be aware of this difficulty when performing experiments to determine accurate kinetic parameters. 

The cuvette must be correctly placed in its holder so that the laser beam is perpendicularly incident upon it. If the cuvette is not fixed correctly the laser beam is deflected from its normal path, which leads to a nonuniform and incorrect diffraction pattern. Many commercial instruments have the ability to adjust the alignment of the laser beam once the cuvette has been correctly inserted into the sample holder, to ensure that it is perpendicularly incident. 

Some coal samples contain a high amount of carbonates (calcite, CaC03) or pyrite (FeS2) or both. In such cases, sulfur retained as sulfates may be both unduly high and nonuniform between duplicate samples. Sulfate sulfur in the ash can be determined (ASTM D-1757) and the requisite correction made, and the ash yield should be reported and designated both as determined and corrected. 

Figure 5. Contours of several diffraction maxima the (2,1,3), (1,0,4), and (3,2,2) before (a,c,e) and after (b,d,f) corrections and background removal. Smoothing by cubic splines is performed during contouring. Note the nonuniformity of fiber tilt distribution appears in the corrected maxima.

---