Gradient image profiles

As mentioned earlier, the COMA positive resists tend to have higher optical absorption at 193 nm than polymethacrylate and COBRA systems, which would produce a tapered image profile. To overcome this potential problem, the T-top formation by absorption of base into the top layer (see above) has been intentionally incorporated in the lithographic process (amine gradient process) [281]. Poly(acrylic acid-co-methyl acrylate) and L-proline were dissolved in water and spin-cast on a COMA resist. During PEB the amine in the overcoat diffuses into the COMA resist layer and compensates for the acid gradient caused by illumination, providing a vertical profile. 

The basic principle underlying the development of images is simple (Lauterber, 1973). Consider a body cavity containing two pools of water in different quantities. In a uniform magnetic field, the NMR spectrum will consist of a single peak, since all the water molecules will process at the same frequency, irrespective of their spatial location. If, however, a linear field gradient is applied in the x -direction, the Larmor frequency of the water will increase linearly across the sample as a function of the x -coordinate, thereby creating a one-dimensional profile, or spectrum, of the sample (Fig. 7.21). 

Figure 7.21 One-dimensional NMR imaging. When a magnetic field gradient is applied across a sample, it gives a spectrum that is a profile of the sample in the direction of the gradient.

Figure 7.22 The principle of creating a two-dimensional NMR image. A number of profiles of the sample are obtained in different orientations in the presence of magnetic field gradients pointing in different directions (designated by arrows). The x -gradient yields an x -profile, and a /gradient generates a y -profile. A combination of these profiles produces a two-dimensional image.

Fig. 2.6.10 Specialized experimental set-up for microfluidic flow dispersion measurements. Fluid is supplied from the top, flows via a capillary through the microfluidic device to be profiled and exits at the bottom. The whole apparatus is inserted into the bore of a superconducting magnet. Spatial information is encoded by MRI techniques, using rf and imaging gradient coils that surround the microfluidic device. They are symbolized by the hollow cylinder in the figure. After the fluid has exited the device, it is led through a capillary to a microcoil, which is used to read the encoded information in a time-resolved manner. The flow rate is controlled by a laboratory-built flow controller at the outlet [59, 60].

A velocity profile u(r) is obtained using MRI flow imaging and, with respect to radial position r, the values of shear rate y(r), ranging from zero at the tube center to a maximum at the tube wall, can be calculated from the velocity profile as local velocity gradients ... 

Fig. 38 (Upper panel) Scanning force microscopy images of gold nanoparticles (diameter 17 nm) adsorbed along a surface-anchored poly(acryl amide) brush with a molecular weight gradient (Edge of each image = 1 p.m). (Lower panel) Dry thickness of poly(acryl amide) on the substrate before particle attachment (right, ) and particle number density profile (left, ). (Reproduced with permission from [140])...

Figure 13.. Comparison of theoretical analysis and empirical NMR imaging of fluid flow during extrusion. Limiting cases for theoretical analysis (a), the velocity profile as a function of position with no pressure gradient in the z-direction (b), the velocity profile as a function of position with no net flow through the extruder. Limiting cases for empirical analysis by NMR flow imaging (c), no pressure gradient in the z-direction (die open) (d), no net flow through the extruder (die closed).[Reproduced with permission from Ref.61].

Cory and Garroway [13] introduced the NMR pulsed gradient stimulated echo method to study compartments which are too small to be observed by conventional NMR imaging. They showed so-called proton displacement profiles of bulk water and dimethyl sulfoxide. The displacements are due to free diffusion and are Gaussian shaped. The profile of water in yeast cells showed restricted diffusion with a characteristic cell width of approximately 5 /xm. 

Bellows et al.28 first used the neutron imaging technique to measure water gradient profiles within the Nation membrane of... 

Not only can errors in absorbance measurements arise from non-linearity in the detector circuitry, but distortion in the linearity of the position of channel detector elements can lead to a corresponding distortion of the measured intensity profile. The geometric distortion of the SIT vidicon, as stated in the specification sheet supplied by the OMA manufacturer, is typically 2 channels between channels 100 and 400 for a 2.5 mm high image centered on the tube. This distortion is sufficient to require correction of data obtained for experiments with steep concentration gradients in our system. 

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