Rayleigh optical system

Optical constant of scattering system (Rayleigh constant) Concentration of adsorbed coagulant [M]... 

The conservation of mass equations are used with refractometric optics. The absorption optical system will give absorbance (optical density) which is directly proportional to concentration. Unless conservation of mass equations are used, one can only obtain concentration differences from refractometric optics. The Rayleigh optical system will give information proportional to cr — cTm thus Equation 20 or 23 would have to be used to obtain cTm. Note also that the initial concentration c0 is needed. This must be measured by differential refractometry, by boundary-forming experiments, or from ultraviolet light absorption. 

Here h is the thickness of the ultracentrifuge centerpiece (usually 12 mm), n — n0 is the refractive index difference between the solution (n) and the solvent (n0), and A is the wavelength of light used (generally 546 /a). Thus with the Rayleigh optical system one can obtain n, which can be expressed as... 

Figure 1 Sedimentation velocity analysis of the interaction between bisANS and bacteriophage P22 coat protein. Sedimentation was carried out at 56,0(X) rpm at 20 °C in a Beckman Model E centrifuge equipped with a video-based on-line Rayleigh optical system. (TOP) Coat protein alone (cq = 0.4 mg/ml t = 5348 sec) (BOTTOM) Coat protein in the presence of 60 (iM bisANS (A) Co = 0.5 mg/ml t = 5339 sec (B) 0.2 mg/ml t = 5343 sec). The error bars are the standard error of the mean propagated from the averaging process.

Liu, S. and W. F. Stafford (1992). A Real-Time Video-Based Rayleigh Optical System for an Analytical Ultracentrifuge Allowing Imaging of the Entire Centrifuge Cell. Biophys. J. 61, A476, 2745. 

Yphantis, D. A., W. F. Stafford, S. Liu, P. H. Olsen, J. W. Lary, D. B. Hayes, T. P. Moody, T. M. Ridgeway, D. A. Lyons and T. M. Laue (1994). "On line Data Acquistion for the Rayleigh Interference Optical System of the Analytical Ultracentrifuge." in MODERN ANALYTICAL ULTRACENTRIFUGATION Acquisition and Interpretation of Data for Biological and Synthetic Polymer Systems Eds. T. M. Schuster and T. M. Laue. Boston, Birkhauser Boston, Inc. 

Other optical techniques have also been used to monitor analytical ultracentrifugation experiments. These included refractive index (Schlieren optics) as well as interference patterns produced using Rayleigh- or Lebedev-type optics.11 In both cases, data are acquired using photographic or video recording equipment. Examples of data obtained with these different optical systems are shown in Figure 13.11. 

The exposure of the coated wafers is done through a complicated optical system. The size of the features is given by the Rayleigh equation, and is directly proportional to the exposure wavelength (X) and inversely proportional to the numerical aperture (NA), while k is a constant that depends on the equipment used (with values between 0.4 and 1.0)... 

AUC systems are available commercially with several optical systems. The ProteomeLab XL-I model (Beckman Coulter, Inc.) is equipped with two optical detection systems. A Rayleigh interference system, driven by a 660 nm laseg measmes concentration by monitoring refractivity, and a 190-800 nm xenon-lamp system measmes sample absorbance. An XLA version, equipped with absorbance-optics only, is also available. 

Lord Rayleigh considered this problem and concluded that in any optical system an unwanted pathlength of A/4 or less can be tolerated, as having an extremely small affect on the size of the Airy disk. 

The order parameter was arguably first introduced by Landau at the equilibrium thermodynamic level to study phase behavior. Order parameter models can also be motivated through classical bifurcation theory, and several physical systems have been recently modeled in this way. They include Rayleigh-Benard convection, Faraday waves,or pattern formation in optical systems. Close to a bifurcation point, these models asymptotically describe the system under study, but they are now routinely used, in a phenomenological feshion, to describe highly nonlinear phenomena. 

To calculate the aperture (a) required by an optical system to resolve two objects with known linear separation, the Rayleigh criterion for resolution is used as... 

The improvement in optical resolution can be achieved either by inaeasing the numerical aperture or by reducing the wavelength of the illuminating light. This is a consequence of equation 10.7. The theoretical resolution of an optical system for projection printing is limited by Rayleigh diffraction ... 

---