Optical null method

In double-beam instruments compensation was, with one or two exceptions, by the optical null method whereby a servomotor drove a comb into the reference beam to minimize the signal difference between it and the sample beam as it was attenuated to varying degrees by absorbance. Movement of the comb was mechanically geared to a pen, which thus recorded the spectrum as a trace on a moving chart. 

Absorbance may be derived from the photoelectric signal either directly on a precalibrated meter scale or by a null method where a reference signal is provided optically or electrically. In null methods, readings... 

This instrument is used to measure the difference in refractive index or in optical path length between two liquids by a null method. The measurement is converted into a difference in composition by means of a calibration curve. The use of the instrument is restricted to systems with a small difference in refractive index, otherwise a large number of standard mixtures have to be made up for calibration purposes. 

Figure 5 shows a typical arrangement of ellipsomteter which consists of a light source, polarizer (P), phase compensator (C), reflection surface (S), analyzer (A), and photo-detector. In the nulling method, azimuths of the three optical elements (polarizer, compensator, and analyzer) are adjusted for the light intensity of the photo-detector to be zero or minimum. For example, when one fixes the azimuths of the compensator at C = (ti/4) or -(ti/4) and its... 

The optical null spectrometer is the simpler and less expensive spectrometer. In the optical null spectrometer, an amplifier registers the difference in energy between the radiation in the sample beam and the reference beam, and drives a non-transparent comb or wedge into the reference beam until the energies are equal in both beams. The recorder, either a pen drawing on a chart or a computer, is attached to the optical comb, and as the optical comb is driven into the beam, the recorder registers less transmission. The main problem with this method is apparent when the sample... 

The simplest method of beam microbalance operation is to measure the deflection of the ends of the beam by optical magnification. This method has the disadvantage that the maximum weight change that can be observed is limited and the vacuum system must usuaUy be opened to reset the zero point. However, a beam microbalance can be readily converted to a null point instrument by electromagnetic adjustment. A commercially available instrument which features electromagnetic compensation and automatic recording is shown schematicaUy in Fig. 10. 

To perform unbiased analyses, a collaboration-wide policy of blindness was established, where cut selections are optimized on a fraction of data or on time-scrambled data set. We present upper confidence limits for null results following the treatment described in (Feldman and Cousins, 1998) and incorporate systematic uncertainties into the calculation of confidence intervals according to (Conrad et al., 2003). The contributions to systematic uncertainties is predominantly due to variations of the optical properties of the ice, the absolute sensitivity of the OM, the neutrino cross section and the muon propagation. The combined systematic uncertainty is typically 30%, although the value varies slightly with the analysis method. 

Because the servosystem always drives to a null signal, the spectrum is basically independent of time or spatial changes in source intensity, amplifier drift, and most important of all, atmospheric absorption bands. The optical systems for this method of photometry are designed to ensure symmetry of the reference and sample beams with respect to path length, number of reflections, etc. However, the operator of such an instrument must keep in mind the fact that insertion of a sample cell may introduce a sufficient asymmetry between the reference and sample beams so that atmospheric absorption bands may appear in the spectrum. The degree to which these appear depends on the difference in absorption path length introduced, on the concentration of CO2 and H2O vapor in this path difference, and on the resolution of... 

The contributions of Zheng [276,277], Zheng and Strom [279], and Zheng and Shao [278] demonstrated the applicability of the null-field method to particles with complex geometries and optical properties. The above formalism can be extended to nonaxisymmetric particles in which case, the domain of analysis can be discretized into many volume elements with different shapes and optical constants. 

In the first chapter, we recapitulate the fundamentals of classical electromagnetics and optics which are required to present the theory of the null-field method. This part contains explicit derivations of all important results and is mainly based on the textbooks of Kong [122] and Mishchenko et al. [169]. 

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