Minimum deviation

Abstract: This paper describes a modification of a nondestructive ultrasonic method for measurements of the phase velocity of bulk waves in arbitrary directions in generally anisotropic materials. In the conventional method the through‐transmission technique is used for velocity measurements at a specified angle of incidence. When this angle is changed by rotation of the sample, the transmitted beam changes position, and so the position of the receiving transducer must be changed. This leads to experimental difficulties and loss of precision. In the double‐transmission technique, the ultrasonic wave is reflected from reflector plates behind the sample and returns via the same path to the same position on the transmitter/receiver working in pulse‐echo mode, which eliminates the necessity of readjusting the receiver position. It is also shown that for arbitrary direction of measurement in anisotropic materials, time‐delay measurements give phase velocity regardless of the angle of deviation between phase and group ve...

Abstract: Manufactured features generally deviate in size, form and relations with respect to other features from the features desired by the designer. Designers specify certain limits for these deviations that depend on functional requirements. The specification of different form errors is dealt with by the International Organization for Standardization (ISO). ISO also specifies that an ideal geometric feature must be established from the actual measurements such that the maximum deviation between it and the actual feature concerned is the least possible value. In practice, the least squares (LS) method is sometimes used for establishing the ideal feature, as this method is based on sound mathematical principles. However, the least squares procedure does not yield a minimum value. Therefore some attempts have been made to arrive at a form error based on the minimum deviation (MD) principles. A stray peak or valley on the actual feature introduces considerable variation in the results obtained by the minimum deviation method. This paper suggests a new approach based on the minimum average deviation (MAD). In this method, the ideal feature is established by using a search technique for different geometric features such as straight lines, circles, planes, cylinders and spheres. Using simple numerical examples, the values obtained by this approach are compared with the values obtained by the least squares and minimum deviation methods.

Abstract: Two techniques are presented for measuring the refractive index of fluids. The first is a reflective technique where liquid is applied to a rough surface to hold the liquid during measurement. Ellipsometric psi and delta data are acquired and analyzed to determine the fluid refractive index. The second technique is refractive and uses a hollow prism cell to contain the liquid. The fluid index is then determined using the prism minimum deviation technique. Both techniques have been applied over a very wide spectral range from the vacuum ultraviolet to the infrared and have been implemented on a research spectroscopic ellipsometer system (VUV-VASE®) with continuously variable angle of incidence. The refractive index of several candidate immersion fluids for 157 and 193nm immersion lithography are reported over the spectral range from 156to1700nm in a nitrogen-purged environment. The advantages and disadvantages of both techniques are discussed. Results were checked against values measured on very accurate p...

Abstract: Although the spectra of drop radii in rain showers are broad, the supernumerary bows are caused by only those drops with radii of about 0.25 mm. The angle of minimum deviation, the rainbow angle, is a function of drop size, being large for big drops, owing to drop distortion, and large for small drops, owing to interference. Between these extremes, there is a minimum rainbow angle. The drops that cause it give rise to the supernumerary bows.