Abstract: A correction method for an electronic instrument accessory probe utilizes an error correction equation wherein at least one term contains an exponent less than unity. One simple such equation is: S=Cs2+Bs+A+b|s|x (where 0<x<1), but additional terms may be added, either with integer exponents greater than 2, or with other fractional exponents less than one. In the most simple embodiment, there are only four coefficients and the only term with a fractional exponent has an exponent of ½ (i.e., x=0.5). A second set of coefficients may be needed for the correction of negative values.

Abstract: In a multi-axis machine tool (M) including an angular dividing head (HD) having a spindle head (9) mounted thereto, the positional correction includes determining an error representative vector componentwise representative of a plurality of positional errors with respect to a plurality of axes of the spindle head at a respective angular position dividable by the angular dividing head, and correcting an arbitrary positional error of the spindle head by calculating a component vector of the error representative vector associated with the respective angular position.

Abstract: A system and method of calibrating an S parameter measurement instrument (such as a vector network analyzer) in which the number of calibrations required to fully characterize the error model of an n-port system is n/2 calibrations for an even number of ports and (n+1)/2 calibrations for an odd number of ports. Each test port in the system is involved in at least one full calibration, thus n/2 test paths are fully calibrated. For each measured test path, the error terms of the applicable error model are calculated. These error terms are then decoupled from the associated test path into error parameters that are localized to the individual test ports of the test path. Having localized the error parameters, the error model for each test port can then be treated independently from the other test ports. The error terms for the test paths that are not calibrated are then constructed using the localized error parameters for the individual test ports.

Abstract: A forming method for a calibration curve in an infrared gas analyzer. The forming method minimizes the systematic error that occurs in the infrared gas analyzer improves measuring precision. The forming method modifies a method in which gases having different concentrations are supplied to an infrared gas analyzer. The gas analyzer has the outputs corresponding to the gas concentrations, and samples the gas concentrations as a plurality of points, the number of which is not less than four. A calibration curve is approximated by up to a fourth-order polynomial using a method of least squares based upon the measured values of not less than 4 points thus sampled. In carrying out the above-mentioned polynomial approximation, an inverse number of the square of the divided ratio at each point of the calibration curve is used so as to carry out a weighting operation.

Abstract: A signal processor (10) receives both open and closed field values for elements of a detector (11) and corrects for non-uniformities in offset response between the elements prior to converting the signal via an A to D converter (15). The corrected signal is then digitally processed to compensate for linear and higher order non-uniformities in the response of the element. The invention enables the A to D converter to have relatively low resolution for a given output radiation.

Abstract: A technique to modify the input data to any system so as to cancel errors in the transfer function of that system. The system error response to each possible input amplitude transition is determined. A compensating input sequence is calculated which compensates for this error. The error-correcting sequence is stored in memory for each possible transition. These pattern sequences exactly cancel errors in the response to each of the possible, individual sample-to-sample transitions. For each of any series of input data sample transitions, the appropriate correction sequence is recalled from memory. The composite corrected input is the sum of Y correction sequences from Y preceding sample transitions.

Abstract: A method is provided for the fractal representation of data in which the data (902) is divided into a first series of overlapping regions. A weighting function is applied to the regions. The weighted regions are expanded onto an orthonormal basis, and the orthonormal expansion is truncated at a predetermined point. A residue is formed between the data (902) and the truncated orthonormal expansion, and a fractal approximation to the residue is determined.

Abstract: A method for providing a standard Raman spectrum from a sample uses a particular Raman spectrometry apparatus or any similar Raman spectrometry apparatus, which is used to simultaneously irradiate a reference material and at least one sample, thereby obtaining their respective convolved Raman spectra. Using a defined standard energy dispersion characteristic and a standard Raman spectrum of the reference material, a convolution function is determined and applied to produce a deconvolved Raman spectrum of the sample. This deconvolved spectrum is multiplied by a defined standard photometric response function to produce a standard Raman spectrum of the sample.

Abstract: A method for calibrating a circuit analyzer includes determining a plurality of initial technology parameters characterizing the circuit according to a timing model of the circuit. A delay along an entire logic path of the circuit is expressed as a function of the technology parameters. A benchmark set of circuit paths is determined which has fixed topology, device sizes, and wire capacitances. The technology parameters are then optimized to minimize error over the set of circuit paths to obtain optimized parameters for use in the timing model. The optimized technology parameters minimize the average error for the benchmark set of paths relative to SPICE or physical measurements. Average error is significantly reduced on a representative set of paths when compared to the conventional approach of separately measuring each parameter.