Patent ID: 8126673
Filing Date: 2012-02-28
Classification: G01J,G01N

Abstract:
1. A method for increasing the speed of line-by-line calculations of multiple overlapping absorption lines, said method comprising: (1) a step of dividing a domain of a Voigt function representing the shape of an absorption line into a first range around the peak of the Voigt function and a skirt portion not contained in the first range, replacing the first range with a cubic function whose function values and derivative values match with those of said Voigt function at the connection points with said Voigt function, and calculating the values and derivative values of said cubic function and the Voigt function in the skirt portion for each of first predetermined intervals; (2) a step of adding together the results of step (1) for a plurality of absorption lines; (3) a step of interpolating the results of step (2) to calculate the function values and derivative values in second predetermined intervals smaller than said first predetermined intervals; (4) a step of dividing said first range into a second range near the peak of said cubic function and a skirt portion not contained in the second range, replacing said second range of a “function representing the difference between the Voigt function and said cubic function” with a second cubic function whose function values and derivative values match with those of said “function representing the difference between the Voigt function and said cubic function” at the connection points with said “function representing the difference between the Voigt function and said cubic function”, and calculating the values and derivative values of said second cubic function replacing said second range and the “function representing the difference between the Voigt function and said cubic function” in the skirt portion for said second predetermined intervals; (5) a step of adding the results of step (4) to the results of step (3) for a plurality of absorption lines; (6) a step of interpolating the results of step (5) to calculate the function values and derivative values for intervals smaller than said second predetermined intervals; and (7) a step of adding the values and derivative values of the “function representing the difference between the ”“function representing the difference between the Voigt function and said cubic function”“and said second cubic function” to the results of step (6) for a plurality of absorption lines in said second range.