Patent ID: 7783458

Claim:
A method for using an optical system employing filtered broad band light to determine the specific components in a material sample, which comprises: forming an n by r matrix C representing measurements made by the optical system of m samples of the material to be analyzed at n different light frequencies, each sample of the material containing r principal components, each sample containing known quantities of the r principal components in the material being analyzed where n is a finite number related to the number of measurement channels in the optical system and is selected to reduce the cost of the optical system and to increase the speed of measurement associated with the optical system while maintaining beneath a selected value the uncertainty associated with the measurements, measuring m different samples at n different frequencies using the optical system, each of said m samples containing unknown quantities of r specific components in the material, where “m” is a selected integer representing the number of samples and r represents the number of principal components in the material; using the measured results from the m samples, each sample containing unknown quantities of the r principal components, to form an n by m matrix P, where P=C·R, where R is an r by m matrix representing unknown values of the r principal components which are being measured in the m material samples; and further wherein said matrix R is found from said matrix P and said matrix C as in the expression R =( C T ·C ) −1 ·C T ·P.