A regularization approach for the determination of remission curves

Abstract

In this paper, based on a new indirect measuring procedure we present an adapted regularization approach for the determination of remission curves. Applications occur in the visible light spectral analysis of material samples. The obtained remission curves can be used to identify and distinguish colours in various fields of colourimetry, for example in automobile industry and medicine. The traditional technique of measuring remission curves directly is based on complex hardware that combines a monochromator and a photometer. The aim of our considerations is to replace this traditional technique by a more efficient software approach. Our alternative procedure uses only simple electronic components as light emitter diodes and photodiodes which provide series of indirect measurements of the remission curves in integral form. From a mathematical point of view the inverse problem under consideration can be interpreted as the solution of a discretized Fredholm integral equation of the first kind. We present a stable numerical approach that allows finding sufficiently precise approximations for the remission curves.

Keywords:

• Remission curves
• Optical spectral analysis
• Regularization

^*Corresponding author [email protected]

^*Corresponding author [email protected]

Notes

^*Corresponding author [email protected]