Analytical calculation of the light-collection efficiency of an optical emission spectrometer with the effective solid-angle method

A method is proposed for calculating the optical emission spectrometer (OES) light-collection efficiency using the effective solid angle from an arbitrary point source. Based on the point source-OES relative positioning, the effective solid angle is derived for four cases: (1) on axis and on the object plane; (2) on axis and outside the object plane; (3) off axis and on the object plane; and (4) off axis and outside the object plane. The results were in good agreement with those obtained through Monte Carlo ray tracing. After calculating the OES geometrical collection efficiency with respect to the object plane distance in three different-sized cylindrical volume sources, we suggest a simple strategy to increase this efficiency in plasma process monitoring.