We have modeled the path-length distribution in an integrating sphere used as a multipass optical cell for absorption measurements. The measured radiant flux as a function of analyte concentration is nonlinear as a result, deviating from that expected for a single path length. We have developed a full numerical model and introduce a new analytical relationship that describes this behavior for high reflectivity spheres. We have tested both models by measuring the optical absorption of methane at $1651\mathrm{nm}$ in a $50\mathrm{mm}$ diameter sphere, with good agreement with experimental data in the absorption range of $0–0.01{\mathrm{cm}}^{-1}$. Our results compare well with previous work on the temporal response of integrating spheres.

We present the results of a detailed analysis of the noise behavior of two CCD spectrometers in common use, an AvaSpec-3648 CCD UV spectrometer and an Ocean Optics S2000 Vis spectrometer. Light sources used include a deuterium UV/Vis lamp and UV and visible LEDs. Common noise phenomena include source fluctuation noise, photoresponse nonuniformity, dark current noise, fixed pattern noise, and read noise. These were identified and characterized by varying light source, spectrometer settings, or temperature. A number of noise-limiting techniques are proposed, demonstrating a best-case spectroscopic noise equivalent absorbance of $3.5\times {10}^{-4}\mathrm{AU}$ for the AvaSpec-3648 and $5.6\times {10}^{-4}\mathrm{AU}$ for the Ocean Optics S2000 over a 30 s integration period. These techniques can be used on other CCD spectrometers to optimize performance.