Using confidence intervals to evaluate the focus alignment of spectrograph detector arrays

High-resolution spectrographs extract detailed spectral information of a sample and are frequently used in astronomy, laser-induced breakdown spectroscopy, and Raman spectroscopy. These instruments employ dispersive elements such as prisms and diffraction gratings to spatially separate different wavelengths of light, which are then detected by a charge-coupled device (CCD) or complementary metal-oxide-semiconductor (CMOS) detector array. Precise alignment along the optical axis (focus position) of the detector array is critical to maximize the instrumental resolution; however, traditional approaches of scanning the detector through focus lack a quantitative measure of precision, limiting the repeatability and relying on one's experience. Here we propose a method to evaluate the focus alignment of spectrograph detector arrays by establishing confidence intervals to measure the alignment precision. We show that propagation of uncertainty can be used to estimate the variance in an alignment, thus providing a quantitative and repeatable means to evaluate the precision and confidence of an alignment. We test the approach by aligning the detector array of a prototype miniature echelle spectrograph. The results indicate that the procedure effectively quantifies alignment precision, enabling one to objectively determine when an alignment has reached an acceptable level. This quantitative approach also provides a foundation for further optimization, including automated alignment. Furthermore, the procedure introduced here can be extended to other alignment techniques that rely on numerically fitting data to a model, providing a general framework for evaluating the precision of alignment methods.