A high-speed anamorphic pupil-conjugate slit spectrograph for rapid, self-luminous sources
We present a slit imaging spectrograph whose wavelength registration is a property of the instrument rather than of the pointing of the fore-optic or the position of the source. An internal telecentric 4f relay places the system stop within the instrument while a cylindrical lens places the slit aperture at a plane where transverse position encodes source angle only (an $A = 0$ conjugate in the ABCD matrix formulation). As a result, the lateral motion of the source or the pointing of the fore-optic does not cause the spectral image illuminating the sensor to wander, thus eliminating any non-physical registration of chemical species not present in the event and the need for on-the-fly recalibration. Additionally, the use of a high-speed CMOS camera eliminates temporally averaged spectral lines and aliasing noise. We characterize wavelength calibration (He discharge lamp, quadratic fit, RMS residual 0.12 nm, verified with Ne discharge lamp, same calibration, RMS residual 0.13 nm), spectral resolution (R $\approx$ 639, FWHM 0.92 nm at the optimal slit width setting, R $\approx$ 783, FWHM 0.75 nm at the instrument profile floor), and pointing invariance (He 587.6 nm line wander 0.29 nm RMS, 1.03 nm peak-to-peak, a nearly 100x reduction relative to the same instrument with the aperture stop at the fore-optic pupil). We perform combustion spectroscopy on ignited nitrocellulose at 10 kHz, 99 $μ$s exposure time, identifying Na, K, Ca, CaOH, and Rb chemical species using the unchanged wavelength calibration transferred from the helium discharge lamp.