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Differential spectroscopy is spectroscopy of the difference between two similar spectra, the two from slightly different circumstances, to gain information about this difference. Essentially, the values obtained from one spectrograph observation are subtracted from those of the other. Transit spectroscopy basically refers to differential spectroscopy between a spectral energy distribution (SED) of electromagnetic radiation from some source versus EMR which also has passed through some particular gas, e.g., for the analysis of extra-solar planet atmospheres through analysis of the difference between SED of the host star with and without the planet in front of it: the ratio of the amount of EMR blocked at a given wavelength depends upon whether the atmosphere is opaque to that wavelength, and full comparison of the two SEDs (during the transit versus not) can reveal spectral lines and spectral bands imposed by the atmosphere, providing clues to its constituents, temperature, layering, and over time, transient phenomena such as the presence of clouds (analogous to those in the Earth's sky). The term also applies to spectroscopy near versus during the time of the secondary eclipse to compare the SED of the host star with that when some light reflected from the planet is added to it. In both these cases, the technique produces results even though the star and planet are not resolved.
Various forms of differential spectroscopy for other (e.g., non-astronomical) purposes are carried out with a specialized instrument that performs the comparison during observation, e.g., analysis of material in Earth atmosphere such as pollutants.