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Specific intensity (or spectral intensity) is intensity (per astrophysics) per unit wavelength or frequency, i.e., a measure of the amount (energy) of electromagnetic radiation (EMR) striking a surface from a given direction, at a given wavelength or frequency. Like intensity, it is defined in such a way that it does not fall off with distance, a means of characterizing EMR along a line. It is the value of a distribution function and the only possible measurement (e.g., from a galaxy) is that of its average over a finite wavelength-range and finite region of an extended source. The term spectral radiance means the same thing: usage of the terms varies in astronomy, to a large extent according to the type of EMR (e.g., radio vs. visible light).
Note that specific intensity values per wavelength versus per frequency are different values. Various branches of astrophysics likely each have a convention regarding which it generally uses, but when both values are used, one must carry out a conversion in order to compare them; for example, the numerical value at a particular wavelength "per unit wavelength" is not the same as the numerical value at that same wavelength "per unit frequency". See Wien's displacement law for more detail.