Ignoring spatial and time dependences, let 
be the
effective instrumental response for the rows extracted, 
the
atmospheric transmission
and 
the spectrum of the target object. The
observed spectrum of the target object is
Since one is interested in 
only, one has to correct
for 
and for 
.
If an astronomical standard object with a known spectrum
is
observed in the same conditions as the target object then its observed
spectrum is
Ratioing the two spectra one obtains:
As can be seen, correcting a spectrum for the
atmospheric transmission and for the
instrumental response implies dividing the observed spectrum of the
target object
by that of an object for which its actual spectrum is known, i.e.
a
standard star, and
multiply the result by the actual spectrum of the latter. Apart from the
hydrogen lines, early
type stars are known to have an almost featurless IR
spectrum. Therefore, using an
early type star as a standard star one obtains the flux density of the
target object by dividing the observed spectrum of the standard star by
before ratioing the two observed spectra.