The Umkehr measurement is known as customarily N-value and is given by the logarithm base 10 of the ratio of cloudless zenith sky intensities at two different wavelengths scaled by a multiplicative factor 100 plus a constant which depends on instruments and extraterrestrial radiation.
In 1964, Carlton Mateer provided analysis on information content in umkehr measurements.
The effective scattering height depends on the ozone absorption coefficient and on the solar zenith angle, increasing as with each of these.
This reversal (Umkehr) or inversion implies the existence of maximum of ozone concentration at some level in the atmosphere.
[1] The resulting ozone profile derived from reduction of these measurements is quite dependent on the algorithm used.