The MAF has a very thin wire through the centre that is used by the ECU
It uses a well established hot-wire principle. A hot wire and an air temperature probe are mounted together in the inlet duct. The hotwire is maintained at 200°C hotter than the air temperature probe, and the current needed to maintain this temperature is connected to a precision resistor.
The principle is simple. The heated probe is cooled proportionally by the mass of air which passes it in the duct, so the current required to heat the probe varies according to the mass of the air passing through. From the voltage reading in the resistor the PCM can then assign an accurate measurement of the air flow and map the quantity of fuel to be emitted by the injectors
The oil from the filter "coats" the wire and stops it performing its job. It is EXCEEEDINGLY sensitive, so any contaminant is bad news.
I can't find an Omega piccy but this one, from a Ford Scorpio site gives some information that might be usefull
http://www.fordscorpio.co.uk/cleanmaf.htm