hmm, the strip is a good idea, but cant be used, the port is moving longer than its own length, so it would move off the scale. And it folds too, so a big area isn't possible to use. Should then use two sensors, but that might be a mess to work with too.
By "port", I am assuming you are meaning "door" - ie, a "garage door" to let an automobile in/out of the garage.
You don't say what kind of door this is, nor what is moving it. Here in the US, we have two typical kinds of garage doors - one that is basically a slab that moves on special hinges and large springs to tilt it up and over:http://www.remodelguide.com/improve/garage/garage_intro.gif
...and one that is composed of segmented pieces that moves on a curved track, typically with a coiled spring and cable counterweights to carry the extra load:http://garagedoorrepairhelp.com/wp-content/uploads/2009/06/garage_door_parts_diagram.jpghttp://www.easyrollgaragedoors.co.uk/garage_doors_yorkshire_images/garage-doors-sectional-doors2.jpghttp://earlcarterlumber.com/images/affina_interior_432.jpg
...then there are the roll-up doors composed of multiple small segments - but you only see them usually on commercial buildings. There are other options (side swinging, plus some variations on the hinged vs segmented roller), but the majority here are one of the two types above (with the segmented roller version becoming more widely used despite its much higher initial cost - you see them more on new homes and remodels).
Either type of door can be moved by an opener that has the long rail and slider (chain, belt, or screw drive); sometimes on the segmented doors, though, the opener goes in place of the coiled spring and cables counterweight system:http://www.1stdooropeners.com/walljackshaft.jpg
Knowing exactly what type of door you are moving, and what kind of system is moving it, may help us to help you come up with a positioning solution.
I should try to see if I could count the rotations of the motor, to see if it would be possible to use a multi turn pot.
A multi-turn pot with a gearing system might be the best (and simplest) way of implementing a positioning system. You could also do something similar with a regular potentiometer (because really, that is all a multi-turn pot is - a regular pot - sometimes linear travel - that is geared down to the knob).
The idea of a gray-scale line could be done, but doing it would be difficult. What might be better (depending on the door style) would be to set up a simple "bar-code" (look into "Gray Code") along the edge of the door (if on a track) that could be read by a few photo-detectors. You could probably position the door within a few centimeters of precision with such a system (not sure what your needs are, but that seems reasonable to me).
If your door is the "tilting slab/hinged" type, you could connect the potentiometer to one of the moving guide bars on the hinging system via a linkage; since the door moves in a fraction of a circle, a standard pot could be easily used.
Another way to measure the position would be to connect a tape measure tape to the end of the door; as it moves up and down, the tape would move in and out (the torsion spring in the measure would retract it). Add a means to sense the movement of the tape (bar code, contact roller/gear mechanism, etc). Something similar could be done also via a retractable clothes line mechanism.