[bojan]

No way.
This is good for collecting light (heat), for sun furnace for example, or energy generators (because cylindrically shaped reflective sheet is cheaper than rotational paraboloid), but not for imaging of any significant field - too many distortions to deal with (astigmatism, to start with, then coma...).
Could be also useful for spectroscopy, where you do not need the image of an object... but not for imaging.

For imaging, you have to have the wave front dot disturbed (meaning, all distances from focus towards the entry aperture must be the same expressed in wavelenghts, down to 1/10 at least.
This can't be done with cylindrical system of mirrors in all orientations relative to optical axis.