electromagnetic radiation - Double slit experiment- light intensity

The standard explanation for the interference pattern is one of constructive and destructive interference between the light waves from the two slits. But, am I right in thinking that light intensity is due to the number of photons in the wave at any position? i.e. in the light bands, there are the maximum number of photons hitting the screen and in the dark bands there are zero photons impacting the screen? In which case, although you can have constructive interference between light rays, you can never have destructive interference, since photons in one beam cannot be reduced to zero just because there are none in the other beam. If this is right, then I must deduce the dark bands are in fact the two wave troughs aligning and not a peak aligning with a trough. I would appreciate confirmation or otherwise please.