UK research at BLEU in the late 70’s supported the theory of not using landing lights during Cat 3 landings. Some test with lights set downwards suggested some improvement but the best results for pilot vision / awareness was achieved by adjusting the approach and runway light intensity.
In general, whilst high approach and runway light intensities could give the earliest point of contact, the very high levels of glare made height and position more difficult to assess, particularly if a manual landing was authorised in the event of autopilot failure. Thus whilst a medium approach light setting often gave the best results, the overriding factor was the variability of the fog conditions – layers, thickness / density, etc, thus the policy was to leave the lights set to high intensity. This policy followed the CAA desire to focus on auto land for Cat 3 and the reduction of manual (head down) Cat 2 approaches. (Not allowed now?)
Adjusting the runway light intensity did give beneficial results. The edge lights could be at higher intensities, but the touchdown and centreline lights should be set to low intensity. These settings gave the best results at night. In daytime fog, the light intensity made little difference, except for the first point of contact, which improved at high intensities, but this was mainly true for coloured approach lights. Some tests used reduced lighting patterns; this data has been in the minimum approach light requirements. At least one daytime landing, auto approach – manual touchdown, was completed without any approach or runway lights at all - from a 50 ft DH.
Use of landing lights? The options to turn them off was given to the operators, but most were reluctant to switch them off just in case they missed the approach and suffer commercial consequences, but actually landing lights-off operations make the crew’s judgment task much easier. I suspect that this is even truer with the higher intensity lights used today. Approach strobes are good for Cat 1 + visibilities but are disturbing in low vis; aircraft strobes should be off in fog.