Daniel Kripke, a professor of psychiatry at UC San Diego, has done lots of research on the effect of exposure to varying amounts of natural light. His subjects often wear meters that record the illumination level. His latest paper (2004) on the connection between outside light and sleep reports several weak correlations between amount of light exposure and sleep quality:
mesor log10[lux] [a measure of light exposure] was . . . positively correlated with sleep quality (rp = 0.17, p < 0.005), and negatively correlated with reported trouble falling asleep (rp= -0.17, p < 0.005), waking up several times a night (rp= -0.18, p < 0.001), waking up earlier than planned (rp= -0.09, p < 0.10), and trouble getting back to sleep (rp = -0.11, p < 0.025).
The introduction states:
Bright light has been recommended for treatment of various sleep disorders [13], but very few experimental trials have been reported.
“Very few” seems to mean none, given the absence of citations.
The paper ends:
In conclusion, low illumination has a small relationship to . . . sleep disturbances.