From the journal Opthamology:
According to World Health Organization criteria, the relationship between fluoroquinolone therapy and diplopia is “possible.” This causality assessment is based on the time relationship of drug administration and ADR development, the multiple positive dechallenge and rechallenge reports, and the plausible mechanism by which diplopia could occur: Possible tendinitis of the extraocular muscles.
Link here:
http://www.ophsource.org/periodicals/ophtha/article/S0161-6420%2809%2900655-1/abstract