USAGE:

api.php?what=<search string>&where=<search field>&exact=[yes:no]

where search field is one of:

name
identifier
sub_identifier
prosopographical_reference
prosopographical_reference_id
work
edition
edition_id
passage
book
casaubon_reference
kaibel_reference

e.g.: 

http://digitalathenaeus.org/tools/OlsonIndex/api.php?what=Theopompus%20of%20Chios&where=Name&exact=yes
http://digitalathenaeus.org/tools/OlsonIndex/api.php?what=Homer&where=Name&exact=no