Mongo DB Collection - Count values of an attribute

I have a mongo db with companies with the following data structure:

{'Beschreibung': [],
 'Branche': ['Doctor'],
 'Homepage': 'http://www.doctorsdomain.de',
 'Mail': None,
 'Name': ['Companyname'],
 'Ort': 'Doctors City',
 'PLZ': '12345 ',
 'StrHausnummer': 'Doctors Street',
 'Telefonnummer': '1235345646',
 '_id': ObjectId('sadfsdfawdfawedfbad5f'),
 'domain': 'doctorsdomain',
 'doctors': [{'Salutation': 'Dear Madame', 'Name': 'Maximiliane Mustermann'},
                    {'Salutation': 'Dear Mister', 'Name': 'Bernd Beispiel'}],
'other information'

I don't find the query to count how many names (doctors) I have in my database.

I tried something like

collection.find({"doctors":{"$exists":1}}).count() 

but than I only get the number of the companies where doctors exists.

Need help please!

Thanks a lot!