From Syntax:

$count

This is a new accumulator which returns the number of documents in the current window/partition. In $group, it is identical to {newField: {$sum: 1}} but will only be exposed as a window function. It is an error to specify an input expression to $count, but a non-default window may be specified.

{newField: {$count: {}, window: ...}}

From Technical Design Document: 

A $count window function will be desugared to a $sum with an input expression of the constant '1'. The window definition will remain the same.