Ultimate backlash free reduction

What is the best way of acheiving approximately 5:1 gear ratio with
as little backlash as humanly possible?

The application is the increase of optical rotary encoder resolution
so there are no large forces involved. You can also assume the
encoder has ball bearings or is at least coupled to a shaft with
them. The encoders are already 2500CPR/10000PPR so we are talking a
requirement of 0.007 degrees of backlash.

If this is going to cost the earth then knowing the best possible
method without it costing the earth would be a help.

Thanks

Graham