[Laser] -FL lens

[Tom Becker]

For a TOF laser ranging experiment receiver, I've mounted a 12"-diameter 
16" FL Fresnel on the end of an appropriate tube.  I'll use two such 
assemblies, one to transmit, one to receive.  I'd like to fully 
illuminate the transmit Fresnel with a laser diode module to expand and  
yield a ~12-inch diameter collimated beam.

I think I have two ways to do that:
 - disburse the collimated laser output to a ~40-degree elliptical cone 
with a negative lens, or
 - remove the laser module lens and reduce the radiated ~120 degree 
elliptical cone to ~40 degrees.

I have a pile of positive lenses but not a single negative lens, so I 
need to determine the -FL of an appropriate lens for the first method.  
Can someone point me to some math to calculate what lens is appropriate?

Thanks.

Tom Becker
Cape Coral