Lens to increase angular responsivity of optical sensor

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AndreyG
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How to specify a lens to increase angular responsivity of optical sensor? Sensor I presently use has angular responsivity +/-60 degrees at 50% level and I would like to increase it to +/- 80 degrees at 50% level or more.

Which lens should I use?

Please advice on design guidance for this procedure.

PS: (Angular responsivity = Angle of acceptance =~ sensitivity of sensor to light arriving from different angles)
 
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Here's a simulator you can run that might help find what you need.

http://phet.colorado.edu/en/simulation/geometric-optics"

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