Need Help lamp distance

Is there a general rule of thumb for how far a sign face should be from the lamps for even illumination? I currently have a project involving a 3' x 10' x 9" deep wall mounted cabinet that needs a new face. The t12 fluorescent lamps are about halfway in, about 4" from the face. The sign currently has a flat face, but it is hard to tell if a new .177 polycarbonate face could be used or if the client will need a pan face (the client wants to do their own installation, the sign needs relamping, and I'm trying to avoid an hour long field survey at night).
Naturally, the client does not want to pay for a pan face. I know I can re-wire the cabinet to put the fluorescents at the back of the cabinet, or that I could remove the fluorescent lighting and install LEDs. Perhaps a flat face will be fine 4" from the lamps. Any advice, and is anyone aware of any kind of standard reference?