I found a hint in this thread http://positech.co.uk/forums/phpBB3/viewtopic.php?f=19&t=5410 that optimum range is where the weapon does 100% damage and from there to both minimum and maximum range scales down to 50% Is this correct?
And for extra credit:
Is this scaling a straight line?
Is there any other effect on accuracy or tracking?
Can the optimum range is set to match either the minimum or maximum?
Does it only work on beam and bullet modules?
Aaaaalllllllrighty then, TKK; class is now in session! 
Yes, you’re correct.
I’m unsure if I fully understand this question. Allow me to reply with a thought-experiment. Go through it step by step, and tell me if it addresses your concerns…
Weapon 1 has the following ranges–
Maximum = 500
Optimum = 475
Minimum = 25
Draw the concentric circles of these ranges on a sheet of paper, centered upon a dot in the very middle which represents the exact location of Weapon 1’s turret on your ship.
Draw a straight line from that point, heading outwards from the turret’s location and at right angles to the range circles.
You now have two sets of line segments: min-to-opt, and opt-to-max.
Min-to-opt is 450 units long.
Opt-to-max is 25 units long.
Despite their gross disparity in length, the damage degradation along each line segment will follow the same relative amount of damage growth or damage decay.
Min-to-opt will have the quality of a very slow, boring, annoyingly gradual increase in maximum possible damage as it begins at range 25 from the turret with 50% damage and eventually reaches 100% damage once it reaches its outer end at range 475 from the turret. The halfway point will be at range 250 (range 25 + 225 = range 250).
Opt-to-max will have the quality of an amazingly rapid decrease in maximum possible damage as it begins at range 475 with 100% damage and very quickly drops to 50% damage when it reaches range 500, which is barely two fighter-hull lengths from start to end! The halfway point will be around range 487 (range 475 + 12 = range 487).
In the first example, the scaling effect is very drawn-out. In the second example, the scaling effect is drastically compressed. Proportionately, both are equal.
No. Optimum range only governs the amount of damage inflicted after a successful hit has occurred. It has no effect on the weapon’s attempt to score that hit itself.
Absolutely yes. If you do something that radical, you need to be sure you fully understand how the weapon’s radical new ability will be a part of that ship’s tactical effectiveness – or lameness, as the case might be. Tweak with care.
It works with beams, bullets, kinetics and plasmas. It has no function at all with any form of missile, rocket or torpedo.
Point Defense systems, EMP Cannons and target painters have no optimum range AND no minimum range – they go from max range straight inward to range zero right in front of the turret’s barrel muzzle. 
Yes - you are spot on
Again yes - so at the half way point between optimum and Min/Max you will deal 75% damage
The only other thing that effect tracking is the Target Booster Modules.
Yes - I have used it as a nerf for some over powered weapons, I would only suggest caution
It works for anything that uses an optimum range
For example missiles do not have an optimum range so they always do max damage
::Edit::
Ah, i see that Archduke has not only beaten me to the punch, his explanation is better 
My thanks to you both for explaining this. It looks like this will be quite handy in implementing SFB style phasers (and plasma torpedoes!)
I always thought optimum range doesn’t apply to plasma…?!?
Agree with everything else.
Then you haven’t been paying attention when designing and using your fleets. But don’t take my word for it. Confirmation is as simple as opening up your game’s folders and reading the contents of any textfile for a plasma weapon. Most if not all of the parameters are in alphabetical order, so just scroll down until you see a parameter starting with letter ‘O’. For example…
[config]
unlockcost = 400
lockable = 1
animationgap = 10
armour_penetration = 52
category = "WEAPONS"
classname = "SIM_PlasmaLauncherModule"
cost = 115
crew_required = 18
damage = 30
description = "There's lots to like about plasma, but those big launchers can't hit a planet at twenty meters. These smaller ones are less wasteful."
fire_interval = 3000
frames = 4
fuel = 2000
guiname = "Cruiser Plasma Launcher"
hitpoints = 105
icon = turret
max_range = 950
min_range = 330
name = "cruiser plasma"
optimum_range = 800
powerconsumed = 8
shield_penetration = 44
size = "CRUISER"
sound = data/sounds/laserblasts_crt05_06_1.ogg
soundvolume = 1.0
speed = 12.0
spritesize = 14.0
tracking_speed = 0.6
turnspeed = 0.5
turret_sprite = "turret_plasma_v2"
turretsize = 10.0
weight = 97
slot_type = TURRET
style = STANDARD
uisortpos = 1190
It’s right there, in black and white:
[size=150]optimum_range = 800[/size]
I knew it’s written in the plasma weapons’ textfiles, but i thought it wasn’t working ingame, i [size=150]really[/size] thought it all the time!
Now I checked it ingame and you are right, optimum range affects plasma. Good to know… thanks!