Microstepping, Gearing, and Torque

[SquidPhysics]

So for my current project, I need to hold a crystal on a platform that needs to turn on the scale of microradians. I'm accomplishing this with a 1.8 degree/full step stepper motor that I'll be microstepping by 1/256 full step. To get to microradians, I'll need an additional division of steps that I'll be achieving with a gearbox. I'm fairly certain that to get 1 microradian steps, the gear ratio needs to be 125:1. The holding torque of the motor I'm considering is 7.5 oz-in with a detent torque of 0.5 oz-in. The platform and crystal weights should be less than 7.5 oz and will be further designed later. The experiment is kept at about 6E-6 torr in a vacuum chamber. To clarify, the motor only needs to make very small, very accurate movements and won't be used for full rotations. I've done more research into this than I can stand for a day so the questions I'm left with are:
1) how much driving torque am I losing to the microstepping process and the gearing?
2) Is the torque I'm left with enough to overcome the detent?
3) How do I calculate these things myself? I've not found much helpful info regarding this question.
4) Is there a better way to go about achieving these very small steps? The gear ratio is a bit troubling.

 

[Nidum]

The proposed system will not give you anywhere near the accuracy required .

There is a large amount of information about how high precision motion systems are designed available on the internet .

High resolution turntable stages are commercially available .

Do some research and please come back if you have specific questions .

 

[CWatters]

Just for info... Gearing down reduces rpm but multiplies the available torque. So a high ratio reduction gearbox can magnify the torque of a motor enormously. But see Nidum's reply.