Accuracy - The difference between a commanded position and an actual position of a positioning stage. Accuracy is typically specified in microns that represent specified number of standard deviation "Sigma" (see definition below), per given travel, at a specified height above the stage mounting plate. For example: a +3 micron accuracy, 3 Sigma, per 500 mm travel means that if the controller commands the positioning stage to move to a location 500mm away from a known "home" position in space, then, in 99.8% of the times that this move will be made, the actual position of the stage, at 25mm above the mounting surface, will end up being between 499.997 and 500.003mm.
Repeatability - Repeatability represents the maximum deviation between actual position values, obtained in repetitive moves of a positioning stage, to a desired position. Repeatability, like accuracy, corresponds to a specified number of "Sigma", per specified travel, at a specified height above the mounting surface of the stage.
Resolution (Encoder) - The smallest increment of the position feedback signal that can be measured by a feedback device (e.g., encoder).
Standard Deviation ("sigma") - The average deviation of a Random Variable (a variable such as position error, whose outcome is of a statistical nature) from its average value ("mean"). The chart below represents a Standard Normal distribution of a random variable with zero mean and sigma of 1. The X Axis represents the random variable in units of "sigma" , and the Y Axis represents the Probability Density function of the random variable. The density function is used to calculate the probability that the random variable will occur between two values on the X Axis. More specifically, the probability of a random variable occurring between two values on the X Axis equals to the area under the Probability Density Function between these two values. The total area under the curve equals 1. Some important areas are as follows: the area between +1 sigma is 0.84, between +2 sigma it is 0.977 and between +3 sigma it is 0.998. This means, for example, that the probability of a random variable occurring between +3 Sigma is 99.8%. (see image below)