As a primer (if you need) here are some sites:
http://www.fourmilab.ch/cship/aberration.html
http://en.wikipedia.org/wiki/Aberration_of_light
http://www.newtonphysics.on.ca/Aberration/Aberration.html
There are two ways to measure “aberration of light”. The first involves knowing the exact position of two objects/stars in space, A and B, and from the vector BA measure the angle that a telescope on B must be inclined to view A. The second involves changing the velocity of B and measuring the change in the inclination angle needed to view A. However the second method will only measure the “aberration of light” due to the change in B’s velocity.
Aberration of light is based on the fact that a photon travels in a straight line in space-time (space-time may be curved but the photon doesn't notice). The velocity of the emitter does not matter to the photon’s direction of travel (the photon does not travel sideways). The telescope is designed to magnify/collect photons that travel parallel to the optic axis of the telescope. The velocity of the telescope with respect to the photon is all that matters.
Absolute aberration of light can only be determined by the first method or if we had a way to measure the instantaneous change in aberration angle. Since light/photons travel in straight lines and is/are independent of the source then I will propose a method for discussion to measure absolute aberration of light via instantaneous change (or close to it) of the angle of aberration.
Take a long rotating cylinder with a laser at one end and a CCD photo detector at the other end. As the cylinder rotates the path of the laser on the CCD will change and will form a circle for the output of the CCD. The orientation of the rotating axis is then changed and the diameter of the output recorded. When the circle is at a maximum diameter then the axis of rotation is at right angle to the absolute linear velocity (Vc) of the cylinder through space. When the circle is at minimum diameter then the axis of rotation is parallel to Vc. The difference between the maximum/minimum diameters, the length of the cylinder, and the speed of light can be used to determine Vc.