# Sensitivity of Space Telescopes and Instruments

I have been doing a bit of light reading on space telescopes and have been amazed by the reported sensitivity of some of the instruments. In particular, the Laser Interferometer Space Antenna (LISA) which is said to be able to detect a relative change in displacements of 20 picometres over a distance of 1 million km. I'm keen to understand what is the technology/underlying physics behind detectors such as this?

I understand that this is a very broad question as detectors are chasing many different things but a general overview will suffice.

If possible, specifically, what gives rise to the phenomenal resolution of LISA?

LISA (long PDF) uses interferometry. This is a method that allows very accurate measurement of the difference between two lengths.
Basically, a laser beam is split. Each half of the beam travels a different path. A small difference in path lengths causes a phase difference between the beams. Both beams are combined in a heterodyne detector, which produces an output signal proportional to the difference in either frequency or phase of the two beams (I'm not sure which is used in LISA yet).
The laser produces a frequency on the order of $10^{14} Hz$, a frequency difference of 0.1 Hz is easily measured and yields an accuracy of $10^{-15}$.

Paper that calculates the accuracy of this method. (long PDF)
Report on the underlying technology of LISA (even longer PDF)

Edit: my initial answer was incorrect.

• Are the two resulting beams perpendicular to one another in that case? May 21, 2014 at 9:43
• Not necessarily. May 21, 2014 at 10:19
• It is a long way from the naive 400 nm accuracy of an inteferometer to the 80 pm accuracy claimed. I'm sure that multiple passes are the first part of this, but it also takes very accurate measurement of the peaks. May 22, 2014 at 15:42
• @RossMillikan There is a great deal of technology in bridging that gap. Indeed, the Einstein Telescope Design Study Document summarizes this. Brute force signal to noise is one part of it: one uses powerful lasers with fantasically sophisticated noise control so that the measurement has huge dynamic range. The use of squeezed light to trade off amplitude accuracy for phase accuracy (a manifestation of the Heisenberg Uncertainty Inequality) is a small, but significant part of it. I'm pretty sure LISA is to use only one pass - in space you have, well, .... Dec 23, 2014 at 11:42
• @RossMillikan .... lots of space, so you don't need to fold the beam up as you do in LIGO and the Einstein telescope. The experimental study of relativity has been the most amazing driver of interferometry technology over the last 20 years. LISA and LIGO and the ET seek the gravitational waves foretold by GTR, but equally impressive are the modern replications of the Michelson-Morley experiment, which measure $c$ and its non-dependence on inertial frame to within better than $\Delta c/c\leq 10^{-17}$. The technologies for the MME replication and gravitational wave sensing are highly related .. Dec 23, 2014 at 11:47