Obtaining a measurement very indirectly While answering a question I came to reflect on the fact that in science experimental setups measure things indirectly.
Example: the setup of the Pound-Rebka experiment.
The amount of absorption was assessed by obtaining a measure of the flux of gamma rays that were not absorbed. The gamma rays were registered using a scintillation counter.
As an historical contrast:
When Rutherford set out to measure deflections of alpha particles, the setup involved direct visual observation of scintillation. In order to see the scintilations an assistent would spend something like 20 minutes in total darkness, so that his eyes would be at maximum sensitivity to light. That is how a measure of number of alpha particles hitting the scintillation screen was obtained.
Example: The Gravity probe B experiment. 
I saw the animations of the how the spheres had been moving around. They were all over the place. There were classical mechanics effect going on, on a scale that swamped the sought after signals by many orders of magnitude. To subtract those classical effects they had to be modeled to a new level of sophistication. That work delayed public announcement of the results by something like a year. Getting out the goods took a huge data-mining effort.

Experiments probe deeper and deeper, the setups become more and more elaborate. Often supporting measurements are made for the purpose of subtracting other effects signal from the sought after data. 
Out of sheer curiosity: can you think of other examples where it took even more steps, extensive data-mining, etc. to produce the goods?
 A: I'm not sure this is the exact type of answer you were looking for, but without getting into specific experiments, most experiments in many fields must be done indirectly. One of these such fields is Astrophysics, although I would say most of the things here are more of measurements than an experiment in a lab. Even so, the measurements are often made indirectly, especially with topics such as dark energy. 
Another such field would be quantum mechanics, where many behaviors were predicted mathematically much before they could be experimentally proven. This is because of the difficulty in conducting experiments about things that are on such a small scale.
This list could go on and on, but the point is, planning an experiment is all about what data can easily and accurately be obtained and what relations can be made with that data to get to a desired point. 
Also experiments must obviously conform to what is possible; with your example of the gamma rays, the gamma rays on one side of a material can be measured as well as the gamma rays on the other side of the material, but there's no real way to measure the absorption of the gamma rays into the materials. Likewise, people can't go up into space with a dark energy measurement device, or at least not at this time. But the presence of dark energy can be theoretically shown by other measurements.
To add to my answer, the Millikan oil drop experiment is one famous example of an experiment that indirectly measures something, in this case the specific charge of an electron. Without indirect measurement, it would be pretty much impossible to measure the charge of a single electron.  
