Spatial resolution of silicon pixels

Question

There is a variety of silicon pixels being used in very high energy particle applications. I would like to know, if I have a detector with silicon pixels of dimensions $N \times M$, how can I calculate what is the maximum spatial resolution I can obtain in every of these directions

Answer 1

When you’re trying to measure exactly where a track went through a silicon detector plane, the resolution depends on the readout.

If you just have a one-bit digital readout, I.e. “this one was hit”, the RMS resolution is N or M over $\sqrt{12}$. That factor is due to averaging over the cell: the most you can be wrong is N/2, and it’s usually less.

With more complicated readout, you can do better. With an analog readout (read charge deposited in each element) that has a good SNR, you can do things like “hmm, mostly in 23, with nothing in 22 and a little in 24; let’s call it 23.82”. Resolutions like N or M over 8 have been achieved in large systems; over 20 in small systems.

You might be interested in this 2018 LBNL paper: “Ultimate position resolution of pixel clusters with binary readout for particle tracking” it starts with a nice intro, and then goes to some advanced work on readout of multiple (small) binary cells for very high resolution.

Sometimes, cost and logistical (heat load, readout space) leads to optimizing around more complicated readout systems that still meet resolution goals (given by what the experiment is trying to do), but don't provide the full resolution that the sensor is capable of:

Answer 2

You need two points (detectors) to determine a spatial frequency (really a sinusoid). Note that you cannot distinguish between alias that happen when the wave varies spatially faster then your detector spacing.

In a typical rectangular array, the pixel size gives you the spacing of these two points.

The fastest sinusoidal then becomes propositional to the inverse of the pixel spacing. That is to say the inverse of the pixel size.