Preparing a suitable nanoparticle position file with ImageJ/FIJI is straightfoward. I won't detail how to use Find Foci plugin here as the the creators put together a detailed user manual of their own. If you do opt for the plugin, you'll still want to output the position file via "Measure" (see below) rather than Find Foci's more expansive native output (which contains a lot of data not needed for this analysis).
Find Foci can be used to automatically find particle centers (with a load of parameters to tweak) -- though you may still need to manually add or remove some of what it finds -- or you can just manually identify them using ImageJ's multi-select tool (the multi-select is the same button as select, just right-click it to choose which one is active):
For ImageJ, once each nanoparticle has been indicated, go "Analyze" > "Set Measurements" and uncheck everything.
Then go "Analyze" > "Measure" (or press ctrl+M). Save the table that appears.
If your image has calibrated pixels (i.e., if it is showing distances in non-pixel units -- see the ovals below), then before you "Measure", go to "Analyze" > "Set Scale" and select "Remove Scale".
That's it!