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Particles count rates at given Earth location and altitude result from theconvolution of (i) the interstellar (IS) cosmic-ray fluxes outside the solarcavity, (ii) the time-dependent modulation of IS into Top-of-Atmosphere (TOA)fluxes, (iii) the rigidity cut-off (or geomagnetic transmission function) andgrammage at the counter location, (iv) the atmosphere response to incoming TOAcosmic rays (shower development), and (v) the counter response to the variousparticles/energies in the shower. Count rates from neutron monitors or muoncounters are therefore a proxy to solar activity. In this paper, we review allingredients, discuss how their uncertainties impact count rate calculations,and how they translate into variation/uncertainties on the level of solarmodulation $\varphi$ (in the simple Force-Field approximation). The mainuncertainty for neutron monitors is related to the yield function. However,many other effects have a significant impact, at the 5-10\% level on $\varphi$values. We find no clear ranking of the dominant effects, as some depend on thestation position and/or the weather and/or the season. An abacus to translateany variation of count rates (for neutron and $\mu$ detectors) to a variationof the solar modulation $\varphi$ is provided.

advances in space research

Neutron monitors and muon detectors for solar modulation studies:  Interstellar flux, yield function, and assessment of critical parameters in  count rate calculations