Background correction

Two different things are called “background” in μSR, and they must not be confused. The first is the uncorrelated, time-independent count rate in the raw histograms — particles unrelated to a muon decaying in the sample (for example decay positrons from muons stopped upstream) that survive the coincidence logic. This page is about removing that rate from the counts before the asymmetry is formed. The second is the background asymmetry from muons that genuinely stop in the sample holder or cryostat — a real muon signal, handled in the fit model (and calibrated with silver/hematite reference measurements), not by the corrections here.

Subtracting a count-rate background matters because the asymmetry is a ratio: a flat rate \(\eta\) added to both groups pulls \(A(t)\) toward zero by a factor that grows as \(e^{t/\tau_\mu}\) relative to the muon signal. At a continuous source (PSI, TRIUMF) the uncorrelated rate is significant and limits useful data to roughly 8 μs; at a pulsed source (ISIS) the beam duty factor of about \(1.6\times10^{-3}\) suppresses it to nearly nothing — but “nearly nothing” can still matter when fitting weak relaxation out to 20–32 μs, which is exactly the regime pulsed sources exist for.

The grouping dialog’s Background selector chooses the mode per dataset; modes that cannot apply to the data type are greyed out. The correction is applied to the grouped forward/backward counts before the asymmetry ratio, with the subtraction’s uncertainty propagated into the per-bin errors.

Choosing a mode

Data in hand	Mode
Continuous-source data	Range average — the pre-t0 bins measure the uncorrelated rate directly
Pulsed-source data	Tail fit — no pre-t0 region exists; estimate from the late-time spectrum
Dedicated reference run	Background run — sample-holder / silver / laser-off measurement
Known constants	Fixed values (from a stored grouping)

Range average (pre-t0)

The mean count over a window of bins before time zero, subtracted per group — the musrfit convention, with its default window from \(0.1\,t_0\) to \(0.6\,t_0\) and beam-period-aware trimming at PSI and TRIUMF. Only continuous-source data have a pre-t0 region: muons arrive continuously, so the histogram records the uncorrelated rate before each muon’s own clock starts. Pulsed files begin at the muon pulse, so this mode is unavailable for them.

When to use this. The default for PSI/TRIUMF data. It is a direct measurement, not a fit — prefer it over the tail fit whenever a pre-t0 region exists.

Tail fit (late-time)

Fits the late half of the good-data window with the muon decay plus a flat rate,

\[C(t) = \left[ p_1\, e^{-t/\tau_\mu}\, \frac{\sinh(w/2\tau_\mu)}{w/2\tau_\mu} + p_2 \right] w,\]

where \(w\) is the bin width (the bracketed factor averages the exponential across each bin), and subtracts the flat rate \(p_2\). The fit maximises the Poisson likelihood, which remains correct in the late-time bins that hold only a handful of counts — the regime where least-squares weighting fails. The fitted rate is reported with its uncertainty, e.g. 0.23(11) counts/μs, and flagged when it is consistent with zero.

When to use this. Pulsed-source (ISIS) data analysed to long times. The expected result at ISIS is a rate consistent with zero — the duty factor suppresses the background below measurability in most runs — so treat a significantly non-zero rate as a diagnostic worth understanding (light leak, detector noise, upstream stops) rather than as routine. Two caveats: the asymmetry must have relaxed away by the fit window (a persistent oscillation or slow relaxation biases \(p_2\)), and the window needs enough bins to constrain two parameters; both produce explicit failure messages rather than silent numbers.

This is WiMDA’s auto BG mode (and equivalent to Mantid’s “Auto” flat + exp-decay correction). WiMDA weights bins by \(\sqrt{N}\) and deletes bins holding ≤ 4 counts, which removes essentially the whole tail at fine binning; the Poisson-likelihood fit needs no such surgery (study record: divergence D4).

Background run

Subtracts a designated reference run — an empty sample holder, a silver plate, or the laser-off partner of a photo-excitation measurement — from the data, scaled by the ratio of good frames:

\[N_{\text{corr}}(t) = N(t) - \frac{F_{\text{sample}}}{F_{\text{ref}}}\, N_{\text{ref}}(t), \qquad \sigma^2 = N + \left(\frac{F_{\text{sample}}}{F_{\text{ref}}}\right)^2 N_{\text{ref}}.\]

Good frames measure beam exposure, so the ratio puts both runs on the same exposure footing. The reference is chosen from the loaded datasets (or browsed from disk), recorded with the grouping, and re-resolved when the project is reopened. Both runs receive identical deadtime treatment before the subtraction, and each run’s own time zero is used for alignment.

When to use this. Separating holder/mount signal when its shape (not just a flat rate) must be removed — the reference subtraction removes the full time-dependent spectrum of the unwanted component, which neither constant mode can do. The cost is doubled statistical noise where the reference dominates: the errors grow by the second term above. For period-mode data (light on/off within one run), prefer period mapping — periods share the exposure exactly, with no scaling assumption.

WiMDA’s File BG subtracts the raw reference counts from deadtime-corrected sample counts and leaves the error bars untouched; both are corrected here (study record: divergences D6, D7).

References

• S. J. Blundell, R. De Renzi, T. Lancaster, and F. L. Pratt, Muon Spectroscopy: An Introduction (Oxford University Press, Oxford, 2022).

• 1. Suter and B. M. Wojek, Phys. Procedia 30, 69 (2012).

• 6. 12. Pratt, Physica B 289–290, 710 (2000).