= Instrument response function
An <instrument response function> describes how a <scientific instrument> spreads or weights a specified ideal input. For a linear, time-invariant measurement system its temporal form $h(t)$ is the output produced by a unit impulse. An input signal $s(t)$ then gives
$$
y(t)=\int_{-\infty}^{\infty}h(t-u)s(u)\,du+b(t),
$$
where $b(t)$ is a background contribution. This <convolution> model requires linearity and time invariance; detector saturation or changing instrument settings can invalidate it. A spectral instrument similarly spreads a narrow input line across recorded <wavelengths>.
In <time-correlated single-photon counting>, a short <laser> pulse does not produce an infinitely narrow recorded event distribution. The pulse duration, <photodetector> timing and recording electronics all contribute to the measured <instrument response function>. Prompt scattered excitation can characterize the combined response under suitable measurement conditions. Extracting a <fluorescence lifetime> then often means fitting a decay after convolving it with the measured response, rather than treating the recorded histogram as the unblurred decay.<What is the IRF and how to measure it in fluorescence spectroscopy? by PicoQuant>[What is the IRF?; reconvolution and IRF measurement sections]{ref}
An elementary example makes the distinction visible. If $h$ is a normalized Gaussian with standard deviation $\sigma$ and the normalized physical decay is $s(t)=\tau^{-1}e^{-t/\tau}$ for $t\ge0$, the convolved distribution has variance $\sigma^2+\tau^2$. Its width therefore combines instrumental broadening with the sample lifetime. A measured broad peak need not imply a slow physical process. Measuring the response, background and their uncertainties is part of learning the physical signal, not an optional cosmetic correction.
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