## 1 Introduction  
Ultrashort laser pulses are playing an ever-increasing role in important scientific experiments and applications. Multiphoton microscopy, made possible specifically by ultrashort pulses, has become very popular as a result of its many unique advantages over conventional microscopy techniques [1]. Novel ultrashort-pulse-based techniques that achieve spatial super-resolution, such as stimulated-emission-depletion imaging, are yielding spectacular views into the nanoscopic world never before imagined [2]. In addition, most molecular processes occur on ultrafast timescales and so their study requires ultrashort laser pulses using methods like excite-probe spectroscopy [3,4]. For all such applications, it is crucial to be able to measure ultrashort pulses in time, or at least measure their length, complexity, and pulse-to-pulse stability. Multiphoton-microscopy contrast is inversely proportional to the pulse length, and ultrafast spectroscopy and super-resolution methods require simple, short, and stable pulses. Variations in the pulse shape from shot to shot introduce uncertainty in the temporal resolution of excite-probe measurements and yield inconsistent peak power, adding noise to measurements in all techniques that use ultrashort pulses. It is therefore necessary to ensure that ultrafast lasers emit stable, consistent pulses. Unstable double-pulsing and other common types of instabilities are unacceptable in essentially all applications. Indeed, variationsin the duration, shape, and peak power of ultrashort pulses can have significant impacts on all applications of ultrashort pulses. Because there is no such thing as a \"pulse-shape stability meter\", it is necessarily the responsibility of ultrashort-pulse measurement techniques to also determine whether or not the pulse temporal profile is consistent from shot to shot. Techniques that ignore fluctuating components of the pulse shape and see only the consistent component are said to measure the \"coherent artifact\", which is typically the shortest possible temporal profile consistent with the spectrum of the pulse [5; 6]. It is shorter than and often much shorter than the actual average pulse length, and wishful thinking (desiring the shortest pulse length) has frequently resulted in its misinterpretation as the actual pulse length. A measurement technique that yields only the coherent artifact yields results that are, at worst, wrong and, at best, unconvincing. Recently, a few papers have addressed the unfortunate consequences of averaging over a train of pulses with fluctuating pulse shapes in attempts to measure them using modern ultrashort-pulse measurements [7; 8; 9; 10]. Also, shockingly, modern techniques based on interferometry were found to measure only the coherent artifact. This happens because fluctuations in the pulse shape yield fringes that cancel out and so are not measured, leaving only the shorter, coherent component in the resulting measurement. As a result, these techniques are at risk of significantly under-estimating the pulse length and pulse complexity. Our recent publications used simulations to understand how the many ultrashort pulse-measurement techniques behave in the presence of pulse-shape instability. Figure 1 shows an example of these results, comparing frequency-resolved optical gating [11] (FROG) measurements and spectral interferometry for direct electric field reconstruction [12] (SPIDER) measurements of stable and unstable pulse trains. These studies focused on noise bursts, that is, pulses approximating incomplete mode-locking. Figure 1: Simulated measurements of stable and unstable pulse trains (**left**) using spectral interferometry for direct electric field reconstruction (SPIDER) (**middle**) and second-harmonic-generation (SHG) (frequency-resolved optical gating (FROG) (**right**). Reprinted with permission from [8], WILEY-VCH Verlag GmbH & Co., 2013. Of course, lasers can exhibit instability in many other ways. Another simple, very common, and important type of instability is multiple pulsing.