## 1 Introduction  
Femtosecond laser pulse generation has progressed rapidly since the advent of the Ti/sapphire femtosecond laser. The laser wavelength now extends from short, i.e., deep ultraviolet or X-ray, to long, i.e., the middle-infrared or terahertz range [1; 2; 3; 4; 5; 6; 7], the pulse duration has been compressed to subcycle femtoseconds [8; 9], and the peak power can reach petawatt (PW) level [10; 11; 12; 13; 14; 15; 16]. These kinds of femtosecond laser pulses are widely used in research in physics, materials science, chemistry, biology, and bioengineering. For example, laser plasma physics [17; 18], ultrafast reaction dynamics in chemistry, biomacromolecules [19; 20], solid-state [21; 22; 23; 24], and two-photon laser microscopy [25; 26; 27] require femtosecond pulses as a laser excitation source. Pulse duration or the complete temporal profile of a femtosecond pulse is a very important parameter in applications of the above-mentioned fields, because it is indicative of not only the speed but also the peak power of the pulse. Thus, methods to characterize the temporal profile of femtosecond pulses improved with the development of femtosecond laser technology [28]. A fast, accurate, and easy-to-setup method for characterizingfemtosecond pulses is always important for improving the efficiency of research in which femtosecond laser pulses are used. The most widely used techniques for characterizing the temporal profile of femtosecond pulses are frequency-resolved optical gating (FROG) [29] and spectral phase interferometry for direct electric field reconstruction (SPIDER) [30]. With FROG, introduced in 1993, data acquisition usually takes a relatively long time and a blind iterative reconstruction algorithm is used to calculate the spectral phase and the temporal profile. SPIDER, introduced in 1998, entails a relatively complicated optical setup, because it needs a dispersive chirped pulse and uses sum-frequency generation to achieve spectral shear. Since their introduction, a significant effort was focused on improving the reliability, accuracy, simplicity, and temporal resolution of both methods [28; 31]. Commercial products based on these two methods have been developed. Other methods, such as two-dimensional spectral shearing interferometry (2 DSI) [32], multiphoton intrapulse interference phase scan (MIIPS) [33], and d-scan [34], with their own advantages in characterizing femtosecond pulses, were developed over the past few decades. The self-referenced spectral interferometry (SRSI) technique, introduced in 2010 [35], has several advantages over the FROG and SPIDER methods. As an extension of the spectral interferometry (SI) technique [36], SRSI is an analytical, sensitive, accurate, and fast technique with a dramatically simplified setup and reconstruction algorithm for obtaining the temporal profile of a femtosecond pulse [37]. Initially, the development of the SRSI method was based on the cross-polarized wave generation (XPW) process [38]. Subsequently, its performance has been greatly improved. Because of its heterodyne nature, with the spectrum of the self-generated reference pulse broader than that of the input pulse, the SRSI method can be used to characterize pulses accurately, even when the input pulse intensity is lower than the noise level of the spectrometer. SRSI can be used to characterize a dynamic range up to 50 dB with a \(\pm\)400 fs time window, even when using a common 25 dB signal-to-noise-ratio (SNR) spectrometer [39]. The pulse duration limitation caused by the dispersion of the optical elements in SRSI has been studied in detail [40]. With a low-dispersion optical setup, pulses as short as 4 fs have been measured successfully [41]. SRSI possesses a wide wavelength range of validity measurements when suitable spectrometers are used 2.5-cycle pulses with spectra covering 1.3-2 \(\upmu\)m and a sub-10 fs pulse at 400 nm have been measured successfully using SRSI [42; 43].