In a turbid medium, the distance (step size) that a photon travels before it hits a scatterer is determined by $\mu s\u2032$. Since the scatterers are randomly distributed, it is impossible to predict the exact step size for each photon collision. However, the probability of a given photon step size is deterministic in simple cases and the function that describes such probability over different photon step sizes is known as probability density function (PDF). In the case of a turbid medium with uniformly distributed microbubbles having the same size, the corresponding $\mu s,b\u2032$ is also uniformly distributed before the ultrasound is switched on and the PDF has a negative exponential distribution^{10} as shown in Fig. 1(a). When the ultrasound is switched on, microbubbles vary in size spatially and temporally, causing $\mu s,b\u2032$ to vary as well. Figure 1(b) depicts the scenario when an ultrasound plane wave propagates vertically downwards in the $z$-direction. The variation of $\mu s,b\u2032$ over three acoustic wavelengths in the $z$-direction is also shown here. In this scenario, the PDF has a more complicated shape. The “humps” in the PDF correspond to the photon traveling a distance of several wavelengths, experiencing varying $\mu s,b\u2032$ along the way. The PDF shown in Fig. 1(b) was obtained by launching photons in the $z$-direction, calculating the first step sizes using Eq. (6) and the methodology introduced in the last paragraph, and binning the step sizes to form a histogram. In the subsequent steps, when the photons are within the medium, the direction of travel may not be along the $z$-direction. As a result, the corresponding PDF will look different from the one shown in Fig. 1(b). Also, the microbubble sizes and therefore $\mu s,b\u2032$ vary over time, again resulting in different PDFs. Therefore, the PDF of the photon step size in a turbid medium with insonified microbubbles is temporally and spatially varying.