## 2 Methods  
### Interferometric Synthetic Aperture Microscopy (ISAM)  
A schematic diagram illustrating the interaction between incident light beam and tissue is shown in Figure 1a [18]. The Gaussian beam \(E_{i}(\overrightarrow{r_{0}},k)\) generated from a focused lens is incident on the green plane \(z=z_{0}\) shown in Figure 1a. The incident field entering the tissue interacts with the scatterer at the position of \((\overrightarrow{r},z^{\prime})\) to produce a scattered field, and this scattered field can be expressed as \(E_{i}(\overrightarrow{r^{\prime}}-\overrightarrow{r_{0}},k)\eta( \overrightarrow{r^{\prime}})\) on the basis of the first-order Born approximation, where \(\eta(\overrightarrow{r^{\prime}})\) is scattering potential function of sample. The secondary source can now be propagated through space using the Green's function \(G(\overrightarrow{r},\overrightarrow{r},k)\) based on [PERSON] theory. The scattered field is then collected by a detection lens at the position of \((\overrightarrow{r},z)\), and the focused detection field is defined as \(E_{b}(\overrightarrow{r}-\overrightarrow{r_{0}},k)\). Consequently, the signal collected by the detection lens is given by [17]  
\[S(\overrightarrow{r}_{0},k)=A(k)\oint\limits_{\Sigma}d^{2}r\int\limits_{V}d^{ 3}r^{\prime}G(\overrightarrow{r}^{\prime},\overrightarrow{r},k)E_{i}( \overrightarrow{r}^{\prime}-\overrightarrow{r}_{0},k)\eta(\overrightarrow{r} ^{\prime})E_{b}(\overrightarrow{r}-\overrightarrow{r}_{0},k), \tag{1}\]  
where \(A(k)\) is the power spectrum function of the light source. If the detection lens is chosen to be the same as the illumination lens, the \(E_{i}\) and \(E_{b}\) are the same pattern of Gaussian function. After applying a fast Fourier transform (_FFT_) over the lateral direction and making some modifications, Equation (1) can be transformed into [18]  
\[\overrightarrow{S}(\overrightarrow{Q_{//}},k)=A(k)H(\overrightarrow{Q_{//}},k)\overrightarrow{\eta}(\overrightarrow{Q_{//}},-2k_{z}(\overrightarrow{Q_ {//}}/2)), \tag{2}\]  
in which \(k_{z}(\overrightarrow{Q_{//}}/2)=\sqrt{k^{2}-(\overrightarrow{Q_{//}}/2)^{2}}\). Equation (2) relates the spectral data at the lateral spatial frequency \(\overrightarrow{Q_{//}}\) and wavenumber \(k\) to the 3D _FFT_ of \(\eta(\overrightarrow{r})\) of tissue. In traditional SD-OCT, the detected scattered signal at each lateral position is considered to be independent and one-dimensional, which can be expressed as  
\[S(\overrightarrow{r}_{0},k)=A(k)C\int\eta(\overrightarrow{r}_{0},z)\exp(i2 kz )dz, \tag{3}\]  
where \(C\) is a parameter related to the system. Taking the 2D _FFT_ of \(S(\overrightarrow{r}_{0},k)\) with respect to the lateral components of \(\overrightarrow{r}_{0}\), Equation (3) now becomes  
\[\overrightarrow{S}(\overrightarrow{Q_{//}},k)=A(k)\widetilde{\eta}( \overrightarrow{Q_{//}},-2k). \tag{4}\]  
Comparing Equation (2) and Equation (4), it can be easily found that the point \((\overrightarrow{Q_{//}},k)\) in the collected spectral data is assumed to correspond to the point \((\overrightarrow{Q_{//}},-2k)\) in the 3D Fourier representation  
Figure 1: **(a)** The three-dimensional (3D) schematic diagram illustrating the interaction between the incident field and sample. The coordinates \((\overrightarrow{r}_{0},z_{0})\), \((\overrightarrow{r}^{\prime},z^{\prime})\), and \((\overrightarrow{r},z)\) represent the incident position of the beam, the position of the scattered particle, and the position at which the scattered field is detected, respectively. The green dot in **(a)** represents a scattering particle. (**b,c**) Simulation results of Spectral domain optical coherence tomography (SD-OCT) and interferometric synthetic aperture microscopy (ISAM) applied to a scattering particle sample, respectively. of the object. This assumption in SD-OCT causes the spot to diffuse heavily as the distance from the focus increases.