Algorithm 1.

3D coherent imaging reconstruction

Require: $I_{c,\mathcal{l}z}$, ${\mathbf{r}}_{\mathcal{l}}$, $\mathcal{l}=1,\dots ,N_{\text{img}}$
1:	initialize $t_1^{\left(1,0\right)},\cdots ,t_M^{\left(1,0\right)}$, $p_c^{\left(1,0\right)}$, ${\tilde{h}}_c^{\left(1,0\right)}$; normalize $I_{c,\mathcal{l}z}$
2:	for $k=1:K_c$ do
3:	Sequential gradient descent
4:	for $j=1:(N_{\text{img}}\cdot N_z)$ do
5:	$z=z_{\text{mod}(j,2)}$; $\mathcal{l}=\text{mod}(j,N_{\text{img}})$
6:	if $j<N_{\text{img}}\cdot N_z$ then
7:	for $m=1:M$ do
8:	$t_m^{(k,j)}=t_m^{\left(k,j-1\right)}-{\nabla }_{t_m}{e}_{c,\mathcal{l}z}(t_1^{(k,j-1)},\cdots ,t_M^{\left(k,j-1\right)},p_c^{\left(k,j-1\right)},{\tilde{h}}_c^{\left(k,j-1\right)})/4\max {\left(\left|p_c^{\left(k,j-1\right)}\right|\right)}^2$
9:	end for
10:	$p_c^{\left(k,j\right)}=p_c^{\left(k,j-1\right)}\left(\mathbf{r}\right)-{\nabla }_{p_c}{e}_{c,\mathcal{l}z}(t_1^{\left(k,j-1\right)},\cdots ,t_M^{\left(k,j-1\right)},$
	$p_c^{\left(k,j-1\right)},{\tilde{h}}_c^{\left(k,j-1\right)})/\max {\left(|t_1^{\left(k,j-1\right)}|,\cdots ,|t_M^{\left(k,j-1\right)}|\right)}^2$
11:	$\xi =\mathcal{F}\{G_{\mathcal{l}}^{\left(k,j-1\right)}\}$
12:	${\tilde{h}}_c^{\left(k,j\right)}={\tilde{h}}_c^{\left(k,j-1\right)}-{\nabla }_{{\tilde{h}}_c}{e}_{c,\mathcal{l}z}(t_1^{\left(k,j-1\right)},\cdots ,t_M^{\left(k,j-1\right)},p_c^{\left(k,j-1\right)},{\tilde{h}}_c^{\left(k,j-1\right)})\cdot |\xi |/\left[\max (|\xi |\right)\cdot ({|\xi |}^2+\delta )]$, where δ is chosen to be small
13:	else
14:	Do the same update but save to $t_1^{\left(k+1,0\right)},\cdots ,t_M^{\left(k+1,0\right)},p_c^{\left(k+1,0\right)},{\tilde{h}}_c^{\left(k+1,0\right)}$
15:	end if
16:	end for
17:	Filter $t_1^{\left(k+1,0\right)},\cdots ,t_M^{\left(k+1,0\right)}$ with Gaussian filter to damp down high-frequency artifacts
18:	end for