## Appendix A  
The CDI reconstruction analysis was based on three similar algorithms, each of them refining the CDI details at a different level. All three algorithms follow the work flow diagram presented in Figure A2. Initially, the magnitude \(|F|\) is obtained from the experimental CDI picture as the square root of the signal intensity for each pixel. Additionally, a starting guess for the phase of each pixel is given, along with \(|F|\), as an input to the algorithm, thus forming the diffraction function \(G^{\prime}=|F|e^{-i\varphi}\) in inverse space at the detector plane. Then, by applying an inverse Fourier transformation, \(\mathcal{F}^{-1}\), the object density distribution function, \(g^{\prime}\), is obtained in real space at the object plane. In the next step, certain geometrical and methodological constraints, which depend on the algorithm in use, are applied, thus resulting in a new object density distribution function, \(g\), at the object plane. The latter is then subject to a Fourier transformation, \(\mathcal{F}\), resulting in a new diffraction function, \(G=|G|e^{-i\varphi}\), in inverse space at the detector plane. The retrieved phase, \(\varphi\), from this function, \(G\), is inserted into the initial diffraction function \(G^{\prime}=|F|e^{-i\varphi}\), which has the experimentally measured magnitude \(|F|\) as the input, thus initiating the next iteration step. The calculation is repeated for a predetermined iteration number of steps, which result in the final reconstructed image of the object. As a first step, a support area at the object domain, \(S(x,y)\), is defined as follows: Initially, a Gaussian filter with a unity amplitude and standard deviation \(\sigma\) is applied to \(g^{\prime}\). Then, by defining a threshold value \(\theta\), the value at the \((x,y)\) point of the support area \(S(x,y)\) is set to zero or one for the \(g^{\prime}\) filtered values below or above the threshold value of \(\theta\), respectively, i.e.,  
\[S(x,y)= \begin{cases}1&g^{\prime}(x,y)\geq\theta\\ 0&g^{\prime}(x,y)<\theta\end{cases} \quad. \tag{1}\]  
The three similar algorithms used in this study, namely the error reduction (ER), hybrid input-output (HIO), and shrink-wrap (SW), differ by the object domain constraints applied. Specifically, the object domain constraint for ER is [12]  
\[g_{k+1}(x,y)= \begin{cases}g^{\prime}_{k}(x,y)&(x,y)\in S\quad\&\quad g^{\prime }_{k}(x,y)\geq 0\\ 0&(x,y)\
otin S\quad\text{or}\quad g^{\prime}_{k}(x,y)<0\end{cases} \quad, \tag{2}\]  
while for HIO, it is [12]  
\[g_{k+1}(x,y)= \begin{cases}g^{\prime}_{k}(x,y)&(x,y)\in S\quad\&\quad g^{\prime }_{k}(x,y)\geq 0\\ g_{k}(x,y)-\beta g^{\prime}_{k}(x,y)&(x,y)\
otin S\quad\text{or}\quad g^{\prime }_{k}(x,y)<0\end{cases} \quad, \tag{3}\]  
where \(k\) is the \(k\)-th iteration. The definition of the SW algorithm is identical to HIO, except that, in SW, the support area \(S\) is updated after a certain number of iterations. This is performed by applying a Gaussian filter with smaller \(\sigma\), so that the object support \(S\) approaches the shape of the object distribution [13]. The reconstruction process initiates using the SW algorithm with a starting value of \(\sigma=7.5\), reduced to \(\sigma=0.8\) during 120,000 iterations, while changing the support \(S\) every 20 iterations. The values of \(\theta\) and \(\beta\) were empirically set to 0.15 and 0.9, respectively,in accordance with the values from the literature [26]. Finally, using the ER algorithm, 200 additional iterations were applied to obtain the final result [45]. * _[PERSON] et al. (2009)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; et al. Tabletop coherent diffractive microscopy with extreme ultraviolet light from high harmonic generation. In Proceedings of the Metrology, Inspection, and Process Control for Microlithography XXIII, SPIE, San Jose, CA, USA, 22-27 February 2009; Volume 7272, pp. 126-133. [CrossRef]
* _[PERSON] et al.