## 2 Experimental Setup
For the reconstruction, the combined distance \(d_{comb}\) of the illumination and recording scheme was used in the implementation of the direct Fresnel propagation:  
\[d_{comb}=\frac{d_{ill}d_{rec}}{d_{ill}+d_{rec}} \tag{4}\]The application of illumination sources with different curvature acts like a magnification to the recorded diffraction pattern, and in that manner, resulting in a changed pixel size \(\overline{\Delta x}^{\prime}\) that will have to be applied in the reconstruction instead of the sensor's pixel size \(\Delta x^{\prime}\):  
\[\overline{\Delta x^{\prime}}=\frac{d_{ill}\Delta x\prime}{d_{ill}+d_{rec}} \tag{5}\]  
The relationship between the illumination distance and the resulting projected pixel size \(\overline{\Delta x}\) has graphically been represented in Figure 2. However, the pixel size in the reconstruction plane when employing the direct Fresnel method is the same for all illumination distances as pointed out in Reference [9]. \[\Delta x^{\prime\prime}=\frac{\lambda d_{rec}}{N\Delta x\prime} \tag{6}\]  
Figure 1: Opto-mechanical setup used for the comparison of the digital holography and iterative phase retrieval via curved illumination: (**a**) schematic setup, and (**b**) experimentally implemented setup. The iterative approach was implemented in the conventional manner, replacing the recovered amplitude with the square root of the recorded intensity pattern at each plane while preserving the phase. In addition, [PERSON]'s theorem was implemented to ensure the correct contribution of each diffraction pattern to the recovered complex wave. The off-axis holograms were first Fourier filtered for the extraction of the image term only [11]. Afterwards, the numerical reconstruction was performed using the direct Fresnel method [11]. The reconstruction distance \(d_{recon}\) that had to be employed, represents a function of the combined distance \(d_{comb}\) and the reference source point distance \(d_{ref}\) (with the virtual path length \(d_{ref}=103\) mm to the source of the reference wave):  
\[d_{recon}=\frac{d_{comb}\cdot d_{ref}}{\left|d_{comb}-d_{ref}\right|} \tag{7}\]  
Furthermore, the magnification adjusted pixel-size \(\overline{\Delta x}\), see Equation (5), was used in the reconstruction process. A recorded diffraction pattern and a recorded digital hologram are shown in Figure 3a,b, including a zoomed-in region at the bottom-right corner. The zoomed-in region highlights the effect of self-interference as encountered in the diffraction pattern and the interference with a separate reference wave, which arise at the off-axis hologram leading to the characteristic carrier frequency. The corresponding amplitude reconstructions are shown in Figure 3c,d. The averaged cross-section plots of the test target element that can still be resolved are shown at the bottom corner. The abscissa represents the pixel position and the ordinate represents the normalized averaged amplitude value. The resolution obtained has been evaluated with respect to [PERSON]'s resolution criterion. Care was taken to ensure that the ratio between the smallest maximum and largest minimum of the investigated averaged test target element was always smaller than 0.81. For the phase retrieval approach group 5's 5 th and 6 th element could be resolved for vertical and horizontal orientation, respectively, which corresponded to the recovery of structural details of 9.84 \(\upmu\)m and 8.77 \(\upmu\)m in width. Test target element 6 in group 5 could be resolved for both horizontal and vertical orientation when employing digital holography, which corresponded to resolving structural details of 8.77 \(\upmu\)m in width. In conclusion, the iterative approach and the phase retrieval method performed similarly well. \[l_{vir}=l_{geo}/n \tag{1}\]0 Change of projected pixel size \(\overline{\Delta x}\) with respect to the object–illumination source distance. Besides the possibility to enable lensless imaging, the most prominent advantage of quantitative phase imaging is its high sensitivity to changes in the phase.