## 2 Experimental Setup  
The experimental setup for both systems, iterative phase retrieval and digital holography, was configured on a breadboard in order to enable transportation to our medical partners in Tubingen to investigate human samples on site. The setup is shown in Figure 1. Light is launched from a HeNe Laser (Spectra-Physics, Irvine, CA, USA) (632.83 nm) into a single mode fibre coupler. One end of the fibre coupler is used as a point source. The wavelength and the distance to the object define the illumination function impinging upon the object. An aperture is positioned in close proximity to the object in order to restrict the field of view to ensure that the frequencies in the detector plane are below the Nyquist limit. The object-diffracted light and the reference wave are combined via a beam splitter cube of 20 mm length (Thorlabs BS016, 50:50 Non-Polarizing Beamsplitter Cube, 400-700 nm, Thorlabs, Newton, NJ, USA) and directed at slightly different angles to the sensor, at which an off-axis digital hologram is recorded. The distance between the illumination point source and the object is 85 mm. The sensor employed is Ximea Modell MQ013 RG-E2 (1280 \(\times\) 1024, 5.3 um pixel size). For the iterative phase retrieval system, the reference fibre is removed from the setup and the motorized actuator (Physik Instrumente M125.11, Physik Instrumente, Karlsruhe, Germany) holding the point source is axially displaced to different predefined positions to ensure the recording of speckle decorrelated diffraction patterns, as pointed out in Reference [9]. For the sake of a fair comparison, the beam splitter cube was not removed between the two different experiments, which resulted in the same effect on the object beam and its wavefront. Due to the smaller refraction angle in the glass (NBK7), the divergent wavefronts leaving the beam splitter have a stronger curvature compared to an equivalent passage of light through air. Therefore, the interference pattern appears to have been recorded from a shorter recording distance than the geometrical path length. Considering the refractive index of glass, the interferometrically recorded path length can be calculated, which we from now on refer to as virtual path length:  
\[l_{vir}=l_{geo}/n \tag{1}\]  
The actuator and the sensor are controlled using the in-house developed software ITOM [10], which enables an automated procedure. At first, the resolution was investigated employing a United States Air Force resolution test target. The sensor was positioned at a virtual path length distance of 93 mm with respect to the object, and the point source at distances ranging from 73 mm to 85 mm with respect to the object. In accordance with the Nyquist criterion:  
\[X=\frac{\lambda d_{rec}}{2\Delta xt} \tag{2}\]  
The object size \(X\) was restricted to 5.5 mm, with \(d_{rec}\) being the object to camera distance, and \(\Delta x^{\prime}\) the sensor's pixel size. The minimum displacement \(d_{sp\_axial}\) applied to the actuator in order to obtain speckle decorrelation was:  
\[d_{sp\_axial}=\frac{4\lambda{d_{ill}}^{2}}{X^{2}} \tag{3}\]  
which was equal to 0.6 mm, with \(\lambda\) being the wavelength (632.83 nm), \(d_{ill}\) the longest illumination distance (85 mm) and \(X\) being the object size. Speckle represented high-frequency information, which hence decorrelated quicker than low-frequency components. In order to likewise obtain sufficient decorrelation of low-frequency components, the available displacement of the actuator was employed, with the recording of 10 diffraction patterns separated by 1.33 mm.