## 3 Application to Medical Imaging  
After demonstrating the functionality of the iterative phase retrieval technique on a USAF test target, it was then applied for biomedical applications with the motivation to assist the discrimination between cancerous and normal tissue for histopathology, which currently necessitates the time-consuming staining process (roughly 15 min) in order to visualize cell structures, by which the discrimination is made possible. An intraoperative measurement technique based on quantitative phase imaging, which is sensitive to the slightest change in the propagation of the light due to refractive index changes, will reduce the time to a few seconds, which consequently results in decreasing costs and less stress/harm on the patient and the surgeon. Three thin paraffine tissue sections of 5-7 um thickness from cancerous and healthy renal tissue of oncologic surgeries have been investigated. Two different wavelengths have been employed to  
Figure 4: Phase reconstructions for a specifically engineered phase USAF test target with a phase step of \(\uppi/4\) at 633 nm for the target elements: (**a**) iterative phase retrieval and (**b**) digital holography. investigate those samples: 633 nm and 1064 nm (Nd:YAG) (see Figure 5). To track the convergence of the iterative algorithm, an error measure, represented by the root mean square difference between the measured diffraction pattern intensity and the iteratively retrieved intensity, was introduced. A quickly declining error measure over the number of iterations is shown in Figure 5c, which indicates a good convergence of the algorithms. The capital letters A, B, and C represent different diffraction planes. In Figure 5a,b, the quantitative phase reconstructions for normal and tumorous tissue are shown. For the healthy tissue, a smooth and almost regular phase could be reconstructed, which confirmed the findings in Reference [14], where a more regular structure was likewise reported for normal tissue. For the cancerous tissue, a noisy phase reconstruction was obtained for 633 nm, which indicated either that cancerous tissue at such thickness consisted of more scattering layers and/or that cancerous tissue consisted of finer scattering features resulting in large scattering angles, which therefore cannot be recorded by the optical arrangement. The latter has been confirmed by various publications, where a more finely meshed extra cellular matrix has been reported for cancerous tissue in comparison to normal tissue [15; 16]. For comparison, in the case of tumorous tissue, scans resulted in a noisy phase image due to multiple scattering events within the tissue (see Figure 5 b). A possible reason for the increased scattering is the more densely structured extracellular matrix and the hyper-vascularization in tumorous tissue. The changes in scattering behavior on a cellular level have already been reported in Reference [17]. Therefore, it is not too surprising that the changed scattering behavior can likewise be observed on tissue level. In this case, due to multiple scattering events on the cancerous tissue, a very strong difference can be appreciated between the two phase reconstructions. In order to enable visualization of a smooth phase distribution for all samples, a Nd:YAG with 1064 nm was employed, by which the scattering coefficient according to Mie scattering could be reduced by a factor of 8. This was clearly visible in the phase reconstructions. After unwrapping the obtained phase maps, an increase in phase delay was recognized, which indicated that the refractive  
Figure 5: Phase reconstructions at 633 nm: (**a**) healthy, (**b**) cancer, (**c**) error measure curve for different diffraction planes (A = 4, B = 6, C = 8), and unwrapped phase reconstructions for: (**d**) healthy, (**e**) cancer, (**f**) entropy at 633 nm and phase range at 1064 nm. index of the cancerous sample was increased in comparison to the healthy sample (all sections of the same thickness), see Figure 5d,e, which corresponds to the findings in Reference [14].