## 2 Technology
### Principles of QPI  
Apart from a few early studies of biological imaging mounted on reflective surfaces, all QPI set-ups for bio-imaging examine the sample using transmitted light (Table 1). Transmission QPI is based on the interference between the light entering and exiting the sample. A separation between refracted light of the sample (the object beam) and the reference light (the reference beam) can be achieved using either spatial or temporal modulation. There are two types of spatial modulation: In-line holography and off-axis methods. The first type is based on interference of a weakly scattered beam from the object and an un-scattered incident beam [74]. For this optical instrument, the use of heavy algorithms is necessary for image reconstruction, because interferometric information overlaps with unwanted information. In off-axis holography, the optical axis of the reference beam is slightly tilted with respect to the object beam. Thus, unwanted information can be spatially separated [75]. DH is a common off-axis holographic technique for the QPI of cells [31]. Here, a laser beam is spatially separated by a dichroic mirror. The object beam is diffracted by the cells and interferes with the reference beam at a slight angle at the recording sensor, where a fringe pattern characteristic of the object is created. The intensity distribution depends on the phase difference \(\Delta\varphi\)[4]. Temporal modulation, or phase shifting interferometry, involves changing the phase of the reference beam with respect to the object beam. An example of temporal modulation is SLIM [76]. The reconstruction of the phase and amplitude images from the recorded interferometric pattern varies with the hardware set-up. Typically, it consists of one or several reconstruction stages using Fourier Transforms and a focal selection stage, followed by one or more post-processing calculations where modular phase recordings are unwrapped and edge effects removed [4]. The risk of introducing image artefacts in the unwrapping stage is reduced if the sample phase shift is less than one wavelength, or it can be avoided completely by imaging at several wavelengths, thus also allowing for imaging thicker specimens [73; 77; 78]. All image reconstruction and manipulation stages can be performed after capture, as the complete three-dimensional information of the sample is stored in the interferometricrecording. The result is an image (Figure 1b) where pixel intensity is directly proportional to the phase shift \(\Delta\Phi\) (Equation (1), with wavelength \(\lambda\) and refractive index in optical path direction \(n(z)\) as parameters. The image is well suited for automated image analysis for two reasons. Firstly, the image background can be used to offset the phase shift and allow comparison between images. Secondly, the images themselves display intensity gradients at cellular boundaries, making it possible to segment the image and extract information on each imaged cell separately (Figure 1c). \[\Delta\Phi=\frac{2\pi}{\lambda}\cdot\int n(z)dz \tag{1}\]  
All image reconstruction and manipulation stages can be performed after capture, as the complete three-dimensional information of the sample is stored in the interferometric recording. Despite these appealing traits, several challenges persist. Thick cellular coverage may make it difficult to establish image background, and the choice not to use dyes will also reduce the ability to artificially enhance image contrast or specific image content, such as highlighting a specific molecule or intracellular structure. As a consequence, QPI images of very thin cells or cell structures may be undetectable due to noise. The phase delay measured is directly related to cellular dry mass and is the only physical property measured. Using image analysis, it is possible to extract further information using the recorded two-dimensional mass distribution within each cell.