Microscopic visualisation of optically transparent samples has been a topic of interest for several decades. Features such as density or chemical composition can influence the optical phase of transmitted light, and phase contrast can reveal these structures. Several methods of phase contrast have been developed, which can be categorised as either interferometric or non-interferometric, based on the type of coherence properties of the light used. In this work, I focus on incoherent based phase contrast, in particular Differential Phase Contrast (DPC). The choice of incoherent light brings benefits such as the absence of distortions like speckle patterns and ringing patterns, increased spatial resolution, and a simpler setup that can be used for in-vivo applications. Moreover, DPC allows reconstruction of quantitative phase maps of the samples. On the other hand, coherent-based techniques demonstrate superior performance in terms of phase sensitivity. The first part of this thesis offers a quantitative analysis of the phase sensitivity of DPC and investigates the influence of optical parameters and sample characteristics. With simulations and experiments, a relation between numerical aperture and phase sensitivity is demonstrated, and the concept of spectral matching is introduced to enhance the contrast. The methods can be generalised to any DPC setup, and allow a-priori investigation of the sensitivity of a DPC microscope at the design stage rather than through testing. Comparison between the best sensitivity that can be achieved in DPC and state-of-the-art interferometric techniques, shows that it is not possible to reach comparable single-shot performances. In this thesis, it is shown that the reason for this limitation is the strong background in DPC images, which degrades the dynamic range. DPC images are obtained with mirrored illuminations, for which the background is identical and the phase term switches in sign. The difference between these pairs of images is computed digitally, which does not improve the limited dynamic range. Lock-in DPC is proposed as a solution: instead of sampling different illumination states, lock-in DPC demodulates the phase signal when the illumination is switched, and the background is never encoded. This is enabled by periodical switching of sources coupled with a smart pixel detector, the so-called "lock-in camera". Part of this work is dedicated to the theoretical description of this method, and the analysis of the expected benefit. Experiments are also described, that demonstrate a factor of 8 improvement in single-shot sensitivity compared to standard DPC. DPC is not the only imaging technique to suffer from high intensity background: it is easy to see how the use of a lock-in camera for differential imaging can be generalised to any situation where weak modulations can be induced over a strong background. Here, an example is presented with lock-in Shifted Excitation Raman Difference Spectroscopy (SERDS). SERDS is an established Raman spectroscopy technique that takes advantage of the Raman emission spectrum being relative to the excitation wavelength to remove unwanted fluorescence emission. Two spectra with shifted excitation wavelengths are measured, their difference is computed, and the fluorescence is thus digitally removed. The parallel with DPC is immediately apparent. Both simulations and experiments are used to demonstrate the advantage of analog demodulation.