This article presents an overview of recent advances in the field of digital holography, ranging from holographic techniques designed to increase the resolution of microscopic images, holographic imaging using incoherent illumination, phase retrieval with incoherent illumination, imaging of occluded objects, and the holographic recording of depth-extended objects using a frequency-comb laser, to the design of an infrastructure for remote laboratories for digital-holographic microscopy and metrology. The paper refers to current trends in digital holography and explains them using new results that were recently achieved at the Institute for Applied Optics of the University Stuttgart.

Fluorescence correlation spectroscopy (FCS) is a powerful technique for quantification of molecular dynamics, and it has been widely applied in diverse fields, e.g., biomedicine, biophysics, and chemistry. By time-correlation of the fluorescence fluctuations induced by molecules diffusing through a focused light, FCS can quantitatively evaluate the concentration, diffusion coefficient, and interaction of the molecules in vitro or in vivo. In this review, the basic principle and implementation of FCS are introduced. Then, the advances of FCS variants are reviewed, covering dual-color FCCS, multi-focus FCS, pair correlation function (pCF), scanning FCS, focus-reduced FCS, SPIM-FCS, and inverse-FCS. Besides, the applications of FCS are demonstrated with the measurement of local concentration, hydrodynamic radius, diffusion coefficient, and the interaction of different molecules. Lastly, a discussion is given by summarizing the pros and cons of different FCS techniques, as well as the outlooks and perspectives of FCS.

Quantitative phase microscopy (QPM), a technique combining phase imaging and microscopy, enables visualization of the 3D topography in reflective samples, as well as the inner structure or refractive index distribution of transparent and translucent samples. Similar to other imaging modalities, QPM is constrained by the conflict between numerical aperture (NA) and field of view (FOV): an imaging system with a low NA has to be employed to maintain a large FOV. This fact severely limits the resolution in QPM up to $0.82\lambda /\mathrm{NA}$, $\lambda$ being the illumination wavelength. Consequently, finer structures of samples cannot be resolved by using modest NA objectives in QPM. Aimed to that, many approaches, such as oblique illumination, structured illumination, and speckle illumination (just to cite a few), have been proposed to improve the spatial resolution (or the space–bandwidth product) in phase microscopy by restricting other degrees of freedom (mostly time). This paper aims to provide an up-to-date review on the resolution enhancement approaches in QPM, discussing the pros and cons of each technique as well as the confusion on resolution definition claims on QPM and other coherent microscopy methods. Through this survey, we will review the most appealing and useful techniques for superresolution in coherent microscopy, working with and without lenses and with special attention to QPM. Note that, throughout this review, with the term “superresolution” we denote enhancing the resolution to surpass the limit imposed by diffraction and proportional to $\lambda /\mathrm{NA}$, rather than the physics limit $\lambda /(2n_{\mathrm{med}})$, with $n_{\mathrm{med}}$ being the refractive index value of the immersion medium.

Super‐resolution optical microscopy, which gives access to finer details of objects, is highly desired for fields of nanomaterial, nanobiology, nanophotonics, etc. Many efforts, including tip optimization and illumination optimization etc., have been made in both near‐field and far‐field super‐resolution microscopy to achieve a spatial resolution beyond the diffraction limit. The development of vector light fields opens up a new avenue for super‐resolution optical microscopy via special illumination modes. Cylindrical vector beam (CVB) has been verified to enable resolution improvement in tip‐scanning imaging, nonlinear imaging, stimulated emission depletion (STED) microscopy, subtraction imaging, superoscillation imaging, etc. This paper reviews recent advances in CVB‐based super‐resolution imaging. We start with an introduction of the fundamentals and properties of CVB. Next, strategies for CVB based super‐resolution imaging are discussed, which are mainly implemented by tight focusing, depletion effect, plasmonic nanofocusing, and polarization matching. Then, the roadmap of super‐resolution imaging with CVB illumination in the past two decades is summarized. The typical CVB‐based imaging techniques in fields of both near‐field and far‐field microscopy are introduced, including tip‐scanning imaging, nonlinear imaging, STED, subtraction imaging, and superoscillation imaging. Finally, challenges and future directions of CVB‐illuminated super‐resolution imaging techniques are discussed.

Structured illumination microscopy (SIM), is a wide-field, minimally-invasive super-resolution optical imaging approach with optical sectioning capability, and it has been extensively applied to many different fields. During the past decades, SIM has been drawing great attention for both the technique development and applications. In this review, firstly, the basic conception, instrumentation, and functionalities of SIM are introduced concisely. Secondly, recent advances in SIM which enhance SIM in different aspects are reviewed. Finally, the variants of SIM are summarized and the outlooks and perspectives of SIM are presented.