Fresnel Incoherent Correlation Holography (FINCH) allows digital reconstruction of incoherently illuminated objects from intensity records acquired by a Spatial Light Modulator (SLM). The article presents wave optics model of FINCH, which allows analytical calculation of the Point Spread Function (PSF) for both the optical and digital part of imaging and takes into account Gaussian aperture for a spatial bounding of light waves. The 3D PSF is used to determine diffraction limits of the lateral and longitudinal size of a point image created in the FINCH set-up. Lateral and longitudinal resolution is investigated both theoretically and experimentally using quantitative measures introduced for two-point imaging. Dependence of the resolving power on the system parameters is studied and optimal geometry of the set-up is designed with regard to the best lateral and longitudinal resolution. Theoretical results are confirmed by experiments in which the light emitting diode (LED) is used as a spatially incoherent source to create object holograms using the SLM.

We demonstrate a new imaging method enabling a selective edge contrast enhancement of three-dimensional amplitude objects with spatially incoherent light. The imaging process is achieved in a spiral modification of Fresnel incoherent correlation holography and uses a vortex impulse response function. The correlation recordings of the object are acquired in a one-way interferometer with the wavefront division carried out by a spatial light modulator. Two different methods based on applying a helical reference wave in the hologram recording and a digital spiral phase modulation in image reconstruction are proposed for edge enhancement of amplitude objects. Results of both isotropic and anisotropic spiral imaging are demonstrated in experiments using an LED as an incoherent source of light.

Fresnel incoherent correlation holography (FINCH) was a milestone in incoherent holography. In this roadmap, two pathways, namely the development of FINCH and applications of FINCH explored by many prominent research groups, are discussed. The current state-of-the-art FINCH technology, challenges, and future perspectives of FINCH technology as recognized by a diverse group of researchers contributing to different facets of research in FINCH have been presented.

Optical metasurfaces have emerged as a new generation of building blocks for multi-functional optics. Design and realization of metasurface elements place ever-increasing demands on accurate assessment of phase alterations introduced by complex nanoantenna arrays, a process referred to as quantitative phase imaging. Despite considerable effort, the widefield (non-scanning) phase imaging that would approach resolution limits of optical microscopy and indicate the response of a single nanoantenna still remains a challenge. Here, we report on a new strategy in incoherent holographic imaging of metasurfaces, in which unprecedented spatial resolution and light sensitivity are achieved by taking full advantage of the polarization selective control of light through the geometric (Pancharatnam-Berry) phase. The measurement is carried out in an inherently stable common-path setup composed of a standard optical microscope and an add-on imaging module. Phase information is acquired from the mutual coherence function attainable in records created in broadband spatially incoherent light by the self-interference of scattered and leakage light coming from the metasurface. In calibration measurements, the phase was mapped with the precision and spatial background noise better than 0.01 rad and 0.05 rad, respectively. The imaging excels at the high spatial resolution that was demonstrated experimentally by the precise amplitude and phase restoration of vortex metalenses and a metasurface grating with 833 lines/mm. Thanks to superior light sensitivity of the method, we demonstrated, for the first time to our knowledge, the widefield measurement of the phase altered by a single nanoantenna, while maintaining the precision well below 0.15 rad.

Incoherent correlation microscopy is recently discovered technique for digital imaging of three-dimensional objects in a quasimonochromatic spatially incoherent light. Its operation is based on wavefront division carried out by a spatial light modulator and capturing correlation recordings of the observed scene. To achieve image reconstruction, at least a partial overlapping of the signal and reference waves created by the spatial light modulator is necessary. In the known experimental configurations, the overlapping of interfering beams is strongly reduced in off-axis areas of the object and the image can be reconstructed only in a very small portion of the field of view provided by the used microscope objective lens. Here, we propose and successfully demonstrate modified experimental system working with two-component relay optics inserted between the microscope objective and the spatial light modulator and providing full overlapping of correlated beams in all areas of the field of view of the objective lens. The benefits and applicability of the proposed system design are clearly demonstrated on the imaging of the USAF resolution targets.

In the past decade, probe-based super-resolution using temporally resolved localization of emitters became a groundbreaking imaging strategy in fluorescence microscopy. Here we demonstrate a non-diffractive vortex microscope (NVM), enabling three-dimensional super-resolution fluorescence imaging and localization and tracking of metal and dielectric nanoparticles. The NVM benefits from vortex non-diffractive beams (NBs) creating a double-helix point spread function that rotates under defocusing while maintaining its size and shape unchanged. Using intrinsic properties of the NBs, the dark-field localization of weakly scattering objects is achieved in a large axial range exceeding the depth of field of the microscope objective up to 23 times. The NVM was developed using an upright microscope Nikon Eclipse E600 operating with a spiral lithographic mask optimized using Fisher information and built into an add-on imaging module or microscope objective. In evaluation of the axial localization accuracy the root mean square error below 18 nm and 280 nm was verified over depth ranges of 3.5 μm and 13.6 μm, respectively. Subwavelength gold and polystyrene beads were localized with isotropic precision below 10 nm in the axial range of 3.5 μm and the axial precision reduced to 30 nm in the extended range of 13.6 μm. In the fluorescence imaging, the localization with isotropic precision below 15 nm was demonstrated in the range of 2.5 μm, whereas in the range of 8.3 μm, the precision of 15 nm laterally and 30–50 nm axially was achieved. The tracking of nanoparticles undergoing Brownian motion was demonstrated in the volume of 14 × 10 × 16 μm3. Applicability of the NVM was tested by fluorescence imaging of LW13K2 cells and localization of cellular proteins.

Light vortices carry orbital angular momentum and have a variety of applications in optical manipulation, high-capacity communications or microscopy. Here we propose a new concept of full-field vortex topographic microscopy enabling a reference-free displacement and shape measurement of reflective samples. The sample surface is mapped by an array of light spots enabling quantitative reconstruction of the local depths from defocused wavefronts. Light from the spots is converted to a lattice of mutually uncorrelated double-helix point spread functions (PSFs) whose angular rotation enables depth estimation. The PSFs are created by self-interference of optical vortices that originate from the same wavefront and are shaped by a spiral phase mask (SPM). The method benefits from the isoplanatic PSFs whose shape and size remain unchanged under defocusing, ensuring high precision in a wide range of measured depths. The technique was tested using a microscope Nikon Eclipse E600 working with a micro-hole plate providing structured illumination and the SPM placed in the imaging path. The depth measurement was demonstrated in the range of 11 µm exceeding the depth of field of the microscope objective up to 19 times. Throughout this range, the surface depth was mapped with the precision better than 30 nm at the lateral positions given with the precision better than 10 nm. Application potential of the method was demonstrated by profiling the top surface of a bearing ball and reconstructing the three-dimensional relief of a reflection phase grating.

We report a study of spatial light modulation in the photonic structure of jewel scarabs, revealing the interplay of the polarization and phase control of light, which is not possible with the current optical technology. Phase measurements performed on jewel scarabs demonstrate that the polarization anomalous (helicity-preserving) reflection of light occurs together with alteration of the dynamic phase associated with the optical path length. This control of light differs from the operation of artificially prepared polarization-sensitive structures, shaping light through the geometric phase altered by the polarization transformation. Challenging three-dimensional imaging of the cuticle, requiring high-resolution quantitative mapping of steep phase changes, has been achieved owing to the optical performance of recently developed geometric-phase microscopy. We find that the cuticle of jewel scarabs is formed of micrometer-sized axicon cells, generating thousands of Bessel beams with subwavelength spot size. The nondiffracting features and the self-healing ability of the Bessel beams originating from the beetle Chrysina gloriosa are demonstrated experimentally. Considering Bragg reflection and shaping of RGB components of white light Bessel beams, we explain the spatial structuring of colors in microscopic images of jewel scarabs and reveal the conversion of colors when changing the distance from the cuticle. The functionality and performance of the cuticle axicon cells are discussed in comparison with high-aperture dielectric meta-axicons, and potential applications in colorimetric refractive index sensing are outlined.