This paper presents a "reinvention" of Gabor Holography that does not suffer optically from the inherent twin-image problem originating back to Gabor's original Nobel Prize awarded invention. In-line or on-axis holography was ironically abandoned by its inventor Dennis Gabor himself and was effectively completely "re-placed" by so-called off-axis holography at the time when Gabor received the Nobel Prize in Physics in 1971. However, Gabor Holography is today the method of choice in modern digital holography due to its inherent on-axis, common-path robustness, lower requirements to resolution of the image sensor (or recording material), shorter exposure time, relaxed mechanical stability and temporal coherence requirements. However, it still inherently suffers from the aforementioned twin-image problem and, hence, one will find an abundance of papers trying to overcome this challenge by iterative phase retrieval or machine learning based approaches. Gabor Holography Reinvented overcomes this long-lasting twin-image problem for the first time by optical means.

We present a phase-only time-reversal framework for steering photonic nanojets without mechanical motion or amplitude modulation. Time-reversed radiation by a synthetic source placed at the target PNJ location helps define a phase-only modulation on a control line, compatible with a spatial light modulator, that produces the desired PNJ. Full-wave finite-difference frequency-domain (FDFD) simulations demonstrate robust lateral and axial steering with subwavelength confinement and low sidelobes across most of the accessible steering range, with the strongest sidelobes confined to the extreme aperture-edge limit. A parametric study of smooth microelement geometries shows that nanojet formation is relatively insensitive within the sampled shape family, with simple shapes providing competitive performance. Robustness to fabrication and alignment errors is confirmed via uncertainty analysis.

We present a phase-only time-reversal framework for steering photonic nanojets without mechanical motion or amplitude modulation. Time-reversed radiation by a synthetic source placed at the target PNJ location helps define a phase-only modulation on a control line, compatible with a spatial light modulator, that produces the desired PNJ. Full-wave finite-difference frequency-domain (FDFD) simulations demonstrate robust lateral and axial steering with subwavelength confinement and low sidelobes. A parametric study of microelement geometries shows that nanojet formation is largely insensitive to moderate boundary variations, with simple shapes providing competitive performance. Robustness to fabrication and alignment errors is confirmed via uncertainty analysis.

A reduced local field model derived from full-wave electromagnetic simulations shows that photonic nanojet formation corresponds to an emergent mesoscopic funnel of propagating power flux sustained by an effective free-space transverse mode structure. This interpretation moves beyond purely geometric-optics or interference-based explanations by identifying a self-consistent redistribution of phase gradients and effective longitudinal wavenumber near the nanojet waist. The model quantitatively captures characteristic nanojet morphology, including the formation and local structure of the jet waist. It also yields a geometry-independent lower bound on the nanojet waist, linking transverse confinement to the effective axial wavenumber through an explicit trade-off. The model establishes a direct connection between full-wave Maxwell fields and a reduced free-space oscillator description, yielding new physical insight into nanojet confinement and suggesting design principles for nanojet-assisted imaging, lithography, and subwavelength field localization.

Abstract Several 3D light-based printing technologies have been developed that rely on the photopolymerization of liquid resins. A recent method, so-called Tomographic Volumetric Additive Manufacturing, allows the fabrication of microscale objects within tens of seconds without the need for support structures. This method works by projecting intensity patterns, computed via a reverse tomography algorithm, into a photocurable resin from different angles to produce a desired 3D shape when the resin reaches the polymerization threshold. Printing using incoherent light patterning has been previously demonstrated. In this work, we show that a light engine with holographic phase modulation unlocks new potential for volumetric printing. The light projection efficiency is improved by at least a factor 20 over amplitude coding with diffraction-limited resolution and its flexibility allows precise light control across the entire printing volume. We show that computer-generated holograms implemented with tiled holograms and point-spread-function shaping mitigates the speckle noise which enables the fabrication of millimetric 3D objects exhibiting negative features of 31 μm in less than a minute with a 40 mW light source in acrylates and scattering materials, such as soft cell-laden hydrogels, with a concentration of 0.5 million cells per mL.

We report the first successful fabrication of three-dimensional models using our fully lensless holographic volumetric additive manufacturing (HoloVAM) platform. In this configuration, tomographic light fields are generated directly from a phase-only spatial light modulator (SLM) and delivered into a rotating vial of photopolymer without any imaging optics, relays, or index-matching bath. Building on the HoloTile framework for tiled Fourier holography and point-spread function (PSF) shaping, the system creates volumetric dose distributions with high photon efficiency and well-controlled axial propagation. Using a simple acrylate resin formulation and a minimalized optical train, we demonstrate reproducible fabrication of complex geometries. These results establish lensless HoloVAM as a practical and mechanically minimal route to volumetric fabrication, opening a new pathway toward compact and application-flexible VAM devices.

This publication extends the HoloTile framework to three dimensions, introducing the ability to generate arbitrary dynamic patterns composed of extended depth-of-field non-diffractive beamlets with theoretically 100% diffraction efficiency. In particular, we demonstrate experimentally the generation of speckle-reduced reconstruction patterns, consisting of spatially multiplexed extended Bessel-like beamlets, implemented on a phase-only spatial light modulator (SLM).Due to the inherent separation of the tiled subhologram and the point spread function shaping hologram in HoloTile, we show that the reconstruction amplitude can be expressed as a simple convolution of the contributions from the two holograms. This results in a discretely sampled reconstruction, with each spatial frequency component exhibiting long DoF with characteristic Bessel beam properties. This separation facilitates spatial and temporal multiplexing of both contributions, and allows for real-time dynamic patterning with extended DoF. Additionally, a geometric analysis is included, allowing for the direct calculation of the propagation characteristics of the beamlets.

We propose a rigorous, physically interpretable, and quantifiable definition of the photonic nanojet (PNJ). This framework resolves longstanding ambiguities in measuring PNJ dimensions and leverages an optimal mass transport-based metric to quantify PNJ quality. Building on this metric, we develop a PNJ steering methodology that requires no opto-mechanical intervention, relying solely on phase-only illumination modulation.

Tomographic volumetric additive manufacturing for 3D Bioprinting is typically based on illuminating a volume of a cell-laden hydrogel with a set of light patterns irradiated from multiple angles. The key advantages of tomographic volumetric printing compared to existing 3D printing methods are the inherently fast processing time and the ability to print complex hollow structures without the need for printing additional supporting structures. However, current illumination systems are based on light inefficient amplitude imaging by so-called Digital Light Projection of powerful multi-mode sources. By rethinking the whole light addressing for tomographic-based additive manufacturing we can circumvent the inherent inefficiency and resolution bottlenecks of current Bioprinting systems and introduce real-time aberration correction by using our recently patent-filed digital holographic projection modality coined HoloTile [1,2] in binary-phase encoded mode on a Digital Micromirror Device. [1] J. Glückstad, HOLOGRAPHIC SYSTEM WITH IMPROVED PROJECTION QUALITY, EP 22169752.7 (2022). [2] A. Madsen and J. Glückstad, Optics Communications 525, 128876 (2022).

3D printing has revolutionized the manufacturing of volumetric components and structures in many areas. Different technologies have been developed including light-induced techniques based on the photopolymerization of liquid resins. In particular, a recently introduced method, so-called Tomographic Volumetric AM (VAM), allows the fabrication of mesoscale objects within tens of seconds without the need for support structures. This method works by projecting thousands of amplitude patterns, computed via a reverse tomography algorithm, into a resin from different angles to produce the desired three-dimensional shape when the resin reaches the polymerization threshold. To date, only amplitude modulation of the patterns has been reported. Here, we show that holographic phase modulation unlocks new capabilities for VAM printing. Specifically, the effective light projection efficiency is improved by at least a factor of 10 over amplitude coding; the resolution can reach the light diffraction limit; and phase encoding allows to control ballistic photons in scattering media, which potentially increases the volume of 3D objects that can be printed in opaque and non-absorbing resins. The approach uses CGH to convert phase, encoded on a 2D modulator to the desired intensity projections by light propagation in a photosensitive resin container. We demonstrate the potential of holographic phase coding using simulations and experiments, the latter by implementing a volumetric printer using a DMD, as the 2D phase modulator in a Fourier configuration. Specifically, we use Lee holograms to encode phase onto a binary DMD. Combining tiled holograms with PSF shaping mitigates the speckle noise typically associated with computer-generated holograms and speed-up their computation. We use these holographic projections to fabricate millimetric 3D objects in less than a minute with a resolution down to 164 um.

HoloTile [1, 2, 3, 4] is a novel digital holographic light sculpting modality with properties well suited to volumetric additive manufacturing (VAM). This paper discusses the consequences of moving from an imaging-based to a holographic-based VAM configuration, and how HoloTile may be used to improve volumetric printing further.

Photonic nanojets (PNJs) are highly localized optical probes that promise label-free measurements beyond the classical diffraction limit. We here demonstrate numerically the feasibility of label-free, self-calibrating, super-resolution optical detection and imaging using far-field scatterometry in conjunction with rapid scanning photonic nanojet excitation achieved with no opto-mechanical intervention. We realize PNJ scanning by computed structured illumination of refractive dielectric micro-elements such as micro-spheres and micro-cubes. Our far-field measurement data are phaseless. In proof-of-concept computations, we use our steerable optical probe to extract information on nanoparticles, aggregates of nanoparticles, and thin-film structures beyond the classical lateral and vertical resolution limits, in the presence of supporting structures such as substrates.

HoloTile is our novel and recently patent-filed approach [1,2] to obtain very fast reconfigurable and strongly speckle-reduced digital holography. Using HoloTile we have experimentally demonstrated more than 90 % photon-efficient phase-only projected dynamic and static far field diffraction both with and without a lens. A key aim for inventing and innovating HoloTile has been to effectively solve the challenge of rapid and speckle-free coherent or semi-coherent light sculpting without the need for time-averaging techniques - a challenge that exists in several fields of optics and photonics. In particular, HoloTile provides four new unique key features as CGH-modality for high-resolution spatial light modulators, reconfigurable DOEs or new meta-surface MOEs: • A 100x speed improvement over standard CGH-modalities • Substantial speckle reduction by matched tiling and PSF-shaping • Real-time dynamic and output 'pixel' discretized digital holograms • Lens-free scaling or zoom by software adapted HoloTile phase-encoding.

Solving the holography equation has long been a numerical task. While effective, the numeric approach has its own set of limitations. Relying solely on numerical approaches often obscures the intricate interplay and influence of the individual terms within the equation. This not only hampers a deeper understanding of the underlying physics but also makes it challenging to predict or control specific outcomes. In this study, wead dress these challenges by leveraging our recently published updated Fraunhofer diffraction expression. This approach allows us to derive an analytic solution for complex-valued phase disks in in-line holography. This solution facilitates the direct computation of each term's influence within the holographic equation, paving the way for a more profound comprehension and application of the holographic process. When compared to experimental results and the numeric Fresnel diffraction solution, our analytic approach shows impressive accuracy, considering the inherent approximations. Notably, it remains precise for Fresnel numbers that extend well beyond the traditionally accepted boundaries of the Fraunhofer regime.

HoloTile is a patented computer generated holography approach with the aim of reducing the speckle noise caused by the overlap of the non-trivial physical extent of the point spread function in Fourier holographic systems from adjacent frequency components. By combining tiling of phase-only of rapidly generated sub-holograms with a PSF-shaping phase profile, each frequency component - or output "pixel" - in the Fourier domain is shaped to a desired non-overlapping profile. In this paper, we show the high-resolution, speckle-reduced reconstructions that can be achieved with HoloTile, as well as present new HoloTile modalities, including an expanded list of PSF options with new key properties. In addition, we discuss numerous applications for which HoloTile, its rapid hologram generation, and the new PSF options may be an ideal fit, including optical trapping and manipulation of particles, volumetric additive printing, information transfer and quantum communication.

We demonstrate the first use of the HoloTile Computer-Generated Holography (CGH) modality on multi-wavelength targets. Taking advantage of the sub-hologram tiling and Point Spread Function (PSF) shaping of HoloTile allows for reconstruction of high-fidelity, pseudo-digital multi-wavelength images, with well-defined discrete output pixels, without the need for temporal averaging. For each wavelength, the target channels are scaled appropriately, using the same output pixel size. We employ a stochastic gradient descent (SGD) hologram generation algorithm for each wavelength, and display them sequentially on a HoloEye GAEA 2.1 Spatial Light Modulator (SLM) in Color Field Sequential (CFS) phase modulation mode. As such, we get full 8-bit phase modulation at 60 Hz for each wavelength. The reconstructions are projected onto a camera sensor where each RGB image is captured in a single shot. While these show impressive color reconstructions, the method can be adapted to any wavelength combination for use in a plethora of multi-wavelength application.

Light-based technologies for 3D printing have recently been developed and are leading the field thanks to their unmatched performance. However, these techniques are still limited to using incoherent light patterning for printing. Here, we present a novel approach that allows us to print using coherent patterns by combining light-beam shaping and tomographic projections. We demonstrate this concept with a volumetric printer based on reverse tomography using a Digital Micromirror Device (DMD) in a holographic configuration. The Lee holograms method allowed us to use the DMD as a fast phase modulator and the HoloTile approach to achieve fast and speckle-reduced holograms.

We report on HoloTile, a new approach to speckle-reduced and rapidly generated holograms. By way of an analytical approach to Gaussian beam shaping, we modify the Point Spread Function (PSF) of a holographic system into flat-top squares. The width of each flat-top output “pixel” is determined from the inter-spectral distance arising from designed tiling on a Spatial Light Modulator (SLM). The resultant hologram consists of the product of a once-calculated PSF shaping hologram and a tiled object hologram. With HoloTile, we achieve speckle-reduced reconstructions and extremely fast hologram generation, due to the reduced resolution of the object hologram.

We demonstrate numerically the feasibility of axial and angular control of the position of a photonic nanojet (PNJ) by lossless phase-only modulation of a fixed Gaussian beam illuminating a fixed 2D circular homogeneous dielectric micro-lens. We furthermore demonstrate that our phase-only modality can be used to calibrate and improve the confinement of PNJ generation.