Efficient and accurate intensity diffraction tomography of multiple-scattering samples.

Optical Diffraction Tomography (ODT) is a label-free method to quantitatively estimate the 3D refractive index (RI) distributions of microscopic samples. Recently, significant efforts were directed towards methods to model multiple-scattering objects. The fidelity of reconstructions rely on accurately modelling light-matter interactions, but the efficient simulation of light propagation through high-RI structures over a large range of illumination angles is still challenging. Here we present a solution dealing with these problems, proposing a method that allows one to efficiently model the tomographic image formation for strongly scattering objects illuminated over a wide range of angles. Instead of propagating tilted plane waves we apply rotations on the illuminated object and optical field and formulate a new and robust multi-slice model suitable for high-RI contrast structures. We test reconstructions made by our approach against simulations and experiments, using rigorous solutions to Maxwell's equations as ground truth. We find the proposed method to produce reconstructions of higher fidelity compared to conventional multi-slice methods, especially for the challenging case of strongly scattering samples where conventional reconstruction methods fail.

Inverse design of gradient-index volume multimode converters.

Graded-index optical elements are capable of shaping light precisely and in very specific ways. While classical freeform optics uses only a two-dimensional domain such as the surface of a lens, recent technological advances in laser manufacturing offer promising prospects for the realization of arbitrary three-dimensional graded-index volumes, i.e. transparent dielectric substrates with voxel-wise modified refractive index distributions. Such elements would be able to perform complex light transformations on compact scales. Here we present an algorithmic approach for computing 3D graded-index devices, which utilizes numerical beam propagation and error reduction based on gradient descent. We present solutions for millimeter-sized elements addressing important tasks in photonics: a mode sorter, a photonic lantern and a multimode intensity beam shaper. We further discuss suitable cost functions for all designs to be used in the algorithm. The 3D graded-index designs are spatially smooth and require a relatively small refractive index range in the order of 10-2, which is within the reach of direct laser writing manufacturing processes such as two-photon polymerization.

Holographic beam shaping of partially coherent light.

We present an algorithmic approach for holographic shaping of partially coherent light, which is described by a mode expansion containing thousands of individual modes. Using gradient descent and algorithmic differentiation, our algorithm is able to find a set of axially separated phase patterns such that each mode undergoes an individually optimized transformation with respect to the formation of a user-defined target intensity distribution. We demonstrate numerically and experimentally that a tandem of two phase patterns can achieve any intensity profile transformation with good accuracy.

Three-Dimensional Single Molecule Localization Microscopy Reveals the Topography of the Immunological Synapse at Isotropic Precision below 15 nm.

T-cells engage with antigen-presenting cells in search for antigenic peptides and form transient interfaces termed immunological synapses. Synapse topography affects receptor binding rates and the mutual segregation of proteins due to size exclusion effects. It is hence important to determine the 3D topography of the immunological synapse at high precision. Current methods provide only rather coarse images of the protein distribution within the synapse. Here, we applied supercritical angle fluorescence microscopy combined with defocused imaging, which allows three-dimensional single molecule localization microscopy (3D-SMLM) at an isotropic localization precision below 15 nm. Experiments were performed on hybrid synapses between primary T-cells and functionalized glass-supported lipid bilayers. We used 3D-SMLM to quantify the cleft size within the synapse by mapping the position of the T-cell receptor (TCR) with respect to the supported lipid bilayer, yielding average distances of 18 nm up to 31 nm for activating and nonactivating bilayers, respectively.

Tomographic refractive index profiling of direct laser written waveguides.

The fabrication of complex integrated photonic devices via direct laser writing is a powerful and rapidly developing technology. However, the approach is still facing several challenges. One of them is the reliable quantitative characterization of refractive index (RI) changes induced upon laser exposure. To this end, we develop a tomographic reconstruction algorithm following a modern optimization approach, relying on accelerated proximal gradient descent, based on intensity images only. Very recently, such algorithms have become the state of the art in the community of bioimaging, but have never been applied to direct laser written structures such as waveguides. We adapt the algorithm to our concern of characterizing these translation-invariant structures and extend it in order to jointly estimate the aberrations introduced by the imaging system. We show that a correct estimation of these aberrations is necessary to make use of data recorded at larger angles and that it can increase the fidelity of the reconstructed RI profiles. Moreover, we present a method allowing to cross-validate the RI reconstructions by comparing en-face widefield images of thin waveguide sections with matching simulations based on the retrieved RI profile.

Diffractive tunable lens for remote focusing in high-NA optical systems.

Remote focusing means to translate the focus position of an imaging system along the optical axis without moving the objective lens. The concept gains increasing importance as it allows for quick 3D focus steering in scanning microscopes, leaves the sample region unperturbed and is compatible with conjugated adaptive optics. Here we present a novel remote focusing approach that can be used in conjunction with high numerical aperture optics. Our method is based on a pair of diffractive elements, which jointly act as a tunable auxiliary lens. By changing the mutual rotation angle between the two elements, we demonstrate an axial translation of the focal spot produced by a NA = 0.95 air objective (corresponding to NA = 1.44 for an oil immersion lens) over more than 140 µm with largely maintained focus quality. We experimentally show that for the task of focus shifting, the wavefront produced by the high-NA design is superior to those produced by a parabolic lens design or a regular achromatic lens doublet.

Two-photon PSF-engineered image scanning microscopy.

We present two-photon fluorescence image scanning microscopy (ISM) with engineered excitation and detection point-spread-functions enabling 3D imaging in a single 2D scan. This demonstration combines excitation using a holographic multispot array of focused femtosecond pulses with a high-efficiency single-helix PSF phase mask detection. Camera detection along with a multiview reconstruction algorithm allows volumetric imaging of biological samples over a depth of field spanning more than 1500 nm with an axial resolution of better than 400 nm. The nonlinear two-photon process improves sectioning and the inherent longer wavelengths increase the penetration depth in scattering samples. Our method extends the performance of 3D ISM towards thicker biological samples.

Modified Alvarez lens for high-speed focusing.

We present a modified configuration of a tunable Alvarez lens with a refocusing frequency of 1 kHz or more. In contrast to the classic Alvarez lens, the approach does not utilize a translational motion of two sub-lenses with respect to each other, but uses a 4f-setup to image two diffractive sub-lenses onto each other. Hereby focus tuning is achieved by rotating a galvo-mirror which affects the overlap of the two sub-lenses which together form an effective lens of refractive power which depends on the rotation angle of the galvo-mirror. We have demonstrated tuning of the optical power in a system where the diffractive Alvarez lens is realized by an LCOS-SLM. We consider our Alvarez setup especially suitable for applications where high refocusing rates are important, as for example in 3D life cell monitoring or tracking.

Deconvolution approach for 3D scanning microscopy with helical phase engineering.

RESCH (refocusing after scanning using helical phase engineering) microscopy is a scanning technique using engineered point spread functions which provides volumetric information. We present a strategy for processing the collected raw data with a multi-view maximum likelihood deconvolution algorithm, which inherently comprises the resolution gain of pixel-reassignment microscopy. The method, which we term MD-RESCH (for multi-view deconvolved RESCH), achieves in our current implementation a 20% resolution advantage along all three axes compared to RESCH and confocal microscopy. Along the axial direction, the resolution is comparable to that of image scanning microscopy. However, because the method inherently reconstructs a volume from a single 2D scan, a significantly higher optical sectioning becomes directly visible to the user, which would otherwise require collecting multiple 2D scans taken at a series of axial positions. Further, we introduce the use of a single-helical detection PSF to obtain an increased post-acquisition refocusing range. We present data from numerical simulations as well as experiments to confirm the validity of our approach.

Colored point spread function engineering for parallel confocal microscopy.

Using the color selectivity of a spatial light modulator (SLM) for both, tailoring the excitation beam at one wavelength, and multiplexing the image at the red-shifted fluorescence wavelength, it is possible to parallelize confocal microscopy, i.e. to simultaneously detect an axial stack (z-stack) of a sample. For this purpose, two diffractive patterns, one steering the excitation light, and the other manipulating the emission light, are combined within the same area of the SLM, which acts as a pure phase modulator. A recently demonstrated technique allows one to combine the patterns with high diffraction efficiency and low crosstalk, using the extended phase shifting capability of the SLM, which covers multiples of 2π at the respective wavelengths. For a first demonstration we compare standard confocal imaging with simultaneous image acquisition in two separate sample planes, which shows comparable results.

High-resolution confocal Raman microscopy using pixel reassignment.

We present a practical modification of fiber-coupled confocal Raman scanning microscopes that is able to provide high confocal resolution in conjunction with high light collection efficiency. For this purpose, the single detection fiber is replaced by a hexagonal lenslet array in combination with a hexagonally packed round-to-linear multimode fiber bundle. A multiline detector is used to collect individual Raman spectra for each fiber. Data post-processing based on pixel reassignment allows one to improve the lateral resolution by up to 41% compared to a single fiber of equal light collection efficiency. We present results from an experimental implementation featuring seven collection fibers, yielding a resolution improvement of about 30%. We believe that our implementation represents an attractive upgrade for existing confocal Raman microscopes that employ multi-line detectors.

How to use a phase-only spatial light modulator as a color display.

We demonstrate that a parallel aligned liquid crystal on silicon (PA-LCOS) spatial light modulator (SLM) without any attached color mask can be used as a full color display with white light illumination. The method is based on the wavelength dependence of the (voltage controlled) birefringence of the liquid crystal pixels. Modern SLMs offer a wide range over which the birefringence can be modulated, leading (in combination with a linear polarizer) to several intensity modulation periods of a reflected light wave as a function of the applied voltage. Because of dispersion, the oscillation period strongly depends on the wavelength. Thus each voltage applied to an SLM pixel corresponds to another reflected color spectrum. For SLMs with a sufficiently broad tuning range, one obtains a color palette (i.e., a "color lookup-table"), which allows one to display color images. An advantage over standard liquid crystal displays (LCDs), which use color masks in front of the individual pixels, is that the light efficiency and the display resolution are increased by a factor of three.

Colour hologram projection with an SLM by exploiting its full phase modulation range.

We demonstrate independent and simultaneous manipulation of light beams of different wavelengths by a single hologram, which is displayed on a phase-only liquid crystal spatial light modulator (SLM). The method uses the high dynamic phase modulation range of modern SLMs, which can shift the phase of each pixel in a range between 0 up to 10π, depending on the readout wavelength. The extended phase range offers additional degrees of freedom for hologram encoding. Knowing the phase modulation properties of the SLM (i.e. the so-called lookup table) in the entire exploited wavelength range, an exhaustive search algorithm allows to combine different independently calculated 2π-holograms into a multi-level hologram with a phase range extending over several multiples of 2π. The combined multi-level hologram then reconstructs the original diffractive patterns with only small phase errors at preselected wavelengths, thus projecting the desired image fields almost without any crosstalk. We demonstrate this feature by displaying a static hologram at an SLM which is read out with an incoherent red-green-blue (RGB) beam, projecting a color image at a camera chip. This is done for both, a Fourier setup which needs a lens for image focusing, and in a "lensless" Fresnel setup, which also avoids the appearance of a focused zero-order spot in the image center. The experimentally obtained efficiency of a two-colour combination is on the order of 83% for each wavelength, with a crosstalk level between the two colour channels below 2%, whereas a three-colour combination still reaches an efficiency of about 60% and a crosstalk level below 5%.

Axial super-localisation using rotating point spread functions shaped by polarisation-dependent phase modulation.

We present an approach for point spread function (PSF) engineering that allows one to shape the optical wavefront independently in both polarisation directions, with two adjacent phase masks displayed on a single liquid-crystal spatial light modulator (LC-SLM). The set-up employs a polarising beam splitter and a geometric image rotator to rectify and process both polarisation directions detected by the camera. We shape a single-lobe ("corkscrew") PSF that rotates upon defocus for each polarisation channel and combine the two polarisation channels with a relative 180° phase-shift on the computer, merging them into a single PSF that exhibits two lobes whose orientation contains information about the axial position. A major advantage lies in the possibility to measure and eliminate the aberrations in the two polarisation channels independently. We demonstrate axial super-localisation of isotropically emitting fluorescent nanoparticles. Our implementation of the single-lobe PSFs follows the method proposed by Prasad [Opt. Lett.38, 585 (2013)], and thus is to the best of our knowledge the first experimental realisation of this suggestion. For comparison we also study an approach with a rotating double-helix PSFs (in only one polarisation channel) and ascertain the trade-off between localisation precision and axial working range.

Broadband suppression of the zero diffraction order of an SLM using its extended phase modulation range.

The diffraction efficiency of a hologram displayed on a phase-only spatial light modulator (SLM) is maximal, if the SLM modulates the phase of the diffracted beam in a range between 0 and 2π. However, if the readout wavelength changes, or a broadband beam is used, due to dispersion this ideal modulation range cannot be maintained, which leads to lower diffraction efficiency and to the appearance of an undesired intense zero diffraction order. Here we show how an SLM with an extended phase modulation range of 4π can be used to display on-axis holograms with a strong suppression of the zero diffraction order in a wide spectral range, extending over 200 nm. The basic idea is to transform the original on-axis hologram into an off-axis hologram by adding a blazed grating and performing a modulo 2π operation, and then transforming it back by adding the conjugate grating, but without performing a subsequent modulo operation. The final hologram then spans over a phase range of 4π. The total diffracted field corresponds to that of the original on-axis hologram, but now the zero-order Fourier component is diffracted away from the optical axis. The same principle can be used to entangle the on-axis hologram with other phase structures, e.g. a random phase mask or a second hologram structure, followed by a subsequent addition of the conjugate mask, which may also suppress higher diffraction orders. The reconstructed holograms show a strong contrast enhancement in a broad wavelength range.

Lensless imaging through thin diffusive media.

Objects imaged through thin scattering media can be reconstructed with the knowledge of the complex transmission function of the diffuser. We demonstrate image reconstruction of static and dynamic objects with numerical phase conjugation in a lensless setup. Data is acquired by single shot intensity capture of an object coherently illuminated and obscured by an inhomogeneous medium, i.e. light diffracted at a specimen is scattered by a polycarbonate diffuser and the resulting speckle field is recorded. As a preparational step, which has to be performed only one time before imaging, the complex speckle field diffracted by the diffuser to the camera chip is measured interferometrically, which allows to reconstruct the transmission function of the diffuser. After insertion of the specimen, the speckle field in the camera plane changes, and the complex field of the sample can be reconstructed from the new intensity distribution. After initial interferometric measurement of the diffuser field, the method is robust with respect to a subsequent misalignment of the diffuser. The method can be extended to image objects placed between a pair of thin scattering plates. Since the object information is contained in a single speckle intensity pattern, it is possible to image dynamic processes at video rate.

Dispersion tuning with a varifocal diffractive-refractive hybrid lens.

We present a hybrid diffractive-refractive optical lens doublet consisting of a varifocal Moiré Fresnel lens and a polymer lens of tunable refractive power. The wide range of focal tunability of each lens and the opposite dispersive characteristics of the diffractive and the refractive element are exploited to obtain an optical system where both the Abbe number and the refractive power can be changed separately. We investigate the performance of the proposed hybrid lens at zero overall refractive power by tuning the Abbe number of a complementary standard lens while maintaining a constant overall focal length for the central wavelength. As an application example, the hybrid lens is used to tune to an optimal operating regime for quantitative phase microscopy based on a two-color transport of intensity (TIE) approach which utilizes chromatic aberrations rather than intensity recordings at several planes to reconstruct the optical path length of a phase object.

Combined holographic optical trapping and optical image processing using a single diffractive pattern displayed on a spatial light modulator.

We demonstrate simultaneous holographic optical trapping and optical image processing using a single-phase diffraction pattern displayed on a liquid crystal spatial light modulator (SLM). The ability of modern SLMs to provide multiorder phase shifts represents a degree of freedom that allows the calculation of diffraction patterns that act in precisely defined but different ways on light beams of different wavelengths. We exploit this property to calculate a single-phase hologram that shapes multiple optical traps at 785 nm while performing double-helix point spread function engineering at 532 nm. Both channels are independent to a large degree and have efficiencies of about 75% compared to the ideal diffractive patterns.

Enhancing diffractive multi-plane microscopy using colored illumination.

We present a method to increase the number of simultaneously imaged focal planes in diffractive multi-plane imaging. We exploit the chromatic properties of diffraction by using multicolor LED illumination and demonstrate time-synchronous imaging of up to 21 focal planes.We discuss the possibilities and limits given by the use of a liquid crystal spatial light modulator to display the diffractive patterns. The method is suitable for wide-field transmission and reflection microscopy.

Wide-field vibrational phase imaging in an extremely folded box-CARS scattering geometry.

We present a method that allows one to measure the real and imaginary parts of the third-order susceptibility in a wide-field coherent anti-Stokes Raman scattering setup using a quadriwave lateral shearing interferometer. This permits the retrieval of the undistorted Raman spectrum and the removal of a nonresonant signal from the surrounding solvent, which otherwise may overwhelm weak resonances.