Search

A novel type of a continuously zoomable telescope is based on two pairs of adjacent toroidal lenses ("saddle lenses") in combination with standard optical components. Its variable magnification is adjusted by a mere rotation of the four saddle lenses around the optical axis. This avoids the necessity of classical zoom systems to shift multiple lenses along the longitudinal axis of the setup. A rotationally tunable pair of saddle lenses consists of two individual saddle lenses (also known as quadrupole lenses, or biconic lenses), which are arranged directly behind each other, acting as a "combi-saddle lens." The transmission function of such a combi-saddle lens corresponds to that of a single saddle lens, but with an adjustable optical power which depends on the mutual rotation angle between its two components. The optical system contains two of these combi-saddle lenses, and acts as a cylindrical Kepler telescope in one plane, and as a cylindrical Galilei telescope in the orthogonal plane. The two orthogonal Kepler/Galilei telescopes stay aligned and change their magnification factors in the same way when the telescope is zoomed by adjusting the optical powers of the two combi-saddle lenses. Altogether this produces a sharp image, which is mirrored with respect to the axis of the Kepler telescope. Thus, in addition to the zooming capabilities of the telescope, it is also possible to rotate the resulting image by a rotation of the whole telescope, or of all included saddle lenses. The operation principle of the telescope will be explained in both a ray-optical and a wave-optical description.

Rotationally tunable diffractive optical elements (DOEs) consist of two stacked diffractive optical elements which are rotated with respect to each other around their central optical axis. The combined diffractive element acts as a highly efficient diffractive lens, which changes its optical power as a function of the mutual rotation angle. Here we show that the principle can be extended to produce polychromatic tunable lenses, i.e. lenses which have the same optical power, and the same diffraction efficiency within the full tuning range at three or more selectable wavelengths. The basic principle is to use higher order DOEs, which will be polychromatic at harmonics of a fundamental wavelength. The method can be applied to other types of optical elements which are tunable by rotation, like axicons, or generalized lenses with arbitrary radial phase profiles, or to elements tunable by a mutual translation, like diffractive Alvarez lenses.

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.

We show that a liquid crystal spatial light modulator (LCOS-SLM) can be used to display amplitude images, or phase holograms, which change in a pre-determined way when the display is tilted, i.e. observed under different angles. This is similar to the tilt-effect (also called "latent image effect") known from various security elements ("kinegrams") on credit cards or bank notes. The effect is achieved without any specialized optical components, simply by using the large phase shifting capability of a "thick" SLM, which extends over several multiples of 2π, in combination with the angular dependence of the phase shift. For hologram projection one can use the fact that the phase of a monochromatic wave is only defined modulo 2π. Thus one can design a phase pattern extending over several multiples of 2π, which transforms at different readout angles into different 2π-wrapped phase structures, due to the angular dependence of the modulo 2π operation. These different beams then project different holograms at the respective readout angles. In amplitude modulation mode (with inserted polarizer) the intensity of each SLM pixel oscillates over several periods when tuning its control voltage. Since the oscillation period depends on the readout angle, it is possible to find a certain control voltage which produces two (or more) selectable gray levels at a corresponding number of pre-determined readout angles. This is done with all SLM pixels individually, thus constructing different images for the selected angles. We experimentally demonstrate the reconstruction of multiple (Fourier- and Fresnel-) holograms, and of different amplitude images, by readout of static diffractive patterns in a variable angular range between 0° and 60°.

We report on the fabrication and the experimental demonstration of Moiré diffractive spiral phase plates with adjustable helical charge. The proposed optical unit consists of two axially stacked diffractive elements of conjugate structure. The joint transmission function of the compound system corresponds to that of a spiral phase plate where the angle of mutual rotation about the central axis enables continuous adjustment of the helical charge. The diffractive elements are fabricated by gray-scale photolithography with a pixel size of 200 nm and 128 phase step levels in fused silica. We experimentally demonstrate the conversion of a TEM(00) beam into approximated Laguerre-Gauss (LG) beams of variable helical charge, with a correspondingly variable radius of their ring-shaped intensity distribution.

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.

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%.

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.

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.

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.

In spiral phase contrast (SPC) microscopy the edge-enhancement is typically independent of the helicity of the phase vortex filter. Here we show that for layered specimens containing screw-dislocations, as are e.g. present in mica or some crystallized organic substances, the intensity distribution in the filtered image acquires a dependence on the rotational direction of the filter. This allows one to map the distribution of phase singularities in the topography of the sample, by taking the intensity difference between two images recorded with opposite handedness. For the demonstration of this feature in a microscopy set-up, we encode the vortex filter as a binary off-axis hologram displayed on a spatial light modulator (SLM) placed in a Fourier plane. Using a binary grating, the diffraction efficiencies for the plus and minus first diffraction orders are equal, giving rise to two image waves which travel in different directions and are Fourier filtered with opposite helicity. The corresponding two images can be recorded simultaneously in two separate regions of the camera chip. This enables mapping of dislocations in the sample in a single camera exposure, as was demonstrated for various transparent samples.

In an earlier publication [Appl. Opt. 47, 3722 (2008)] we suggested an adaptive optical lens, which consists of two cascaded diffractive optical elements (DOEs). Due to the Moiré-effect the combined optical element acts as a Fresnel zone lens with a refractive power that can be continuously adjusted by a mutual rotation of the two stacked DOEs. Here we present an experimental realization of this concept. Four designs of these Moiré-DOEs (MDOEs) were fabricated in thin (0.7 mm) glass slides by lithography and subsequent etching. Each element was realized as a 16 phase level DOE designed for 633 nm illumination. Our experimental investigation shows that the Moiré-lenses have a broad adjustable refractive power range with a high efficiency, which allows one to use them for flexible beam steering and for imaging applications.

In various microscopy applications spatial light modulators (SLMs) are used as programmable Fourier filters to realize different optical contrast enhancement methods. It is often advantageous to use the SLM in off-axis configuration, where the filtered image wave is sent into the first diffraction order of a blazed grating superposed to the phase mask on the SLM. Because of dispersion this approach is, however, typically limited to spectrally narrowband illumination. Here we suggest a method involving a grating for pre-compensation, which allows one to use spectrally broadband (even thermal) light in SLM-based Fourier filtering. The proposed approach is demonstrated by multicolor imaging of amplitude and phase objects, such as a resolution target, onion epidermal cells and human epithelial cheek cells.

Measuring transmission and optical thickness of an object with a single intensity recording is desired in many fields of imaging research. One possibility to achieve this is to employ phase retrieval algorithms. We propose a method to significantly improve the performance of such algorithms in optical imaging. The method relies on introducing a specially designed phase object into the specimen plane during the image recording, which serves as a constraint in the subsequent phase retrieval algorithm. This leads to faster algorithm convergence and improved final accuracy. Quantitative imaging can be performed by a single recording of the resulting diffraction pattern in the camera plane, without using lenses or other optical elements. The method allows effective suppression of the "twin-image", an artefact that appears when holograms are read out. Results from numerical simulations and experiments confirm a high accuracy which can be comparable to that of phase-stepping interferometry.

Microscopic imaging with a setup consisting of a pseudo-random phase mask, and an open CMOS camera, without an imaging objective, is demonstrated. The pseudo random phase mask acts as a diffuser for an incoming laser beam, scattering a speckle pattern to a CMOS chip, which is recorded once as a reference. A sample which is afterwards inserted somewhere in the optical beam path changes the speckle pattern. A single (non-iterative) image processing step, comparing the modified speckle pattern with the previously recorded one, generates a sharp image of the sample. After a first calibration the method works in real-time and allows quantitative imaging of complex (amplitude and phase) samples in an extended three-dimensional volume. Since no lenses are used, the method is free from lens abberations. Compared to standard inline holography the diffuse sample illumination improves the axial sectioning capability by increasing the effective numerical aperture in the illumination path, and it suppresses the undesired so-called twin images. For demonstration, a high resolution spatial light modulator (SLM) is programmed to act as the pseudo-random phase mask. We show experimental results, imaging microscopic biological samples, e.g. insects, within an extended volume at a distance of 15 cm with a transverse and longitudinal resolution of about 60 μm and 400 μm, respectively.

We introduce a widefield CARS microscope implementation that uses a spatial light modulator to obtain extremely precise control over the pump/probe-beam incidence geometry, which provides the possibility to enhance the image contrast at specific target resonances by fine-tuning the incidence angles. We show how this technique can be used to optimize the image contrast between objects of different size and to practically eliminate the undesired signal from the solvent that embeds small target specimens. Changing the numerical aperture of the illumination from 1.27 to 1.24 improved the ratio of the signals of 500 nm polystyrene beads and the agarose solvent by about 20 dB.

We demonstrate "depth of field multiplexing" by a high resolution spatial light modulator (SLM) in a Fourier plane in the imaging path of a standard microscope. This approach provides simultaneous imaging of different focal planes in a sample with only a single camera exposure. The phase mask on the SLM corresponds to a set of superposed multi-focal off-axis Fresnel lenses, which sharply image different focal planes of the object to non-overlapping adjacent sections of the camera chip. Depth of field multiplexing allows to record motion in a three dimensional sample volume in real-time, which is exemplarily demonstrated for cytoplasmic streaming in plant cells and rapidly swimming protozoa.

Holographic optical tweezers typically require microscope objectives with high numerical aperture and thus usually suffer from the disadvantage of a small field of view and a small working distance. We experimentally investigate an optical mirror trap that is created after reflection of two holographically shaped collinear beams on a mirror. This approach combines a large field of view and a large working distance with the possibility to manipulate particles in a large size range, since it allows to use a microscope objective with a numerical aperture as low as 0.2. In this work we demonstrate robust optical three-dimensional trapping in a range of 1mm x 1mm x 2mm with particle sizes ranging from 1.4 mum up to 45 mum. The use of spatial light modulator based holographic methods to create the trapping beams allows to simultaneously trap many beads in complex, dynamic configurations. We present measurements that characterize the mirror traps in terms of trap stiffness, maximum trapping force and capture range.

A modification of the phase contrast method in microscopy is presented, which reduces inherent artifacts and improves the spatial resolution. In standard Zernike phase contrast microscopy the illumination is achieved through an annular ring aperture, and the phase filtering operation is performed by a corresponding phase ring in the back focal plane of the objective. The Zernike method increases the spatial resolution as compared to plane wave illumination, but it also produces artifacts, such as the halo- and the shade-off effect. Our modification consists in replacing the illumination ring by a set of point apertures which are randomly distributed over the whole aperture of the condenser, and in replacing the Zernike phase ring by a matched set of point-like phase shifters in the back focal plane of the objective. Experimentally this is done by illuminating the sample with light diffracted from a phase hologram displayed at a spatial light modulator (SLM). The subsequent filtering operation is then done with a second matched phase hologram displayed at another SLM in a Fourier plane of the imaging pathway. This method significantly reduces the halo- and shade-off artifacts whilst providing the full spatial resolution of the microscope.

A method to remove undesired diffraction orders of computer-generated binary phase holograms is demonstrated. Normally, the reconstruction of binary Fourier holograms, made from just two phase levels, results in an undesired inverted image from the minus first diffraction order, which is superposed with the desired one. This can be avoided by reconstructing the hologram with a diffuse light field with a pseudorandom, but known, phase distribution, which is taken into account for the hologram computation. As a consequence, only the desired image is reconstructed, whereas all residual light is dispersed, propagating as a diffuse background wave. The method may be advantageous to employ ferroelectric spatial light modulators as holographic display devices, which can display only binary phase holograms, but which have the advantage of fast switching rates.

We show how suitable combinations of cascaded diffractive optical elements (DOEs) can form a combined "moiré DOE" of adjustable refractive power and high diffraction efficiency. The optical power can be adjusted continuously by a mutual rotation of one DOE with respect to the other. Fresnel lenses and axicons of variable refractive power or spiral phase plates of adjustable helical charge can be realized this way.

Recently we demonstrated the applicability of a holographic method for shaping complex wavefronts to spatial light modulator (SLM) systems. Here we examine the potential of this approach for optical micromanipulation. Since the method allows one to shape both amplitude and phase of a trapping light field independently and thus provides full control over scattering and gradient forces, it extends the possibilities of commonly used holographic tweezers systems. We utilize two cascaded phase-diffractive elements which can actually be display side-by-side on a single programmable phase modulator. Theoretically the obtainable light efficiency is close to 100%, in our case the major practical limitation arises from absorption in the SLM. We present data which demonstrate the ability to create user-defined "light pathways" for microparticles driven by transverse radiation pressure.

We present an implementation method for noiseless holographic projection of precalculated light fields with a spatial light modulator. In the reconstructed image, both the spatial amplitude and phase distributions can be programmed independently. This is achieved by diffracting the light from two successive phase holograms that are located in conjugate Fourier planes. The light path is folded such that the two corresponding phase masks can be displayed side by side at a single phase-only spatial light modulator. Such a device has relevant applications in holographic display-or projection systems, and for optical micromanipulation in laser tweezers.

We investigate holographic optical tweezers manipulating micro-beads at a suspended air-liquid interface. Axial confinement of the particles in the two-dimensional interface is maintained by the interplay between surface tension and gravity. Therefore, optical trapping of the micro-beads is possible even with a long distance air objective. Efficient micro-circulation of the liquid can be induced by fast rotating beads, driven by the orbital angular momentum transfer of incident Laguerre-Gaussian (doughnut) laser modes. Our setup allows various ways of creating a tailored dynamic flow of particles and liquid within the surface. We demonstrate examples of surface manipulations like efficient vortex pumps and mixers, interactive particle flow steering by arrays of vortex pumps, the feasibility of achieving a "clocked" traffic of micro beads, and size-selective guiding of beads along optical "conveyor belts".

Recently a spatial spiral phase filter in a Fourier plane of a microscopic imaging setup has been demonstrated to produce edge enhancement and relief-like shadow formation of amplitude and phase samples. Here we demonstrate that a sequence of at least 3 spatially filtered images, which are recorded with different rotational orientations of the spiral phase plate, can be used to obtain a quantitative reconstruction of both, amplitude and phase information of a complex microscopic sample, i.e. an object consisting of mixed absorptive and refractive components. The method is demonstrated using a calibrated phase sample, and an epithelial cheek cell.

We demonstrate an optical method for edge contrast enhancement in light microscopy. The method is based on holographic Fourier plane filtering of the microscopic image with a spiral phase element (also called vortex phase or helical phase filter) displayed as an off-axis hologram at a computer controlled high resolution spatial light modulator (SLM) in the optical imaging pathway. The phase hologram imprints a helical phase term of the form exp(i phi) on the diffracted light field in its Fourier plane. In the image plane, this results in a strong and isotropic edge contrast enhancement for both amplitude and phase objects.

We experimentally investigate the size-selective trapping behavior of Laguerre-Gaussian beams ("doughnut-beams") and "cogwheel"-shaped beams which are collinear superpositions of two doughnut beams of equal opposite helical index. Experimentally they are created by diffraction of a Gaussian laser beam at a high resolution refractive spatial light modulator (SLM). In the focus of an optical microscope such a beam looks similar to a "cogwheel", i.e. the light intensity is periodically modulated around the circumference of a sphere with a precisely adjustable diameter. In an optical tweezers setup these modes can be used to trap particles or cells, provided their sizes exceed the ring diameter by a fixed amount. This promises a convenient method of constructing an optical tweezers system in microscopy which acts as a passive sorter for particles of differing sizes.