Tilt-effect of holograms and images displayed on a spatial light modulator.

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°.

Adjustable diffractive spiral phase plates.

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.

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.

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.

Demonstration of focus-tunable diffractive Moiré-lenses.

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.

Quantitative single-shot imaging of complex objects using phase retrieval with a designed periphery.

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.

Lensless digital holography with diffuse illumination through a pseudo-random phase mask.

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.