Phase Holograms Research Articles

Determination of the parameters of a holographic layer from its spectral characteristics

Methods for estimating the main parameters of holographic sensors (refractive index modulation depth and hologram thickness) from transmission spectra in the absence of absorption and light scattering are discussed. The consideration is performed for layers oriented parallel to the holographic layer surface under normal light incidence. Direct numerical solution of the problem of light propagation in a periodic nonabsorbing medium is used to study the reflection and transmission spectra of the holographic layer in a wide range of variation in its thickness and the refractive index modulation depth. A classification of the reflection regimes from the holographic layer is proposed (from weak reflection to the photonic crystal regime). A comparison with the results obtained by the coupled-wave analysis is performed, and the limitations of this method at a significant spectral detuning from resonance and under conditions of strong reflection are revealed. It is shown that the main hologram parameters can be estimated from the experimental transmission spectrum of the phase hologram (in the case of strong reflection) based on the spectral dip parameters.

Creation of Super Long Transversely Polarized Optical Needle Using Azimuthally Polarized Multi Gaussian Beam

The intensity distribution in the focal region of a high-NA lens for the incident azimuthally polarized multi Gaussian beam transmitted through a multi belt spiral phase hologram is studied on the basis of the vector diffraction theory. Here we report a new method used to generate a needle of transversely polarized light beam with sub diffraction beam size of 0.366λ that propagates without divergence over a long distance of about 22λ in free space. We also expect that such a light needle of transversely polarized beam may find its applications in utilizing optical materials or instruments responsive to the transversal field only.

Fabrication of computer-generated holograms using femtosecond laser direct writing.

We demonstrate a single-step fabrication method for computer-generated holograms based on femtosecond laser direct writing. Therefore, a tightly arranged longitudinal waveguide array is directly inscribed into a transparent material. By tailoring the individual waveguide length, the phase profile of an incident laser beam can be arbitrarily adapted. The approach is verified in common borosilicate glass by inscribing a designed phase hologram, which forms the desired intensity pattern in its far field. The resulting performance is analyzed, and the potential as well as limitations of the method are discussed.

Research on encoding multi-gray-scale phase hologram and wavefront reconstruction.

Application of computer-generated holography for wavefront generation is beneficial for optical interferometry and 3D image display. However, there is a noticeable encoding error in computer-generated holograms, which is encoded by using the object's wavefront function in a computer. The encoding error will be transmitted and amplified during fabrication of a hologram, which can cause a reconstructed error in the generated wavefront. A correction method of encoding errors based on the least-squares fitting is proposed. A validating experiment is completed by using a liquid crystal spatial light modulator to reconstruct a group of paraboloid wavefronts. The results show that encoding errors increase the reconstructed error of a wavefront less than optical system errors, and the root-mean-square value drops 0.022λ after the correction of the encoding error, but it falls 0.092λ after the correction of optical system errors. The total error has been reduced by 0.114λ. This research is helpful for prediction of encoding errors and improvement of wavefront reconstruction accuracy.

Non-iterative phase hologram computation for low speckle holographic image projection.

Phase-only spatial light modulators (SLMs) are widely used in holographic display applications, including holographic image projection (HIP). Most phase computer generated hologram (CGH) calculation algorithms have an iterative structure with a high computational load, and also are prone to speckle noise, as a result of the random phase terms applied on the desired images to mitigate the encoding noise. In this paper, we present a non-iterative algorithm, where simple Discrete Fourier Transform (DFT) relations are exploited to compute phase CGHs that exactly control half of the desired image samples (those on even - or odd - indexed rows - or columns) via a single Fast Fourier Transform (FFT) and trivial arithmetic operations. The encoding noise appearing on the uncontrolled half of the image samples is reduced by the application of structured, non-random initial phase terms so that speckle noise is also kept low. High quality reconstructions are obtained under temporal averaging of several SLM frames. Interlaced video within half of the addressable image area is readily deliverable without frame rate division. Our algorithm provides about 6X and 20X reduction in computational cost compared to IFTA and FIDOC algorithms, respectively. Simulations and experiments verify that the algorithm constitutes a promising option for real-time computation of phase CGHs.

A method of achieving the maximum diffraction efficiency of holograms based on optimizing the form factor

For the case of 3D phase holograms, the impact of the form factor on the hologram diffraction efficiency is shown. The form factor concept is introduced by analogy with the classical definition, which is used for calculating the averaged interaction of complex-shaped objects. In the present context, the form factor concept is used for determining the average diffraction efficiency of the holograms formed with the help of beams distributed non-uniformly over the hologram field. It is shown that after calculating the corrections, they can be used in the same way as coefficients in the classical formulas of the diffraction efficiency. The impact of such a form factor only comes into play when there are two factor present at the same time, i. e. non-linearity of photoresponse and non-uniformity of the light beam distribution over the hologram field.

Quality assessment of combined quantization-shot-noise-induced decorrelation noise in high-speed digital holographic metrology.

this paper discusses on the influence of decorrelation noise induced by quantization and shot-noise when recording digital holograms at very high frame rate. A criterion based on the coherence factor of the hologram phase difference is proposed. The main parameters of interest are the ratio between the reference and the object waves and the sensor dynamics, depending on the photo-electron capacity of pixels. The study is based on a full numerical simulation of the holographic process, which provides useful rules. This leads to define the optimal conditions for recording at very-high frame rate with minimization of the decorrelation noise. Experimental results obtained with frame rate at 50kHz confirm the proposed approach.

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°.

Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram

We generate various kinds of arrays of Gaussian vortex, Bessel and Airy beams, respectively, with digital phase holograms (DPH) based on the fractional-Talbot effect by using the phase-only spatial light modulator (SLM). The linear and nonlinear transmissions of these beam arrays in strontium barium niobate (SBN) crystal are investigated numerically and experimentally. Compared with Gaussian vortex arrays, Bessel and Airy beam arrays can keep their patterns unchanged in over 20mm, realizing non-diffracting transmission. The Fourier spectra (far-field diffraction patterns) of the lattices are also studied. The experimental results are in good agreement with the numerical simulations.

Applying gray-scaled detour phase hologram on liquid crystal on silicon spatial light modulator (LCoS-SLM)

In order to solve the representation problem of computer-generated holograms, multiple algorithms have been devised. One of which is the well-known detour phase method. This method has recently been modified to be optimized to display the generated hologram on twisted nematic spatial light modulators. In this paper, we apply the modified gray-scaled detour phase holograms on another type of spatial light modulators, which is of utmost importance in the field, namely the reflective liquid crystal on silicon spatial light modulator.

Acoustic phase hologram with labyrinthine metamaterials

Acoustic metamaterials offer large degree of design freedom and precise control over amplitude and phase at subwavelength scales. In the past, we have demonstrated a family of labyrinthine metamaterial unit cells as premium building blocks for phase modulation devices, as well as several 1D wavefront shaping devices based on these unit cells. Here we extend the complex modulations to 2D by demonstrating a computer generated metamaterial-based phase hologram. Through spatially modulating the phase of the wavefront, the hologram projects the incident wave to a designed three-dimensional amplitude pattern. The hologram is designed with a two-step process: first, an iterative holographic reconstruction algorithm is used to obtain the optimal phase pattern of the hologram; second, unit cells with desired phase modulations are designed and fabricated. Ray tracing and full-wave simulations have been performed to verify the design. The measurements of reconstruction in an anechoic chamber will be taken for a hologram designed to operate around 4 kHz. The metamaterial-based hologram creates a three-dimensional acoustic illusion with only passive structures. The designing process can also be extended to devices such as multi-focal lenses and wave-based analog processing/computing interfaces.

Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission.

Metasurfaces are planar structures that locally modify the polarization, phase and amplitude of light in reflection or transmission, thus enabling lithographically patterned flat optical components with functionalities controlled by design. Transmissive metasurfaces are especially important, as most optical systems used in practice operate in transmission. Several types of transmissive metasurface have been realized, but with either low transmission efficiencies or limited control over polarization and phase. Here, we show a metasurface platform based on high-contrast dielectric elliptical nanoposts that provides complete control of polarization and phase with subwavelength spatial resolution and an experimentally measured efficiency ranging from 72% to 97%, depending on the exact design. Such complete control enables the realization of most free-space transmissive optical elements such as lenses, phase plates, wave plates, polarizers, beamsplitters, as well as polarization-switchable phase holograms and arbitrary vector beam generators using the same metamaterial platform.

Holographic Generation of Highly Twisted Electron Beams

Free electrons can possess an intrinsic orbital angular momentum, similar to those in an electron cloud, upon free-space propagation. The wave front corresponding to the electron’s wave function forms a helical structure with a number of twists given by the angular speed. Beams with a high number of twists are of particular interest because they carry a high magnetic moment about the propagation axis. Among several different techniques, electron holography seems to be a promising approach to shape a conventional electron beam into a helical form with large values of angular momentum. Here, we propose and manufacture a nanofabricated phase hologram for generating a beam of this kind with an orbital angular momentum up to 200ℏ. Based on a novel technique thevalue of orbital angular momentum of the generated beam is measured and then compared with simulations. Our work, apart from the technological achievements, may lead to a way of generating electron beams with a high quanta of magnetic moment along the propagation direction and, thus, may be used in the study of the magnetic properties of materials and for manipulating nanoparticles.

Specific features of electrical conductivity of LiTaO3 and LiNbO3 crystals in the temperature range of 290–450 K

The electrical conductivity of single crystals of lithium tantalate and lithium niobate of the congruent composition not subjected to special thermochemical treatments has been investigated in the temperature range of 290–450 K. It has been shown that the charge transfer mechanisms and carrier types in these crystals are identical in the temperature range under study. The presence of mobility anisotropy of conduction electrons has been revealed and its influence on the recording and storage of optical phase holograms in these crystals has been established.

Holographic fluorescence microscopy with incoherent digital holographic adaptive optics.

Introduction of adaptive optics technology into astronomy and ophthalmology has made great contributions in these fields, allowing one to recover images blurred by atmospheric turbulence or aberrations of the eye. Similar adaptive optics improvement in microscopic imaging is also of interest to researchers using various techniques. Current technology of adaptive optics typically contains three key elements: a wavefront sensor, wavefront corrector, and controller. These hardware elements tend to be bulky, expensive, and limited in resolution, involving, for example, lenslet arrays for sensing or multiactuator deformable mirrors for correcting. We have previously introduced an alternate approach based on unique capabilities of digital holography, namely direct access to the phase profile of an optical field and the ability to numerically manipulate the phase profile. We have also demonstrated that direct access and compensation of the phase profile are possible not only with conventional coherent digital holography, but also with a new type of digital holography using incoherent light: selfinterference incoherent digital holography (SIDH). The SIDH generates a complex—i.e., amplitude plus phase—hologram from one or several interferograms acquired with incoherent light, such as LEDs, lamps, sunlight, or fluorescence. The complex point spread function can be measured using guide star illumination and it allows deterministic deconvolution of the full-field image. We present experimental demonstration of aberration compensation in holographic fluorescence microscopy using SIDH. Adaptive optics by SIDH provides new tools for improved cellular fluorescence microscopy through intact tissue layers or other types of aberrant media.

Recording and thermo developing of latent phase holograms in the photosensitive polymer material based on anthracylacetonatoboron difluoride

The diffraction efficiency of photoinduced gratings recorded in polymethylmethacrylate doped with anthracylacetonatoboron difluoride was shown to be increased from 8% to 70% due to the post-exposure heating of the material to 75°C. Mechanism of the thermal development was determined to be the diffusion of the initial photoactive additives molecules and the photoproduct. This process shifts the minimum of the material frequency-contrast characteristic into the low-frequency region as well as significantly increases the amplitude of the refractive index modulation for gratings with the spatial frequencies up to 2500mm−1.

Photothermal Conversion of Color Centers in $$\hbox {CaF}_{2}$$ CaF 2 Crystals: A Process Underlying the Use of Crystals as a Holographic Medium

Photothermal effects in a holographic medium of calcium fluoride crystals with color centers \((\hbox {CaF}_{2})\) are discussed. It is shown that photochromism of this crystal makes it possible to record volume holograms within its volume and to change their physical properties by photothermal treatments. The diffusion–drift mechanism of a hologram recording in \(\hbox {CaF}_{2}\) includes the conversion of centers and their redistribution over the crystal bulk. Depending on the readout wavelength, it is possible to read out amplitude, amplitude phase, or phase holograms. The opportunity to record thick holograms in \(\hbox {CaF}_{2}\) and their high resistance with respect to non-coherent illumination at an elevated temperature allows forming narrow-band angular and spectral holographic filters in \(\hbox {CaF}_{2}\).

GPC-enhanced read-out of holograms

The Generalized Phase Contrast (GPC) method has been demonstrated to reshape light efficiently to match the input beam profile requirements of different illumination targets. A spatially coherent beam can be GPC-shaped into a variety of static and dynamic profiles to match e.g. fixed commercially available modulation systems or for more irregular and dynamic shapes such as found in advanced optogenetic light-excitations of neurons. In this work, we integrate a static GPC light shaper to illuminate a phase-only spatial light modulator encoding dynamic phase holograms. The GPC-enhanced phase-holograms are encoded to create reconfigurable spot arrays and arbitrary extended patterns. For a given laser power, our experimental results show a significant intensity gain in the resulting diffraction patterns when we illuminate the holograms with a GPC-shaped beam as compared to the more common practice of hard truncation. The phase flatness of the GPC-enhanced readout beam has also been investigated.

Laser microsculpting for the generation of robust diffractive security markings on the surface of metals

We report the development of a laser-based process for the direct writing (‘microsculpting’) of unique security markings (reflective phase holograms) on the surface of metals. In contrast to the common approaches used for unique marking of the metal products and components, e.g., polymer holographic stickers which are attached to metals as an adhesive tape, our process enables the generation of the security markings directly onto the metal surface and thus overcomes the problems with tampering and biocompatibility which are typical drawbacks of holographic stickers. The process uses 35ns laser pulses of wavelength 355nm to generate optically-smooth deformations on the metal surface using a localised laser melting process. Security markings (holographic structures) on 304-grade stainless steel surface are fabricated, and their resulted optical performance is tested using a He–Ne laser beam of 632.8nm wavelength.

Ultrafast laser beam shaping for material processing at imaging plane by geometric masks using a spatial light modulator

We have demonstrated an original ultrafast laser beam shaping technique for material processing using a spatial light modulator (SLM). Complicated and time-consuming diffraction far-field phase hologram calculations based on Fourier transformations are avoided, while simple and direct geometric masks are used to shape the incident beam at diffraction near-field. Various beam intensity shapes, such as square, triangle, ring and star, are obtained and then reconstructed at the imaging plane of an f-theta lens. The size of the shaped beam is approximately 20µm, which is comparable to the beam waist at the focal plane. A polished stainless steel sample is machined by the shaped beam at the imaging plane. The shape of the ablation footprint well matches the beam shape.