Iterative Fourier Transform Algorithm Research Articles

Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm

Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm

An improved Fourier modal method for design of metasurface diffractive optical elements

An improved Fourier modal method (FMM) is developed for the design of metasurface diffractive optical elements (DOEs), which combines the iterative Fourier transform algorithm (IFTA) with FMM. In which, the IFTA is executed for a coarse solution; then, FMM is for a precise solution. We take a 5 × 5 metasurface DOE with nanorods as an example to explore the improved FMM (IFTA + FMM). By varying the diameter of the nanorods on the metasurface DOE, a 5 × 5 spot array DOE has been created with a diffraction angle of 48°× 48° in the far field. The analysis results show that the improved FMM (IFTA + FMM) requires fewer iterations, about 17 times, while direct FMM requires about 70 times. The DOE designed with an improved FMM achieves a diffraction efficiency of 79.6% with a uniformity of 24.2%, while the DOE designed with a direct FMM shows a diffraction efficiency of 76.9% with a uniformity of 27.7%. The improved FMM (IFTA + FMM) shows a similar accuracy, but is more timesaving, simple, and intuitive.

Suppression of alias and replica noises in phase holograms using fractal topologies.

Two-dimensional fractal topologies featuring (scaling) self-similarity, dense set of Bragg (diffraction) peaks, and inherent rotation symmetry, which are not achievable with regular grid-matrix geometries, exhibit optical robustness against structural damage and noise immunity of optical transmission paths. In this work, we numerically and experimentally demonstrate phase holograms using fractal plane-divisions. By taking advantage of the symmetries of the fractal topology, we propose numerical algorithms to design the fractal holograms. This algorithm solves the inapplicability of the conventional iterative Fourier transform algorithm (IFTA) method and enables efficient optimizations of millions of adjustable parameters in the optical element. Experimental samples show that the alias and replica noises in the image plane of fractal holograms are clearly suppressed, facilitating applications for high-accuracy and compact requirements.

Fast generation of arbitrary optical focus array

We report a novel method to generate arbitrary optical focus arrays (OFAs). Our approach rapidly produces computer-generated holograms (CGHs) to precisely control the positions and the intensities of the foci. This is achieved by replacing the fast Fourier transform (FFT) operation in the conventional iterative Fourier-transform algorithm (IFTA) with a linear algebra one, identifying/removing zero elements from the matrices, and employing a generalized weighting strategy. On the premise of accelerating the calculation speed by >70 times, we demonstrate OFA with 99% intensity precision in the experiment. Our method proves effective and is applicable to systems in which real-time OFA generation is essential.

Discrimination between normal and cancer white blood cells using holographic projection technique.

White blood cells (WBCs) play a vital role in the diagnosis of many blood diseases. Such diagnosis is based on the morphological analysis of blood microscopic images which is performed manually by skilled hematologist. However, this method has many drawbacks, such as the dependence on the hematologist’s skill, slow performance, and varying accuracy. Therefore, in the current study, a new optical method for discrimination between normal and cancer WBCs of peripheral blood film (PBF) images is presented. This method is based on holographic projection technique which is able to provide an accurate and fast optical reconstruction method of WBCs floating in the air. Besides, it can provide a 3D visualization map of one WBC with its characterization parameters from only a single 2D hologram. To achieve that, at first, WBCs are accurately segmented from the microscopic PBF images using a developed in-house MATLAB code. Then, their associated phase computer-generated holograms (CGHs) are calculated using the well-known iterative Fourier transform algorithm (IFTA). Within the utilized algorithm, a speckle noise reduction technique, based on temporal multiplexing of spatial frequencies, is applied to minimize the speckle noise across the reconstruction plane. Additionally, a special hologram modulation is added to the calculated holograms to provide a 3D visualization map of one WBC, and discriminate normal and cancer WBCs. Finally, the calculated phase-holograms are uploaded on a phase-only spatial light modulator (SLM) for optical reconstruction. The optical reconstruction of such phase-holograms yields precise representation of normal and cancer WBCs. Moreover, a 3D visualization map of one WBC with its characterization parameters is provided. Therefore, the proposed technique can be used as a valuable tool for interpretation and analysis of WBCs, this in turn could provide an improvement in diagnosis and prognosis of blood diseases.

Machine learning-based error compensation for high precision laser arbitrary beam splitting

A method for error compensation based on machine learning is developed for high-precision laser arbitrary beam-splitting technology. The preliminary approach in laser arbitrary beam splitting is to generate a phase hologram using the iterative Fourier transform algorithm (IFTA) and modulate the incident light beam into multiple beams using a spatial light modulator (SLM). The inherent error in the algorithm and experiment described above prevents beam splitting from improving precision. Error compensated machine learning is developed to mitigate the aforementioned impact and improve beam splitting precision. The corresponding supervised learning regression task on the Numerical simulation dataset, and the SLM experimental dataset establishes two types of mapping relationships between the target image and the detection result image. With the benefit of error compensated machine learning, the mean absolute error (MAE) of beam splitting was reduced by 28% in theory and 21% in the experiment. The error compensated machine learning method is an efficient way to achieve high precision laser arbitrary beam splitting.

LCOS-SLM Based Intelligent Hybrid Algorithm for Beam Splitting

The iterative Fourier transform algorithm (IFTA) is widely used in various optical communication applications based on liquid crystal on silicon spatial light modulators. However, the traditional iterative method has many disadvantages, such as a poor effect, an inability to select an optimization direction, and the failure to consider zero padding or phase quantization. Moreover, after years of development, the emergence of various variant algorithms also makes it difficult for researchers to choose one. In this paper, a new intelligent hybrid algorithm that combines the IFTA and differential evolution algorithm is proposed in a novel way. The reliability of the proposed algorithm is verified by beam splitting, and the IFTA and symmetrical IFTA algorithms, for comparison, are introduced. The hybrid algorithm improves the defects above while considering the zero padding and phase quantization of a computer-generated hologram, which optimizes the directional optimization in the diffraction efficiency and the fidelity of the output beam and improves the results of these two algorithms. As a result, the engineers’ trouble in the selection of an algorithm has also been reduced.

Three-dimensional beam shaping by means of a spatial phase modulator for two-photon-polymerization

Two-photon-polymerization is an additive manufacturing method to produce parts with high resolution. With reachable voxel sizes below the optical diffraction limit, it is of particular interest for biomedical or micro-optical applications. Despite its high resolution, the spreading of this method is hindered by its low productivity in the µm³/s range. Scaling up productivity is in principle possible with already available laser sources with high pulse energy and beam shaping such as multi-spot approaches. This beam shaping is limited in the processable volume and has to be expanded to arbitrary beam shapes in three dimensions to make use of the next generation laser sources with higher pulse energy and higher average laser power. In this work, a three-dimensional Iterative Fourier Transform Algorithm for optimizing arbitrary three-dimensional intensity distributions using a spatial phase modulator was investigated for suitability for 2PP.

Numerical optimization of writing computer-generated holograms in threshold media

Recent developments in binary photo-magnetic materials showed efficient and ultra-fast rewriting of holograms where the intensity threshold allows for a dense, sub-diffraction limit packing of hologram points. This paper describes the numerical optimization of the process of writing and reconstructing of 2-D images in a binary-phase computer-generated holograms stored in the said threshold-like medium. Global optimization of the free parameters of the writing process is shown, including the intensity threshold level, propagation distance, hologram spot size and the shape of the boundary regions of the written spots. We present the optimal set of parameters for the best possible writing quality. Full Text: PDF ReferencesA. Stupakiewicz, K. Szerenos, D. Afanasiev et al., "Ultrafast nonthermal photo-magnetic recording in a transparent medium", Nature 542, 71 (2017). CrossRef J. Starobrat, A. Frej, J. Bolek, R. Trybus, A. Stupakiewicz, and M. Makowski, "Photo-magnetic recording of randomized holographic diffraction patterns in a transparent medium", Opt. Lett. 45, 5177 (2020). CrossRef V. Ostroverkhov, et al., "Micro-Holographic Storage and Threshold Holographic Recording Materials", Jap. J. App. Phys. 48.3S1, 03A035 (2009). CrossRef K. Matsushima, T. Shimobaba, "Band-Limited Angular Spectrum Method for Numerical Simulation of Free-Space Propagation in Far and Near Fields", Opt. Express 17, 19662 (2009). CrossRef F. Wyrowski, O. Bryngdahl, "Iterative Fourier-transform algorithm applied to computer holography", JOSA A 5.7, 1058 (1988). CrossRef I. Ducin, T. Shimobaba, M. Makowski, K. Kakarenko, A. Kowalczyk, Jaroslaw Suszek, M. Bieda, A. Kolodziejczyk, M. Sypek, "Holographic projection of images with step-less zoom and noise suppression by pixel separation", Opt. Comm. 340, 131 (2015). CrossRef M. Makowski, "Minimized speckle noise in lens-less holographic projection by pixel separation", Opt. Express 21, 29205 (2013). CrossRef

Design and Simulation of 1xN Optical Switch Based on LCoS SLM by Using Iterative Fourier Transform Algorithm with the Optimization Method

Proceedings of the International Display Workshops Volume 28 (IDW '21),Design and Simulation of 1xN Optical Switch Based on LCoS SLM by Using Iterative Fourier Transform Algorithm with the Optimization Method

Ultrahigh-aspect-ratio beam generation with super-resolution spot

Focusing to a small spot along a large depth of focus (DOF) beyond the limits imposed by diffraction has attracted extensive theoretical as well as practical interest. The aspect ratio, defined as the DOF divided by the diameter of spot, has been extended by several schemes with reasonable success, but there is no report that enables one to modulate the aspect ratio as long as possible with sidelobe suppression. In this Letter, we propose a method to generate ultrahigh-aspect-ratio beams (UARBs) by introducing an analytic procedure using Zernike polynomials in the modified iterative Fourier-transform algorithm, and a super-resolution spot is also realized to further extend the aspect ratio. We design the diffractive optical elements that generate UARBs with sidelobe suppression and further experimentally demonstrate a stretched 1602:1 aspect ratio of UARBs with a lateral super-resolution spot, suggesting potential applications for further super-resolution imaging or precision fabrication.

Reprogrammable and high-precision holographic optical addressing of trapped ions for scalable quantum control

High-precision, individually programmable manipulation of quantum particles is crucial for scaling up quantum information processing (QIP) systems such as laser-cooled trapped-ions. However, restricting undesirable “crosstalk” in optical manipulation of ion qubits is fundamentally challenging due to micron-level inter-ion separation. Further, inhomogeneous ion spacing and high susceptibility to aberrations at UV wavelengths suitable for most ion-species pose severe challenges. Here, we demonstrate high-precision individual addressing (λ = 369.5 nm) of Yb+ using a reprogrammable Fourier hologram. The precision is achieved through in-situ aberration characterization via the trapped ion, and compensating (to λ/20) with the hologram. Using an iterative Fourier transformation algorithm (IFTA), we demonstrate an ultra-low (<10−4) intensity crosstalk error in creating arbitrary pair-wise addressing profiles, suitable for over fifty ions. This scheme relies on standard commercial hardware, can be readily extended to over a hundred ions, and adapted to other ion-species and quantum platforms.

Quasi-Continuous Metasurface Beam Splitters Enabled by Vector Iterative Fourier Transform Algorithm.

Quasi-continuous metasurfaces are widely used in various optical systems and their subwavelength structures invalidate traditional design methods based on scalar diffraction theory. Here, a novel vector iterative Fourier transform algorithm (IFTA) is proposed to realize the fast design of quasi-continuous metasurface beam splitters with subwavelength structures. Compared with traditional optimization algorithms that either require extensive numerical simulations or lack accuracy, this method has the advantages of accuracy and low computational cost. As proof-of-concept demonstrations, several beam splitters with custom-tailored diffraction patterns and a 7 × 7 beam splitter are numerically demonstrated, among which the maximal diffraction angle reaches 70° and the best uniformity error reaches 0.0195, showing good consistency with the target energy distribution and these results suggest that the proposed vector IFTA may find wide applications in three-dimensional imaging, lidar techniques, machine vision, and so forth.

Alternative Design of Binary Phase Diffractive Optical Element with Non-π Phase Difference

It was found that binary phase diffractive optical element (DOE) with non-π phase difference had higher diffraction efficiency and adjustable zero-order intensity than a 0-π one. However, existing design methods are all based on the simulated annealing algorithm and thus computationally expensive. In this paper, a simple and efficient method using the iterative Fourier transform algorithm (IFTA) is proposed. In this method, the target pattern is first modified via reducing the zero-order intensity. Then, the IFTA is adopted to design the conventional 0-π DOE. Subsequently, the phase distribution remains unchanged and the phase difference is carefully adjusted to increase the zero-order intensity so that the reconstructed pattern is consistent with the target. To verify this method, several typical DOEs for beam splitting were designed and fabricated, and the result showed that the proposed method is effective.

Light-shaping design by a fourier pair synthesis: the homeomorphic case.

From a physical-optics point of view, the far-field light-shaping problem mainly requires a Fourier pair synthesis. The Iterative Fourier Transform Algorithm (IFTA) is one of the algorithms capable of realizing this synthesis, however, it may lead to stagnation problems when the fields of the Fourier pair exhibit a homeomorphic behavior. To overcome this problem, we use a mapping-type relation for the Fourier pair synthesis. This approach results in a smooth phase response function in a single step, without requiring an iterative procedure. The algorithm is demonstrated with examples and the results are investigated via physical-optics modeling techniques.

Diffractive optical elements in single crystal diamond.

We demonstrate the design, fabrication, and experimental characterization of near-field binary phase transmission diffractive optical elements (DOEs) in single crystal diamond. Top-hat and arbitrary pattern DOE beam shapers were numerically optimized using an iterative Fourier transform algorithm (IFTA). Commercially available single crystal diamond plates (3mm×3mm×0.3mm) were patterned using hardmask deposition (α-Si), e-beam lithography, and O2 plasma-based diamond reactive ion etching. The resulting binary phase relief patterns were characterized using scanning electron microscopy (SEM) and atomic force microscopy (AFM). Experimental characterization of the single crystal diamond DOEs in transmission at λ=532nm confirms excellent uniformity of the resulting top-hat beam profile as required in copper welding applications.

A Hybrid Algorithm for Multi-Beam Steering of LCOS-Based Wavelength Selective Switch

Iterative Fourier transform algorithm (IFTA) has been widely applied to achieve holograms in diffractive optical elements, however it is insufficient for designing holograms uploaded on liquid crystal on silicon (LCOS) to steer multi-beams in a wavelength selective switch (WSS). In this paper, a three-step hybrid algorithm including IFTA, Symmetrical IFTA with both phase and amplitude freedoms (SIFTA-2) and Genetic algorithm (GA) is developed to optimize the multi-casting hologram and experimentally demonstrated the multi-casting function of WSS. The reconstructed output field not only has max 128 fan-out patterns with flexible power ratio, but also can be adjusted to balance multi-indicators like reconstructed root mean square error (RMSE), diffraction efficiency and crosstalk power by setting flexible weightings of fitness functions in GA.

Rapid phase calibration of a spatial light modulator using novel phase masks and optimization of its efficiency using an iterative algorithm

ABSTRACT We develop an improved phase calibration method of a reflective SLM using interferometry by employing novel phase masks. In the process, we definitively determine the actual maximum phase throw of our SLM which provides a recipe for users to verify supplier specifications. We generate optimised phase masks by using Iterative Fourier Transform Algorithm (IFTA) and compare their performance with global linear corrections in the look-up table (LUT) and find that the former perform with around 20 better efficiency. Besides obtaining an array of 1D/2D spots having high uniformity (90) using IFTA, our result exemplifies the use of iterative algorithms for improving efficiency of phase limited SLMs. Finally, our improved phase calibration method enables threefold faster phase measurements, and to the best of our knowledge, is the first endeavour directed towards enabling rapid phase characterisation of an SLM using interferometric measurements. We believe that it can have very useful applications in settings which may require fast phase calibrations as well as for real-time, multi-wavelength spectroscopic applications.

Light shaping from a physical-optics point of view

In the design of optical element for light shaping, a geometric-optics assumption is usually used, where the validity of the assumption is rarely discussed in literature. In this work, the field tracing techniques for modeling light-shaping systems are presented, which reveals the optical element resulted from those geometric-base algorithm is not always accurate enough for the design task. An example is demonstrated with the functional embodiment of the element. The simulation result shows that diffraction effect may occur, especially in paraxial situation. However, the designed result start with the assumption is well-introduced initial guess for further optimization with the iterative Fourier transform algorithm (IFTA).

Projection of holographic images in volumetric fluorescent fluids for near-eye displays

The optical setup for holographic projection on the scatterings in fluorescent liquids is presented. Such media can be used as volumetric screens for near-eye holographic displays, solving the problem of speckle noise and very small exit pupils in existing setups. Three different oils (canola, olive and engine oil) with 532 nm laser and tonic water with 405 nm laser are used for projecting holographic fields, the quality of such images is investigated. The laser wavelength is cut out from acquisition on a camera and only filtered fluorescent light is observed. The best and brightest results are obtained with engine oil. Full Text: PDF ReferencesX. Li, C. P. Chen, H. Gao, et al. "Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal", Journal of display technology 10(6), 438-443 (2014). CrossRef X. Li, Z. Song, F. Li, X. Dong, W. Liu, "79‐3: Video‐rate Holographic Display in ZnSe layer‐assisted Quantum Dot Doped Liquid Crystal with High‐photorefractive Sensitivity", SID Symposium Digest of Technical Papers. Vol. 48. No. 1. 2017, CrossRef Sasaki, Takeo, et al. "Real-time dynamic hologram in photorefractive ferroelectric liquid crystal with two-beam coupling gain coefficient of over 800 cm–1 and response time of 8 ms", Applied Physics Letters 6(2) (2013) CrossRef N. Tsutsumi, K. Kinashi, A. Nomura, W. Sasaki, "Quickly Updatable Hologram Images Using Poly(N-vinyl Carbazole) (PVCz) Photorefractive Polymer Composite", Materials 5.8: 1477-1486 (2012) CrossRef M. Makowski, "Simple holographic projection in color", et al. Optics express 20.22: 25130-25136 (2012) CrossRef A. Yagi, M. Imura, Y, Kuroda, O. Oshiro, "360-degree fog projection interactive display", SIGGRAPH Asia 2011 Emerging Technologies. ACM, (2011) CrossRef C.H. Hsu, K. L. Hua, W. H. Cheng. "Omni-Tube: a low-cost portable omnidirectional interactive 3D display", SIGGRAPH Asia 2012 Posters. ACM, (2012) CrossRef Z. Zeng, H. Zheng, X. Lu, H. Gao, Y. Yu, "Dynamic holographic three-dimensional projection based on liquid crystal spatial light modulator and cylindrical fog screen", Opt Rev (2015) 22: 853 CrossRef I. Rakkolainen, "Feasible mid-air virtual reality with the immaterial projection screen technology", 3DTV-Conference, Tampere (2010) CrossRef S. Yanfeng, et al. "A multi-plane optical see-through holographic three-dimensional display for augmented reality applications", Optik 157: 190-196 (2018) CrossRef G. Li, D. Lee, Y. Jeong, J. Cho, B. Lee, "Holographic display for see-through augmented reality using mirror-lens holographic optical element", Opt. Lett. 41(11), 2486-2489 (2016) CrossRef C. L. Lin, Y. Z. Su, M. W. Hung, K. C. Huang "Augmented reality system", Proc. SPIE 7798, Applications of Digital Image Processing XXXIII, 779826 (2010) CrossRef A. Maimone, A. Georgiou, J. S. Kollin, "Holographic near-eye displays for virtual and augmented reality", ACM Trans. Graph. 36, 4, 1-16 (2017) CrossRef M. Quinten, Optical properties of nanoparticle systems: Mie and beyond (John Wiley &amp; Sons 2010). CrossRef J.-W. Liaw, S.-W. Tsai, H.-H. Lin, T.-C. Yen, B.-R. Chen, "Wavelength-dependent Faraday–Tyndall effect on laser-induced microbubble in gold colloid", Journal of Quantitative Spectroscopy and Radiative Transfer 113(17), 2234-2242 (2012), CrossRef T. Mu et al. "Classification of edible oils using 532 nm laser-induced fluorescence combined with support vector machine", Anal. Methods 5, 6960 (2013) CrossRef T. Mu et al. "Classification of Motor Oil Using Laser-Induced Fluorescence and Phosphorescence", Analytical Letters 49:8, 1233-1239 (2015) CrossRef V. Rostampour, M. J. Lynch, "Quantitative Techniques To Discriminate Petroleum Oils Using LED-induced Fluorescence", WIT Transactions on Ecology and the Environment 95, 265 262 (2006) CrossRef F. Wyrowski and O. Bryngdahl, "Iterative Fourier-transform algorithm applied to computer holography", Opt. Soc. Am. A 5(7), 1058-1065 (1988) CrossRef