Fourier Optical System Research Articles

Transmissive nonlocal multilayer thin film optical filter for image differentiation

AbstractIt is well-known that a Fourier optical system can be used to perform specific computing tasks, such as image differentiation, with a superior speed and power consumption in comparison with digital computers, despite bulky optical components that are often required. Recently, there has been a surge in the interest to design much more compact nanophotonic structures, such as dielectric and metallic thin films, photonic crystals, and metasurfaces with a tailored angle-dependent (nonlocal) optical response, to directly perform image differentiation without additional lenses for Fourier transformation. Here, we present a straightforward platform, a multilayer dielectric thin film optical filter, fabricated using mature wafer-scale thin film deposition technique, with an optimized nonlocal optical response, for isotropic image differentiation in transmission mode for arbitrary input polarization. The proposed thin film filter may be conveniently coated at various transparent surfaces and inserted in machine vision or microscopy systems for enhanced, real-time image processing.

CMOS-compatible integrated 4-f system for mode-transparent spatial manipulation.

To exploit spatial dimension, on-chip optical modes with various spatial profiles have been utilized in optical interconnects and spatial analog computing. An integrated Fourier optical system is able to perform spatial operations. However, the reported schemes based on a subwavelength structure pose difficulty in fabrication, and the fabrication-friendly structure has been investigated only with a fundamental mode. With the complementary metal-oxide-semiconductor process, we propose an integrated 4-f system with simple geometry and a moderate minimum feature size to manipulate the mode's spatial size and position in a mode-transparent way. A size magnification of 2.5 and center-to-center position offset of 7 µm are experimentally demonstrated. Reasonable insertion loss and low inter-mode crosstalk are measured over a 30 nm bandwidth. The work in this Letter paves the way for an on-chip Fourier optical system with convenient fabrication and broadband operation.

Compensating inhomogeneous potential fields using two orthogonal spatially modulated laser beams

The inhomogeneous potential residual field is the main impediment that prevents atomic samples from reaching sub-nanokelvin temperatures in deep cooling experiments. In this study, we propose a method to reduce the potential inhomogeneity using a pair of perpendicular spatially modulated laser beams. Two 2D distributions have been calculated by decomposing the required 3D compensation field and generated by employing Fourier optical systems. The proposed approach can be used to experimentally investigate Efimov physics in ultracold K-Rb mixtures.

Fourier optical cryptosystem using complex spatial modulation

Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter.

Метод компьютерного синтеза микроголограмм Фурье и оптическая система их записи на голографический диск памяти

Метод компьютерного синтеза микроголограмм Фурье и оптическая система их записи на голографический диск памяти

Gerchberg-Saxton algorithm applied to a translational-variant optical setup

The standard Gerchberg-Saxton (GS) algorithm is normally used to find the phase (measured on two different parallel planes) of a propagating optical field (usually far-field propagation), given that the irradiance information on those planes is known. This is mostly used to calculate the modulation function of a phase mask so that when illuminated by a plane wave, it produces a known far-field irradiance distribution, or the equivalent, to calculate the phase mask to be used in a Fourier optical system so the desired pattern is obtained on the image plane. There are some extensions of the GS algorithm that can be used when the transformations that describe the optical setup are non-unitary, for example the Yang-Gu algorithm, but these are usually demonstrated using nonunitary translational-invariant optical systems. In this work a practical approach to use the GS algorithm is presented, where raytracing together with the Huygens-Fresnel principle are used to obtain the transformations that describe the optical system, so the calculation can be made when the field is propagated through a translational-variant optical system (TVOS) of arbitrary complexity. Some numerical results are shown for a system where a microscope objective composed by 5 lenses is used.

Calculation method of CGH for Binocular Eyepiece-Type Electro Holography

We had researched about eyepiece-type electro holography to display 3-D images of larger objects at wider angle. We had enlarged visual field considering depth of object with Fourier optical system using two lenses. In this paper, we extend our system for binocular. In the binocular system, we use two different holograms for each eye. The 3-D image for left eye should be observed like the real object observed using left eye and the same for right eye. So, we propose a method of calculation of computer-generated hologram (CGH) transforming the coordinate system of the model data to make two holograms for binocular eyepiece-type electro holography. The coordinate system of original model data is called the world coordinate system. The left and the right coordinate system are transformed from the world coordinate system. We also propose the method for correcting the installation error that occurs when placing the electronic and optical devices. The installation error is calculated and the model data is corrected using the distance between measured position and setup position of the reconstructed image Optical reconstruction experiments were carried out to verify the proposed method.

Ray matrix analysis of anamorphic fractional Fourier systems

In this work we extend the application of the ray matrix approach to analyse anamorphic fractional Fourier systems, i.e., fractional Fourier optical systems where the fractional power is different for two orthogonal directions. The application of the ray matrix approach allows for easily obtaining the properties of the optical system, and it is therefore a powerful tool to design and simplify complicated systems. For simplicity we consider fractional Fourier systems with real orders and systems without apertures. We start by presenting the analysis of some previously reported anamorphic Fourier and fractional Fourier systems, and we end by proposing a simple optical system with tunable anamorphic fractional orders that can be varied continuously without changing the input and output planes.

Intelligent reduction of zero-order diffraction in Fourier optical systems

A simple and intelligent technique of reducing the zero-order diffraction in an optical spectrographic processor is discussed and the corresponding nonbias optical architecture, by which spectrograms can indeed be obtained, is proposed. Reduction of zero-order diffraction in a Fourier optical system arises from the removal of the dc bias, which is usually needed when a conventional optical spectrographic processor is utilized. We have shown that discrimination sensitivity of the optical spectrograms is significantly enhanced and the dynamic range (DR) requirement for the spectrogram capturing device is also notably reduced due to the removal of the dc bias. In addition, energy utilization efficiency in the optical signal processing is drastically improved by our nonbias architecture. Simulated demonstration is provided.

Soft blocking of the dc term in Fourier optical systems

A technique utilizing an electron-trapping (ET) film to block the extended dc term in a Fourier optical system film is proposed and demonstrated. Since the blocking process is actually based on the sub- tracting property of the ET film, it is a soft blocking, which differs from, and is better than, simple hard blocking with a stop. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)01401-9)

Plateau tank apparatus for the study of liquid bridges

An apparatus has been constructed and used to study the equilibrium and dynamical behavior of liquid bridges under reduced effective gravity. Liquid bridges are created and manipulated using six independent computer controlled stepper motors which drive linear motion tables. The bridges are visualized with a high magnification coherent Fourier optical system and in an orthogonal view using incoherent white light. By calibrating a density hydrometer and measuring the interfacial energy between the bridge and bath, reliable Bond numbers as low as 10−4 can be created and held stable for extended periods of time. Dimensional control of the liquid bridges approaches one part in 10−4 for the aspect ratio and volume. The apparatus has been tested by measuring the static stability limits of axisymmetric bridges and comparing the results with previous theoretical predictions. Experimental error for the apparatus is δBo/Bo=0.03, δΛ/Λ=0.001 and δV/V =0.001, where Bo is the Bond number, Λ is the aspect ratio of the bridge, and V is the dimensionless (relative) volume of the bridge.

Every Fourier optical system is equivalent to consecutive fractional-Fourier-domain filtering

We consider optical systems composed of an arbitrary number of lenses and filters, separated by arbitrary distances, under the standard approximations of Fourier optics. We show that every such system is equivalent to (i) consecutive filtering operations in several fractional Fourier domains and (ii) consecutive filtering operations alternately in the space and the frequency domains.

Digital Fourier optics

Analog Fourier optical processing systems can perform important classes of signal processing operations in parallel, but suffer from limited accuracy. Digital-optical equivalents of such systems could be built that share many features of the analog systems while allowing greater accuracy. We show that the digital equivalent of any system consisting of an arbitrary number of lenses, niters, spatial light modulators, and sections of free space can be constructed. There are many possible applications for such systems as well as many alternative technologies for constructing them; this paper stresses the potential of free-space interconnected active-device-plane-based optoelectronic architectures as a digital signal processing environment. Implementation of the active-device planes through hybridization of optoelectronic components with silicon electronics should allow the realization of systems whose performance exceeds that of purely electronic systems.

Measuring the phase function of the fourier spectrum in two dimensions

By using a Fourier-optical system with two orthogonal polarization channels, for a two dimensional real and asymmetrical object function, the real and imaginary part of the Fourier spectrum can be separated and the phase of the Fourier spectrum can be measured. One example is a shifted square, its Fourier phase values measured by experiment agree quite well with the phase values calculated from the displacement of the square.

Coherent Optical Simulation of Radar Imagery

An analytical model of the synthetic aperture radar system is outlined. This model describes the radar image as a spatial two-dimensional bandpass filtering of the radar scene reflectivity density. The offset of the passband along the range frequency axis determines the major wavelength and geometrical properties of the simulated radar image. Through the use of a Fourier optical system, the photographs of radar target models and an aerial scene were bandpass filtered. The resulting images exhibit the characteristics of radar imagery, including texture (fading) and image dependence on object orientation. Use of the model and optical processing to simulate radar imagery from aerial photographs is discussed.

Reduction of diffraction of use of a Lyot stop

The efficiency of a Lyot stop in reducing the effects of diffraction is analyzed for a Fourier optical system. The problem reduces to the evaluation of an integral whose integrand is the product of two Bessel functions of different order and argument. An analytic series solution is found for the reduction of diffracted light reaching the focal plane.

Linear Vector Operations in Coherent Optical Data Processing Systems

The generation of a two-dimensional linear vector space in a coherent optical data processing system and its specific application to the gradient operator is discussed using theoretical and experimental results. The vector space is created by superposing the outputs of two Fourier optical systems having light of mutually orthogonal polarizations. As a result, the total amplitude of the signal in the output plane is a vector sum of the signals from the systems. If each one of the systems performs one of the partial derivative operations of the transverse gradient, and if the inputs to both systems are identical, then the output is the vector sum of the partial derivatives or the transverse gradient operation. The experimental program is heavily oriented toward the realization of the optimum approximation to the jomega(x)î and jomega(y)j; filters, rather than using various binary-type filters. Problems with film and lens noise are also discussed.