Design Of Holograms Research Articles

Pixelated phase masks and their synthesis

An approach to the design of holograms and masks for optical lithography is proposed on the basis of digitizing an image and dividing the sample into three phase components defined on a special bitmap. The equivalence conditions of the continuous and discrete methods of specifying a transmission function are studied. Computer modeling is used to reconstruct the images generated by means of the discrete phase masks synthesized. The locality principle has proven to hold: the transmission function at a given mask point is determined by the position of the nearest aperture.

Design and fabrication of a high-efficiency extreme-ultraviolet binary phase-only computer-generated hologram

As the development of extreme-ultraviolet (EUV) lithography progresses, interest grows in the extension of traditional optical components to the EUV regime. The strong absorption of EUV by most materials and its extremely short wavelength, however, make it very difficult to implement many components that are commonplace in the longer wavelength regimes. One such component is the diffractive optical element used, for example, in illumination systems to efficiently generate modified pupil fills. The fabrication and characterization of an EUV binary phase-only computer-generated hologram is demonstrated, allowing arbitrary far-field diffraction patterns to be generated. Based on reflective architecture, the fabricated device is extremely efficient. Based on an identically fabricated null hologram, the absolute efficiency into one diffracted order of 22% has been demonstrated. In the case where axially symmetric diffraction patterns are desired (both positive and negative diffraction orders can be used), the efficiency can be twice as high.

Iterative design of multiplane holograms: experiments and applications

We present an experimental confirmation of optical properties of multiplane holograms designed with our novel iterative method. The method allows encoding many input intensity distributions into a single phase-only hologram. The object planes can be placed at variable distances, and their content is fully customizable. The reconstructed three-dimensional (3D) scenes exhibit high contrast and low noise level in all designed image planes. The results of numerical simulations are compared with those of a reconstruction in an optical setup. Holograms for optical reconstructions were manufactured using two methods: photographic and electron beam lithography (EBL). Experimental results achieved with both methods are compared. We present our research on a new class of iterative holograms, containing up to eleven object planes, designed in close distance to each other. The elements exhibit unusual light focusing possibilities and extraordinary imaging properties, thus introducing a number of possible practical applications, which are discussed.

Design of a novel hologram for full measurement of large and deep convex aspheric surfaces

We proposed a valid method with a novel computer-generated hologram (CGH) to test large-aperture convex aspheric. The CGH consisted of two zones with different amounts of power: the central zone has a larger amount of power than the marginal zone. Compared with other CGHs used for convex aspheric testing [SPIE.2576.258 (1995)], it could overcome the difficulty of measuring the central region of the convex surface under test, while relaxing the requirement for the illumination optics and CGH of the test system. We have designed an optical test system with the novel CGH to test a 150 mm-diameter convex surface with full aperture by using optical design software Zemax. The simulated result verified the efficiency of the novel CGH. It is believed that this kind of CGHs can be used to measure any large and deep convex surface with full aperture.

Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors

Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). The etching of the CGH pattern must be highly accurate to create desired wavefronts. Variations of line width, etching depth, and surface roughness cause unwanted wavefront errors. The sensitivity to these manufacturing errors is studied using scalar diffraction analysis. We provide a parametric model that can be used for optimizing the CGH design to give good diffraction efficiency and limited sensitivity to manufacturing errors.

A multipurpose WDM holographic device for filtering, wavelength multiplexing and routing applications

This work describes the theory, design, and experimental results of a generic multipurpose device that can operate as a tunable wavelength filter, wavelength multiplexer and wavelength router. This device could be especially useful in optical networks applications based in both Coarse and Dense Wavelength Division Multiplexing technology (CWDM/DWDM). The enabling component is a Ferro-electric Liquid Crystal (FLC) Spatial Light Modulator (SLM) where dynamic holograms are implemented in real time. As a consequence, the device will be able to carry out different functions according to the hologram recorded on the SLM. The great advantage of this device is a polarization insensitivity operation, allowing low cross-talk and simple handling. Also some topics on Computer Generated Holograms (CGHs) design process are commented and general guidelines also are done. Laboratory experiments have demonstrated the capability of a phase FLC-SLM, with the great advantage of a polarization insensitivity operation, to diffract the incident light according its wavelength and hologram patterns, for the use in the former applications.

Interactive approach to optical tweezers control

We have developed software with an interactive user interface that can be used to generate phase holograms for use with spatial light modulators. The program utilizes different hologram design techniques, allowing the user to select an appropriate algorithm. The program can be used to generate multiple beams and can be used for beam steering. We see a major application of the program to be in optical tweezers to control the position, number, and type of optical traps.

Aberration correction in holographic optical tweezers

Holographic or diffractive optical components are widely implemented using spatial light modulators within optical tweezers to form multiple, and/or modified traps. We show that by further modifying the hologram design to account for residual aberrations, the fidelity of the focused beams can be significantly improved, quantified by a spot sharpness metric. However, the impact this improvement has on the quality of the optical trap depends upon the particle size. For particle diameters on the order of 1 microm, aberration correction can improve the trap performance metric, which is the ratio of the mean square displacement of a corrected trap to an uncorrected trap, in excess of 25%, but for larger particles the trap performance is not unduly affected by the aberrations typically encountered in commercial spatial light modulators.

Aberration correction in holographic optical tweezers

Holographic or diffractive optical components are widely implemented using spatial light modulators within optical tweezers to form multiple, and/or modified traps. We show that by further modifying the hologram design to account for residual aberrations, the fidelity of the focused beams can be significantly improved, quantified by a spot sharpness metric. However, the impact this improvement has on the quality of the optical trap depends upon the particle size. For particle diameters on the order of 1 microm, aberration correction can improve the trap performance metric, which is the ratio of the mean square displacement of a corrected trap to an uncorrected trap, in excess of 25%, but for larger particles the trap performance is not unduly affected by the aberrations typically encountered in commercial spatial light modulators.

Three-plane phase-only computer hologram generated with iterative Fresnel algorithm

A novel iterative method of generating three-plane, phase-only computer-generated holograms is presented. It is based on the iterative Fresnel ping-pong two-plane algorithm. A modification is introduced to extend the method for three planes, i.e., two object planes and a hologram itself. The described method enables the design of low-noise and high-efficiency phase-only holograms using a numerical Fresnel propagation algorithm. The source method is described, followed by the modified algorithm. Numerical simulation results and algorithm parameters are discussed, followed by a discussion of the method limitations.

Assembly of 3-dimensional structures using programmable holographic optical tweezers

The micromanipulation of objects into 3-dimensional geometries within holographic optical tweezers is carried out using modified Gerchberg-Saxton (GS) and direct binary search (DBS) algorithms to produce the hologram designs. The algorithms calculate sequences of phase holograms, which are implemented using a spatial light modulator, to reconfigure the geometries of optical traps in many planes simultaneously. The GS algorithm is able to calculate holograms quickly from the initial, intermediate and final trap positions. In contrast, the DBS algorithm is slower and therefore used to pre-calculate the holograms, which are then displayed in sequence. Assembly of objects in a variety of 3-D configurations is semi-automated, once the traps in their initial positions are loaded.

Practical implementation of the phase-quantization technique in an iterative Fourier-transform algorithm.

Implementation of the phase-quantization method in the design of computer-generated holograms (CGHs), especially binary CGHs, is a major influence on the diffraction efficiency of the CGHs. We describe the use of various quantization methods in the various steps of an iterative Fourier-transform algorithm and compare the root-mean-square (RMS) errors of the CGHs. As a result of the practical quantization technique, the most effective RMS value of a binary CGH should be decreased by at least 13% to retain maximum diffraction efficiency.

Design, fabrication and characterization of subwavelength computer-generated holograms for spot array generation

We report the analysis, design, fabrication and experimental characterization of novel subwavelength computer-generated holograms that produce uniform symmetric spot array. We distinguish between a polarization-sensitive and polarization-insensitive far-field reconstruction and show that a linearly polarized incident illumination is required in the former case in order to generate a symmetric reconstruction. The polarization-insensitive case generates a symmetric response independent of the illumination polarization. We show that this response is equivalent to that of a scalar-based computer-generated hologram but with an additional, independent, term that describes the undiffracted zeroth order. These findings simplify the design and optimization of form birefringent computer-generated holograms (F-BCGH) significantly. We present experimental results that verify our analysis and highlight the advantage of these novel elements over scalar-designed elements.

Area encoding for design of phase-only computer-generated holograms

A new encoding method of phase-only computer-generated holograms (CGH) is proposed in this paper, which is based on the division of each sampling cell into two sub-cells as well as the area modulation of each sub-cell. The holographic function to be recorded is expressed by a sum of two component complex quantities, each allocated to one sub-cell that displays a uniform phase value. Area partitioning of two sub-cells contained in each cell is determined by the relative module value of two component complex variables. Methods of error reduction and improvements are provided, and the computer simulation is presented, proving the capability of the proposed encoding technique.

On-axis computer-generated holograms based on centrosymmetric partitioning of the pixel

A novel, to our knowledge, configuration for the design and fabrication of zero-order computer-generated holograms in which each pixel is split into two centrosymmetric equal-sized regions is proposed and tested. In a manner similar to other approaches this configuration also permits the encoding and the reconstruction of a complex function that exhibits phase as well as amplitude variations by use of a phase-only filter. A detailed mathematical analysis is followed by evaluation of the error of the encoding approach, which is calculated and compared with the error exhibited by other approaches. Computer simulations as well as optical experiments demonstrate the capabilities of this novel configuration.

Simulator for computer-aided design of holograms

A simulator for the computer-aided design of holograms is developed. The direction and intensity of the reconstructed beam are calculated using the Kirchhoff diffraction integral and Kogelnik's coupled- wave theory. Grating distortions induced by physical changes in the re- cording medium are evaluated using the diffraction integrals, and imag- ing characteristics are analyzed using ray tracing. Simulator results can be used to evaluate wavefront aberrations of the reconstructed images, and holograms that compensate for aberrations can be designed by the simulator. Examples are given where recording and reconstruction wave- lengths are different and where the grating is distorted by nonuniform shrinkage of the medium. Also, to illustrate practical application, a holo- graphic optical element lens and a wavelength demultiplexer are de- signed and evaluated.9 © 2001 Society of Photo-Optical Instrumentation Engineers. Holographic optical elements ~HOEs! are useful for assem- bling compact optical systems. Since a hologram is a kind of diffractive optical element, the position of the recon- structed image is changed and aberrations are induced when the reconstruction conditions are different from the recording conditions. Also, the intensity of the recon- structed beam is reduced when the physical properties of the recording medium are changed during the development process. Therefore it is necessary to take the reconstruction and imaging characteristics into consideration when design- ing holograms. The reconstruction characteristics of holograms can be analyzed using the Kirchhoff diffraction integral 1 or coupled-wave theory. 2 The imaging characteristics of holo- grams can be analyzed using wavefront matching 3-5 or ray tracing. 6,7 However, it is difficult to design holograms by analytical methods because of the nonlinearity of the evalu- ation function, but computer-aided design can be effective. Latta's ray-tracing program can be used to design holograms, 8,9 but is inconvenient because of its specializa- tion for the analysis of imaging characteristics. Sweatt has presented the ultra-high-index method 10,11 for designing ho- lograms using general optical design tools. However, com- mercially available tools are not suitable because they em- phasize the design of bulk-type lenses. Therefore a computer-aided design tool specialized for holography is needed.

Design of Computer-Generated Hologram With Ring Focus for Nonmechanical Corneal Trephination With Er:YAG Laser in Penetrating Keratoplasty

Purpose: To calculate a beam-shaping optical element for homogeneous intensity distribution within a focal ring to be used in nonmechanical trephination with the Er:YAG laser in penetrating keratoplasty instead of a spot guiding device. Methods: The phase distribution behind a holographic optical element (HOE) kΨ( u) can be described by the addition of the hologram phase Φ H ( u) to the beam phase Φ E( u ): k Ψ( u ) = Φ H( u ) + Φ E( u ), k = 2 π/ λ , where u denotes the coordinates inside the hologram aperture, k an integer, and λ the laser wavelength. To avoid discontinuous wavefronts leading to speckle noise, a smooth phase function is necessary. After transforming the hologram aperture coordinates into the focal plane x in a focal distance f, Ψ can be retrieved from the slope equation: ▿ Ψ( u ) = x( u ) − u /f . Results: Creating a ring focus can be reduced to an essentially one-dimensional problem by separation of variables due to the symmetry condition. We calculated a computer-generated eight-level phase-only HOE with 4096 × 4096 pixels from a Gaussian-distributed 2.94 Er:YAG laser spot with a beam diameter of 10 mm and a focal distance of 100 mm. Thereby, a ring focus with an inner/outer radius of 7/8 mm can be created. To avoid Poisson's spot, the symmetry of the problem was broken by circular modulation of the phase leading to a spiral-like structure. The calculated efficiency of the HOE relating the energy within the ring to the total energy was 91%. Conclusion: With an HOE it is possible to redistribute the energy along the desired focal ring. The HOE design can be adapted to the intensity distribution of the impinging laser beam with its characteristic aperture shape. A circular homogeneous corneal trephination depth is possible, because the energy fluctuation from pulse to pulse does not locally affect the ablation process. A ring focus for the Er:YAG laser has the potential to render superfluous a manual beam control via micromanipulator and to allow a more rapid and more regular corneal trephination along aperture masks.

Two-dimensional, three-dimensional, and gray-scale images reconstructed from computer-generated holograms designed by use of a direct-search method

A direct-search method for the computer design of holograms is demonstrated. Two-dimensional, three-dimensional, and containing holograms with different levels of intensity (gray scales) were designed, fabricated, and optically reconstructed. The number of effective gray levels and the image-intensity noise and contrast are discussed. A modification of the state-variables cost function used in the direct-search algorithm that permits reliable control of gray scales is presented. Optical reconstructions of two-dimensional, three-dimensional, and gray-scale binary phase computer-generated holograms are presented.

Applications of FLC SLM dynamic holograms to WDM network components

This paper presents an overview of ferroelectric liquid crystal spatial light modulator (FLC SLM) dynamic digital holographic filtering technology and its application to WDM network components. Early work demonstrated a dynamically tunable filter and, in conjunction with an erbium-doped fibre amplifier (EDFA), a fibre laser[1]. The hologram design algorithm was subsequently expanded to yield a multiple variable amplitude passband filter, or spectral equaliser, for four[2] or six[3] WDM channels. Latest results for eight-channel equalisation are presented in this article, together with a demonstration of flattening the spectral shape of an individual passband. The paper concludes with a discussion of future work, including the redesign of filter parameters to meet ITU standards, and further improvements in computerised hologram design to achieve finer tuning resolution.

Modifications of detour phase computer-generated holograms

The detour phase method for the design of computer-generated holograms can be modified to achieve multichannel reconstruction along various diffraction orders. It is shown how a single hologram can be used to display two patterns of different intensities along two diffraction orders. This is achieved by the release of any requirement on the phase distributions of these patterns, thus leaving them as free parameters. Various algorithms are suggested to make possible nonidentical reconstructions along two different off-axis diffraction orders. The two reconstruction orders can be chosen arbitrarily. The case of four-channel reconstructions for generating four different images is discussed as well. Computer simulations and optical experiments were carried out to demonstrate the capabilities of the proposed approaches.