Fabrication Of Computer-generated Holograms Research Articles

The Wavefront Power Spectral Density Measurement of Aspheric Lens with Long Focal-Length Using a Computer-Generated Hologram

To ensure the performance of the optical system, the machining accuracy of lens with long focal lengths is required to ensure the image quality. A new method for lens transmission wavefront power spectral density (PSD) in mid-frequency domain measurement using binary phase computer-generated hologram (CGH) is presented. This technique is widely applicable and is particularly useful for measuring large-size lenses with long focal lengths. A comparison experiment of the CGH measurement with results from a Fizeau sphere interferometry method is carried out to verify the accuracy and convenience of the measurement. Furthermore, measurement uncertainty due to CGH fabrication process is analysed. Analysis of the CGH test showed the overall accuracy of less than 1 nm RMS for a sphere lens with over 30 m focal length and Φ410 mm clear aperture. CGH can provide reference spheres with high precision, in the meantime greatly shorten air space, thus reducing the effect of vibration and air turbulence, therefore is of great importance for lens transmission wavefront PSD measurement. The realization of high precision, high efficiency and nondestructive testing of long focal-lens wavefront PSD ensure the ultra-precision and certainty level of machining, hence improving the comprehensive performance of the optical system.

Diffractive Sensor Elements for Registration of Long-Term Instability at Writing of Computer-Generated Holograms.

The research and development of methods using of the specialized diffractive microstructure sensors embedded in the pattern of computer-generated holograms (CGH) manufactured on circular and X-Y laser writing systems is discussed. These microstructures consist of two parts: one of which is written before the CGH in the field of future hologram and the second one is written during the long-term writing of the CGH. The shift between the first and second part of the microstructure is the trace of the writing errors and allows one to determine and calculate the error of CGH fabrication along both orthogonal coordinates. The developed method is based on the principle of diffraction-based overlay with 1D and 2D built-in diffractive microstructure-sensors. Mathematical modeling and results of experimental test writings of such diffractive microstructure sensors are described. The efficiency of using these types of build-in sensors for the writing errors estimation for CGHs is demonstrated.

Scanning ion beam etching: A method for the fabrication of computer-generated hologram with nanometric accuracy for aspherical testing

The phase type computer generated hologram (CGH) plays an important role in aspherical surface optical testing, especially for low reflectivity material mirror surfaces, owing to its high diffractive efficiency. With the increasing demand for high precision CGHs, traditional methods such as reactive ion etching and focusing ion beam, have difficulty realizing the fabrication of a large aperture and high accuracy phase type CGH. In this study, fabrication of a high precision CGH has been demonstrated via a new method called scanning ion beam etching (SIBE), which is suitable for most common optical materials and the fabrication of high performance CGH. On the basis of the movable radio frequency ion source, we determine an etching depth calculation method to realize high accuracy etching regardless of whether the removal function is a perfect Gaussian distribution. Experiments are conducted to verify the etching depth accuracy. Moreover, the linewidth, sidewall angle, roughness, and etching uniformity results of the CGH are superior to the fabrication of CGH via the conventional method. As a proof of concept, a phase type CGH with an aperture of 80 mm is fabricated, and the wavefront accuracy is 6.2 nm, which can meet the processing requirements of a high precision aspheric mirror. Thus, a SIBE method is developed for high performance CGH, which may aid in the development of high accuracy diffractive optics.

Machine learning based technique towards smart laser fabrication of CGH

Fabrication of Computer-Generated Holograms (CGHs) on metal surfaces is a challenging procedure, given the nature of the laser-matter interaction specified for metals, and the power requirements for silver laser machining. A machine learning approach is derived for engraving of CGHs on silver surfaces with a 1070 nm fiber laser. The proposed method paves the way towards an automated solution for the fabrication of CGH on silver surfaces that accounts for, in terms of manufacturability. Sophisticated image-based descriptors are extracted from digital holographic masks produced by commercial CGH design software to predict, using machine learning, a “quality score” from ‘1’ to ‘5’, estimating the fabrication feasibility of a CGH's mask. Based on this idea, the procedure of CGH engraving on silver is remarkably improved.

Testing the mid-spatial frequency error of a large aperture long-focal-length lens with CGH.

We present the use of a computer-generated hologram (CGH) to test the mid-spatial frequency error of a large aperture long-focal-length lens. In order to verify this test approach, a 450 mm × 450 mm reflective CGH is designed and fabricated for testing the 440 mm × 440 mm spatial filter lens. Both 0th and 1st order diffraction wavefront of CGH are measured, and the 0th order diffraction wavefront is used to calibrate the substrate error. The mid-spatial frequency wavefront error caused by the CGH fabrication errors are evaluated using the binary linear grating model and power spectral density (PSD) theory. Experimental results and error analysis show that the CGH test approach is also feasible for the measurement of mid-spatial frequency error, and the measurement accuracy of PSD1 can reach 0.8832 nm RMS.

Fabrication of a high-accuracy phase-type computer-generated hologram by physical vapor deposition.

With the development of optical systems used in astronomical and earth observation, aspherical and free-form surfaces are increasingly used because they are lightweight and have improved image quality. As a highly accurate, aberrationless technique, computer-generated hologram (CGH) plays an important role in wavefront testing. At present, the main way to fabricate phase CGH is reactive ion etching, which suffers from low accuracy. To improve the accuracy, physical vapor deposition (PVD) is applied in the fabrication of phase CGH. The wavefront errors of PVD-fabricated phase CGH were analyzed. Testing results indicate that the wavefront error of the CGH is 0.020λ root mean square (RMS), mainly caused by the machine tool orthogonality error rather than the PVD process. The diffraction efficiency of the +1st order is 22.4%.

Testing the effect of computer-generated hologram fabrication error in a cylindrical interferometry system

This paper presents a method of testing the effect of computer-generated hologram (CGH) fabrication error in a cylindrical interferometry system. An experimental system is developed for calibrating the effect of this error. In the calibrating system, a mirror with high surface accuracy is placed at the focal axis of the cylindrical wave. After transmitting through the CGH, the reflected cylindrical wave can be transformed into a plane wave again, and then the plane wave interferes with the reference plane wave. Finally, the double-pass transmitted wavefront of the CGH, representing the effect of the CGH fabrication error in the experimental system, is obtained by analyzing the interferogram. The mathematical model of misalignment aberration removal in the calibration system is described, and the feasibility is demonstrated via the simulation system established in Zemax. With the mathematical polynomial, most of the possible misalignment errors can be estimated with the least-squares fitting algorithm, and then the double-pass transmitted wavefront of the CGH can be obtained by subtracting the misalignment errors from the result extracted from the real experimental system. Compared to the standard double-pass transmitted wavefront given by Diffraction International Ltd., which manufactured the CGH used in the experimental system, the result is desirable. We conclude that the proposed method is effective in calibrating the effect of the CGH error in the cylindrical interferometry system for the measurement of cylindricity error.

Analysis of wavefront errors introduced by encoding computer-generated holograms

The fabrication of computer-generated holograms (CGH) by e-beam or laser-writing machine specifically requires using polygon segments to approximate the continuously smooth fringe pattern of an ideal CGH. Wavefront phase errors introduced in this process depend on the size of the polygon segments and the shape of the fringes. In this paper, we propose a method for estimating the wavefront error and its spatial frequency, allowing optimization of the polygon sizes for required measurement accuracy. This method is validated with computer simulation and direct measurements from an interferometer.

Design and fabrication of computer-generated holograms for testing optical freeform surfaces

Freeform optical surfaces (FOSs) will be the best elements in the design of compact optical systems in the future. However, it is extremely difficult to measure freeform surface with sufficient accuracy, which impedes the development of the freeform surface. The design and fabrication of computer-generated hologram (CGH), which has been successfully applied to the tests for aspheric surfaces, cannot be directly adopted to test FOSs due to their non-rotational asymmetry. A novel ray tracing planning method combined with successively optimizing even and odd power coefficients of phase polynomials in turn is proposed, which can successfully design a non-rotational asymmetry CGH for the tests of FOSs with an F-θ lens. A new eight-step fabrication process is also presented aiming to solve the problem that the linewidth on the same circle of the CGH for testing freeform surface is not uniform. This problem cannot be solved in the original procedure of CGH fabrication. The test results of the step profiler show that the CGH fabricated in the new procedure meets the requirements.

Design of diamond-turned holograms incorporating properties of the fabrication process

Recently, the fabrication of computer-generated holograms by diamond face turning with a nanometer-stroke fast tool servo (nFTS) has been demonstrated. Existing methods for the design of diamond-turned holograms account for their spiral-shaped surface topology and the fact that only the phase of a wave field can be modulated. Here we present an algorithm enabling the additional consideration of two important fabrication-related properties: the shape of the diamond tool used and the limited control frequency of the nFTS. Our method is based on the generalized projections method and enables the design of holograms for the reconstruction of arbitrary intensity distributions in the far field. Experimental results are presented, demonstrating the advantages of the method.

Fabrication error analysis and experimental demonstration for computer-generated holograms

Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). For precise measurement, the wavefront errors caused by the CGH must be known and characterized. A parametric model relating the wavefront errors to the CGH fabrication errors is introduced. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given. The calibration of these effects for a CGH null corrector is demonstrated to cause measurement error less than 1 nm.

Fast data preparation for high-quality and large-area computer generated hologram fabrication

Fast data preparation for high-quality and large-area computer generated hologram fabrication

Laser Beam Shaping by Computer Generated Hologram

A computer generated hologram (CGH) is a useful tool for various optical applications, such as beam multiplexing, patterning, beam homogenizer, etc. The precise technologies are important issue for the fabrication of CGH, and the algorithm is more essential for designing it. I discuss the detailed consideration on the CGH design which is required to reconstruct a complex image. I also introduce efficient methods to design a hologram which creates a desired pattern at the Fresnel region and on a spherical surface.

J. Turunen and F. Wyrowski (eds.), Diffractive Optics for Industrial and Commercial Applications, Akademie Verlag, Berlin, Germany, 1997. 426 pp.

The field of diffractive optics is at the same time old and young. Diffraction gratings have been known for two centuries and used extensively in spectroscopy, for example. Also the theoretical understanding of the basic properties of grating diffraction has been well developed since that time. Until the 1960s, the technological foundation of grating manufacture used to be precision mechanics. It was then, when with the advent of the laser, things gradually started to change. On the one hand, laser interferometry became an additional tool to fabricate grating structures with very small periods. On the other hand, many new applications for optics started to develop based on the use of different types of laser sources. Some examples that may be mentioned are—besides modern spectroscopic techniques—areas like material processing, optical communications and information processing, optical data storage, etc. Consequently, the term “diffractive optics” has obtained a different flavor during the past 20–30 years. New types of diffractive elements were being developed with new technologies. This started in the mid-1960s with the invention of computer-generated holography which allowed to create “arbitrary” wavefronts (this means, within practical limits) by diffracting a light wave at an irregular binary structure. The computation and fabrication of computer-generated holograms was made possible by then newly available digital computers and plotting equipment. Since the early 1970s, people started to make diffractive elements using microfabrication techniques (lithography, etching, etc.) adapted from the processing of electronic circuits. These ideas were initially demonstrated in industrial research laboratories like Philips and Thomson-CSF.

Physical models and algorithms for optoelectronic MCM layout

Future computers will need to incorporate the parallelism of optical interconnections in order to achieve projected performance within reasonable size, power and speed constraints. This is necessary since optical interconnections have advantages in size, power, and speed over "long" distance communication. These features make optical interconnects ideal for inter-module connections in multichip module systems. Free-space optical interconnection can be one form of optical interconnections. Computer generated holograms (CGHs) are extremely attractive optical components for use in free space optical interconnections due to their ability to be computer designed. We will show that the fabrication limitations of CGHs for general interconnection networks require the need for placement algorithms for large processing element (PEs) arrays. In this paper, we will demonstrate that these fundamental CGH fabrication limitations greatly influence the computer aided design of optoelectronic interconnect networks that utilize CGHs for optical interconnections. Specifically, we show that the minimum feature size directly affects the logical placement of processing elements. Various physical models for free-space optical interconnects in parallel optoelectronic MCM systems are then identified from which we derive several logical models for analysis. We then analyze these cases and present algorithms to solve the associated layout problems. Design examples are given to illustrate the benefits of utilizing these placement algorithms in real optoelectronic interconnection networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Holograms For Optical Interconnects For Very Large Scale Integrated Circuits Fabricated By Electron-Beam Lithography

High performance holograms are a crucial part of realizing the predicted benefits of optical interconnection of electronic circuits. Fabrication of computer-generated holograms using electron-beam lithography provides access to the needed performance but presents new challenges in design, encoding, and data handling. Two holograms are described that represent different approaches in each of these areas. The first hologram connects a single laser source to several widely separated detectors. A paraxial imaging arrangement allows the holographic interferogram to be encoded as concentric circles of a Fresnel zone plate. The second hologram was designed to replace the row address lines on a 1 kbit RAM chip. In this case, broad separation of the sources prohibits use of the paraxial approximation. Instead, a piecewise approximation to the optimal phase function is encoded with a closed-contour fringe-tracing algorithm. Both holograms were evaluated in experimental systems involving photodetectors integrated onto a VLSI circuit chip and a discrete semiconductor laser.

Electron Beam Fabrication Of Computer-Generated Holograms

We report here the development of an integrated capability for writing computer-generated holograms (CGHs) using either of two commercially available electron-beam lithography systems. These binary, chrome-on-glass holograms have been used extensively for aspheric optical testing and also have applications to the interferometric recording of holograms. Algorithms are described for encoding CGHs for drawing by e-beam systems. Limitations of e-beam CGH fabrication are discussed. A self-contact lithography and ion milling process is described for con-verting chrome-on-glass holograms into 40% efficient, environmentally durable all-glass holograms.

Computer Generated Holography

The article reviews the state of art of the computer generated holography. Sec. 2 deals with the various coding schemes to record both the amplitude and phase of the field at the hologram plane. Special emphasis is given to those coding schemes which are used for the generation of binary holograms. The theory of discrete Fourier transform (DFT) hologram and its optical reconstruction are treated in Sec. 3. The introdution of randomizer in front of the object while computing the D.F.T. and its influence on the reconstructed image have been discussed. Sec. 4 contains some of the major applications of the computer generated holograms (CGH). For examples, the generation of filters for coherent optical processing, fabrication of CGH’s for testing unconventional optics and GGH’s as generalised optical elements etc. have been discussed in detail.