Use Of Computer-generated Holograms Research Articles

Subaperture stitching test for large aperture mild acylinders

Large aperture acylinders are typical optical elements in synchrotron radiation systems and laser shaping devices. The manufacture of such ultra-precision optical elements requires ultra-precision measurement of the surface figure. The use of computer-generated hologram (CGH) customized for the acylindrical surface can only achieve a “one-to-one” test. Limited by the aperture of CGH, it also cannot meet the requirements for large aperture acylinders. In order to realize flexible test of large aperture acylinders with mild aspherical departure, a method of surface figure reconstruction for subaperture measurements under near-null test is proposed. It is based on ray tracing and rigid body transformation. By using a general CGH for cylindrical surface, near-null test for various acylindrical surfaces can be realized. Subaperture stitching test can overcome the problem of the limited CGH aperture which cannot meet the requirement of large aperture acylinders. Finally an elliptical cylindrical mirror with an aperture of 240mm (sagittal) × 350mm (tangential) is measured. And the cross test is realized by using a customized CGH to verify the validity and precision of the proposed method.

Testing the transmitted wavefront of large aperture long-focallength lens using a multizone computer-generated hologram

A method for testing the transmitted wavefront of large aperture long-focal-length lens with a multizone computer-generated hologram (CGH) is proposed. The multizone CGH has 5 zones: one main zone for the null testing of long-focal-length lens and four auxiliary zones for the pre-alignment of measured lens. Both 1st order wavefront and 0th order wavefront of CGH are measured, and 0th order wavefront is used to calibrate the substrate error. To verify this test approach, a 450mm×450mm multizone CGH is designed and fabricated for testing the spatial filter lens. Experiments and error analysis are carried out. The results show that the desired precision can be reached with use of CGH.

Testing the transmitted wavefront of large aperture and long-focal-length lens with computer-generated hologram.

A method for testing the transmitted wavefront of large aperture and long-focal-length lens with a multizone computer-generated hologram (CGH) is proposed. The multizone CGH has 5 zones: one main zone for the null testing of long-focal-length lens and four auxiliary zones for the pre-alignment of measured lens. Both 1st order wavefront and 0th order wavefront of CGH are measured, and 0th order wavefront is used to calibrate the substrate error. To verify this test approach, a 450mm × 450mm multizone CGH is designed and fabricated for testing the spatial filter lens. Experiments and error analysis are carried out. The results show that the desired precision can be reached with use of CGH.

Use of Computer-Generated Holograms in Security Hologram Applications

Abstract The article discusses the use of computer-generated holograms (CGHs) for the application as one of the security features in the relief-phase protective holograms. An improved method of calculating CGHs is presented, based on ray-tracing approach in the case of interference of parallel rays. Software is developed for the calculation of multilevel phase CGHs and their integration in the application of security holograms. Topology of calculated computer-generated phase holograms was recorded on the photoresist by the optical greyscale lithography. Parameters of the recorded microstructures were investigated with the help of the atomic-force microscopy (AFM) and scanning electron microscopy (SEM) methods. The results of the research have shown highly protective properties of the security elements based on CGH microstructures. In our opinion, a wide use of CGHs is very promising in the structure of complex security holograms for increasing the level of protection against counterfeit.

Computerized interferometric surface measurements [Invited

The addition of electronics, computers, and software to interferometry has enabled enormous improvements in optical metrology. This paper discusses four areas in which computerized interferometric measurement improvements have been made in the measurement of surface shape and surface roughness: (a) The use of computer-generated holograms for the testing of aspheric optics, (b) phase-shifting interferometry for getting interferometric data into a computer so the data can be analyzed, (c) computerized interference microscopes, including multiple-wavelength and coherence scanning, for the precision measurement of surface microstructure, and (d) vibration-insensitive dynamic interferometers for enabling precise measurements in noncontrolled environments.

Efficient testing of segmented aspherical mirrors by use of a reference plate and computer-generated holograms II Case study, error analysis, and experimental validation

Segmented mirrors present unique challenges to fabrication and testing that are absent for monolithic optics. Since traditional asphere tests do not address segmented optics adequately, we validate a previously developed method to test large quantities of segments accurately, quickly, and economically. In this test, the aspheric shape of each segment is controlled to high accuracy by use of computer-generated holograms, and the radius of curvature is tightly controlled by use of the reference plate. In an adjoining paper [Appl Opt 43, 5303 (2004)] we developed the theory for this test, and now we present a complete system design and optimization for measuring the 1.4-m segments from a 30-m F/1 primary. A complete tolerance analysis predicts a test accuracy of 4.8-nm rms surface and excellent accuracy for controlling the geometry of the segment. In addition, a laboratory demonstration using 30-cm optics is presented that demonstrated 3.9-nm rms surface accuracy.

Entanglement of orbital angular momentum for the signal and idler beams in parametric down-conversion

We calculate the anticipated correlation between measurements of the orbital angular momentum of the signal and idler beams for parametric down-conversion. These calculations apply to the experiments where the orbital angular momentum state is measured by the use of computer-generated holograms. Displacement of these holograms with respect to the beam axis allows the measurement of superpositions of Laguerre—Gaussian modes. The correlations between such superposition modes of the signal and idler beams show their entanglement and could be used for Bell-type tests of nonlocality.

Dynamic array generation and pattern formation for optical tweezers

The generalised phase contrast approach is used for the generation of optical arrays of arbitrary beam shape, suitable for applications in optical tweezers for the manipulation of biological specimens. This approach offers numerous advantages over current techniques involving the use of computer-generated holograms or diffractive optical elements. We demonstrate a low-loss system for generating intensity patterns suitable for the trapping and manipulation of small particles or specimens.

Diffraction-limited laser beam shaping by use of computer-generated holograms with dislocations

A new method that reshapes a Gaussian laser beam into a polygon of diffraction-limited size with a flat or a pyramidal top is presented. The technique is based on the use of computer-generated holograms with phase dislocations (singularities).

Space-variant optical interconnection through the use of computer-generated holograms

A space-variant optical interconnection through the use of computer-generated holograms is proposed, and specific configurations to increase the number of parallel channels are analyzed. To this end, the well-known method based on a matrix composed of subholograms is applied. The field diffracted by each channel (assumed to be square apertures) is calculated through the angular-spectrum technique, and the resulting fields are suitably superimposed to obtain a hologram matrix with a reduced bandwidth. Results show that a compact transmissive planar configuration can be handled; in particular, the small interconnect distance between the array planes and the hologram yields a limited system volume.

Optical elements for efficient one-dimensional image transmission through a single multimode fiber

Optical elements, including continuous surface and multiple-ring types, are considered to improve the efficiency of one-dimensional imaging by angular multiplexing in a single multimode fiber. The limiting resolution of the multiple-ring method, determined by ring width, fiber diameter, etc., is discussed. Results are presented for a holographic implementation, with up to ten concentric rings, operating in monochromatic light. The use of computer-generated holograms is suggested.

Computer-generated holograms: display using one-dimensional transforms

The use of computer-generated holograms to display three-dimensional images is suggested. To simplify the calculation of the hologram, the parallax in the vertical direction is eliminated where a projection of the object onto the hologram plane is performed. The synthesis of the horizontal parallax involves one-dimensional transforms. This procedure reduces computer-memory requirements and permits a high-speed generation.

Wigner distribution function and optical geometrical transformation

The Wigner distribution function is applied to optical geometrical transformations, which are implemented by the use of computer-generated holograms under coherent illumination.

Hybrid optical processor for pattern recognition and classification using a generalized set of pattern functions

A pattern recognition and classification system has been studied which computes the inner products of an input pattern with a generalized set of pattern functions. The system utilizes a filter whose impulse response consists of an amplitude superposition of a set of generalized pattern functions in phase-coded form and has a space-bandwidth product the same as that of a matched filter for one pattern function. Each pattern function in the general set may correspond to a different variation (e.g., scale or rotation) of the object to be detected. Because the amplitude superposition of the phase-coded pattern functions takes place in the digital computer, and the filter is created as a computer-generated hologram, the biasing problem of conventional, multiple exposure (intensity superposition) holograms is significantly reduced. This makes it possible to encode many more pattern functions than was previously possible using multiple exposure techniques. Furthermore, the use of computer-generated holograms eliminates the need to generate a transparency for each pattern function and complex phase code. To facilitate real-time operation a hybrid system was constructed consisting of a liquid crystal light valve for incoherent-to-coherent image conversion, a TV camera and image digitizer for image analysis, and a laser scanner to produce the computer-generated holograms. Both the TV camera/digitizer and the laser scanner systems were interfaced to a digital computer for automatic operation. Experimental results using the hybrid system are presented for pattern recognition of rotated and scaled objects and pattern classification. In the second half of the paper we provide an analysis on the SNR of the processor employing the coded-phase technique, on the diffraction efficiencies of computer-generated filters (amplitude superposition) vs conventional filters (intensity superposition), and on the number of pattern functions required for a certain recognition task.

A method of incoherent optical-image processing using synthetic holograms*

Under coherent illumination, the interference between signal and noise produces an amplification of the noise. That is why image processing by optical methods may be done better with incoherent light than with coherent light. A method is described where image deblurring is performed in spatially incoherent illumination. The two main features are an additional step of illuminance subtraction to simulate negative intensities, and the use of computer-generated holograms of a low number of cells.

Computer generated holograms for processing radiographic data

Accurate images of body cross sections can be obtained from certain straightforward but lengthy computational operations on X-ray shadowgrams (projections). It is suggested that clinical radiographic data could be processed rapidly and economically by making use of computergenerated holograms. A simple method is described for constructing such holograms by overprinting teletype characters with a standard lineprinter. Preliminary experimental results are reported. Reconstructed images of an aluminium cylinder and a bovine shin bone are presented.