A numerical method for decomposing discrete wavefront aberration data into their individual azimuthal orders is presented. The approach utilizes the multi-angle averaging method, where the wavefront error is averaged under m equally spaced angular positions. This angular averaging cancels out all those contributions that are not integer multiples of the number of angular positions. Generally, the sampling theorem gives the maximum angular order that can be resolved by the given discrete data set. By combining the multi-angle averaging method at different m with the sampling theorem one can extract not only any distinct azimuthal order including their harmonics but in particular also each fundamental angular order. The basic algorithm is explained and numerically demonstrated. It is also shown how this approach compares to other angular decomposition methods such as Fourier filtering and Zernike decomposition.
Over the last decade, various technologies for visualizing
three-dimensional (3D) scenes on displays have been
technologically demonstrated and refined, among them such of stereoscopic, multi-view, integral imaging, volumetric,
or holographic type. Most of the current approaches utilize the conventional stereoscopic principle.
But they all lack of their inherent conflict between vergence and accommodation since scene depth cannot be
physically realized but only feigned by displaying two views of different perspective on a flat screen and delivering
them to the corresponding left and right eye. This mismatch requires the viewer to override the physiologically
coupled oculomotor processes of vergence and eye focus that may cause visual discomfort and fatigue.
This paper discusses the depth cues in the human visual perception for both image quality and visual comfort
of direct-view 3D displays. We concentrate our analysis especially on near-range depth cues, compare visual
performance and depth-range capabilities of stereoscopic and holographic displays, and evaluate potential depth
limitations of 3D displays from a physiological point of view.
Large real-time holographic displays with full color are feasible with SeeReal's new approach to holography and today's
technology. The display provides the information about the 3D scene in a viewing window at each observer eye. A
tracking system always locates the viewing windows at the observer eyes. This combination of diffractive and refractive
optics leads to a significant reduction of required display resolution and computation effort and enables holographic
displays for wide-spread consumer applications. We tested our approach with two 20 inch prototypes that use two
alternatives to achieve full color. One prototype uses color filters and interlaced holograms to generate the colors
simultaneously. The other prototype generates the colors sequentially. In this paper we review our technology briefly,
explain the two alternatives to full color and discuss the next steps toward a consumer product.
This paper illustrates one of the various capabilities of static diffractive optical elements (DOE) beneficial to realtime
holographic displays. Custom kinoform-type DOE can be used as elements for illumination of the spatial
light modulator, i.e. the display where the video hologram is encoded. For an RGB application of diffractive
optical elements, particular issues concerning the inherent wavelength-dependence have to be addressed. Multiorder
DOE offer a way to compensate for chromatic as well as monochromatic aberrations. We will discuss
concepts and performance of multi-order DOE, show their application in holographic displays, describe issues of
fabrication and replication, and give experimental results of the multi-order DOE performance.
A miniaturized photoplethysmographic sensor system which utilizes the principle of pulse oximetry is presented.
The sensor is designed to be implantable and will permit continuous monitoring of important human vital
parameters such as arterial blood oxygen saturation as well as pulse rate and shape over a long-term period
in vivo. The system employs light emitting diodes and a photo transistor embedded in a transparent elastic
cu. which is directly wrapped around an arterial vessel. This paper highlights the specific challenges in design,
instrumentation, and electronics associated with that sensor location. In vitro measurements were performed
using an artificial circulation system which allows for regulation of the oxygen saturation and pulsatile pumping of
whole blood through a section of a domestic pig's arterial vessel. We discuss our experimental results compared to
reference CO-oximeter measurements and determine the empirical calibration curve. These results demonstrate
the capabilities of the pulse oximeter implant for measurement of a wide range of oxygen saturation levels and
pave the way for a continuous and mobile monitoring of high-risk cardiovascular patients.
A fiber-optic-based, time-domain optical coherence tomography (OCT) system coupled with a pneumatically actuated
micro-lens is demonstrated. The OCT system uses a superluminescent diode emitting at a center
wavelength of &lgr; ≈ 1300 nm. Microsystem fabrication technologies employing polydimethylsiloxane (PDMS) are used to fabricate the micro-lens with an aperture of 2 mm. A B-scan is carried out while dynamically shifting the focal length of the micro-lens along the axial scan. The OCT scan results show a higher lateral resolution and higher contrast of the backscattered interference signals when using the tunable lens; hence, deeper axial scans are possible. The ability to miniaturize the dimensions of the micro-lens will allow the system to be applicable to en-face optical coherence tomography and endoscopic applications.
Self-calibration techniques in interferometry imply the absolute determination of the interferometer's systematic error without the need for a high-quality, precisely-known calibration standard. By taking separate measurements at different positions and under different orientations, the interferometer's error can be determined in an absolute manner even with non-perfect optical elements. This paper discusses the versatile possibilities of using diffractive optical elements as calibration tools in wavefront testing interferometry.
Interferometric testing of micro-optical components involves some challenges due to problems such as Fresnel diffraction artefacts, the non-common path interferometer configuration, coherent noise as well disturbing interferences, and uncertainties in distance measurements. Recently we have developed a versatile Mach-Zehnder / Twyman-Green hybride interferometer for micro-optics testing. The system combines the
advantages of both interferometer types and allows full characterization of lens and surface figure errors as well as radius of curvature and focal length measurements. The interferometer system is explained and measurement results of micro-lenses are presented. Furthermore, this paper is concerned with the metrology challenges of interferometric testing on microscopic scales.
Active and adaptive optics are becoming more important in the field of beam shaping and wave front analysis. One of the main reasons for the progress and recent activities in active optics is the availability of new active elements like deformable mirrors, micro mirrors and liquid crystals. The application of spatial light modulators for wave front adaption, shaping and sensing will be discussed. An important application is a flexible testing procedure for testing aspheric surfaces using adaptive optics such as deformable mirrors liquid crystals and micro mirrors.
With surface-relief structures, optical functions that are required for radiation power management such as antireflection, light trapping, or light distribution and redirection can be obtained for new applications in solar energy systems and in displays. There, structures with submicrometer features must be distributed over large areas homogeneously. We address the design and the whole experimental process chain from the microstructure origination on large areas to the replication and the system integration in the specific application. Topics are antireflective surfaces for solar systems and displays, light trapping in polymer solar cells, sun protection systems for facades, and diffusers for projection displays and in glazing. For the microstructure origination we investigate the suitability of holographic recording in photoresist using a large-scale interferometer. We use an argon ion laser as a coherent light source at a wavelength of 364 nm. Periodic and stochastic interference patterns are recorded in positive photoresist with the interferometer setup. In the case of periodic structures, grating periods between 200 nm and 20 µm are realized. By carefully modeling the resulting resist profiles it is possible to originate even prismatic surface-relief profiles. Structures with good homogeneity are originated on areas of up to 4800 cm2 by optimizing the interferometer setup and the photoresist processing.
A complete absolute interferometric test of aspheres is presented. The method is based on a specially designed computer-generated hologram (CGH), which reconstructs an aspherical wave as well as auxiliary waves. The auxiliary waves are used for calibration. The aberrations of the auxiliary waves are measured absolutely by means of established absolute testing methods. The errors of the auxiliary waves can be transferred to those of the aspheric wave. Methods for absolute testing of aspheric surfaces using multiplex CGHs are described. Test procedures are explained and equations are derived. For axially symmetric aspheres, experimental results are presented and a comparison with the established N-position rotation test is given.
The expansion of the field of diffractive optics applications is accompanied by toughening performance requirements for CGHs. Optical testing sets especially high requirements, concerning wavefront accuracy and diffraction efficiency. The key point in fabrication technology is the writing system creating the photomask or the profiled pattern. The diffractive optics fabrication facility at ITO (University of Stuttgart) is based on the circular laser writing system CLWS-300. This flexible and high-accurate tool was originally designed for binary diffractive optics fabrication. This paper presents novel enhancements of this system allowing direct laser writing of a wide range of binary and continuous-relief CGHs on photoresist layers, chromium films and LDW-glass. Main topics of the enhancements were the scanning accuracy and exposure control.
Many types of CGHs (binary precision holograms for optical testing, Shack-Hartmann arrays, microlens discs for confocal microscopy, diffractive interferometer objectives, doughnut generators etc.) have been manufactured using the developed algorithms and hardware.
It has been shown that high precision diffractive objectives are an alternative to their refractive counterparts for application in interferometers. A design for an all-diffractive, double-sided objective that fulfills the Abbe sine condition has been proposed. It allows eliminating aberrations due to a finite field angle. Ray tracing simulations show that field angles up to 0.1 ° cause aberrations less than ?/20 PV in single pass. A single-sided prototype (diameter - 80 mm; NA. - 0.158; designed wavelength - 632.8 nm) has been fabricated by direct laser writing on photoresist. It was written on a polar coordinate laser system CLWS-300 that is capable of writing high precision DOEs up to a diameter of 300 mm. The blazed diffractive structures were written directly into a photoresist layer that was spinned on a high-precision substrate. Recalibration of the radial coordinate by reading marker positions on the substrate was used to eliminate machine drifts. The writing parameters were optimized by modelling the writing process in order to maximize the diffraction efficiency. The fabricated objective has a rms wavefront error of less than ?/2O in single pass. The residual errors are predictable using manufacturing data that is recorded during the writing process for each element. This permits to supply calibration data for each element. Measurements of the fabricated DOE show excellent agreement between the predicted and measured wavefront quality.
The entire process of designing the test setup with a computer-generated hologram (CGH) and performing the CGH-null test of an asphere will be described in detail. Critical aspects in testing aspherics with CGH-nulls e.g. caustic of the asphere, influence of alignment errors, lateral distortion and lateral resolution of the measurement are discussed. Detection, specification and calibration methods of fabrication errors of the CGH-null are analyzed with respect to the fabrication technology of the CGH. For a high accuracy CGH-null test of an asphere, the errors of the CGH must be negligible or well calibrated. Techniques to calibrate the systematic error of the test setup are presented with examples. Experimental results of interferometric CGH-null tests of an asphere are presented.
Computer-generated holograms (CGHs) are increasingly used in optical shop testing, especially for testing aspheric surfaces. For precise interferometrical measurements the error influence of the CGHs must be known and needs to be characterized. Different error types of two-level binary CGHs are identified and their contribution to the reconstructed wavefront are discussed: pattern errors of the CGH structure, duty cycle errors, surface figure errors of the CGH-substrate, etching depth variations in phase holograms and thickness variations of the chromium layer of amplitude chrome-type holograms. Methods to determine all these different errors are explained and an error budget of the total CGH error is given. Since the pattern error of a CGH is the most critical error it will be discussed in detail. This error depends on the writing technology (e-beam, laser beam) and on the type of the CGH (inline, off-axis). As examples of the two CGH-types a test method for measuring the pattern errors of Fresnel zone plates and linear gratings is presented. Experimental results of the tests are discussed.
Diffractive optics is a field where the progress is defined by fabrication technology. Diffractive optical elements (DOEs) are generally planar structures, typically fabricated using X-Y image generators designed for semiconductor industry. However there are some kinds of DOEs for which the polar scanning geometry, where the optic rotates under a writing beam, is more preferable. In some cases polar coordinate machines provide the only practical method of fabricating DOEs with the required accuracy. It is necessary to take into account the DOE specification when choosing the fabrication method. The present paper considers peculiarities of polar coordinate laser systems for large size and high precision DOEs fabrication. The specific error sources for these systems are described and compared with those of X-Y systems. An optimal writing strategy is discussed. The wavefront aberrations of rotationally symmetric DOEs caused by fabrication errors were measured interferometrically. Different types of aberrations were identified and can be referred to certain writing errors. Interferometric measurements of the wavefront errors for binary zone plates with a 64 mm diameter and 0.45 numerical aperture have shown that the wavefront root-mean-square error does not exceed 0.009 (lambda) wavelength.
Aspheric surfaces are becoming interesting for the reduction of elements in optical systems as well as for improving the quality of the image forming system. The fabrication process of aspheric surfaces has been improved. For optical testing of aspheric surfaces computer generated holograms (CGHs) are interesting and already used. To perform aspheric testing in the same accuracy as spherical surface testing, further improvements of the CGH-null test method are required. A new concept for testing aspheric surfaces with CGH-nulls, including a calibration of the system, will be described. To specify and verify CGH quality, systematic errors due to fabrication inaccuracies of the CGHs will be analysed. On the other hand, alternative methods that provide more flexibility but possibly less accuracy than the CGH-null technique are required. Potential alternative testing methods of aspherics will be discussed.