Abstract: An approach is proposed for removing the wave front curvature introduced by the microscope imaging objective in digital holography, which otherwise hinders the phase contrast imaging at reconstruction planes. The unwanted curvature is compensated by evaluating a correcting wave front at the hologram plane with no need for knowledge of the optical parameters, focal length of the imaging lens, or distances in the setup. Most importantly it is shown that a correction effect can be obtained at all reconstruction planes. Three different methods have been applied to evaluate the correction wave front and the methods are discussed in detail. The proposed approach is demonstrated by applying digital holography as a method of coherent microscopy for imaging amplitude and phase contrast of microstructures.

Abstract: In this paper, an alternative to classical pupil apodization techniques (use of an amplitude pupil mask) is proposed. It is shown that an achromatic apodized pupil suitable for imaging of extrasolar planets can be obtained by reflection of an unapodized flat wavefront on two mirrors. By carefully choosing the shape of these two mirrors, it is possible to obtain a contrast better than 10 9 at a distance smaller than 2λ/d from the optical axis. Because this technique preserves both the angular resolution and light gathering capabilities of the unapodized pupil, it allows efficient detection of terrestrial extrasolar planets with a 1.5 m telescope in the visible.

Abstract: Numerical simulation of high frequency acoustic, elastic or electro-magnetic wave propagation is important in many applications. Recently the traditional techniques of ray tracing based on geometrical optics have been augmented by numerical procedures based on partial differential equations. Direct simulations of solutions to the eikonal equation have been used in seismology, and lately approximations of the Liouville or Vlasov equation formulations of geometrical optics have generated impressive results. There are basically two techniques that follow from this latter approach: one is wave front methods and the other moment methods. We shall develop these methods in some detail after a brief review of more traditional algorithms for simulating high frequency wave propagation.

Abstract: In this paper, an alternative to the classical pupil apodization techniques (use of an amplitude pupil mask) is proposed. It is shown that an apodized pupil suitable for imaging of Extrasolar planets can be obtained by reflection of an unapodized flat wavefront on 2 mirrors. By carefully choosing the shape of these 2 mirrors, it is possible to obtain a contrast better than 10^{9} at a distance smaller than 2 \lambda/d from the optical axis. Because this technique preserves both the angular resolution and light gathering capabilities of the unapodized pupil, it allows efficient detection of terrestrial extrasolar planets with a 1.5m telescope in the visible.

Abstract: Single-beam optical gradient force traps created by focusing helical modes of light are known as optical vortices. Modulating the helical pitch of such a mode's wave front yields a new class of optical traps whose dynamically reconfigurable intensity distributions provide new opportunities for controlling motion in mesoscopic systems. An implementation of modulated optical vortices based on the dynamic holographic optical tweezer technique is described.

Abstract: The effects of wavefront distortions induced by acoustic heterogeneities in breast thermoacoustic tomography (TAT) are studied. Amplitude distortions are shown to be insignificant for different scales of acoustic heterogeneities. For wavelength-scale, or smaller, heterogeneities, amplitude distortion of the wavefront is minor as a result of diffraction when the detectors are placed in the far field of the heterogeneities. For larger-scale heterogeneities at the parenchyma wall, by using a ray approach (geometric optics), we show that no refraction-induced multipath interference occurs and, consequently, that no severe amplitude distortion, such as is found in ultrasound tomography, exists. Next, we consider the effects of phase distortions (errors in time-of-flight) in our numerical studies. The numerical results on the spreads of point sources and boundaries caused by the phase distortions are in good agreement with the proposed formula. After that, we demonstrate that the blurring of images can be compensated for by using the distribution of acoustic velocity in the tissues in the reconstructions. The effects of the errors in the acoustical velocities on this compensation also are investigated. An approach to implement the compensation using only TAT data is proposed. Lastly, the differences in the effects of acoustic heterogeneity and the generation of speckles in breast TAT and breast ultrasound imaging are discussed.

Abstract: A method of designing a multifocal ophthalmic lens with one base focus and at least one additional focus, capable of reducing aberrations of the eye for at least one of the foci after its implantation, comprising the steps of: (i) characterizing at least one corneal surface as a mathematical model; (ii) calculating the resulting aberrations of said corneal surface(s) by employing said mathematical model; (iii) modeling the multifocal ophthalmic lens such that a wavefront arriving from an optical system comprising said lens and said at least one corneal surface obtains reduced aberrations for at least one of the foci. There is also disclosed a method of selecting a multifocal intraocular lens, a method of designing a multifocal ophthalmic lens based on corneal data from a group of patients, and a multifocal ophthalmic lens.

Abstract: The phase retrieval algorithm has been used in this paper for whole reconstruction of the optical wave fields. The quantitative information of the phase distribution as well as the intensity distribution of the reconstruction field at different locations along the propagation direction has been achieved from double or multi in-line holograms. Numerical reconstructions of the wave fields from experimentally recorded in-line holograms are presented. This technique can be potentially applied for aberrated wave front analyzing and 3D imaging.

Abstract: Purpose To investigate the lateral alignment accuracy needed in wavefront-guided refractive surgery to improve the ocular optics to a desired level in a percentage of normally aberrated eyes. Setting Department of Ophthalmology, University of Zurich, Zurich, Switzerland. Methods The effect of laterally misaligned ablations on the optical outcome was simulated using measured wavefront aberration patterns from 130 normal eyes. The calculations were done for 3.0 mm, 5.0 mm, and 7.0 mm pupils. The optical quality of the simulated correction was rated by means of the root-mean-square residual wavefront error. Results To achieve the diffraction limit in 95% of the normal eyes with a 7.0 mm pupil, a lateral alignment accuracy of 0.07 mm or better was required. An accuracy of 0.2 mm was sufficient to reach the same goal with a 3.0 mm pupil. Conclusion Procedures must be developed to ensure that the ablation is within a tolerance range based on each eye’s original optical error. Rough centration based on the surgeon’s judgment might not be accurate enough to achieve significantly improved optical quality in a high percentage of treated eyes.

Abstract: Synthesizing computer-generated holograms (CGHs) of a general three-dimensional (3D) object is usually a heavy computational task. We propose and demonstrate a new algorithm for computing CGHs of 3D objects. In our scheme, many different angular projections of computer-designed 3D objects are numerically processed to yield a single two-dimensional complex matrix. This matrix is equivalent to the complex amplitude of a wave front on the rear focal plane of a spherical lens when the object is located near the front focal point and illuminated by a plane wave. Therefore the computed matrix can be used as a CGH after it is encoded to a real positive-valued transparency. When such CGH is illuminated by a plane wave, a 3D real image of the objects is constructed. The number of computer operations are equivalent to those of a two-dimensional Fourier CGH. Computer and optical constructions of 3D objects, both of which show the feasibility of the proposed approach, are described.

Abstract: An image processing method includes the steps of wavefront coding a wavefront that forms an optical image, converting the optical image to a data stream, and processing the data stream with a filter kernel to reverse effects of wavefront coding and generate a final image. By example, the filter set kernel may be a reduced filter set kernel, or a color-specific kernel. Methods and systems are also disclosed for processing color images, such as by separating color and spatial information into separate channels. Methods and systems herein are for example useful in forming electronic devices with reduced opto-mechanical, opto-electronic and processing complexity or cost.

Abstract: We report, for the first time to our knowledge, experimental demonstration of wave-front analysis via the Hartmann technique in the extreme ultraviolet range. The reference wave front needed to calibrate the sensor was generated by spatially filtering a focused undulator beam with 1.7- and 0.6-microm-diameter pinholes. To fully characterize the sensor, accuracy and sensitivity measurements were performed. The incident beam's wavelength was varied from 7 to 25 nm. Measurements of accuracy better than lambdaEUV/120 (0.11 nm) were obtained at lambdaEUV = 13.4 nm. The aberrations introduced by an additional thin mirror, as well as wave front of the spatially unfiltered incident beam, were also measured.

Abstract: We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functions reproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.

Abstract: An optical wavefront correction plate incorporates a unique, three-dimensional spatial retardation distribution utilizing the index of refraction change of resin mixture in its cured state. The optical wave plate comprises a pair of transparent plates, containing a layer of a monomers and polymerization initiators, such as resin mixture. This resin mixture exhibits a variable index of refraction as a function of the extent of its curing. Curing of the resin mixture may be made by exposure to light, such as ultraviolet light, and may be varied across and through the surface of the resin mixture to create a particular and unique three-dimensional wavefront retardation profile. The optical wave plate provides improved performance in large area mirrors, lenses, telescopes, microscopes, and ophthalmic diagnostic systems.

Abstract: Purpose. The aim of this study was to investigate the effect of contact lenses on the optical performance of the eye by measuring wavefront aberrations for the eyes with or without contact lenses. Method. A sensitive aberrometer was used to measure wavefront aberrations for 54 eyes in 27 subjects for three conditions: with no contact lens (non-CL), with soft-contact lenses (soft-CL) and with rigid gas permeable contact lenses (RGP-CL). The root mean square (RMS) value of the wavefront aberrations and Zernike aberrations were calculated. Results. A change in the RMS values of wavefront aberrations with CL wear was observed for every eye. The change in wavefront aberrations with CL wearing was found to vary substantially from individual to individual. Relative to the mean RMS value of the group for the non-CL condition, the mean RMS value was increased for the soft-CL condition and was significantly reduced for the RGP-CL condition. A significant increase in mean RMS for the soft-CL condition was found when astigmatisms were removed. Although soft-CL wearing resulted in significant increases in higher orders of Zernike aberrations (fourth, fifth, and higher), the RGP-CL condition led to a significant decrease in second-order Zernike aberrations. For the eyes with low wavefront aberrations in the non-CL condition, either soft-CL wearing or RGP-CL wearing results in increases in the RMS values. Conclusion. Contact lens wearing, either with soft lenses or the RGP lenses, causes changes in the wavefront aberrations of the eye. The changes in wavefront aberrations vary substantially from eye to eye. Although soft-CL wearing tends to induce more higher-order aberrations, RGP-CL effectively reduces the astigmatisms. Both soft-CL and RGP-CL induce more aberrations for the eyes that have low wavefront aberrations. The change in wavefront aberrations due to contact lens wearing may explain the changes in visual performance for contact lens wearers reported previously. (Optom Vis Sci 2003;80:135-141)

Abstract: PURPOSE: Corneal topography data expressed as corneal aberrations are frequently used to report corneal laser surgery results. However, the optical image quality depends on all optical elements of the eye, including the human lens. We investigated correlations between corneal and total wavefront aberrations and the relevance of corneal aberrations for representing the optical quality of the total eye. METHODS: Thirty-three eyes of 22 myopic patients were measured using a corneal topography system and a Tscherning-type wavefront analyzer. Pupils were dilated to at least 6 mm in diameter. All measurements were centered with respect to the line of sight. Corneal and total wavefront aberrations were calculated up to the 6th Zernike order in the same reference plane. RESULTS: Statistically significant correlations (P<.05) between corneal and total wavefront aberrations were found for astigmatism (C3,C5) and all 3rd Zernike order coefficients such as coma (C7,C8). No statistically significant correlations were found for 4th, 5th, or 6th order Zernike coefficients. On average, all Zernike coefficients for corneal aberrations were larger than the Zernike coefficients for total wavefront aberrations. CONCLUSIONS: Due to the lack of correlation between corneal and total wavefront aberrations in most of the higher order aberrations, measurement of corneal aberrations are of limited use for representation of the optical quality of the human eye, especially after corneal laser surgery. Corneal aberrations and optical elements within the eye are optically balanced. As a consequence, ideal customized ablations must take both corneal and total wavefront aberrations into consideration. [J Refract Surg 2003;19:104-112]

Abstract: Wedescribe and evaluate the performance of a phase diversity wavefront sensor used to measure the staticaberrations of the VLT instrument NAOS-CONICA. The main limitations of this phase diversity technique are compiled. We investigate the systematic errors due to the experimental implementation and the design restrictions. Further error sources stem from the imperfect knowledge of the system, and from limitations of the algorithm. The influence of these errors on the wavefront estimation is evaluated on numerical and experimental data. This study highlights the essential verifications and calibrations needed to obtain accurate results and gives a practical guideline for the application of a phase diversity wavefront sensor. The comprehensive calibration results and the final gain in optical performance are presented and discussed in a complementary paper (Hartung et al. 2003).

Abstract: A remote, non-contact system for detecting a defect in a railroad wheel as the wheel is stationary or moving along a railroad track includes; (1) a pulsed, laser light source for generating an ultrasonic wave in the wheel, the ultrasonic wave having a direct portion and reflected and transmitted portions if the direct portion encounters a defect in the wheel, (2) an optical component in the path of the light from the light source for forming the light into a specified illumination pattern so that the generated ultrasonic wave has a specified wavefront, (3) an air-coupled transducer or a group of transducers for sensing the acoustic signal emanating from the wheel that results from the ultrasonic wave traveling through the wheel, and (4) a signal processor, responsive to the sensed acoustic signal, capable of distinguishing whether the sensed signal has a component that indicates the existence of a reflected portion in the ultrasonic wave, wherein the presence of such a component in the acoustic signal indicates the existence of a defect in the railroad wheel.

Abstract: The work presented here addresses the problem of target detection against spatially structured interference composed of jamming plus noise, where for practical reasons, the received target wavefront may also deviate from the traditional plane wave model. This detection problem arises in over-the-horizon (OTH) radar systems where spatially distributed targets often compete for detection against directional interference that is spread over the entire range-Doppler search space. Conventional detection processing schemes are compared with a recently proposed adaptive subspace detector (ASD) that takes both the spatial structure of the interference and the possibility of target wavefront distortions into account. Experimental array data recorded by the Jindalee sky-wave and Iluka surface-wave OTH radar systems, located in central and northern Australia respectively, is used to evaluate detection performance.

Abstract: The multi-conjugate adaptive optics (MCAO) systems proposed for future giant telescopes will require new, computationally efficient, concepts for wavefront reconstruction due to their very large number of deformable mirror (DM) actuators and wavefront sensor (WFS) measurements. Preliminary versions of such reconstruction algorithms have recently been developed, and simulations of MCAO systems with 9000 or more DM actuators and 33000 or more WFS measurements are now possible using a single desktop computer. However, the results obtained to date are limited to the case of open-loop wavefront reconstruction, and more work is needed to develop computationally efficient reconstructors for the more realistic case of a closed-loop MCAO system that iteratively measures and corrects time-varying wavefront distortions. In this paper, we describe and investigate two reconstruction concepts for this application. The first approach assumes that knowledge of the DM actuator command vector and the DM-to-WFS influence matrix may be used to convert a closed-loop WFS measurement into an accurate estimate of the corresponding open-loop measurement, so that a standard open-loop wavefront reconstructor may be applied. The second approach is a very coarse (but computationally efficient) approximation to computing the minimum variance wavefront reconstructor for the residual wavefront errors in a closed-loop AO system. Sample simulation results are presented for both concepts with natural guide star (NGS) AO and laser guide star (LGS) MCAO systems on 8- and 32-meter class telescopes. The first approach yields a stable control loop with closed-loop performance comparable to the open-loop estimation accuracy of the classical minimum variance reconstructor. The second approach is unstable when implemented in a type I servo system.

Abstract: A wide-angle zoom lens with as few as two plastic elements codes the wavefront produced by the imaging system such that the imaging system is substantially invariant to aberrations related to misfocus. Signal processing is used to decode the wavefront to form the final image. A first type of zoom lens configuration uses as few as two lens elements. In this type, image processing may be modified to take into account the positioning of the lenses.

Abstract: Scanning laser ophthalmoscope optimized for selective retinal microphotocoagulation A combination of a confocal scanning laser ophthalmoscope and external laser sources is used for microphotocoagulation purposes. An opto-mechanical linkage device and beamsplitter is used to align the pivot point of the Maxwellian view of the scanning laser ophthalmoscope with the pivot point of non-scanning external laser beams. The same pivot point is necessary to minimize wavefront aberrations and to enable precise focussing of a therapeutic laser beam on the retina. An AOM and/or two-dimensional AOD can be inserted in the pathway of the Gaussian therapeutic beam to control intensity and spatial pattern of small and short-duration pulses. The location of the external laser beam on the retina is determined with the help of two synchronized detectors and image processing. One detector is used to localize moving fiducial landmarks of the retina. A second detector is used to locate on the retina the external laser aiming beam. Two different confocal apertures are used. Polarizing the aiming beam is necessary to further reduce unwanted reflections from the anterior corneal surface.

Abstract: Holography and shearography are two useful whole-field non- contacting optical tools for nondestructive flaw detection and precision measurements. Holography serves as a displacement transducer since it gives direct measurements on displacements whereas shearography serves as a strain gage since it gives direct measurements on displace- ment gradients. This paper views holography and shearography and their variations as a single optical technique having the same basic mathematical formulation and instrumentation. A key optical component used in both techniques is a doubly-refractive prism that combines two angularly separated laser rays to interfere at near collinearity, thereby permitting the use of a low-resolution CCD camera for recording the interference pattern. Shearography uses a doubly-refractive prism with small image shearing so that two neighboring points on the test surface are brought to interfere at the image plane of the camera, whereas ho- lography, on the other hand, uses a doubly-refractive prism with large image shearing so that light scattered from two different objects—a test object and a reference surface (serving as a reference beam)—are brought to interfere at the image plane of the camera. Hence, testing and measurements made using holography may also be made using shearography, and vice versa. © 2003 Society of Photo-Optical Instrumentation

Abstract: Purpose To measure the wavefront aberration at different locations in progressive-power lenses (PPL's) isolated and in situ (PPL's plus eye). Methods A Hartmann-Shack wavefront sensor was used to measure progressive-power lenses and human eyes either independently or in combination. In each selected zone, the lens was placed and tilted accordingly to simulate natural viewing conditions. We measured 21 relevant locations across an isolated PPL (plano lens of power addition of 2 D). In six of the locations, the wavefront aberration of the eye plus PPL were obtained in two ways: (1) by direct measurement of the system and (2) by adding the individual wavefront aberrations of the eye and the lens for each appropriate zone. In every case, we obtained the wavefront aberration as Zernike polynomials expansions, the root mean square error, the point-spread function, and the Strehl ratio. Results Along the corridor of the PPL, third-order coma and trefoil, and astigmatism were the dominant aberrations. In areas of the PPL outside the corridor, astigmatism increased, whereas other aberrations remained similar to the lens center. Small differences were found between the direct and calculated methods used to obtain the wavefront aberration of the eye with the lens, and the possible sources of errors were discussed. In some lenses zones, the aberrations of the lens may be compensated by the particular aberrations of the eye, yielding improved optical performance over that present in the lens alone. Conclusions We designed and built a wavefront sensor to perform spatially resolved aberration measurements in ophthalmic lenses, in particular in PPL's, either isolated or in combination with the eye. The aberrations appearing in the PPL were compared with those in normal aged eyes.

Abstract: An enhanced resolution scanned image of an object is produced by a scanning laser microscope which includes an illumination arm for scanning an object with a focused probe beam and a detection arm for receiving light from the object. The detection arm includes a detector which collects and detects light from the object to produce pixel data for a plurality of pixels. In addition, the detection arm includes a wavefront sensor for sensing phase variations of the light from the object to produce wavefront data for scanned pixel locations. From the wavefront shape of the collected light at each pixel location, a high frequency spectrum is determined which corresponds to uncollected scattered light from small scale features of that pixel location. An enhanced resolution image of a region of interest is produced based on the high frequency spectra of the scanned pixel locations.

Abstract: This paper presents an approach for computing the symmetries (skeletons) of an edge map consisting of a collection of curve segments This approach is a combination of analytic computations in the style of computational geometry and discrete propagations on a grid in the style of the numerical solutions of PDE's Specifically, waves from each of the initial curve segments are initialized and propagated as a discrete wavefront along discrete directions In addition, to avoid error built up due to the discrete nature of propagation, shockwaves are detected and explicitly propagated along a secondary dynamic grid The propagation of shockwaves, integrated with the propagation of the wavefront along discrete directions, leads to an exact simulation of propagation by the Eikonal equation The resulting symmetries are simply the collection of shockwaves formed in this process which can be manipulated locally, exactly, and efficiently under local changes in an edge map (gap completion, removal of spurious elements, etc) The ability to express grouping operations in the language of symmetry maps makes it an appropriate intermediate representation between low-level edge maps and high level object hypotheses

Abstract: As the first generation of laser interferometric gravitational wave detectors near operation, research and development has begun on increasing the instrument’s sensitivity while utilizing existing infrastructure. In the Laser Interferometer Gravitational Wave Observatory (LIGO), significant improvements are being planned for installation in ∼2007 to increase the sensitivity to test mass displacement, hence sensitivity to gravitational wave strain, by improved suspensions and test mass substrates, active seismic isolation, and higher input laser power. Even with the highest quality optics available today, however, finite absorption of laser power within transmissive optics, coupled with the tremendous amount of optical power circulating in various parts of the interferometer, result in critical wavefront deformations which will cripple the performance of the instrument. Discussed is a method of active wavefront correction via direct thermal actuation on optical elements of the interferometer; or, “thermally adaptive optics”. A simple nichrome heating element suspended off the face of an affected optic will, through radiative heating, remove the gross axisymmetric part of the original thermal distortion. A scanning heating laser will then be used to remove any remaining non-axisymmetric wavefront distortion, generated by inhomogeneities in the substrate’s absorption, thermal conductivity, etc. This work includes a quantitative analysis of both techniques of thermal compensation, as well as the results of a proof-of-principle experiment which verified the technical feasibility of each technique. Thesis Supervisor: Rainer Weiss Title: Professor of Physics