Extracting Wavefront Error From ShackHartmann Images Using Spatial Demodulation


 Russell Lester
 1 years ago
 Views:
Transcription
1 Etracting Wavefront Error From ShackHartmann Images Using Spatial Demodulation Edwin J. Sarver, PhD; Jim Schwiegerling, PhD; Raymond A. Applegate, OD, PhD ABSTRACT PURPOSE: To determine whether the spatial demodulation processing of ShackHartmann images is suitable for etracting wavefront gradients for ocular wavefront sensors. METHODS: We developed a custom software program to implement the spatial demodulation technique. To test the algorithm s performance, we generated simulated spot images and obtained an eye eamination image. We generated a collection of simulated aberrated spot images corresponding to: astigmatic wavefront ( ), highly aberrated defocus ( diopters [D]), highresolution defocus ( 0.01 D), and thirdorder aberrations (trefoil and coma). The eye eamination image and its measured Zernike coeffi cients were obtained from a ShackHartmann ocular aberrations system. We evaluated the output from the algorithm in terms of comparing the results to the known Zernike coeffi cients (for the simulated images) or the previously measured Zernike coeffi cients (for the eye eamination image). RESULTS: The spatial demodulation algorithm was able to correctly recover the aberrations to better than 1/100 (0.01) D for the simulated spot images. The processing of the eye eamination image yielded results within approimately 1/4 (0.25) D to the values provided by the ShackHartmann system. CONCLUSIONS: From the set of simulated images and the eye eamination image used to test the spatial demodulation technique, it appears that the method is suitable for application in ocular wavefront aberrations ShackHartmann systems. The method appears capable of accurately processing high levels of aberrations ( D) as well as providing high resolution as evidenced by fi nding the 0.01 D defocus. The method may be especially well suited for processing highly aberrated wavefronts. [J Refract Surg. 2006;22: ] T he ShackHartmann wavefront sensor uses a twodimensional micro lens array to measure the gradient of the wavefront. A twodimensional image sensor is located at the focal plane of the micro lens array and the array of spots (regular array for an incident plane wave and an irregular array for an aberrated incident wavefront) is digitized for subsequent computer processing. In this technique, local slopes of the wavefront are sampled by the individual lenses of the micro lens array, and by eamining the location of the spots produced for each micro lens relative to its nominal position for an incident plane wave, the gradients of the wavefront can be determined. From these gradients the wavefront can be reconstructed using, for eample, a Zernike or Fourier epansion. The imageprocessing step is typically performed by finding the centroid of each spot and directly calculating the partial derivatives of the local wavefront slope in the and y directions. 1 It is also possible to obtain the gradients of the wavefront using twodimensional Fourier transform analysis of the spots image. 2 In this method, which we refer to as the Fourier transform method, there is no need to find the individual spots in the spots image. The Fourier transform method as used here refers to a method to reconstruct the gradient field from the sensor spot image and not simply a method to reconstruct the wavefront from the gradient field. A third method of obtaining the wavefront gradients is closely related to the Fourier transform technique but only involves operations directly on the spots image. 3 We refer to this third method as spatial demodulation processing of ShackHartmann spot images. The purpose of this study is to determine whether the spatial demodulation processing of ShackHartmann spot images the third method mentioned above is a suitable technique for etracting the ocular wavefront error. From Sarver and Associates Inc, Carbondale, Ill (Sarver); Ophthalmology & Vision Sciences, University of Arizona, Tucson, Ariz (Schwiegerling); and Visual Optics Institute, College of Optometry, University of Houston, Houston, Te (Applegate). The authors have no financial or proprietary interests in the materials presented herein. Correspondence: Edwin J. Sarver, PhD, Sarver and Associates Inc, 131 Phillips Rd, Carbondale, IL Tel: ; Fa: ; JRSS1106SARVER.indd /26/ :58:18 PM
2 Figure 1. Basic geometry of coordinate mapping at a micro lens. Figure 2. Basic spectrum of aberrated spots image with spectral regions of interest identified. MATERIALS AND METHODS Eplaining the operation of the Fourier transform technique first facilitates the eplanation of the spatial demodulation technique to follow. Thus, we begin with a discussion of the Fourier transform technique. It is convenient to represent the ShackHartmann spot image for an incident plane wave as the infinite cosine function product g 0 (,y) times a spatial domain aperture function that has a value of 1 inside the pupil and 0 outside. The function g 0 (,y) is given by Eq.(1). 950 g 0 (,y) = ( cos ( 2 p ) ) ( cos ( 2 p y y ) ) (1) In this equation, p and p y are the period of the micro lens array spacing in the and y directions. Although Eq.(1) is not the spots image predicted by diffraction theory, this particular model was selected for its simplicity and its ability to capture the primary spectral peaks of interest that are required for our purposes. The corresponding Fourier transform G 0 (u,v) is a twodimensional array of weighted delta functions: G 0 (u,v)= 1 4 (0,0) 1 8 ( ( u p 1,v ) ( u p 1,v y ) ) (2) For a sufficiently wide aperture, the Fourier transform of the aperture function times the function g 0 is only slightly different from the simple delta functions of Eq.(2). When the local slope of the incident wavefront is not zero, the irradiance distribution can be thought of as being warped by a coordinate transformation as illustrated in Figure 1. In this figure, the value of dely (and similar for delx) is given by dely = dw(y) f (3) dy The irradiance distribution for the aberrated incident wavefront is denoted g 1 (,y) and is given by g 1 (,y) = g 0 [ A(,y), y B(,y)] = ( cos ( 2 p ( A(,y)) ) ) ( cos ( 2 p y (y B(,y)) ) ) (4) where A(,y) and B(,y) are proportional to the partials of the wavefront (see Eq.[3]) with respect to and y. Now, writing the cosine functions as a sum of comple eponentials and taking the Fourier transform, we see that the function A(,y) appears as the argument of a comple eponential shifted to the frequency 1/p along the u ais in the Fourier domain. Likewise, the function B(,y) appears as the argument of a comple eponential shifted to the frequency 1/p y along the v ais in the Fourier domain. This is illustrated in Figure 2. Note that two regions must be processed: one for wavefront derivatives with respect to and the other for wavefront derivatives with respect to y. Now we can enumerate the top level steps used in the Fourier transform technique: 1. Compute the Fourier transform of the ShackHartmann image. 2. Isolate the region of interest in the Fourier domain and shift the center of the region of interest to the origin. 3. Compute the inverse Fourier transform and compute the comple angle to yield the wrapped phase. Two additional steps are needed to complete the process. 4. Unwrap the phase and normalize to yield the wavefront gradient; and 5. Reconstruct the wavefront from the gradients. In step 4, we need to unwrap the phase from the arrays (one for dw/d and the other for dw/dy) computed in step 3 and then normalize the arrays to account for the micro lens focal length. Note that the normalization must be performed after the unwrapping. When journalofrefractivesurgery.com JRSS1106SARVER.indd /26/ :58:21 PM
3 there are no jump discontinuities (called residues) in the phase arrays, the unwrapping can be accomplished with a simple and fast algorithm as illustrated in Figure 3. In this case, the unwrapping algorithm (in one dimension with U = unwrapped and W = wrapped) can be described as: Set U(0) = W(0) For n=1 to the end of the array do the following D = W(n) W(n 1) If D then D = D 2 If D then D = D 2 U(n) = U(n 1) D This algorithm can be applied down the center of the array and then to the left and right to the edges of the arrays. Where there are phase discontinuities, more elaborate phase unwrapping techniques must be used. 4 Detecting phase discontinuities can be accomplished with a simple and quick test involving the sum of phase deltas around a closed contour of four samples. 4 After unwrapping and normalizing to obtain the wavefront slopes in the and y directions, the wavefront is constructed by fitting to a Zernike or Fourier epansion. SPATIAL DEMODULATION The previous processing using Fourier transforms can also be accomplished entirely in the spatial domain. In this method, the spots image is multiplied by a comple eponential to shift the desired neighborhood to the origin in the frequency domain. This operation can be described by the Fourier shift theorem shown in Eq.(5). e j2 a f() F(s a) (5) FT Figure 3. Simple unwrapping of a wrapped phase array. In Eq.(5), the parameter a is referred to as the shift constant. One comple eponential with the shift constant equal to 1/p is used to obtain the neighborhood for the wavefront slopes with respect to, and another with shift constant equal to 1/p y is used to obtain the neighborhood for the wavefront slopes with respect to y. These multiplications will lead to two complevalued arrays. A lowpass filter is then used to isolate the desired frequency band. The cutoff frequency of this lowpass filter is set to a fraction of the epected width of energy about the main peaks in the Fourier domain. We have empirically set this to 1/(2p ) in this study based on the separation of the main peaks (see Fig 2). This produces the wrapped phase arrays as we obtained in the Fourier method. The remaining steps of unwrapping the phase and reconstructing the wavefront are the same as for the Fourier method. To be practical, the lowpass filter must be efficient as it is computed in the spatial domain using convolution. One eample of such a computationally efficient lowpass filter is the bo filter in which all coefficients of the impulse response are equal. When implemented as a sliding sum, the filter is computed using only 2 adds and 2 subtracts per output sample. We use two passes of this filter to provide a triangleshaped impulse response, which has much less energy in the side lobes of the filter s frequency response compared to the bo filter. The width of the lowpass filter leads to a region near the edge of the valid data (the edge of the pupil) that has phase errors due to convolution with zero values outside the pupil. Thus, we limit processing to the portion of the pupil inside a contour that accounts for this compromised region. We refer to this valid processing region as the region of interest. In Figure 4A, we denote the edge of the detected pupil with a red circle and the region of interest to be processed by a green region. The main steps in the spatial demodulation technique are: 1. Multiply the spots image by a comple eponential (one for and the other for y). 2. Isolate the region of interest by applying a lowpass filter. 3. Unwrap the phase and normalize to yield the wavefront gradient. 4. Reconstruct the wavefront from the gradients. We developed a custom program to implement the spatial demodulation algorithm above. TEST IMAGES To evaluate the spatial demodulation method, we used simulated spot images for known aberrated wavefronts and also an eamination image acquired from a ShackHartmann wavefront sensor. The simulated 951 JRSS1106SARVER.indd /26/ :58:21 PM
4 Figure 4. Spatial demodulation processing steps of an astigmatic wavefront. A) Spots image with bounding contour identified. B) Wrapped phase corresponding to dw/d. C) Wrapped phase corresponding to dw/dy. D) Unwrapped phase corresponding to dw/d. E) Unwrapped phase corresponding to dw/dy. F) Wavefront map for reconstructed Zernike epansion. spot images were for an astigmatic wavefront, high dynamic range defocus ( diopters [D]), highresolution defocus ( 0.01 D), and thirdorder aberrations (trefoil and coma). The eye image had a large amount of background noise, but otherwise represented a normal eye. The amount of noise in the eye image is not uncommon for 50yearold eyes with typical levels of nuclear opalescence. The simulated spot images were noise free. RESULTS Using the spatial demodulation algorithm, the wavefronts calculated from the simulated aberrated spot 952 images were virtually identical to the incident wavefronts. An eample is illustrated in Figure 4. Figure 4A shows the simulated spots image for a wavefront corresponding to Figures 4B and 4C show the wrapped phase for dw/d and dw/dy, respectively. Figures 4D and 4E show the unwrapped phase for dw/d and dw/dy, respectively. Figure 4F shows a map for the reconstructed aberrations. The tet in the upper right corner of this image shows the sphere, cylinder, and ais (calculated from the secondorder coefficients), which is equal to the wavefront used to simulate the spots image. The rootmeansquare (RMS) errors in the calculated Zernike coefficients for the as journalofrefractivesurgery.com JRSS1106SARVER.indd /26/ :58:22 PM
5 tigmatic and the other simulated cases are shown in the Table. In the Table, we considered only the second order and above coefficients as is typical for reporting ocular aberrations. The errors in the Table are small for all cases. The calculated sphere, cylinder, and ais values for the first four simulation cases were found to be better than 1/100 D compared to that entered in the calculation of the simulation image. For the ShackHartmann eamination image (not one of the simulated images shown in the Table), the background noise posed no problem for the spatial demodulation technique. The Zernike coefficients calculated from this technique were not identical to the coefficients calculated from the spot centroids as reported by the ShackHartmann instrument, but they were within approimately 1/4 (0.25) D. The spatial demodulation processing yielded a correction of compared to for the spots centroid method. The difference between our calculation and the ShackHartmann system calculation could be due to differences in pupil center calculation, image processing to find the centroids not being perfect, or differences in actual system optical parameters (such as calibration data) compared to the values we estimated for the system. The difference may also be due to how our software and the ShackHartmann system software calculated the correction from the Zernike coefficients. DISCUSSION The spectrum illustrated in Figure 2 helps identify requirements for successful wavefront reconstruction using the Fourier transform or spatial demodulation technique. First, the wavefront spectrum must be band limited. In particular, the wavefront slope frequency must be low compared to the micro lens array spot frequency, ie, the value of the wavefront slope should not vary much over the region of a single micro lens. In addition, the width of the spot pattern should be large relative to the spot pitch, ie, a large number of spots should be present across the image. Both the Fourier transform and spatial demodulation techniques compute the wavefront without finding the locations of the individual spots. To shift the spectral region of interest to the center, the Fourier transform method computes the Fourier transform of the spots image and then shifts the array to the center. In the spatial decomposition method, this is accomplished by multiplying by a comple eponential. To isolate the desired band of frequencies of interest, the Fourier transform method sets all samples outside the central region of interest to zero. In the spatial decomposition method, this is accomplished by applying the lowpass filter. To obtain the wrapped wavefront TABLE RootMeanSquare (RMS) Error in Calculated Zernike Coefficients for the Simulated Spot Images Simulation Case RMS Error (µm) Astigmatic wavefront ( ) D defocus D defocus D defocus µm trefoil µm coma 0.01 derivatives, the Fourier transform method computes the inverse Fourier transform and then calculates the comple phase. In the spatial decomposition method, we calculate the comple phase. The remaining steps for both techniques are the same. Although not discussed in the algorithm steps above, other processing required includes finding the bounding contour of the region in the spots image to process and adjustments to the wavefront (,y location and derivative scaling) due to the ShackHartmann system optical layout. Compared to the ShackHartmann spot centroid method, the Fourier transform and spatial demodulation methods do not require finding the location of individual spots, easily allow spots to move outside their initial aperture region, but do require phase unwrapping algorithms. Because of this, the Fourier transform and spatial demodulation methods are especially suited for measuring highly aberrated wavefronts. From the set of simulated images and the eye eamination image used to test the spatial demodulation technique, it appears that the method is suitable for application in an ocular wavefront aberrations ShackHartmann system. The method appears capable of accurately processing high levels of aberrations ( D) as well as providing high resolution as evidenced by finding the 0.01 D defocus. The method may be especially well suited for processing highly aberrated wavefronts. REFERENCES 1. Tyson RK. Principles of Adaptive Optics. 2nd ed. New York, NY: Academic Press; Carmon Y, Ribak EN. Phase retrieval by demodulation of a HartmannShack sensor. Optics Communications. 2003;215: Talmi A, Ribak EN. Direct demodulation of HartmannShack patterns. J Opt Soc Am. 2004;21: Talmi A, Ribak EN. TwoDimensional Phase Unwrapping. New York, NY: John Wiley; JRSS1106SARVER.indd /26/ :58:23 PM
Testing spherical surfaces: a fast, quasiabsolute technique
Testing spherical surfaces: a fast, quasiabsolute technique Katherine Creath and James C. Wyant A technique for measuring the quality of spherical surfaces that provides a quasiabsolute result is presented.
More informationImproving visual function diagnostic metrics. Charles Campbell
Improving visual function diagnostic metrics Charles Campbell Metrics  What are they? What are they used for? A metric assigns a numerical value or a set of values to characterize some chosen phenomenon
More informationWilliam J. Donnelly III, PhD. Jon A. Herlocker, PhD.  Sr. Optical Engineer.  Sr. Optical Scientist
Applications of Nonsequential Ray Tracing to Investigate Lenslet Image Point Spread Function Uniformity Under Geometrical & Physical Optical Coherent & Incoherent Source Modeling 22307 William J. Donnelly
More informationNull test for a highly paraboloidal mirror
Null test for a highly paraboloidal mirror Taehee Kim, James H. Burge, Yunwoo Lee, and Sungsik Kim A circular null computergenerated hologram CGH was used to test a highly paraboloidal mirror diameter,
More informationCity Research Online. Permanent City Research Online URL:
Gruppetta, S, Koechlin, L, Lacombe, F & Puget, P (0015). Curvature sensor for the measurement of the static corneal topography and the dynamic tear film topography in the human eye.. Opt Lett, 30(20),
More informationOPTI 513R / Optical Testing
OPTI 513R / Optical Testing Instructor: Dae Wook Kim Meinel Building Rm 633, University of Arizona, Tucson, AZ 85721 EMail: dkim@optics.arizona.edu Website: sites.google.com/site/opti513r/ Office Hours:
More informationLens Design I. Lecture 11: Imaging Herbert Gross. Summer term
Lens Design I Lecture 11: Imaging 20150629 Herbert Gross Summer term 2015 www.iap.unijena.de 2 Preliminary Schedule 1 13.04. Basics 2 20.04. Properties of optical systrems I 3 27.05. 4 04.05. Properties
More informationOn the quality of measured optical aberration coefficients using phase wheel monitor
On the quality of measured optical aberration coefficients using phase wheel monitor Lena V. Zavyalova *, Aaron R. Robinson, Anatoly Bourov, Neal V. Lafferty, and Bruce W. Smith Center for Nanolithography
More informationA software simmulation of HartmannSchack patterns for real corneas
A software simmulation of HartmannSchack patterns for real corneas L. A. Carvalho*, Jarbas C. Castro*, P. Schor, W. Chamon *Instituto de Física de São Carlos (IFSC  USP), Brazil lavcf@ifsc.sc.usp.br
More informationImage Sampling and Quantisation
Image Sampling and Quantisation Introduction to Signal and Image Processing Prof. Dr. Philippe Cattin MIAC, University of Basel 1 of 46 22.02.2016 09:17 Contents Contents 1 Motivation 2 Sampling Introduction
More informationImage Sampling & Quantisation
Image Sampling & Quantisation Biomedical Image Analysis Prof. Dr. Philippe Cattin MIAC, University of Basel Contents 1 Motivation 2 Sampling Introduction and Motivation Sampling Example Quantisation Example
More informationHolographic imaging with a ShackHartmann wavefront sensor
Holographic imaging with a ShackHartmann wavefront sensor Hai Gong, 1,4 Oleg Soloviev, 1,2,3 Dean Wilding, 1 Paolo Pozzi, 1 Michel Verhaegen 1 and Gleb Vdovin 1,2,3,5 1 Delft University of Technology,
More informationDiffraction. Singleslit diffraction. Diffraction by a circular aperture. Chapter 38. In the forward direction, the intensity is maximal.
Diffraction Chapter 38 Huygens construction may be used to find the wave observed on the downstream side of an aperture of any shape. Diffraction The interference pattern encodes the shape as a Fourier
More informationOptometer. Subjective Assessment of Refractive Error. Myopia. Far Point. Myopia. Far Point
Optometer Subjective Assessment of Refractive rror Far Point Myopia Far Point Myopia 1 Subjective Assessment of Refractive rror Power φ = 1 / f Far Point Myopia f  Δz d z Subjective Assessment of Refractive
More informationControl of Light. Emmett Ientilucci Digital Imaging and Remote Sensing Laboratory Chester F. Carlson Center for Imaging Science 8 May 2007
Control of Light Emmett Ientilucci Digital Imaging and Remote Sensing Laboratory Chester F. Carlson Center for Imaging Science 8 May 007 Spectroradiometry Spectral Considerations Chromatic dispersion
More informationEvaluation of TwoDimensional Phase Unwrapping Algorithms for Interferometric Adaptive Optics Utilizing LiquidCrystal Spatial Light Modulators
48 The Open Optics Journal, 008,, 485 Open Access Evaluation of TwoDimensional Phase Unwrapping Algorithms for Interferometric Adaptive Optics Utilizing LiquidCrystal Spatial Light Modulators K.L. Baker
More informationTolerance on material inhomogenity and surface irregularity
Opti 521 Wenrui Cai Tolerance on material inhomogenity and surface irregularity Abstract In this tutorial, a case study on tolerance for a focusing doublet is performed by using ZEMAX. First, how to perform
More informationComputer Graphics. Texture Filtering & Sampling Theory. Hendrik Lensch. Computer Graphics WS07/08 Texturing
Computer Graphics Texture Filtering & Sampling Theory Hendrik Lensch Overview Last time Texture Parameterization Procedural Shading Today Texturing Filtering 2D Texture Mapping Forward mapping Object surface
More informationAnalysis of the Gaussian Beam on a Corrugated Dielectric Interface
(An ISO 3297: 27 Certified Organization) Vol. 3, Issue 9, September 214 Analysis of the Gaussian Beam on a Corrugated Dielectric Interface Mohamed B. El_Mashade 1, Adel Shaaban 2 Department of Electrical
More informationCMSC427 Shading Intro. Credit: slides from Dr. Zwicker
CMSC427 Shading Intro Credit: slides from Dr. Zwicker 2 Today Shading Introduction Radiometry & BRDFs Local shading models Light sources Shading strategies Shading Compute interaction of light with surfaces
More informationPrentice Hall. Connected Mathematics 2, 7th Grade Units Mississippi Mathematics Framework 2007 Revised, Grade 7
Prentice Hall Connected Mathematics 2, 7th Grade Units 2006 C O R R E L A T E D T O Mississippi Mathematics Framework 2007 Revised, Grade 7 NUMBER AND OPERATIONS 1. Apply concepts of rational numbers and
More informationAlgorithm for Implementing an ABCD Ray Matrix WaveOptics Propagator
Copyright 007 Society of PhotoOptical Instrumentation Engineers. This paper was published in SPIE Proc. Vol. 66756 and is made available as an electronic reprint with permission of SPIE. One print or
More informationFringe modulation skewing effect in whitelight vertical scanning interferometry
Fringe modulation skewing effect in whitelight vertical scanning interferometry Akiko Harasaki and James C. Wyant An interference fringe modulation skewing effect in whitelight vertical scanning interferometry
More informationCoherent digital demodulation of singlecamera Nprojections for 3Dobject shape measurement: Cophased profilometry
Coherent digital demodulation of singlecamera Nprojections for 3Dobject shape measurement: Cophased profilometry M. Servin, 1,* G. Garnica, 1 J. C. Estrada, 1 and A. Quiroga 2 1 Centro de Investigaciones
More informationIntroduction to Computer Vision. Introduction CMPSCI 591A/691A CMPSCI 570/670. Image Formation
Introduction CMPSCI 591A/691A CMPSCI 570/670 Image Formation Lecture Outline Light and Optics Pinhole camera model Perspective projection Thin lens model Fundamental equation Distortion: spherical & chromatic
More informationFractions. 7th Grade Math. Review of 6th Grade. Slide 1 / 306 Slide 2 / 306. Slide 4 / 306. Slide 3 / 306. Slide 5 / 306.
Slide 1 / 06 Slide 2 / 06 7th Grade Math Review of 6th Grade 20150114 www.njctl.org Slide / 06 Table of Contents Click on the topic to go to that section Slide 4 / 06 Fractions Decimal Computation Statistics
More informationMaterial Made of Artificial Molecules and Its Refraction Behavior under Microwave
Material Made of Artificial Molecules and Its Refraction Behavior under Microwave Tao Zhang College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China (taozhang@bnu.edu.cn)
More informationWAVELENGTH MANAGEMENT
BEAM DIAGNOS TICS SPECIAL PRODUCTS OEM DETECTORS THZ DETECTORS PHOTO DETECTORS HIGH POWER SOLUTIONS POWER DETECTORS ENERGY DETECTORS MONITORS Camera Accessories WAVELENGTH MANAGEMENT UV CONVERTERS UV Converters
More informationx 2 + y 2 + z 2 = 1 = ˆr ŷ = ±y cosθ z (a) The half angle of the cones (inside the material) is just given by the critical angle sinθ c n = 3.
Exercise.6 The results of this problem are somewhat general and apply to any rectangular parallelepiped with source located at any position inside. One can see this as follows. The direction of an arbitrary
More informationCoding and Modulation in Cameras
Mitsubishi Electric Research Laboratories Raskar 2007 Coding and Modulation in Cameras Ramesh Raskar with Ashok Veeraraghavan, Amit Agrawal, Jack Tumblin, Ankit Mohan Mitsubishi Electric Research Labs
More informationSpectrographs. C. A. Griffith, Class Notes, PTYS 521, 2016 Not for distribution.
Spectrographs C A Griffith, Class Notes, PTYS 521, 2016 Not for distribution 1 Spectrographs and their characteristics A spectrograph is an instrument that disperses light into a frequency spectrum, which
More informationEfficient waveoptical calculation of 'bad systems'
1 Efficient waveoptical calculation of 'bad systems' Norman G. Worku, 2 Prof. Herbert Gross 1,2 25.11.2016 (1) Fraunhofer Institute for Applied Optics and Precision Engineering IOF, Jena, Germany (2)
More informationSynthesis Imaging. Claire Chandler, Sanjay Bhatnagar NRAO/Socorro
Synthesis Imaging Claire Chandler, Sanjay Bhatnagar NRAO/Socorro Michelson Summer Workshop Caltech, July 2428, 2006 Synthesis Imaging 2 Based on the van CittertZernike theorem: The complex visibility
More informationModeField Diameter and Spot Size Measurements of Lensed and Tapered Specialty Fibers
ModeField Diameter and Spot Size Measurements of Lensed and Tapered Specialty Fibers By Jeffrey L. Guttman, Ph.D., Director of Engineering, OphirSpiricon Abstract: The ModeField Diameter (MFD) and spot
More informationRay Tracing. Lens Design OPTI 517. Prof. Jose Sasian
Ray Tracing Lens Design OPTI 517 Use of rays In optical design In computer graphics In acoustics In art In photography Lens design raytracing Ray tracing universe Ray tracing It is important to have
More informationSupporting Information: Highly tunable elastic dielectric metasurface lenses
Supporting Information: Highly tunable elastic dielectric metasurface lenses Seyedeh Mahsa Kamali, Ehsan Arbabi, Amir Arbabi, u Horie, and Andrei Faraon SUPPLEMENTAR NOTE : SAMPLING FREQUENC OF THE PHASE
More informationCSPLAT for Photolithography Simulation
CSPLAT for Photolithography Simulation Guoxiong Wang wanggx@vlsi.zju.edu.cn Institute of VLSI Design, Zhejiang University 2001.8.31 Outline Photolithographic system Resolution enhancement technologies
More informationRefraction at a single curved spherical surface
Refraction at a single curved spherical surface This is the beginning of a sequence of classes which will introduce simple and complex lens systems We will start with some terminology which will become
More informationOptimal corneal ablation for eyes with arbitrary Hartmann Shack aberrations
2580 J. Opt. Soc. Am. A/Vol. 15, No. 9/September 1998 Stanley A. Klein Optimal corneal ablation for eyes with arbitrary Hartmann Shack aberrations Stanley A. Klein School of Optometry, University of California,
More informationSupplementary Figure 1 Optimum transmissive mask design for shaping an incident light to a desired
Supplementary Figure 1 Optimum transmissive mask design for shaping an incident light to a desired tangential form. (a) The light from the sources and scatterers in the half space (1) passes through the
More informationAP Physics: Curved Mirrors and Lenses
The Ray Model of Light Light often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric
More information7 Fractions. Number Sense and Numeration Measurement Geometry and Spatial Sense Patterning and Algebra Data Management and Probability
7 Fractions GRADE 7 FRACTIONS continue to develop proficiency by using fractions in mental strategies and in selecting and justifying use; develop proficiency in adding and subtracting simple fractions;
More informationHighresolution 3D profilometry with binary phaseshifting methods
Highresolution 3D profilometry with binary phaseshifting methods Song Zhang Department of Mechanical Engineering, Iowa State University, Ames, Iowa 511, USA (song@iastate.edu) Received 11 November 21;
More informationReconstruction of Images Distorted by Water Waves
Reconstruction of Images Distorted by Water Waves Arturo Donate and Eraldo Ribeiro Computer Vision Group Outline of the talk Introduction Analysis Background Method Experiments Conclusions Future Work
More informationMeasurement of Highly Parabolic Mirror using Computer Generated Hologram
Measurement of Highly Parabolic Mirror using Computer Generated Hologram Taehee Kim a, James H. Burge b, Yunwoo Lee c a Digital Media R&D Center, SAMSUNG Electronics Co., Ltd., Suwon city, Kyungkido,
More informationPlane Wave Imaging Using Phased Array Arno Volker 1
11th European Conference on NonDestructive Testing (ECNDT 2014), October 610, 2014, Prague, Czech Republic More Info at Open Access Database www.ndt.net/?id=16409 Plane Wave Imaging Using Phased Array
More informationEECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines
EECS 556 Image Processing W 09 Interpolation Interpolation techniques B splines What is image processing? Image processing is the application of 2D signal processing methods to images Image representation
More informationCURRICULUM UNIT MAP 1 ST QUARTER
1 ST QUARTER Unit 1: Pre Algebra Basics I WEEK 12 OBJECTIVES Apply properties for operations to positive rational numbers and integers Write products of like bases in exponential form Identify and use
More informationThomas Abraham, PhD
Thomas Abraham, PhD (tabraham1@hmc.psu.edu) What is Deconvolution? Deconvolution, also termed as Restoration or Deblurring is an image processing technique used in a wide variety of fields from 1D spectroscopy
More informationWinCamDLCM 1" CMOS Beam Profiling Camera, SuperSpeed USB 3.0, * nm * modeldependent
Datasheet WinCamDLCM 1" CMOS Beam Profiling Camera, SuperSpeed USB 3.0, 190 1610* nm * modeldependent With an 11.3 x 11.3 mm active area, 4.2 Mpixels, 5.5 x 5.5 μm pixels, optical and electronic triggering
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 40 Review Spring 2016 Semester Matthew Jones Final Exam Date:Tuesday, May 3 th Time:7:00 to 9:00 pm Room: Phys 112 You can bring one doublesided pages of notes/formulas.
More informationPhase. E = A sin(2p f t+f) (wave in time) or E = A sin(2p x/l +f) (wave in space)
Interference When two (or more) waves arrive at a point (in space or time), they interfere, and their amplitudes may add or subtract, depending on their frequency and phase. 1 Phase E = A sin(2p f t+f)
More informationWavefront Prediction using Artificial Neural Networks. By: Steve Weddell
Wavefront Prediction using Artificial Neural Networks By: Steve Weddell 1 Motivation for Research (1 of 2) Turbulence layer #1 Turbulence layer #2 Ground Turbulence Layer Science Object Reference Guide
More informationDerivatives 3: The Derivative as a Function
Derivatives : The Derivative as a Function 77 Derivatives : The Derivative as a Function Model : Graph of a Function 9 8 7 6 5 g()    5 6 7 8 9 0 5 6 7 8 9 0 5   56 7 Construct Your Understanding
More informationDesign of Optical Lens for Quasidiffractionfree beam using Particle Swarm Optimization
Vol. (COMCOMS 5), pp.465 http://dx.doi.org/.457/astl.5..47 Design of Optical Lens for Quasidiffractionfree beam using Particle Swarm Optimization Takafumi Fujimoto and Yoko Maemura Graduate School of
More informationFRESNEL LENS DIMENSIONS USING 3D PROFILOMETRY
FRESNEL LENS DIMENSIONS USING 3D PROFILOMETRY Prepared by Duanjie Li & Benjamin Mell 6 Morgan, Ste156, Irvine CA 92618 P: 949.461.9292 F: 949.461.9232 nanovea.com Today's standard for tomorrow's materials.
More informationTEACHER CERTIFICATION STUDY GUIDE KNOWLEDGE OF MATHEMATICS THROUGH SOLVING...1
TABLE OF CONTENTS COMPETENCY/SKILLS PG # COMPETENCY 1 KNOWLEDGE OF MATHEMATICS THROUGH PROBLEM SOLVING...1 Skill 1.1 Skill 1.2 Skill 1.3 Skill 1.4 Identify appropriate mathematical problems from realworld
More informationOptical Design with Zemax
Optical Design with Zemax Lecture 9: Advanced handling 20140613 Herbert Gross Sommer term 2014 www.iap.unijena.de 2 Preliminary Schedule 1 11.04. Introduction 2 25.04. Properties of optical systems
More informationImproved phaseunwrapping method using geometric constraints
Improved phaseunwrapping method using geometric constraints Guangliang Du 1, Min Wang 1, Canlin Zhou 1*,Shuchun Si 1, Hui Li 1, Zhenkun Lei 2,Yanjie Li 3 1 School of Physics, Shandong University, Jinan
More informationCoherent Gradient Sensing Microscopy: Microinterferometric Technique. for Quantitative Cell Detection
Coherent Gradient Sensing Microscopy: Microinterferometric Technique for Quantitative Cell Detection Proceedings of the SEM Annual Conference June 710, 010 Indianapolis, Indiana USA 010 Society for Experimental
More informationLight: Geometric Optics
Light: Geometric Optics 23.1 The Ray Model of Light Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization,
More informationPHYSICS 1040L LAB LAB 7: DIFFRACTION & INTERFERENCE
PHYSICS 1040L LAB LAB 7: DIFFRACTION & INTERFERENCE Object: To investigate the diffraction and interference of light, Apparatus: Lasers, optical bench, single and double slits. screen and mounts. Theory:
More informationPhase Shifting GratingSlit Test Utilizing A Digital Micromirror Device With an Optical Surface Reconstruction Algorithm
Phase Shifting GratingSlit Test Utilizing A Digital Micromirror Device With an Optical Surface Reconstruction Algorithm Item Type text; Electronic Dissertation Authors Liang, ChaoWen Publisher The University
More informationAUTOMATIC TARGET RECOGNITION IN HIGH RESOLUTION SAR IMAGE BASED ON BACKSCATTERING MODEL
AUTOMATIC TARGET RECOGNITION IN HIGH RESOLUTION SAR IMAGE BASED ON BACKSCATTERING MODEL Wang Chao (1), Zhang Hong (2), Zhang Bo (1), Wen Xiaoyang (1), Wu Fan (1), Zhang Changyao (3) (1) National Key Laboratory
More informationOther Linear Filters CS 211A
Other Linear Filters CS 211A Slides from Cornelia Fermüller and Marc Pollefeys Edge detection Convert a 2D image into a set of curves Extracts salient features of the scene More compact than pixels Origin
More informationOptical Design with Zemax for PhD  Basics
Optical Design with Zemax for PhD  Basics Lecture 8: Advanced handling 20130627 Herbert Gross Summer term 2013 www.iap.unijena.de 2 Preliminary Schedule No Date Subject Detailed content 1 02.05. Introduction
More informationImage Processing and Analysis
Image Processing and Analysis 3 stages: Image Restoration  correcting errors and distortion. Warping and correcting systematic distortion related to viewing geometry Correcting "drop outs", striping and
More informationAccurate and Dense WideBaseline Stereo Matching Using SWPOC
Accurate and Dense WideBaseline Stereo Matching Using SWPOC Shuji Sakai, Koichi Ito, Takafumi Aoki Graduate School of Information Sciences, Tohoku University, Sendai, 980 8579, Japan Email: sakai@aoki.ecei.tohoku.ac.jp
More informationAll Reflective Fly s Eye Illuminators for EUV Lithography
All Reflective Fly s Eye Illuminators for EUV Lithography Blake Crowther, Donald Koch, Joseph Kunick, James McGuire Optical Research Associates Robert Harned, Rick Gontin ASML Presented by Kevin Thompson/
More informationCharles L. Bennett, USA. Livermore, CA 94550
i.., s, co S76,642 tfc RL118 65 IMAGING FOURIER TRANSFORM SPECTROMETER Inventor, Charles L. Bennett, USA 5845 H e i d i Way Livermore, CA 94550 4 0 rl rl I This report was prepared as an account of
More informationMedical Image Segmentation using Level Sets
Medical Image Segmentation using Level Sets Technical Report #CS81 Tenn Francis Chen Abstract Segmentation is a vital aspect of medical imaging. It aids in the visualization of medical data and diagnostics
More informationRadiance Photography. Todor Georgiev Adobe Systems. Andrew Lumsdaine Indiana University
Radiance Photography Todor Georgiev Adobe Systems Andrew Lumsdaine Indiana University Course Goals Overview of radiance (aka lightfield) photography Mathematical treatment of theory and computation Hands
More informationA twomirror design for the high energy section of the Cherenkov Telescope Array
A twomirror design for the high energy section of the Cherenkov Telescope Array Introduction. Optical design studies: Exact Optics. ZEMAX. Mechanical design. Summary. Tim Greenshaw, for Durham, Leeds,
More informationLimits of computational whitelight holography
Journal of Physics: Conference Series Limits of computational whitelight holography To cite this article: Sebastian Mader et al 2013 J. Phys.: Conf. Ser. 415 012046 View the article online for updates
More informationDome and Mirror Seeing Estimates for the Thirty Meter Telescope
Dome and Mirror Seeing Estimates for the Thirty Meter Telescope John S. Pazder a, Konstantinos Vogiatzis b, and George Z. Angeli b, a National Research Council Canada, Herzberg Institute of Astrophysics
More informationThe CAFADIS camera: a new tomographic wavefront sensor for Adaptive Optics.
1st AO4ELT conference, 05011 (2010) DOI:10.1051/ao4elt/201005011 Owned by the authors, published by EDP Sciences, 2010 The CAFADIS camera: a new tomographic wavefront sensor for Adaptive Optics. J.M. RodríguezRamos
More informationTutorial on Fourier Theory
Tutorial on Fourier Theory Yerin Yoo March 2001 1 Introduction: Why Fourier? During the preparation of this tutorial, I found that almost all the textbooks on digital image processing have a section devoted
More informationOptimal local shape description for rotationally nonsymmetric optical surface design and analysis
Optimal local shape description for rotationally nonsymmetric optical surface design and analysis Ozan Cakmakci, Brendan Moore, Hassan Foroosh, Jannick P. Rolland, College of Optics, Center for Research
More informationGrade 9 Math Terminology
Unit 1 Basic Skills Review BEDMAS a way of remembering order of operations: Brackets, Exponents, Division, Multiplication, Addition, Subtraction Collect like terms gather all like terms and simplify as
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 41 Review Spring 2013 Semester Matthew Jones Final Exam Date:Tuesday, April 30 th Time:1:00 to 3:00 pm Room: Phys 112 You can bring two doublesided pages of
More informationUse of beam parameters in optical component testing
Use of beam parameters in optical component testing D. R. Neal *, J. K. Gruetzner *, J.P. Roller * WaveFront Sciences, Inc., 480 Central S.E. Albuquerque, NM 873 ABSTRACT We are investigating the use of
More informationRectification of distorted elemental image array using four markers in threedimensional integral imaging
Rectification of distorted elemental image array using four markers in threedimensional integral imaging Hyeonah Jeong 1 and Hoon Yoo 2 * 1 Department of Computer Science, SangMyung University, Korea.
More informationCoherent Diffraction Imaging with Nano and Microbeams
Diffraction Imaging with Nano and Microbeams Why does lensless need? Mark A Pfeifer Cornell High Energy Synchrotron Source Cornell University Ithaca, NY 14850 map322@cornell.edu XLD 2011 June 28, 2011
More informationEnhanced twofrequency phaseshifting method
Research Article Vol. 55, No. 16 / June 1 016 / Applied Optics 4395 Enhanced twofrequency phaseshifting method JAESANG HYUN AND SONG ZHANG* School of Mechanical Engineering, Purdue University, West
More informationDigital Volume Correlation for Materials Characterization
19 th World Conference on NonDestructive Testing 2016 Digital Volume Correlation for Materials Characterization Enrico QUINTANA, Phillip REU, Edward JIMENEZ, Kyle THOMPSON, Sharlotte KRAMER Sandia National
More informationRectangular Lenslet Array
Rectangular Lenslet Array INTRODUCTION Lenslet arrays are used in a variety of applications that include beam homogenization. This knowledge base article demonstrates the setup of an imaging lenslet array
More informationLight: Geometric Optics (Chapter 23)
Light: Geometric Optics (Chapter 23) Units of Chapter 23 The Ray Model of Light Reflection; Image Formed by a Plane Mirror Formation of Images by Spherical Index of Refraction Refraction: Snell s Law 1
More informationINSPECTION OF MACHINED PARTS FROM CAD MODEL USING 3D PROFILOMETRY
INSPECTION OF MACHINED PARTS FROM CAD MODEL USING 3D PROFILOMETRY Prepared by Duanjie Li, PhD, Erik Steinholt and Jeronimo Silva 6 Morgan, Ste156, Irvine CA 92618 P: 949.461.9292 F: 949.461.9232 nanovea.com
More informationCompliant Baffle for Large Telescope Daylight Imaging. Stacie Williams Air Force Research Laboratory ABSTRACT
Compliant Baffle for Large Telescope Daylight Imaging Steven Griffin, Andrew Whiting, Shawn Haar The Boeing Company Stacie Williams Air Force Research Laboratory ABSTRACT With the recent interest in daylight
More informationFast calculation of phase in spatial npoint phaseshifting techniques
Fast calculation of phase in spatial npoint phaseshifting techniques Joanna Schmit and Katherine Creath Optical Sciences Center University of Arizona, Tucson, AZ 85721 ABSTRACT The npoint technique
More informationMichael Moody School of Pharmacy University of London 29/39 Brunswick Square London WC1N 1AX, U.K.
This material is provided for educational use only. The information in these slides including all data, images and related materials are the property of : Michael Moody School of Pharmacy University of
More informationCHAPTER 3 DISPARITY AND DEPTH MAP COMPUTATION
CHAPTER 3 DISPARITY AND DEPTH MAP COMPUTATION In this chapter we will discuss the process of disparity computation. It plays an important role in our caricature system because all 3D coordinates of nodes
More informationIntroduction to Computer Vision. Week 3, Fall 2010 Instructor: Prof. Ko Nishino
Introduction to Computer Vision Week 3, Fall 2010 Instructor: Prof. Ko Nishino Last Week! Image Sensing " Our eyes: rods and cones " CCD, CMOS, Rolling Shutter " Sensing brightness and sensing color! Projective
More information3DOBJECT DETECTION METHOD BASED ON THE STEREO IMAGE TRANSFORMATION TO THE COMMON OBSERVATION POINT
3DOBJECT DETECTION METHOD BASED ON THE STEREO IMAGE TRANSFORMATION TO THE COMMON OBSERVATION POINT V. M. Lisitsyn *, S. V. Tikhonova ** State Research Institute of Aviation Systems, Moscow, Russia * lvm@gosniias.msk.ru
More informationspecular diffuse reflection.
Lesson 8 Light and Optics The Nature of Light Properties of Light: Reflection Refraction Interference Diffraction Polarization Dispersion and Prisms Total Internal Reflection Huygens s Principle The Nature
More informationComputeroriginated planar holographic optical elements
Computeroriginated planar holographic optical elements Silviu Reinhorn, Yaakov Amitai, and Albert A. Friesem We present novel, to our knowledge, methods for the analytical design and recording of planar
More informationSeventh Grade Mathematics Content Standards and Objectives
Seventh Grade Mathematics Content Standards and Objectives Standard 1: Number and Operations beyond the field of mathematics, students will M.S.7.1 demonstrate understanding of numbers, ways of representing
More informationLight: Geometric Optics
Light: Geometric Optics Regular and Diffuse Reflection Sections 231 to 232. How We See Weseebecauselightreachesoureyes. There are two ways, therefore, in which we see: (1) light from a luminous object
More informationTechnologies of Digital Holographic Display
Technologies of Digital Holographic Display Joonku Hahn Kyungpook National University Outline: 1. Classification of digital holographic display 2. Data capacity, View volume and Resolution 3. Holographic
More informationFast scanning method for onedimensional surface profile measurement by detecting angular deflection of a laser beam
Fast scanning method for onedimensional surface profile measurement by detecting angular deflection of a laser beam Ryo Shinozaki, Osami Sasaki, and Takamasa Suzuki A fast scanning method for onedimensional
More information