Contrast Sensitivity Function of Sine-Wave Gratings in Children With
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Precise and Fast Spatial-Frequency Analysis Using the Iterative Local Fourier Transform
Vol. 24, No. 19 | 19 Sep 2016 | OPTICS EXPRESS 22110 Precise and fast spatial-frequency analysis using the iterative local Fourier transform 1 2 2,* SUKMOCK LEE, HEEJOO CHOI, AND DAE WOOK KIM 1Department of Physics, Inha University, Incheon, 402-751, South Korea 2College of Optical Sciences, University of Arizona, 1630 East University Boulevard, Tucson, Arizona 85721, USA *[email protected] Abstract: The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method’s superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source. ©2016 Optical Society of America OCIS codes: (300.6300) Spectroscopy, Fourier transforms; (070.4790) Spectrum analysis; (070.6760) Talbot and self-imaging effects. References and links 1. L. M. Sanchez-Brea, F. J. Torcal-Milla, J. M. Herrera-Fernandez, T. Morlanes, and E. Bernabeu, “Self-imaging technique for beam collimation,” Opt. Lett. 39(19), 5764–5767 (2014). -
Fourier Optics
Fourier Optics 1 Background Ray optics is a convenient tool to determine imaging characteristics such as the location of the image and the image magni¯cation. A complete description of the imaging system, however, requires the wave properties of light and associated processes like di®raction to be included. It is these processes that determine the resolution of optical devices, the image contrast, and the e®ect of spatial ¯lters. One possible wave-optical treatment considers the Fourier spectrum (space of spatial frequencies) of the object and the transmission of the spectral components through the optical system. This is referred to as Fourier Optics. A perfect imaging system transmits all spectral frequencies equally. Due to the ¯nite size of apertures (for example the ¯nite diameter of the lens aperture) certain spectral components are attenuated resulting in a distortion of the image. Specially designed ¯lters on the other hand can be inserted to modify the spectrum in a prede¯ned manner to change certain image features. In this lab you will learn the principles of spatial ¯ltering to (i) improve the quality of laser beams, and to (ii) remove undesired structures from images. To prepare for the lab, you should review the wave-optical treatment of the imaging process (see [1], Chapters 6.3, 6.4, and 7.3). 2 Theory 2.1 Spatial Fourier Transform Consider a two-dimensional object{ a slide, for instance that has a ¯eld transmission function f(x; y). This transmission function carries the information of the object. A (mathematically) equivalent description of this object in the Fourier space is based on the object's amplitude spectrum ZZ 1 F (u; v) = f(x; y)ei2¼ux+i2¼vydxdy; (1) (2¼)2 where the Fourier coordinates (u; v) have units of inverse length and are called spatial frequencies. -
The Representation of Complex Images in Spatial Frequency Domains of Primary Visual Cortex
9310 • The Journal of Neuroscience, August 29, 2007 • 27(35):9310–9318 Behavioral/Systems/Cognitive The Representation of Complex Images in Spatial Frequency Domains of Primary Visual Cortex Jing X. Zhang,1 Ari Rosenberg,2 Atul K. Mallik,3 T. Robert Husson,2 and Naoum P. Issa4 1Department of Biomedical Engineering, Illinois Institute of Technology, Chicago, Illinois 60616, and 2Committee on Computational Neuroscience, 3Committee on Neurobiology, and 4Department of Neurobiology, University of Chicago, Chicago, Illinois 60637 The organization of cat primary visual cortex has been well mapped using simple stimuli such as sinusoidal gratings, revealing superim- posed maps of orientation and spatial frequency preferences. However, it is not yet understood how complex images are represented across these maps. In this study, we ask whether a linear filter model can explain how cortical spatial frequency domains are activated by complex images. The model assumes that the response to a stimulus at any point on the cortical surface can be predicted by its individual orientation, spatial frequency, and temporal frequency tuning curves. To test this model, we imaged the pattern of activity within cat area 17 in response to stimuli composed of multiple spatial frequencies. Consistent with the predictions of the model, the stimuli activated low and high spatial frequency domains differently: at low stimulus drift speeds, both domains were strongly activated, but activity fell off in high spatial frequency domains as drift speed increased. To determine whether the filter model quantitatively predicted the activity patterns, we measured the spatiotemporal tuning properties of the functional domains in vivo and calculated expected response ampli- tudes from the model. -
Vision: from Eye to Brain (Chap 3, Part B)
Vision: From Eye to Brain (Chap 3, Part B) Lecture 7 Jonathan Pillow Sensation & Perception (PSY 345 / NEU 325) Princeton University, Spring 2015 1 more “channels”: spatial frequency channels spatial frequency: the number of cycles of a grating per unit of visual angle (usually specified in degrees) • think of it as: # of bars per unit length low frequency intermediate high frequency 2 Why sine gratings? • Provide useful decomposition of images Technical term: Fourier decomposition 3 Fourier decomposition • mathematical decomposition of an image (or sound) into sine waves. reconstruction: “image” 1 sine wave 2 sine waves 3 sine waves 4 sine waves 4 “Fourier Decomposition” theory of V1 claim: role of V1 is to do “Fourier decomposition”, i.e., break images down into a sum of sine waves • Summation of two spatial sine waves • any pattern can be broken down into a sum of sine waves 5 Fourier decomposition • mathematical decomposition of an image (or sound) into sine waves. Original image High Frequencies Low Frequencies 6 original low medium high 7 Retinal Ganglion Cells: tuned to spatial frequency Response of a ganglion cell to sine gratings of different frequencies 8 The contrast sensitivity function Human contrast sensitivity illustration of this sensitivity 9 Image Illustrating Spatial Frequency Channels 10 Image Illustrating Spatial Frequency Channels 11 If it is hard to tell who this famous person is, try squinting or defocusing “Lincoln illusion” Harmon & Jules 1973 12 “Gala Contemplating the Mediterranean Sea, which at 30 meters becomes -
Visual Performance Theoretical Limit of Resolution
Visual Performance Aspects Conditions • Resolution Limit • Illumination • Pattern Detection • Monocular vs. Binocular • Pattern Recognition • Distance • Contrast Level • On-axis vs. Off-axis • Color • Single or multiple targets • Temporal Response • Literacy & Verbal ability Theoretical Limit of Resolution θ Rayleigh Criterion 1.22λ θ = radians D For λ = 587.6 nm D ranges from 2 – 8 mm 0.090 ≤θ≤0.358 mrad 0.3 ≤θ≤1.23 minutes of arc 1 Rayleigh Criteria 1 1.6 mm Pupil 0.75 Contrast 14% Airy #1 0.5 Airy #2 Sum Relative Irradiance 0.25 Photorecptor Photorecptor Photorecptor 0 -15 -10 -5 0 5 10 15 20 25 Position (microns) Visual Acuity Visual Acuity is a measure of the smallest detail that can be resolved by the visual system. There are different types of acuity measures. Point Acuity – “Binary Star” test – typically 1 arcmin resolution Vernier Acuity – Two lines slightly offset from each other. Finds smallest detectable offset – typically 10 seconds of arc θ 2 Visual Acuity Grating Acuity – Sinusoidal or Square wave gratings are used to determine the smallest separation between peaks that can be resolved. Typically 2 arcmin. θ Visual Acuity Letter Acuity – Different Letters or Symbols need to be recognized Typically 5 arcmin. E θ F P T O Z L P E D ETDRS Landolt C Tumbling Es Lea 3 Visual Acuity & Pupil Size Visual Acuity Charts 5’ N Visual Acuity Charts are designed so the 20/20 line subtends 5 arcmin. 20/40 subtends 10 arcmin 20/10 subtends 2.5 arcmin 4 Stereo Acuity Given one object slightly closer than the other, find the smallest separation that is resolvable. -
Psychophysical Aspects of Contrast Sensitivity*
S Afr Optom 2013 72(2) 76-85 Psychophysical aspects of contrast sensitivity* Anusha Y Sukhaa and Alan Rubinb a, b Department of Optometry, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa a<[email protected]> b<[email protected]> Received 23 November 2012; revised version accepted 9 June 2013 Abstract demonstrate stereo-pair representation of contrast visual acuities in the context of diabetic eyes. This paper reviews the psychophysical aspects The doctoral research of the first author (AYS) of contrast sensitivity which concerns components that applies similar idea to understanding both of visual stimuli and the behavioural responses inter- and intra-ocular variation of contrast visual and methods used in contrast sensitivity testing. acuities. Some discussion is included of the different types of contrast sensitivity charts available as well Key words: contrast, contrast sensitivity, as a brief background on the different types of contrast visual acuity, vision science, vision graphical representations of contrast sensitivity psychophysics, stereo-pair scatter plots, and contrast visual acuities. Two illustrations also multivariate statistics Introduction (namely spatial frequency, contrast, spatial phase, and orientation) by means of Fourier analysis. Fourier Psychophysics is a scientific discipline designed analysis is an analytical method that calculates to measure internal sensory and perceptual responses simple sine-wave components whose linear sum to external stimuli1. Sensory stimuli and behavioural forms a given complex image2, 3. The visual stimuli responses are the defining or crucial concepts in typically used in contrast sensitivity testing consist of determining contrast thresholds (for example, visual sine-wave or square-wave gratings whose luminance stimuli are used in chart-based contrast sensitivity perpendicular to the bars is modulated in sinusoidal measurements). -
A Tutorial Essay on Spatial Filtering and Spatial Vision
Spatial Filters/Meese/Nov 2000 A Tutorial Essay on Spatial Filtering and Spatial Vision Tim S Meese Neurosciences School of Life and Health Sciences Aston University Feb 2009: minor stylistic and modifications and technical corrections March 2009: referencing tidied up To follow: Final round-up sections and detailed references added. -1- Spatial Filters/Meese/Nov 2000 1. Introduction To the layperson, vision is all about ‘seeing’—we open our eyes and effortlessly we see the world ‘out there’. We can recognize objects and people, we can interact with them in sensible and useful ways and we can navigate our way about the environment, rarely bumping into things. Of course, the only information that we are really able to act upon is that which is encoded as neural activity by our nervous system. These visual codes, the essence of all of our perceptions, are constructed from information arriving from each of two directions. Image data arrives ‘bottom-up’ from our sensory apparatus, and knowledge-based rules and inferences arrive ‘top-down’ from memory. These two routes to visual perception achieve very different jobs. The first route is well suited to providing a descriptive account of the retinal image while the second route allows these descriptions to be elaborated and interpreted. This chapter focuses primarily on one aspect of the first of these routes, the processing and encoding of spatial information in the two-dimensional retinal image. One of the major success stories in understanding the human brain has been the exploration of the bottom-up processes used in vision, sometimes referred to as early vision. -
Session 2. (1) Spatial Frequency and Fourier Transformation
2005 Autumn semester Pattern Information Processing Topic 1. Sampling and digital processing of images Session 2. (1) Spatial frequency and Fourier transformation Organization of digital images is explained in this Diffraction of light and imaging and the next sessions. Although an image is natu- We start from the optical phenomenon of imaging. rally a continuous distribution of brightness, it has to The imaging is defined as a collection of diverged be converted into a discrete set of integers for com- light spread from a point of object into one point by puter processing. The conversion into discrete pixels a lens. This phenomenon can be observed from the is called sampling, and the conversion into integers following point of view: The light has the property of is called quantization. The sampling period is quite diffraction. The diffraction of wave is a phenomenon important issue, and it is evaluated by the concept of that the wave reaches beyond an opaque object ob- spatial frequency. The concept of spatial frequency stracting its path. For example, even if the progress and Fourier transformation are explained in this ses- of wave on a water surface is obstructed by a board, sion. it reaches beyond the board. Since the light is a kind of electromagnetic wave, the light has this property. The radio wave reaches beyond obstructing objects from the broadcasting station by diffraction. wavefronts reach beyond divergence of light the obstruction collection of light Opaque object wavefronts Fig. 2: Diffraction. Fig. 1: Imaging. If the light passes through a diffraction grating, of first order, is obtained in this direction. -
Perceptual Assignment of Opacity to Translucent Surfaces: the Role of Image Blur
Perception, 2002, volume 31, pages 531 ^ 552 DOI:10.1068/p3363 Perceptual assignment of opacity to translucent surfaces: The role of image blur Manish Singhô, Barton L Anderson Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Received 20 June 2000, in revised form 19 June 2001 Abstract. In constructing the percept of transparency, the visual system must decompose the light intensity at each image location into two componentsöone for the partially transmissive surface, the other for the underlying surface seen through it. Theories of perceptual transparency have typically assumed that this decomposition is defined quantitatively in terms of the inverse of some physical model (typically, Metelli's `episcotister model'). In previous work, we demon- strated that the visual system uses Michelson contrast as a critical image variable in assigning transmittance to transparent surfacesönot luminance differences as predicted by Metelli's model [F Metelli, 1974 Scientific American 230(4) 90 ^ 98]. In this paper, we study the contribution of another variable in determining perceived transmittance, namely, the image blur introduced by the light-scattering properties of translucent surfaces and materials. Experiment 1 demonstrates that increasing the degree of blur in the region of transparency leads to a lowering in perceived transmittance, even if Michelson contrast remains constant in this region. Experiment 2 tests how this addition of blur affects apparent contrast in the absence of perceived transparency. The results demonstrate that, although introducing blur leads to a lowering in apparent contrast, the magnitude of this decrease is relatively small, and not sufficient to explain the decrease in perceived transmittance observed in experiment 1. -
AC 150/5320-5C, Surface Drainage Design, September 29, 2006
UFC 3-230-01 AC 150/5320-5C 8/1/2006 9/29/2006 CHAPTER 7 DRAINAGE STRUCTURES 7-1 GENERAL. Certain appurtenant structures are essential to the proper functioning of every storm drainage system. These structures include inlet structures, manholes, and junction chambers. Other miscellaneous appurtenances include transitions, flow splitters, siphons, and flap gates. Many agencies have developed their own design standards for commonly used structures; therefore, it is to be expected that many variations will be found in the design of even the simplest structures. The information in this chapter is limited to a general description of these structures with special emphasis on the features considered essential to good design. 7-2 INLETS. The primary function of an inlet structure is to allow surface water to enter the storm drainage system. As a secondary function, inlet structures also serve as access points for cleaning and inspection. The materials most commonly used for inlet construction are cast-in-place concrete and pre-cast concrete. The structures must ensure efficient drainage of design storm runoff to avoid interruption of operations during or following storms and to prevent temporary or permanent damage to pavement subgrades. The material, including the slotted drain corrugated metal pipe to handle surface flow (if employed), should be strong enough to withstand the loads to which it will be subjected. 7-2.1 Configuration. Inlets are structures with inlet openings to receive surface water. Figure 7-1 illustrates several typical inlet structures, including a standard drop inlet (area inlet), catch basin, curb inlet, and combination inlet. The hydraulic design of surface inlets is covered in detail in Chapter 3. -
Contrast Sensitivity and Spatial Frequency Response of Primate Cortical Neurons in and Around the Cytochrome Oxidase Blobs DAVID P
Vision Res. Vol. 35, No. 11, pp. 1501-1523, 1995 Pergamon Copyright © 1995 Elsevier Science Ltd 0042-6989(94)00253-3 Printed in Great Britain. All rights reserved 0042-6989/95 $9.50 + 0.00 Contrast Sensitivity and Spatial Frequency Response of Primate Cortical Neurons in and Around the Cytochrome Oxidase Blobs DAVID P. EDWARDS,* KEITH P. PURPURA,*t EHUD KAPLAN*:~ Received 26 January 1994; in revised form 26 September 1994 The striate cortex of macaque monkeys contains an array of patches which stain heavily for the enzyme cytochrome oxidase (CO blobs). Cells inside and outside these blobs are often described as belonging to two distinct populations or streams. In order to better understand the function of the CO blobs, we measured the contrast sensitivity and spatial frequency response of single neurons in and around the CO blobs. Density profiles of each blob were assessed using a new quantitative method, and correlations of local CO density with the physiology were noted. We found that the CO density dropped off gradually with distance from blob centers: in a typical biob the CO density dropped from 75% to 25% over 100 pm. Recordings were confined to cortical layers 2]3. Most neurons in these layers have poor contrast sensitivity, similar to that of the parvocellular neurons in the lateral geniculate nucleus. However, in a small proportion of layers 2]3 neurons we found higher contrast sensitivity, similar to that of the magnocellular neurons. These neurons were found to cluster near blob centers. This finding is consistent with (indirect) parvocellular input spread uniformly throughout layers 2/3, and (indirect) magnoceHular input focused on CO blobs. -
Nanophotonics Enhanced Coverslip for Phase Imaging in Biology Lukas Wesemann1,2, Jon Rickett1, Jingchao Song1, Jieqiong Lou1, Elizabeth Hinde1, Timothy J
Wesemann et al. Light: Science & Applications (2021) 10:98 Official journal of the CIOMP 2047-7538 https://doi.org/10.1038/s41377-021-00540-7 www.nature.com/lsa LETTER Open Access Nanophotonics enhanced coverslip for phase imaging in biology Lukas Wesemann1,2, Jon Rickett1, Jingchao Song1, Jieqiong Lou1, Elizabeth Hinde1, Timothy J. Davis1 and Ann Roberts 1,2 Abstract The ability to visualise transparent objects such as live cells is central to understanding biological processes. Here we experimentally demonstrate a novel nanostructured coverslip that converts phase information to high-contrast intensity images. This compact device enables real-time, all-optical generation of pseudo three-dimensional images of phase objects on transmission. We show that by placing unstained human cancer cells on the device, the internal structure within the cells can be clearly seen. Our research demonstrates the significant potential of nanophotonic devices for integration into compact imaging and medical diagnostic devices. Introduction Theinventionofthephase-contrastmicroscopebyFrits Phase-contrast microscopy has had a profound impact on Zernike14 earned him the Nobel Prize for Physics in 1953. biology, enabling weakly absorbing microscopic organisms The invention came from Zernike’sanalysisofthephase to be observed without staining or fixing1. Recently, profile of light that he describesasasumofplanewaves fi 15 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; nanostructured thin- lm devices have been developed with travelling in different directions . The absence of intensity the potential to replace the bulky optics used in traditional contrast results from an ideal convolution of all the plane phase-contrast microscopes. These devices perform mathe- wave components, such that a perturbation to any one of matical operations on wavefields, such as first- and second- them disrupts the convolution creating contrast.