Class 7 Arrays - Stanford University
Class 7: ArraysRad225/Bioe225UltrasoundFall 2019ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing1
Class 7Rad225/Bioe225UltrasoundFall 2019ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing2
form of energy to another. In ultrasound, atransducer or transducer array convertsDefinitionselectrical energy to mechanical and vice versa.Rad225/Bioe225UltrasoundFall 2019apertureheightwidthpitchkerf3
Rad225/Bioe225UltrasoundFall 2019TransducerArrays ArraysTransducerTransducerArraysMost thoraxLow Frequency LowHighFrequencyHigh Frequency High FrequencyLowFrequencyLowFrequencyFrequency Low Frequency Low Frequency 4cm field of-wideview-wide field of view-small acoustic window 4cmfieldview-wideof view-small acoustic window 4cm field of viewfieldof ofview-smallfieldacousticwindow-wideat field of view at-wide-wide field of viewat field of viewdepthdepthdepthBeam Origins Linear – beam origins shift across field of view, beamdirection (steering remains the same)Beam Origins Linear – beam origins shift across field of view, beamdirection (steering remains the same)4
Back to Huygen’s principle:Array BeamformingRad225/Bioe225UltrasoundFall 2019Translate whichelements are usedImage one lineat a time5
Beam From SubapertureRad225/Bioe225UltrasoundFall 2019Elevation/Slice Thickness (y)Azimuth/Lateral (x)θAxial/Depth (z)LensSlice ThicknessLateral res./Beam width6
Rad225/Bioe225UltrasoundFall 2019Linear Array ImagingFOV smaller thanarrayTime-delayedelectrical pulsesfor focusingArraySubapertureOne focusedultrasound beam isused to form oneimage scan-lineScanning DirectionFocal PointPictureField ofViewWider beam, anyone object goesinto multiple lines,lower resolutionChoice ofsubaperture sizepresents atradeoff betweenresolution andFOV1.22λ FW D7
Class 7Rad225/Bioe225UltrasoundFall 2019ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing8
Rad225/Bioe225UltrasoundFall 2019Single Element Rectangular ApertureExamplesRectangular Aperture:FT x Lx u rect sin c λ Lx rect(x) sin c( Lx f )Lxu fλ9
Ideal Array of point sourcesRad225/Bioe225UltrasoundFall 2019FT x u comb comb p λ / p grating lobesSzabo
Subaperture Array of Point SourcesRad225/Bioe225UltrasoundFall 2019FT comb x Lx u u x rect comb sin c p Lλ/p λ x grating lobesSzabo
Rad225/Bioe225UltrasoundFall 2019Subaperture Array of Finite Width SourcesFT comb x Lx u x u u x *rectrect combsinc sinc w λ / p λ / w L λ p xenvelope on the grating lobesSzabo
Class 7Rad225/Bioe225UltrasoundFall 2019ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing13
Back to Huygen’s principle:SteeringRad225/Bioe225UltrasoundFall 201914
Utilizes the entire aperture foreach scan lineElectronic sector scanning isachieved through varying thesteering angle θθBeam SteeringScanningDirection
Steered Subaperture Array of Finite WidthSourcesRad225/Bioe225UltrasoundFall 2019Phase x Lx u x x u u comb*rectrect combsinc sinc p w λ / p λ / w L λ xlinear phase translationgrating lobes modulated by the envelopeSzabo
Beam pattern follows the envelopeGrating lobes at 60 Steered 15 to rightMain lobe intensity decreasesGrating lobe intensity increasesRad225/Bioe225UltrasoundFall 2019
Rad225/Bioe225UltrasoundFall 2019Grating LobesEnergy goes into the near field from grating lobes nλ θ g sin p 1p
Correcting for Grating LobesRad225/Bioe225UltrasoundFall 2019If the element spacing is less than λ, the grating lobe is greater than 90 degreesArrayφθgg90 MainLobedSide Lobe-90 λ sin(θ g ) p IntensityGrating LobeAngle19
Rad225/Bioe225UltrasoundFall 201900-5-5-10-10-15-15Amplitude (dB)Amplitude (dB)What is the gle (degrees)406080-40-80-60-40-20020Angle (degrees)406080 λ sin(θ g ) p λ sin(40 ) p d 1.55λ λ sin(90 ) d d λ20
Grating Lobe ArtifactsRad225/Bioe225UltrasoundFall 2019
Class 7Rad225/Bioe225UltrasoundFall 2019ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing22
Pulse - EchoRad225/Bioe225UltrasoundFall 2019Ultrasonic Imaging Because US is pulse-echo, we are concernedwith both the transmitted pressure field (Tx)and the receiver sensitivity (Rx)– Rx sensitivity is the locations in the field where thereceiver is sensitive to incoming waves Rx can be determined using the principle ofacoustic reciprocity23
Rad225/Bioe225UltrasoundFall 2019Acoustic ReciprocityAcoustic Reciprocity The receiver sensitivity is equal to thetransmit diffraction pattern of the receiveracting as a sourceDRx cos( Dfx)24
Rad225/Bioe225UltrasoundFall 2019Pulse Echo SensitivityThe Radar Equation The pulse-echo beam pattern (i.e. thesensitivity of the ultrasound system) is equalto the product of the transmit diffractionpattern and the receive sensitivity pattern:B( x, y) Tx( x, y) Rx ( x, y)cos( Dfx)cos2( Dfx) 1 2cos(2 Dfx)25
Transmit Beamforming: Plane WaveRad225/Bioe225UltrasoundFall 2019Transmit Beamforming26
Rad225/Bioe225UltrasoundFall 2019Transmit Beamforming: Focused WaveTransmit Beamforming27
Transmit BeamRad225/Bioe225UltrasoundFall 2019Fixed Focus Beamforming28
Receive BeamformingReceive BeamformingRad225/Bioe225UltrasoundFall 2019 Transmit beamforming in reverse:Use same equation as before to compute time delays for receiving!29
Rad225/Bioe225UltrasoundFall 2019Transmit Focusing at Different DepthsDynamic Receive Focusing30
Rad225/Bioe225UltrasoundFall 2019Raw (undelayed)Channels/elementsDynamic Receive FocusingDepth/TimeContinuously adjust the delaysBeamformingDynamic Receive FocusingDepth/Time31
Dynamic Focusing on Receive
Rad225/Bioe225UltrasoundFall 2019Dynamic Receive FocusingContinuously adjust the delaysDynamic Receive FocusingBeamformingdelayedentsDepth/Time33
Transmit beamforming in reverse:Rad225/Bioe225UltrasoundFall 2019Receive se same equation as before to compute time delays for receiving!Unfocused signal received fromthe near fieldFocused signal using time-delays:Note how wavefronts appear as“plane waves”RF Sum34
Transmit Beamforming OnlyRad225/Bioe225UltrasoundFall 2019Fixed Focus Beamforming35
Dynamic Receive BeamformingRad225/Bioe225UltrasoundFall 2019Dynamic Receive Beamforming36
Class 7 Fall 2019 8 Arrays Grating Lobes with Linear Arrays Phased Arrays and More Grating Lobes Pulse-Echo or Transmit-Receive and Dynamic Receive Focusing. Rad225/Bioe225 Ultrasound Single Element Rectangula
Hooray for Arrays: A Mini Reference Guide Hooray for Arrays: What Do You Say, Let's Make an Array! * Hooray for Arrays: Repeat Addition * Hooray for Arrays: Multiplication Fact Practice * Hooray for Arrays: Equal Group Problems * Hooray for Arrays: Repeated Addition and Multiplication * Hooray for Arrays:
SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity Qingyuan Zhao Stanford University qyzhao@stanford.edu Murat A. Erdogdu Stanford University erdogdu@stanford.edu Hera Y. He Stanford University yhe1@stanford.edu Anand Rajaraman Stanford University anand@cs.stanford.edu Jure Leskovec Stanford University jure@cs.stanford .
Super Teacher Worksheets - www.superteacherworksheets.com 1. Arrays Arrays 3. Arrays 4. Arrays 2. Write a multiplication fact that is shown by the array. Write a multiplication fact that is shown by the array. Mr. Rule is a 4th grade teacher. He sets up 4 rows of desks in his classroom. Each
2 Lesson 9: Introduction To Arrays Objectives: Write programs that handle collections of similar items. Declare array variables and instantiate array objects. Manipulate arrays with loops, including the enhanced for loop. Write methods to manipulate arrays. Create parallel arrays and two- dimensional arrays.
Arrays in Java Arrays in Java are objects Only 1D arrays are directly supported Multidimensional arrays are arrays of arrays General, but slow - due to memory layout, difficulty of compiler analysis, and bounds checking Subarrays are important in AMR (e.g., interior of a grid) – Even C and C don’t support these well
Computer Science Stanford University ymaniyar@stanford.edu Madhu Karra Computer Science Stanford University mkarra@stanford.edu Arvind Subramanian Computer Science Stanford University arvindvs@stanford.edu 1 Problem Description Most existing COVID-19 tests use nasal swabs and a polymerase chain reaction to detect the virus in a sample. We aim to
Domain Adversarial Training for QA Systems Stanford CS224N Default Project Mentor: Gita Krishna Danny Schwartz Brynne Hurst Grace Wang Stanford University Stanford University Stanford University deschwa2@stanford.edu brynnemh@stanford.edu gracenol@stanford.edu Abstract In this project, we exa
Alfredo López Austin (1993:86) envisioned the rela - tionship between myth, ritual, and narrative as a triangle, in which beliefs occupy the dominant vertex. They are the source of mythical knowledge
