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LAGRANGIAN PARTICLE TRACKING IN ISOTROPIC TURBULENT FLOW VIA HOLOGRAPHIC AND INTENSITY BASED STEREOSCOPY By Kamran Arjomand
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Page 1: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

LAGRANGIAN  PARTICLE  TRACKING  IN  ISOTROPIC  TURBULENT  FLOW  VIA  HOLOGRAPHIC  AND  

INTENSITY  BASED    STEREOSCOPY  

By  Kamran  Arjomand  

Page 2: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

I.  Background

A.  Holographic Imaging 1.  Acquire Hologram 2.  Preprocessing 3.  Numerical Reconstruction 4.  Particle Extraction 5.  Velocity Extraction

B.  Turbulence

II.  Minimum Goals A.  Holographic Simulation with Gaussian Blur

B.  Single particle holographic image and intensity based image correspondence

C.  Single particle velocity calculation at given time step

III.  Additional Goals if time permits

A.  Multiple Particle Image Correspondence

B.  Multiple Velocity Particle Extraction

C.  Particle Matching for a non-uniform particle field IV.  References

Page 3: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Holography

•  Concept of using a wave front imaging to do a three dimensional reconstruction first introduced by (Gabor,1949)

•  After introduction of the laser in the 1960’s did holography really start to flourish(Collier ,1971;Vikram,1992).

I.  Film Based Holography A.  Intensity only reconstruction

B.  Time consuming to reconstruct Holograms from Film

II.  Digital Holography A.  Easier acquisition of Data analysis (Intensity as well as complex amplitude)

B.  Resolution restricted due to angular aperture as well as size

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 4: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Digital holographic Process

Preprocessing

Numerical Reconstruction

Particle Extraction

Acquire Raw Hologram Matlab image processing toolbox

1.  Subtract Background Image 2.  Smooth with imfilter 3.  Contrast-limited adaptive

histogram equalization (adapthisteq)

 Particles imaged range between 8-20 micrometers  Optical Recording Schemes

• In-line • Off-axis (our group)

Based on Huygens Principle which states that if the wave front is known in one plane, it is known in any other 3D space

Rayleigh-Sommerfeld diffraction theory

(use Fourier Transform) Velocity Extraction

Intensity Based Image

Improve Depth Location/Determine

Particle Size

Region building base on connectivity relationships between adjacent foreground pixels in three dimensions(DeJong,2008)

• Nearest Neighbor • Particle Relaxation Method

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 5: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Raw Hologram

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 6: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Raw Hologram Acquisition

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 7: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Angular Aperture

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

•  angular aperture is a function of the camera pixel size, ∆, and the image size, a function of the number of pixels, N. Given the system parameters: ,

Critical Pixel Size:

•  Our CCD camera is 2650x2650 pixels with an effective pixel size of 2 micrometers with a long distance microscopic lens system

Page 8: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

In-Line Recording Object Beam Configurations

(Pan,2003)

On-axis Reference beam

Off-axis Reference beam

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 9: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Advantages/Disadvantages of In-line

Advantages •  Greater Intensity Hologram •  Complex amplitude Particle Extraction •  Potential for particle size determination

Disadvantages •  Excessive Speckle Noise from particles outside of

region of interest resulting in large depth resolution errors

•  Low Particle Seeding Density

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 10: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Off-Axis Recording Object Beam Configurations

Pan,2003

On-axis Reference beam

Off-axis Reference beam

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 11: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Advantages/Disadvantages of Hybrid Holographic Recording

Advantages

•  Speckle Noise suppression resulting from smaller imaged region

•  Lower resolution requirement then off-axis reference wave configuration

•  Facilities with higher particle concentrations can be imaged

•  More accurate z location

Disadvantages •  No complex amplitude particle extraction methods

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 12: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Subtraction with Background Image

-

Raw Hologram Background Image Image after I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 13: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Contrast-limited adaptive histogram equalization and Imfilter

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 14: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Holography with on-axis reference wave

R= reference wave O=object wave Z= distance from focus plane r = radial coordinate in the hologram recording system = wavelength = phase shift

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 15: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Numerical Reconstruction (Direct Method(Takaki,1999))

Fourier Transforms:

Diffraction kernel

Fourier Transform of:

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

m,n= matrix indices Nx,Ny= number of pixels , = pixel size in x an y directions

Discrete Form

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 16: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Particle Extraction

Particle Extraction using Intensity(PEI)

•  Only available method for side scattering due to irregular distribution of scattered wave in side scattering

The intensity based centroid of the particle (xp,yp,zp) is calculated from the relationships,

where a moment of order (p+q+r) of the intensity I is given by,

(DeJong,2008)

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 17: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Problems with particle centroid calculation

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 18: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

3D Reconstructed Particle Field

(DeJong,2008)

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 19: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Velocity Extraction

Nearest Neighbor(Ouellette,2006)

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 20: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

What is Turbulence ?

•  Rotational and Dissipative •  Non-linear •  Stochastic(random) •  diffusive

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 21: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Isotropic Turbulence

Singlepoint Velocity Correlations

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

Homogeneous Turbulence in which all the fluctuation statistics have no preferred directionality. All statistics are independent of coordinate rotations and reflections

Page 22: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

My Research

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 23: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

For my experiment (first assume perfectly orthogonal setup has been completed)

Inte

nsity

Bas

ed Im

age

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 24: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Simulation of Holographic Particle (completed)

Synthesized Hologram

Hologram after Gaussian Blurr

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 25: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Correspondence of Reconstructed Hologram with Intensity Based Image (currently working on)

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 26: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Other Minimum goals to be completed

•  Determination of Particle Size via pixel count •  Simulate Movement of particles for a given

Time Step

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step D. Determination of Size via Pixel Count IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References

Page 27: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

Long Term Goals

•  Multiple Particle Image Correspondence •  Multiple Particle Velocity Extraction •  Particle matching for a non-uniform particle field

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step D. Determination of Size via Pixel Count IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle Velocity Extraction C. Particle matching for a non-uniform particle field V. References

Page 28: LAGRANGIAN’PARTICLE’TRACKING’IN’ISOTROPIC ......By’Kamran’Arjomand’ I. Background A. Holographic Imaging 1. Acquire Hologram 2. Preprocessing 3. Numerical Reconstruction

References

Gabor D. 1949. Microscopy by reconstructed wave fronts. Proc. R. Soc. Lond. Ser. A 197:454–87

Collier RJ, Burckhardy CB, Lin LH. 1971. Optical Holography. New York: Academic

Vikram CS. 1992. Particle Field Holography. Cambridge, UK: Cambridge Univ. Press

Takaki Y;Ohzu H(1999) “Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy,” Appl Ot 38:2204-2211.

Pan,G (2003)”Digital Holographic Imaging for 3D Particle and Flow Measurements”, thesis.

DeJong,J(2008)”Particle Field Clustering and Dynamics Experiments with Holographic Imaging.thesis

Ishihara,(2009)” Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation

I Background A . Holographic Imaging 1.Aqure raw hologram 2. Preprocessing 3.Numerical Reconstruction 4. Particle Extraction 5. Velocity Extraction B. Turbulence

III Minimum Goals A. Holographic Simulation with Gaussian Blur B. Single particle holographic image and intensity based image correspondence C. Single Particle Velocity calculation at given time step D. Determination of Size via Pixel Count IV. Additional Goals if time permits A. Multiple Particle image correspondence B. Multiple Particle matching by Neighbor V. References


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