Eceu692 subsurface imaging course notes part 12 imaging with light 4 diffusive optical tomography
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ECEU692 Subsurface Imaging Course Notes Part 12: Imaging with Light (4): Diffusive Optical Tomography. Profs. Brooks and DiMarzio Northeastern University Spring 2004. Topic Outline. Goal: “Find the Matrix Elements” A Bit of Radiometry Terminology and Units Radiative Transport

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Eceu692 subsurface imaging course notes part 12 imaging with light 4 diffusive optical tomography

ECEU692Subsurface ImagingCourse NotesPart 12: Imaging with Light (4):Diffusive Optical Tomography

Profs. Brooks and DiMarzio

Northeastern University

Spring 2004

Chuck DiMarzio, Northeastern University


Topic outline

Topic Outline

  • Goal: “Find the Matrix Elements”

  • A Bit of Radiometry

    • Terminology and Units

    • Radiative Transport

  • Approximation to Radiative Transport Equation

    • Diffusion Approximation

    • Wave Solution

    • Generating the Diffusive Waves

  • Examples

  • Adding Ultrasound

  • Solving for the Matrix Elements

Chuck DiMarzio, Northeastern University


The matrix elements

P

P

t

t

The Matrix Elements

DC

AC Amplitude

AC Phase

Chuck DiMarzio, Northeastern University


Radiometric quantities

Radiometric Quantities

Chuck DiMarzio, Northeastern University


Radiometry and photometry

Radiometry and Photometry

M, Flux/Proj. Area

Notes: Spectral x=dx/dn or dx/dl: Add subscript n or w, divide units by Hz or mm.

F, Flux

Radiant Flux

Watts

Luminous Flux

Lumens

Radiant Exitance

Watts/m2

Luminous Exitance

Lumens/m2=Lux

1 W is 683 L at 555 nm.

Radiance

Watts/m2/sr

Luminance

Lumens/m2/sr

1 Lambert=

(1L/cm2/sr)/p

I, Flux/W

L,Flux/AW

Radiant Intensity

Watts/sr

Luminous Intensity

Lumens/sr

E, Flux/Area Rcd.

Irradiance

Watts/m2

Illuminance

Lumens/m2=Lux

1 ftLambert= (1L/ft2/sr)/p

1mLambert= (1L/m2/sr)/p

1 Ft Candle=1L/ft2

1 Candela=1cd=1L/sr

Chuck DiMarzio, Northeastern University


What is radiative transport

What Is Radiative Transport?

  • The Radiative Transport Equation

L+dL

dW

dW

L

ds

Chuck DiMarzio, Northeastern University


Solutions to rte

Solutions to RTE

  • Monte-Carlo

  • Low Scattering

  • High Scattering

    • Diffusion Approximation

    • Usually Valid in Tissue, Except...

      • Certain Tissue Types

      • Certain Imaging Modalities (eg. Confocal, OCT)

      • Close to Source or to Rapid Changes in Parameters

Chuck DiMarzio, Northeastern University


Resolution limits m c

Resolution Limits (M-C)

Tissue Parameters

ma = 0.03 /cm

ms = 200 /cm

g = 0.95

d = 1 cm

  • Approach

    • Monte-Carlo

    • Reciprocity

    • Fourier Transform

  • Parameters

    • Depth 1 cm.

    • Thickness 2 cm.

  • Transillumination

MTF

125

150

200-ps Gate

Spatial Frequency, /cm

Dunn, Andrew, and Charles A. DiMarzio, “Efficient Computation of Time--Resolved Transfer Functions for Imaging in Turbid Media,” Journal of the Optical Society of America A 13, No. 1, January 1996. Pp. 65--70.

Chuck DiMarzio, Northeastern University


Photon diffusion approximation

Photon Diffusion Approximation

  • The Radiative Transport Equation

  • Taylor Series: f is Fluence Rate, J is Flux

  • Result

Chuck DiMarzio, Northeastern University


Fluence rate

Fluence Rate?

  • Another Radiometric Quantity

    • Fluence is Energy/Area

    • Fluence Rate is Energy/Area/Time

      • =Power/Area

      • Units Like E or M, but Different Meaning

  • Relation to Absorbed Power/Volume

    • A=fma

    • Used to Determine f in Monte-Carlo

Chuck DiMarzio, Northeastern University


Dispersion equation

F

(

)

Ñ

·

D

Ñ

F

-

-

a

F

=

0

Dispersion Equation

  • The Diffusion Equation

  • Wave Solution

t

k

  • k2

Im

=0

Re

Chuck DiMarzio, Northeastern University


Dispersion results

Dispersion Results

Chuck DiMarzio, Northeastern University


Spherical waves

Spherical Waves

Chuck DiMarzio, Northeastern University


Different types of waves

8

10

Light

(Real)

6

10

-1

4

10

DPDW

Sound

), Wavenumber, m

(Imag)

(Imag)

2

10

p

(Real)

0

k/(2

10

-2

10

-4

10

0

5

10

15

20

10

10

10

10

10

f, Frequency, Hz.

Different Types of Waves

1mm

1mm

1m

1km

10059_1

Chuck DiMarzio, Northeastern University


Physical reason for dispersion

Physical Reason for Dispersion

Imaginary part

of k increases

with frequency

Easy to understand in terms of multiple paths.

m100574a.m

Chuck DiMarzio, Northeastern University


Watch the photons migrate

20 Photon Tracks

20,000 Photon Tracks

Pabs=0.1

Pext=0.3

Watch the Photons Migrate!

  • Received Photons

90

80

70

60

Photons in Box

50

40

30

20

10

0

0

20

40

60

80

100

Time Step

Chuck DiMarzio, Northeastern University


How diffuisve waves begin

How Diffuisve Waves Begin?

Tissue

Extrapolated

Boundary

  • Generation

    • From Light Wave

  • Wave Behavior

    • Absorption

    • Reflection

    • Refraction

    • Diffraction

    • Interference

    • Scattering

Detector

Image

Source

Image

Source

Effective

Source

Input

Chuck DiMarzio, Northeastern University


Noise issues

Noise Issues

Noise proportional

to square root of

DC signal.

m100574a.m

Chuck DiMarzio, Northeastern University


Dot instrumentation at mgh imaging center

DOT Instrumentation at MGH Imaging Center

  • TECHNOLOGY

  • Near-infrared light

  • Fiber optics

  • Computed Tomography

  • ADVANTAGES

  • Optical contrast

  • Portable - bedside, ambulance

  • Continuous

  • Inexpensive

  • DISADVANTAGES

  • Resolution

  • Depth penetration

From David A. Boas - MGH NMR Center

Chuck DiMarzio, Northeastern University


Functional imaging of a neonate

Detectors

Sources

Functional Imaging of a Neonate

6 cm

Mid-line

4 cm

Passive movement of

right arm

Passive movement of

right arm

At Rest

Data Set I - 98-05-14

From David A. Boas - MGH NMR Center

Chuck DiMarzio, Northeastern University


Keeping the matrix rank up

0

-1

Z axis

-2

-3

-4

6

-5

5

4

6

3

5

2

4

3

1

2

1

0

0

X axis

Y axis

0.15

0

-1

0.1

0.05

-2

0

0

0.14

-3

0.05

0.12

0.04

-1

-1

-4

Reconstruction with

Reflection only

(Top Sources)

0.1

-5

0

0.03

-2

-2

0

2

4

6

0.08

-3

-3

0.06

0.02

0.04

-4

-4

Reflection and

Transmission

(All Sources)

0.01

0.02

-5

-5

0

1

2

3

4

5

6

0

0

1

2

3

4

5

6

Keeping the Matrix Rank Up

Source

z

y=4

Detector

Object

x

  • DiMarzio, et. al., Presented at Photonics West, Jan 1999

Chuck DiMarzio, Northeastern University


Api virtual source

API Virtual Source

Ultrasound

Beam

Optical

Source

Optical

Source

Optical

Source

Optical

Receiver

Optical

Receiver

Optical

Receiver

Ultrasound

Focal Point

Light from Source to Receiver

Light from Source to Receiver through Ultrasound Focus

All Light from

Source Fiber

Chuck DiMarzio, Northeastern University


Solving the wave equation 1

Solving the Wave Equation (1)

Chuck DiMarzio, Northeastern University


Solving the wave equation 2

Solving the Wave Equation (2)

Chuck DiMarzio, Northeastern University


The first born approximation

The First Born Approximation

Chuck DiMarzio, Northeastern University


Why do we want a model

Why Do We Want a Model?

  • Applications

    • Forward Model

      • Will it work?

    • Inverse Algorithms

      • How Much Does k Change?

        • ie. Is there a Tumor?

      • And Where?

  • Understanding

    • What is k?

    • See Panel to Right.

Chuck DiMarzio, Northeastern University


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