Shadowgraphy

Diode Laser

Beam Expander

Mirror

Screen

ICCD Camera

Nd: YAG beam

Shadowgraphy is an optical method that reveals non-uniformities in transparent media

Works on the refractive effect of light and generates corresponding intensity patterns

Shadowgraphy Principle

n = 1.12 ×1013 λ–2

Sensitivity

2

21

x

n

gx

gxd

g

I

IS

Sensitivity ~10-4

g

a

D plume length

Differences in light intensity are proportional to the second spatial derivative

of refractive index field

Shadowgraphy for temperature measurement

The refraction in the plume is given by ideal gas relation

plume

medium

medium

plume

medium

plume

T

T

P

P

n

n

Or by Gladstone-Dale formula, which gives

T =293 x 2.73 x 10-4 /(n-1) K

Requires beforehand knowledge of plasma plume refractive index and temperature

Shadowgraphy for temperature measurement

Other methods

1. By point to point comparison of shadowgraphic image with the simulated image

2. Using Abel transformation

The picture of the plasma plume obtained by using the high-speed camera is the projection of the real, 3-dimensional plume onto a plane. The density of species in the volume of the plume can be calculated from this information using the inverse Abel transform.

Shadowgraphy for density measurement

According to Gladstone-Dale formula

n-1 =K

K=Gladstone-Dale coefficient=plasma density

22

22

2

2

2 i

ii

e

f

Mmc

LeK

K=0.2259 cm3/g at T=288K and =670.4nm in air

Again beforehand knowledge of plasma plume refractive index is required

Or Abel transform can be used

e= electronic chargeMe= electron massM = molar weight of the fluidL= 2.687 x 1019 cm-3 is Loschmidt’s numberfi is oscillator strengthi is resonant wavelength

Plasma Shadowgram

Intensity distribution after Abel transformation

Corresponding electron density distribution

Resonant and non-resonant shadowgraphy

Resonant shadowgraphy shows enhancement in refractive index and hence enhances the sensitivity of the system as compared to non-resonant case because the refractive index n and absorption depend on the frequency of the probe beam as

Ni is no. density of lower level population

fi is oscillator strength

i is damping constant

me and qe the mass and charge of electron

Shadowgraphy and fast imaging

Photography depends on intensity of emission from the plasma and depends on number density of excited atoms.

Shadowgraphy dependents on change in refractive index in the plasma.

Both techniques could provide information regarding the shape and size of the expanding plume and its density pattern.

Shadowgraphy has following advantages over photography:

Since the plasma emission intensity depends on number density of excited atoms therefore the imaging technique gives only the information about the excited species. On the other hand shadowgraphy gives overall picture of all the species. Accurate information about the plasma boundary, which can be obtained by shadowgraphy, is important from two reasons:

– allows to determine actual sizes and shape of plasma,– determines integration limits in the Abel transformation.

Shadowgraphy Applications

Shadowgraphy is used to visualize:

- Plasma plume dynamics including size, shape of the plume and velocity

-Shock waves

- Refractive index/density gradients

May be helpful for visualization of oscillations in the laser produced plasma

Schlieren method

Diode Laser

Beam Expander

Mirror

Screen

ICCD Camera

Nd: YAG beam

Knife-edge

Knife-edge modifies spatial frequency spectrum and converts phase variations into

intensity variations

Sensitivity higher than shadowgraphic method ~ 10-9

Snell’s law gives

n2 –n1 = (2/2) + tan

Schlieren method

x

n

na

Lf

dzx

n

nI

IySSensitivit

L

L

.

1

2

2

1

f

a

L

n

x

n05.0

min

L= length of plasmaf = focal lengtha = width of source image

Density is given by Gladstone-Dale formula

n-1 =K

22

22

2

2

2 i

ii

e

f

Mmc

LeK

K=0.2259 cm3/g at T=288K and =670.4nm in air