Eindhoven University of Technology

BACHELOR

Light scattering in a dusty plasma

Meulenbroek, Aled

Award date:2015

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Light Scattering in

a Dusty Plasma

Author: A.M.MeulenbroekTechnical University EindhovenElementary Processes in Gas Discharges (EPG)

Supervisors:dr. ir. J. Beckersir. L.P.T. Schepers

July 13, 2015

Abstract

This thesis is about light scattering on dust particles inside dusty plasmas. Dustyplasmas are a perfect environment to alter the density of the particles in a dust cloud.Light scattering on phosphorus particles that are used as transformation layer in blueLight emitting diodes in order to create white light is not understood well. Therefore thisresearch will focus on how the light is scattered in this layer. By changing the density ofthe particles inside the transformation layer light could be scattered differently from theLEDs. This thesis however is about the scatter properties of MF particles since they arespherical and scatter light at a well defined wavelength. It is important to first discoverwhat the scattering profiles of these manageable particles are before research can be doneon the more difficult phosphorus particles.This thesis will document some of the collective knowledge about a new setup, and willoffer a procedure to measure scattering profiles on dust clouds and single dust particlesin plasmas.Measurements are performed on single dust particle scatter profiles and these are com-pared to Mie theory. Though there have been measured Mie scattering profiles there arestill some challenges that need to be overcome. A lot of data is discussed which is usefulfor the understanding of scattering profiles on single dust particles. For instance thereare indications that the particle radius is changed over time. This could be because ofetching. Since it was unknown how dust particle’s scatter properties will change in theplasma. This data is already very useful for understanding how dust particles behave inplasma and how this effects the light scattering profiles.Measurements have been performed on a scatter profile on a dust cloud. These give anindication that there can occur multiple scattering scattering in a cloud of dust particlesin the plasma.Since this thesis is merely the beginning a lot of questions are left unanswered. For thisthis some recommendation are done on how and what the upcoming experiments shouldbe done:

1. The addition of a camera to the setup would increase the possibilities in monitoringthe particles in the plasma

2. Etching can be stimulated in an experiment by changing the gas used to create theplasma.

3. Quantitative information of the density of dust clouds should be compared to theirscattering profiles in order to distinguish between single and multiple scattering.

Contents

1 Introduction 1

2 Theory 22.1 Plasmas and dusty plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1.1 Radio frequent plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1.2 Plasmasheath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.3 Charging of injected dust particle . . . . . . . . . . . . . . . . . . . . . 42.1.4 Forces acting on the dust particles . . . . . . . . . . . . . . . . . . . . 6

2.2 Light scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Single scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Multiple scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Theoretical Mie profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Experimental setup 133.1 Inside of the experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Electrodes and power supply . . . . . . . . . . . . . . . . . . . . . . . 143.1.2 Pressure regulation system and Argon flow regulation . . . . . . . . . 143.1.3 Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.1 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.2 Dust dispenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Operating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.1 Flow control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.2 Dust control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.3 Setup control panel and spectrometer . . . . . . . . . . . . . . . . . . 16

3.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Scattering on a single dust particle 194.1 Particle properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Configuring a single dust particle . . . . . . . . . . . . . . . . . . . . . . . . . 204.3 Measurements on single particle . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.3.1 Two different single particle signals . . . . . . . . . . . . . . . . . . . . 214.3.2 Background signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.3.3 Time dependent signal of a single particle . . . . . . . . . . . . . . . . 244.3.4 Time versus noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.5 Signal to noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3.6 Fitting particle properties on the measured scattering profile . . . . . 26

5 Scattering on a cloud of dust particle 285.1 The method to measure scattering of dust clouds . . . . . . . . . . . . . . . . 285.2 Symmetry of the signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.3 Measurements on dust clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 Conclusion and outlook 32

A Matlab source codes 34

B Matlab Scattermatrix script 43

1 Introduction

Every day we look out of the window to see what type of weather it will be. Are there clouds oris there a clear blue sky? In nature a lot of scattering processes occur, like scattering on rain-clouds and scattering on the gasses inside our atmosphere. In time, the world became moreand more enlightened, after Thomas Edison invented the light-bulb. Having a light sourcein a household became a basic need, and is also a good indicator of the wealth/educationlevel of populations [1], though not all humans posses this need. Nowadays the light-bulbis replaced by the more efficient light emitting diodes (LEDs). The Nobel prize of 2014 wasawarded to the inventors of the blue LED light. ”Since lighting represents 20-30% of ourelectrical energy consumption, and since these new white light sources require ten times lessenergy than ordinary light bulbs, the use of efficient blue LEDs leads to significant energysavings, of great benefit to mankind”[1]. However there is a problem with the LED’s: Theblue coloured light of the LEDs is not the preferred color of lighting. This color would beto cold and is claimed to be unhealthy [2]. Therefore the LED’s are coated with a layerof phosphorus. This coating transforms the blue light in a combination of blue and yellowresulting in a white light source. Although this technique is already widely used there is nogood understanding of what exactly happens when light is scattered on this coating. Themain goal of this research is to get a better understanding of the scattering processes withinthe coating. A setup is built in which a phosphorus layer can be modulated. The last twentyyears a lot of research is done on the structure inside dusty plasmas[3]. This structure isan ideal tool to control the particle density. This particle density is an important propertyof the LED coating. Since the LED should scatter the blue light into the correct color,but should not lose to much of its intensity. There are two types of scattering that couldoccur single scattering and multiple scattering. These two will be discussed in this thesis.In this assay no measurements will be performed on phosphorus particles but on Melamine-Formaldehyde(MF). This particle has an ideal spherical shape and is therefore ideal for Miescattering experiments. Therefore it will only scatter light at same wavelength of the incidentwave. First it is important to gain collective knowledge about how the setup works, this hasbeen done in co-operation with L.Schepers. This research will be on the scattering of lighton a single dust particle to discover the fundamental scatter properties of the particles. Thenit will focus on light scattering on dust clouds/crystalline structures. To obtain fundamentalknowledge about single and multiple scattering processes inside dusty plasmas.

1

2 Theory

The main features of a dusty plasma are addressed in this section. It contains a short overviewof plasma physics which is based on the . For a more detailed theoretical overview shouldbe referred to Beckers [4]. This theory should provide enough knowledge about how a dustyplasma behaves and which parameters are used to change the properties of the dust cloud.Later the theory describing light scattering by these clouds is given.

2.1 Plasmas and dusty plasmas

Plasmas are referred to as the fourth state of matter, in addition to gas, liquid and solid. Allthese states contain small components (molecules and atoms). These molecules or atoms canbe ionized. The fourth state of matter ’Plasma’, the formation of a plasma is based on Bohr’satomic model. In which an electron is orbiting the nucleus of an atom. When the internalenergy of the atom is increased, the energy can realize such levels that the electron separatesfrom its nucleus. This process is called ionization since a positively charged ion is left in thegas. Sir William Crookes identified this state of matter in 1879 in a Crooks Tube and calledit ’radiant matter’, laterin 1928 I.Langmuir called it plasma [9].On top of the normal plasmma species, a dusty plasma is a plasma which is composed ofelectrons, ions and solid particles of nano to micro -meter size. Understanding how theseparticles behave in a plasma is of critical importance to this research. A brief introductioninto plasma physics will be provide you with the knowledge required in this research.

2.1.1 Radio frequent plasma

A radio frequent (RF) plasma is a plasma that operates in the MHz range. The capacity ofthis plasma is coupled to the power source. An RF plasma is able to to accelerate chargedparticles inside the plasma[4]. This property is obtained by the oscillating voltage inside anRF plasma. Initially there will be only few atoms ionized. It is said that there is always anamount of background ionization. Then when the electrons start following the electric fieldthey will collide on neutral atoms with such energy that these atoms become ionized as well.At the frequency we used, it will be more difficult for the ions, due to their inertia, to followthe electric field. The electrons are able to follow the field, because of their low inertia. InMHz range this results in ions with a very small mobility and electrons with a high mobility.Crucial parameters are the electron ωe and ion ωi -frequency they determine whether theelectrons and ions can follow the electric field.

ωe,i =

√ne,iZe,ie2

me,iε0(1)

Here ne is the electron density, ni, is the ion density. These electrons and ions have a chargeZx and mass mx where the subscript ’i’ indicates ion and ’e’ electron. Typically RF-plasmasare operated at low pressures meaning an electron and ion density ne,i ≈ 1015m−3, J.Beckers[4] estimated ωe

2π ≈ 284MHz and ωi2π ≈ 1MHz. This shows that only the electrons are able to

follow the electric fields at a frequency of 13.56MHz.Another crucial parameter is the mean free path λmfp,1 of the ions. This parameter gives the

2

distance between two subsequent collisions, and is dependant on the cross section of the twoparticles (1) and (2) σ12 and the density of particle (2) n2.

λmfp,1 =1

n2σ12(2)

The importance of these parameters will become clear in the next paragraph about the plasmasheath.The third crucial parameter that is introduced is the debye length. The bulk of the plasmais a quasi neutral area. However this means there can be charge gradients in length scalessmaller than the debye length λD which is defined as 3. When the quasi neutral region isaveraged over the debeye length or anything bigger than that it will be neutral:

1

λ2D

=1

λ2D,i

+1

λ2D,e

(3)

Where

λDi,e =

√ε0kBTe,ie2ne0,i0

(4)

Here Te,i are the electron and ion temperature. The values of λDi,e are for the inside the bulkof the plasma since this is the only quasi neutral part of the plasma.

2.1.2 Plasmasheath

In between the electrodes of the plasma can be divided into different areas. The plasma bulk,the plasma sheath and the plasma pre-sheath are defined. This is schematically visualised infigure 1. To begin with the position close to electrodes the sheath region. Here, due to theelectron mobility µe >> µi inside the plasma. The electron flux Γe >> Γi , thus the electrodebecomes negatively charged, then ions are accelerated towards the surface and a space chargeregion will form. This region is typically a few debye lengths thick. The electric field dueto electrons on the surface and ions just above the surface is maintained over time. Thetime that there are many electrons in the sheath is very short compared to the period of theRF electrode. Yet the surface will stay negatively charged as the ion and electron densitieswill reach an equilibrium . Most laboratories use a low pressure plasma where usually thene << ni << nN in the sheath region, where nN is the neutral gas density. Therefore thelight excitation in the sheath plasma is much lower. There are two types of sheaths:

1. The collisionless sheath in which the mean free path of ions is longer than the thicknessof the sheath[8]:

λmfp,i >> ξ where ξ =

√50

27

√2

3λDe(

2φ0

Te)3/4 (5)

Here φ0 is the sheath potential. This sheath thickness by use of the child law for a DCplasma. To factor

√50/27 is to account for the increase in sheath thickness in an RF

plasma compared to DC.

3

Figure 1: Schematic view illustrating the plasma with its three regions. The lower electrode is RF driven theupper electrode is grounded. There is a sheath region at both electrodes. The plasma bulk is indicated withgrey, this tells us in this part of the plasma there is more emission of light.[4]

2. Collision-dominated plasma sheath. Here the mean free path of the ions is lower thanthe sheath thickness λmfp,i << ξc. Other rules apply for the calculation of the sheathtickness in this case [10] [11] :

ξc = 1.155η

35

u250 α

15

(6)

here η = eφ0kBTe

,u0 =ui,sh√kBTemi

and α = λDλmfp

. These are the normalized potential wall,

the normalized ion velocity and the collision parameter.

More information about the pre-sheath region can be found in J.Beckers research [4].

2.1.3 Charging of injected dust particle

When a dusty plasma is by inserting solid particles into the plasma, and the plasma itself ismade out of non-reactive elements, like argon. In there will be a neutral particles with a sizeof roughly 20-10000 nanometres inside the plasma. This particle will interact with the ionsand electrons in the plasma as they move towards its the surface of the neutral particle. Thishappens because of their individual thermal velocities, which has a random movement anddirection. Figure 2 shows a thermal velocity of ion and electron directed towards the particle.This are the only electrons or ions of interest since the others do not move towards the neutralparticle. Because the electrons are more mobile then the ions the surface of the particle willobtain a negative surface charge. This creates an electric field directed towards the particle2. New electrons will then be repelled from the particle and ions accelerated towards which

4

changes the electric field again. This process will reach an equilibrium. The end situation

Figure 2: Schematic illustration of the charging of a dust particle inside a plasma. The electrons will approachthe surface fastest resulting in a negative surface charge which repels other electrons and attracts the ions. Anequilibrium will be reached where the particles surface is negatively charged and it will be surrounded by aspace charge region

will be a particle with negative surface charge surrounded by ions. The charge of a particlecan be obtained solving equation 7:

Qp = Cφp = 4πε0rpφp (7)

where φp is the floating potential of the particle C is the spherical capacity of the particleand rp the particle radius. This result is obtained by the Orbital Motion Limited theory(OML) developed for Langmuir probes [12]. This theory assumes a isolated particle of radiusrp which is surrounded by a sheath of thickness λD >> rp. Important in this theory is theassumption that at steady state (of which we want to know the charge), there will not be achange in charge:

∂Qp∂t

= Γe + Γi = 0 (8)

Where Γe,i are the electron and ion flux respectively. These fluxes where determined to be,

Γe = −πr2pnee

√8kTeπme

exp(eφ(rp)

kTe(9)

Γi = πr2pnie

√8kTeπme

(1− exp(eφ(rp)

kTe) (10)

(11)

according to Laframboise [13]. The OML theory was extended with a Maxwellian distributionfor ions. And assumed the plasma sheath to be collisionless. Now equation 8 can be solvedyielding the floating potential is only depended on ratio ion and electron temperature andmasses.

exp(eφ(rp)

kTe) =

√Time

Temi(1− eφ(rp)

kT i) (12)

5

The floating potential can be kept constant by keeping this ratio TimeTemi

constant. Then thecharge in equation 7 will be linearly dependent on the particle radius. As was measured byJ.Beckers [4].Due to the charge of the particle and the electric field formed in the sheath of the plasmathere will be an electric force working on the particle. This force and other important forceswill be discussed in the next paragraph.

2.1.4 Forces acting on the dust particles

As introduced in the previous paragraph, there will be an electric force on the dust particle.This is not the only force acting on the particle. The magnitude of all these forces aredependent of the particle radius. J.Beckers has calculated the magnitude of the acting forcesdependent on the radius of the particle. These results are shown in graph 3 which is merelyused as an indication. The plasma conditions J.Beckers worked with are roughly the samefor many low pressure plasmas. Some of the forces can be neglected as they are few ordersof magnitude smaller then the other. This is why is immediately disposed of a few forces,which saves time. Since this research is performed with particles in the order of magnitudeof 1-10µm, only those forces that are dominant in this area are discussed. These forces are:

1. The gravitational force Fg

2. The electric force on the particle FE

The gravitational force magnitude can be calculated by:

−→Fg =

4

3πr3

pρp−→g (13)

Here ρp the mass density of the particle and rp is the particle radius. −→g is the gravitationalacceleration.The electric force can be calculated by Coulombs law:

−→FE = Qp

−→E (14)

Where Qp can be calculated via equation 7. The−→E is the present electric field in the sheath

region.Though the other forces are not discussed in detail it is important to remember where theyoriginate from to get a physical understanding of them. Graph 3 is provided to indicate themagnitude of the forces as a function of particle radius.

1. The ion drag force Fi is the force that consists of the momentum transfer from ions thatcollide with the particle.

2. The Neutral drag force FN originates from neutral atoms moving through the plasmaand colliding with the dust particles. In this collision they will transfer momentum tothe dust particle.

3. The thermophoretic force Fth, this is a drag force as well based on momentum transfer.Yet, this momentum transfer is caused by the temperature gradients inside your plasmawhich result in a higher thermal velocity of gas atoms on the warmer side of yourparticle. In our plasma this would be the only other force besides the coulomb force FEdirected upward.

6

Figure 3: Estimated magnitude of the forces acting on the dust particle dependant on the radius [4].

When all these forces are put together a force balance can be created4. An equilibriumwill be reached when the particle is located some distance above the electrode inside theplasma sheath. In this way particles are levitated by the electric force directed upward.

Figure 4: A force balance of the acting forces on the dust particles inside the RF-plasma. [4].

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2.2 Light scattering

When light is incident on particles the light will be scattered from these particles in variousdirections. There exist several methods to describe scattering some are more easy to com-pute then others. In order to determine which kind of scattering is of importance for thisexperiment, two properties of the experiment are of importance: the particle diameter Dp

and wavelength λ of the light.

Ratio =Dp

λ(15)

If this Ratio is below 10% Rayleigh scattering is dominant. This thesis discusses the casewhere DP >> λ and the Ratio is far above the 10%. Then Mie Theory, is the best option todescribe the scattering of the light.Mie theory enables you to determine the:

1. amount of scattered light ;

2. the total optical/scattering cross-section;

3. ”shapefactor”, this parameter indicates where the light is going;

The Mie theory calculates a solution to the Maxwell equations. For the case that an electro-magnetic plane wave is scattered on a homogeneous sphere.For this research it is not required to understand all difficult mathematics of Mie theory. It isonly necessary to be able to reproduce the measured data with corresponding theoretical data.

2.2.1 Single scattering

The amount of light scattered on a single particle is, at first, dependent of the incident beam.A scattering plane is defined parallel to the laser beam. The electric fields, of the laser beam,are spanned up by the two components E‖ and E⊥, representing the components of electricfield parallel and perpendicular to the scattering plane. The relation between the incomingand outgoing electric fields components is[5].(

Es‖Es⊥

)=eik(r−z)

−ikr

(S2 S3

S4 S1

)(Ei‖Ei⊥

)(16)

The subscript i indicates the incoming beam and s means scattered beam. k is the wavevector and r is the particle radius, the z dependency is added to cancel the periodicity inthis parameter of the incoming waves. The matrix containing S1, S2, S3, S4 is the scatteringmatrix.

S1 =

∞∑n=1

2n+ 1

n(n+ 1)(anπn(cosθ) + bnτn(θ)), (17)

S2 =∞∑n=1

2n+ 1

n(n+ 1)(anτn(cosθ) + bnπn(θ)), (18)

Here θ is the scattering angle and an and bn, the scatter coefficients, can be calculated bysolving equation 21 [5]. Since the polarization does not change on spherical particles the off

8

diagonal elements of the scatter matrix S3 and S4 are zero. Simplifying equation 16 to:(Es‖Es⊥

)=eik(r−z)

−ikr

(S2 00 S1

)(Ei‖Ei⊥

)(19)

The expressions for the scatter coefficients an and bn are:

an =m2jn(mx)[xjn(x)]′ − jn(x)[mxjn(mx)]′

m2jn(mx)[xh(1)n (x)]′ − hn(x)[mxjn(mx)]′

, (20)

bn =jn(mx)[xjn(x)]′ − jn(x)[mxjn(mx)]′

jn(mx)[xh(1)n (x)]′ − hn(x)[mxjn(mx)]′

, (21)

Here jn and hn are respectively spherical Bessel functions and Hankel functions of the firstkind. And πn and τn are contain Legendre polynomials P 1

n [5].

πn =P 1n

sinθ, (22)

τn =dP 1

n

dθ, (23)

From the scatter coefficients the scatter and extinction cross section can be calculated:

Cs =2π

k2

∞∑n=1

(2n+ 1)(|an|2 + |bn|2), (24)

Ce =2π

k2

∞∑n=1

(2n+ 1)R {an + bn} , (25)

Where Cs is the scatter coefficient and Ce the extinction cross section.These equations can be used for the single scattering cases. This means that when multiplescattering occurs there should be another mathematical method to describe this.

2.2.2 Multiple scattering

For the propagation of light through a cloud of scatterers the transport theory is used. Picture5 shows how the laser light is scattered and also shows there could be other incident lightscattered in the direction of the detector. Conform to the theory [7] three terms that willadd up to the total scattered intensity on a volume containing scatterers are introduced. Letsfirst consider the spherical volume as in figure 5. The extinction of the spectral intensity ofthe laser beam propagating through this volume in the direction s direction is described bybeers law [7]:

I(r,s)

ds= −ρσtI(r,s). (26)

A second term is introduced since there is also light coming from other directions beingscattered into the the detector. To calculate the amount of light scattered into the detectorthe direction of the light s’ which is scattered to direction s and integrate this over all possibleincoming angles.

Iscattered(r,s)

ds=ρσt4π

∫4π

p(s,s’)I(r,s’)dω′, (27)

9

Figure 5: This schematic shows the laser-light being exposed on a cylindrical scatter volume. Also it indicatesother ’incident light’ which causes light to be scattered in the direction of the detector

Then a source term ε(r,s) is added due to emission or reduced intensity of light. The onlystep left is to notice that the intensity is contained of two part:

I(r,s) = Idiffuse(r,s) + IReducedIntensity(r,s) (28)

We wont turn into the details involved in the reduction of equation these equations. Howevera detailed reduction can be found in [6]. The final equation becomes:

Id(r,s)

ds= −ρσtId(r,s) +

ρσt4π

∫4πp(s,s’)(Id(r,,s’) + IRI(r,s’))dω

′ + ε(r,s’), (29)

Id(r,s) is the diffuse intensity, and IRI(r,s’) is the reduced intensity due to non-scattered lightfrom an external source.Another useful equation arises from the fact that equation 29 is a differential equation. Thistype of equation is difficult to solve in a computational way therefore the differential equationis written as an integral, which is implicit and therefore simplified by the following equation[6]:

Ii+1d (r,s) =

{∫ s0 e−(τ−τ1)[ρσt4π

∫4ı p(s, t)Ir(r1, t)dω]ds1 +

∫ s0 e−(τ−τ1)ε(r1, s)ds1 ifi = 0∫ s

0 e−(τ−τ1)[ρσt4π

∫4π p(s, t)Ir(r1, t)dω]ds1 ifi ≥ 1

(30)

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2.3 Theoretical Mie profile

The comparison of a single dust particle’s spectrum to the theoretical Mie profile can bedone when certain parameters of the particles are known. These are the particle radius andrefractive index. When these values are known a expected Mie profile can be plotted withthe matlab script in appendix B. A profile created with this programme is shown in graph 6.Here three particle radii are plotted at a refractive refractive index of n = 1.68 are used. Theimaginary part of the refractive index is unknown but expected to be close to zero since thereis little absorption. This figure shows that the particle radius is a very indicative property

Figure 6: This graph is an indication of how the measured Mie profile should look like, for three particle radiiand a refractive index of n = 1.68

of the periodicity of the signal. When the radius is increased the periodicity will increase aswell. Further more the scattering profiles that are plotted show a lot of forward scatteringand a lot of backscattering. What’s more it indicates that there are periodic bumps in thesignal. In the polar plot it can be better shown how the light is scattered form the particle.

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Figure 7: Polar plot of the expected Mie profile for green light scattered on a single particle of size 2.5µm

12

3 Experimental setup

This section will address the experimental setup of the experiment. At first there will be anexplanation about the main principle of the setup and how it works. Some of the equipmentwhich is used to create a suitable environment for a plasma is discussed in paragraph 3.2. Inparagraph 3.3 some information will be given on how this equipment can be operated. In thelast paragraph 3.4 of this chapter a description of the data analysis is provided.

3.1 Inside of the experimental setup

Inside the setup, light is scattered on dust particles that are levitated by the electric field inthe sheath of the plasma. This setup is schematically drawn in figure 8. Inside an environmentwhere an argon plasma can be operated is created. An argon plasma is used because this isa non reactive plasma. So the plasma should not interact with the particles. The collimator,which collects the light being scattered from the dust cloud, is able to rotate around theelectrodes to measure at every angle. The particles that are visible in the figure are levitateddue to the conductive ring. This ring changes the potential of the electrode and a ’potential-bucket’ is created.

Figure 8: A schematic view of the setup from the inside of the vacuum vessel. The electrodes create a plasmawhich is given a purple color. The collimator collects the light which is scattered from the dust particles. Alsothe potential bucket in which the particles are levitated is shown.

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3.1.1 Electrodes and power supply

The electrodes are made of conductive stainless steel and the pillars are of non-conductivePEEK. The voltage over the electrodes is altered at a frequency of 13.56 MHz. This frequencyis in between the ion and electron frequencies estimated by J.Beckers [4]. Therefore theelectrons are able to follow the electric field of the electrodes and the ions are not. When theargon density inside the vessel is high enough there will be enough background ionization toinitiate an avalanche of argon atoms being ionized and a plasma will be created.The power supply can be set to a power between 0-100 watts. This can influence the plasma

Figure 9: A schematic view of the setup from the outside

sheath thickness. When a higher power is set there will be a thinner plasma sheath. Thisis because the surface of the electrodes becomes more negative and the ions will move closerto the electrodes. The RF- power supply is attached to a matchbox. This matchbox is adevice which is needed to control the matching of impedance inside the system, to avoidreflections inside the system and increase the power transit. The plasma when turned on willhave a complex impedance that is different from the impedance of the RF-power source. Thematchbox will connect these two different impedances to each other.The shape of the potential lines created by the electrodes can be altered by changing theshape of the electrode. In figure 8 a potential line is created by a cylindrical conductivematerial. This creates an area where the particles are accumulated, a potential bucket.

3.1.2 Pressure regulation system and Argon flow regulation

The experiment takes place in a vacuum vessel. This vacuum can be sustained with twopumps:

1. Primary vacuum pump

2. Roots vacuum pump

These pumps are used to control the pressure in the vessel. The primary vacuum pump isresponsible for the first area namely 1bar-1 mbar. The roots pump is capable to get thepressure to a regime of 1-0.001 mbar.The roots is not build for pressures higher than 1 mbar. This means the pumps must beoperated in series.

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In order to create a plasma argon must be supplied to the vessel this can be done using aflow control unite while the pressures is managed by a pressure valve.

3.1.3 Spectrometer

The spectrometer is mounted on a circular plate which is able to rotate around the electrodes.Figure 8 does not show the spectrometer only the collimator since this is where want tomeasure a scatter signal. The collimator is collecting light scattered from the particles in thehorizontal plane. The rotation of the circular plate can move from -160 to 160 degrees whenchoosing the direction of the unscattered laser light as our 0 degrees point. The spectrometeris able to take a spectrum of each of those angles. From this spectrum a wavelength can bedetermined of which we are sure it is from the laser. These collected wavelengths will thanshow a number of counts. These counts scale with the intensity of the signal.Few important settings of the spectrometer are:

1. The integration time of a measurement can be set. This is the time that the spectrometertakes after starting to count the light intensity. The light is thus integrated over a certaintime period.

2. The number of times the spectroscope averages over a measurement. For instance thereis a lot of variations in your signal over time you want to average this out of your resultsthen this function can be used.

3. The dynamic dark current subtraction this is needed to account for the thermal effectsof the pixels inside the microscope who will measure a signal even when there is none.By turning on this function the spectroscope automatically corrects for this.

3.2 Equipment

All parts of the complete setup need a short explanation concerning their properties andapplication in this setup. Reading this section should provide some familiarity with thesetup. In figure 9 we can see that the laser is stationed outside the vessel and goes through apolariser through a viewpoint in the vessel. The laser beam also exits the vessel via anotherwindow after which it falls onto a photodiode. Through the small viewpoints one can see theparticles between the electrodes. In the schematic view of the setup a pump system is alsoshown which has been discussed before.

3.2.1 Laser

The laser which is used is of type 3B laser emitting green light at a wavelength of λ = 532nm.This laser is used to scatter light on the particles. The best way to secure the alignment ofthe laser seemed to be to open the vacuum vessel and align the laser above the middle of theconductive ring (which was not at the correct place). The intensity of the laser can vary 10%over a time of 4 hours. Therefore it is useful to measure this laser intensity during longermeasurements. This can be done with the photodiods which can be seen in figure 9.The laser beam must also be polarized. This is because only the perpendicular part of theelectromagnetic waves will be taken into account in this measurement. To simplify equation16, there is only an interest in scatter matrix element S2 . This is done by the polariser.

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3.2.2 Dust dispenser

In the schematic in figure 9 the particle dispenser can be seen. This dispenser can be usedwith many different interchangeable heads. These heads are in fact little containers filled withparticles and have different openings. This is useful when different amounts of particles haveto be inserted into the plasma. Or it could be useful for different sized particles.

3.3 Operating systems

A Labview programme is used to control the setup. There are three programmes that controlthree separate components of the plasma setup.

3.3.1 Flow control

The first thing that has to be controlled is the amount of argon going into the vessel. This isdone with the flow control unit and can be operated by the labview program Flowcontrol.vi.This programme is also capable of regulating a valve that opens and closes at the right timesto make sure the pressure inside the vessel is kept constant. The programme also enablesthe user to switch to a higher or lower pressure. In this way the plasma sheath thickness isincreased or decreased, thus a change will be made in the shape of the potential bucket abovethe electrode.When the position indicates 0 it means the valve is closed and that the pressure should beincreasing if there is a gasflow. If position indicates 1000 the valve is completely open. Whenthe valve is completely open the pressure should become lower or stay on the same value ifthis is not the case the gasflow in ml/min is to high.

3.3.2 Dust control

The programme Dust.vi is to control the particle dust dispenser. The program works rathereasily, push the button and particles will be dropped inside the plasma. The programmecontrols the time and the current that is applied to the dust dispenser via a power supply.

3.3.3 Setup control panel and spectrometer

SetupControl.vi is the software which manages the rotation of the spectrometer circling thedust cloud. It is able to move in positive and negative directions, or it can move to an anglewhich is entered. This is the upper part of the programme see figure 10. The part with thespectrum in the lower part of the interface shows the spectrum of the last measurement bythe spectroscope. Here the integration time, maximum integration time and average over arethe options to be filled out. The integration time is regulated by the labview programmesince the amount of light scattered from the particle is very angle dependent. Therefore theprogramme will dynamically adapt to the amount of counts and make sure there is alwaysenough signal and never to many to avoid saturation. To start a measurement over multipleangles the middle part of figure 10 has to be addressed. Here the range can be set, most timesthis would be unchanged -160 to 160. The number of steps taken by the rotator can also beadjusted.The use of a spectrometer for this set-up might seem odd. Why not use a Photomultiplier?The answer is in the scope of my research maybe not be clear. However the setup is build

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Figure 10: The setup control interface used to control the spectroscope and the circular plate which can rotatean angle of 320 degrees.

to offer more possibilities to perform research. L.Schepers will in his PHD-research also usephosphorus dust particles. These particles will be responsible for a shift of the wavelength.When this occurs a photomultiplier is not able to perform measurements on other wavelengths.An important notion is to be made about the spectrometer. As is discussed before thespectrometer adjusts its integration time in order to measure enough signal. The amount ofcounts is therefore divided by the integration time for that angle. The scale for intensity thatis measured is therefore in counts/s.It is worth mentioning that the setup has some practical limitations. The electrode has tobe supported and therefore three pillars are used. These pillars are located at the angles:-87,33 and 155 degrees and are roughly 4 degrees wide. These points do not describe useful dataand can be ignored.

3.4 Data analysis

The data which is collected from a measurement has to be analysed. To start the there aremeasured spectra at every angle where the rotator stopped. Typically this are 320 to 640different ASCI-format. From this several values can be obtained. These are:

1. time of the measurement

2. angle

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3. averaging

4. integration time

5. number of counts at a wavelength of 532 nm.

To read out all the data and subtract the correct wavelength from this pile of informationa MATLAB script is written. This script immediately subtracts the measured backgroundnoise which has to be measured separately .

1. The first script is able to read out the data and will plot the number of counts persecond versus the angle. This file will also save all the data in one single file so thereis no need of reading out the data several times, which is very time consuming. Thisscript is called Rawdata.mat and is added in the appendix A.

2. The second script is able to read out he saved data that was created by Rawdata.mat.It can also read out several different signals at once. Which gives the possibilities ofcomparison of several signal. This script is called SelectData.mat, and is also added inthe appendix A.

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4 Scattering on a single dust particle

As is described in the introduction of this thesis, a primary goal of this research is: tomeasure the scattering profile on a single dust particle inside a plasma. This hasn’t been astraightforward process, and therefore few of the steps taken to do this measurement will beaddressed in this section. This section is the extension part of my bachelor project.

4.1 Particle properties

Mie theory describes the scattering profiles of spherical particles. Therefore it is obliged tocheck the particle radii. This has been done with a simple microscope. The results of thismicroscopic view are visible in the figures 11.

(a) Magnification 40 (b) Magnification 400

(c) Magnification 1600Figure 11: These are microscopic images of the Melamine Formaldehyde particles with a particles diameter4.77 µm ± 0.13 µm. The magnification are x10, x400, x1600 for a,b and c respectively.

At a magnification of 40 numerous single particles can be identified. Some are closetogether. This is because it is not very easy to create a single layer of particles on the retina.When the magnification is increased to 400x it is seen that even when close together theindividual particles can be identified 11b. Increasing the magnification even more it is seenthat the particles are of a spherical shape. What is also seen from 11c is that there is somelight scattering on the particles and there are interference patterns around it. The white dotin the middle of these particles is due to the scattering of light as well. The measured radiusof the particles is 4.77 µm ± 0.13 µm. Which is consistent with what the manufacturer of theparticles tells us (4.79 µm ± 0.08 µm). The difference between these values can be appointed

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to the quality of the microscope that was used. It is a challenge to get a sharp image of theedges of the particles therefore there is more spread in this measurement.

4.2 Configuring a single dust particle

In order to create an environment in which only one particle is present, the following stepsneed to be followed:

1. Create an argon-plasma using two radio frequent electrodes(13.56MHz) in a vacuumvessel with a pressure of 0.05− 0.1 mbar. Use a steady flow of 2 ml/min of argon. Turnon your laser to be able to see the dust particles in the plasma (when present).

2. Inject the particles using the particle dispenser with the settings: 2 Ampere, 100 ms andan opening of 40µm of the dispenser. A cloud of dust particles should now be visibleinside the plasma sheath.

3. Lower the pressure using flow control to obtain a pressure of 0.029− 0.035mbar. Thenexcess particles will be boosted over the top of the potential barrier in figure 8. adjustthe height of the electrodes in such manner that the particles are illuminated until apressure of 0.5mbar. Due to the practical dimensions of our setup it is not possible tomeasure at lower pressures (below 0.4 mbar) because at the edge the waste particles areilluminated by the laser.

4. Increase the pressure again, and look whether there is a single particle visible. If notrepeat the previous step, with a slightly lower pressure (use steps of 0.001mbar). Whenthere are no particles at all, the pressure has become to low, and a start over is inevitable.

The method used to measure the profile of scattered light from a single particle is as follows:

1. turn the laser intensity high enough to obtain a high enough signal (50% − 75% ofmaximum number of counts.

2. Turn on the spectrometer and average over at least 10 measurements. Because thereis only one particle the maximum integration time should be around 2000ms to obtainenough signal at angles where the signal is weak.

3. Then start to measure from angles -160 to 160 using at least 320 steps to measure atevery angle.

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4.3 Measurements on single particle

The process of obtaining the correct procedure to perform measurements on a single dustparticle has proven difficult, lengthy ; yet instructive. Since this is experimental work someof the challenges of obtaining this procedure will be taken into account. These challengeswhere to measure a proper background signal 4.3.2, the time management of a measurementin paragraph4.3.4 and the signal to noise ratio in paragraph 4.3.5. But first in paragraph4.3.1 three measurements on a single dust particle will be discussed. In the final paragraph4.3.6 of this chapter an attempt is made to fit the scattering profiles of these measurements.

4.3.1 Two different single particle signals

This paragraph discusses three of the measurements performed on a single dust particle thatwas configured in the plasma. They were all performed at a pressure of 0.06 mbar withapplied voltage of of 19 watt. The gasflow at every measurement was kept at 2 ml/s. Thefirst measurement was done over an angle of 320 degrees with 320 steps. The other two wereat higher resolution in the angular domain as there were 640 steps taken. The first resultof the measurement is shown in graph 12. The signal is symmetrical, which satisfies the

Figure 12: This graph shows the light intensity of light being scattered at a single dust particle inside a plasma.The intensity is measured as a function of the angle which is on the x-axis.

expectations. A clear Mie profile can be distinguished. The periodic intensity changes arevisible and have a high enough resolution. Yet the figure also shows some discontinuities.These are due to negative data, which is caused by the subtraction of the background signal.The background measurement is done to subtract reflections and other external effects fromour measurement. Thus these points indicate a situation where Ibackground > Isignal. The

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cause of this could be that the integration time of the background signal is different from themeasurement signal. The cause of the negative data will be examined in paragraph 4.3.2.There are done some measurements when the problem of negative data is solved. Under thesame circumstances two measurements are done. Both measurements are plotted in graph 13This result shows that the scattering profiles of particles are totally different. The particle

Figure 13: This graph shows the light intensity of light being scattered at a single dust particle inside a plasma.The intensity is measured as a function of the angle which is on the x-axis. The blue line is from a particlekept overnight in the plasma the red line was a particle a few minutes in the plasma

that was in the plasma for the whole night shows very wide periodic intensity oscillationswhere the other particle shows a very narrow periodicity in the oscillations. The reason forthis could be that there are simply two differently size particles inside the plasma. If this istrue it is expected that the particle with the wide oscillations is the smallest, if the theoreticalMie pattern in graph 6 is compared to graph 13.Different sized particles are not detected on the microscopic pictures. All particles where inthe same order of magnitude 4.77 ± 0.13µm. But what can be seen from the picture is thatsome particles are clustered together. If this is the case in the plasma the difference of the twoparticles could be explained. To examine the size 4.77 ± 0.13µm of a particle in the plasmaa camera with defined magnification should be added to the setup.A second hypothesis is that the particle shrinks over time when inside the plasma. Becauseone of the particles was already inside the plasma the night before it was at least 16 hoursin the plasma before the measurement was started. This hypothesis will be examined inparagraph 15. Here a measurement will be done at a fixed angle to see what happens withthe intensity over time. From this a deduction can be made about what happens with thesize of the particle.A note has to be made here to express the importance of the addition of a camera to thesetup to monitor the size of the particle. This would solve a lot of questions!

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4.3.2 Background signal

A challenge encountered is that the background signal at some angles was higher than thescattering signal. The hypothesis is that this had something to do with the difference be-tween the integration times of both measurements. An experiment to determine the effectsof integration time on the background signal was proposed. The results of this measurementare plotted in graph 14. From this it can be seen that there is an 1/x dependency with x

Figure 14: In this graph there are three background signals of which the intensity is plotted against integrationtime. The blue triangled line is the oldest, and dynamic dark correction was turned off. As the blue line theblack line is a measurement at an angle of 50 degrees, with dynamic dark correction on. The red line is at anangle of 5 degrees (with higher incident light intensity), with dynamic dark correction on.

being the integration time. This calibration could be used to solve the problem. Howeverthe spectroscope that was used offered another solution: Which was turning on the dynamicdark current correction function. This function subtracts the number of counts due to thethermal effects of the spectrometer (the spectrometer always measures a level of white noise).With this function turned on there should not be a dependency of the number of counts tothe integration time. Thus a horizontal line is expected, which is also plotted in the blackline of graph 14. This black line is almost horizontal, only when the integration time is below100 ms the result is unsatisfactory. The fact that these short integration times do not add upwith this horizontal line can be designated to the weakness off the signal at 50 degrees, herenoise becomes dominant. Fortunately the bad working low integration times at low signalswill not be a problem. The Labview programme, SetupControl.vi, will automatically adjustthe integration time to a level where the number of counts of a signal is kept within theboundaries of 50% to 75% of the maximum amount of counts the spectrometer is able to

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detect.Still there is some uncertainty about the operation of the programme at high intensity signalsand low integration times. Therefore a measurement is provided at another angle to deter-mine whether these smaller integration times do make sense when they are in the range ofthe allowed number of counts. As graph 14 shows this is again a flat red line. However theintegration times below 10ms tend to dissociate from the others. Some more research can bedone to see whether these smaller integration times always over or underestimate the signal.For now it is commendable to highlight the lower integration times in the scatter-profile, asthey might deviate 5% of the correct value.The error in the background measurements was not noticed earlier since the first measure-ments where done on a cloud of dust particles that scatter lots of light compared to a singleparticle. This is such a small deviation in the signal on measurements for dust clouds thatthis is neglected. For the previously performed measurements.

4.3.3 Time dependent signal of a single particle

This measurement is done because there are some forecasts that the signal from a singleparticle would have changed over time. To prove whether this is the case it was proposed tomeasure the scattering intensity over a time period at a fixed angle. All the other propertieswere kept the same except the integration time which will change when the intensity of thesignal drops. Although there might be some forecasts it is not expected that the signal willdrops its intensity. Graph 15 shows that the signal intensity drops with a factor 7 in little

Figure 15: This is a graph of how the intensity of a single particle inside a plasma behaves as a function oftime

over 4 hours.The reduced scattering intensity as a function of time can be explained by a proses calledetching. Etching decreases the size of a particle. When this happens it is expected thatthe Mie profile will change drastically as well. The periodic bumps in the scattering profilebecome wider and there will be less of them. This would imply periodic bumps in the signalof graph 15. In graph 16 the intensity fluctuations are plotted as a function particle radius,

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which is decreasing(at the same 30 degree angle as the measurement). Though this graph

Figure 16: Theoretical representation the intensity from a single particle at a fixed angle when the radiusdecreases because of etching

gives us insight in what would happen when etching occurs. There is no certainty about theamount of scattering that occurs and therefore its impossible to say in which region of radiithe signal was during our measurement. Therefore a recommended addition to the setupwould be a camera able of monitoring the particle in the plasma. Because when the particlesize decreases the gravitational force and electric force will change this could be visualized.Another proposal to discover whether etching occurs is changing the plasma properties. Forinstance another gas then argon could be used to stimulate etching because there are otherions in the plasma the momentum of the ions that bombard the surface would be different.A lot of periodicity is visible in the signal of graph 15 yet this is periodicity due to the laserintensity fluctuations. The laser fluctuations are always there and the used laser is also notthe most precise. A laser with less intensity fluctuations would be a useful addition to thesetup. If no better laser is available the integration time and number of averaging could beincreased. This would average out the noise. This is what happened over time in 15 duringthe measurement the integration time increases and the noise becomes less and less dominant.Still using higher integration times should be avoided because it would drastically increasethe measurement time.

4.3.4 Time versus noise

Another important feature of the software that is used is the averaging function of the spec-troscope. This function averages a series of measurements in order to get steadier results.As was previously discussed at lower integration times there is a lot of noise. Then it isrecommended that the averaging is done several times. There is determined a bottom line fornumber of times averaging has to be done this was 10. This has been obtained experimen-tally and was later raised to 15. Still the measurements of graph 15 indicate a lot of noise atlower integration times. Therefore it commendable to determine a bottom line of total time

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a measurement can endure. for example this could be:

(Integration time) ∗ (number averaging) ≥ 10s (31)

Ideally the averaging would be infinite, yet then the measurement would take forever. There-fore a right calculation has to be made on how long a measurement will take and what theallowed averaging boundaries are. An assessment has to be done to find the correct balancebetween time the measurement costs and the amount of noise that is acceptable.

4.3.5 Signal to noise ratio

Intensity is low when light is scattered on a single dust particle. This is because a very longintegration time is needed in order to distinguish between noise and the signal itself. This isa problem which is easily solved: increase the integration time. Yet this solution is limited bythe extra time it consumes. Also the ratio between the signal and the noise doesn’t becomeany different. This problem of a low signal to noise ratio will not be solved, in this thesis. Thehigh level of noise can depend on the amount of light being scattered inside the collimatorthat is not coming from the dust particle. This could be reflections inside the vacuum vesselor light coming from outside the vessel via the viewing windows. Ways to solve this couldbe by attaching a cylindrical beam dump at the height of the collimator. The windows couldalso be replaced by blackout panels.There are some unfortunate side effects of this low signal to noise ratio. The signal is duringthe biggest part of the measurement of the same order as the background noise. Therefore ifthere are variations in the background noise over time, it will cause the corrected signal to befaulty. It is therefore important to keep track of the known variations in the noise as most ofthem scale with the laser intensity fluctuations these can be monitored with the photo diodesin the setup.

4.3.6 Fitting particle properties on the measured scattering profile

It is expected that the scattering profile of a single particle shows a clear Mie shape asthe script appendix B calculated in graph 6. It is know the particles have a diameter of4.77 ± 0.13µm. The real refractive index of the particle nparticle = 1.68. This is enoughinformation to make a theoretical expectation of the scattering profile. Yet if there is onlyas little variation in size as ±0.13µm the scattering profiles change already a lot. Thereforeit is easier to develop a fitting method. This was done by L.Schepers and some of the resultfor now are shown in graph 17. As can be seen from this graph the fit does converge howeverthere is a problem. The expected value for the radius was 2.38 ± 0.13µm the fitted value is4.37µm. This could be because there is an error in the fit. But looking at the periodicity ofthe oscillation it indicates values close to the fit results. There are some attempt made to fitthe other signal that of the single particle but this is something for the future.There are some other future prospects on fitting the scattering profile. For example therefractive index can be fitted as well. The real part of this index is known the imaginary partnot yet. This could be useful information when there are more particles in the cloud.

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Figure 17: A fit on the measured Mie patern. The fitted radius is 4.37µm. The arrow points to the placewhere the fits first oscillation should have started. the blue line is the signal and the red is the fitted

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5 Scattering on a cloud of dust particle

Trying to describe multiple scattering will become difficult quite fast when the number of par-ticles inside the scattering regime is increased. Therefore understanding multiple scatteringbetter is a goal of this research. The first goal of this section is to measure a scatter profileof dust cloud. then by changing the density of the cloud the regimes of single and multiplescattering are to be investigated.

5.1 The method to measure scattering of dust clouds

In order to measure a scattering profile of a dust cloud it is important that the center of thecloud is in the center of the laser beam. Getting a cloud there is very simple. To increasethe cloud particle density, as in the number of dust particles inside the same cloud volume, ismore difficult. For instance when the pressure inside the plasma is changed the shape of thepotential bucket and the shape of the dust cloud will change. Indirectly the volume of thecloud is changed. It is only desirable to change density and not the volume. Therefore its notdesirable to change the pressure. However adding more particles into the plasma will not bethe solution either. Since the extra particles will be dropped on the other dust particles whichwill increase the size of the dust cloud. On top of this the excess particles will be levitatedover the potential barrier.Taking these properties of the potential in consideration there is a solution. If started with acertain cloud shape containing a lot of particles, the potential barrier has a well defined yetunknown volume. With well defined it is meant that this shape of potential is distinctive forthis pressure. If the pressure is lowered and increased again few particles might be pushedout of the bucket’s original shape. Since all particles are negatively charged they will exertrepulsive forces towards each other therefore they will move further apart. This then isa decrease of particle density inside the dust cloud. The dust cloud will not change fromvolume in this method.

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5.2 Symmetry of the signal

The first measurements where done on dust clouds of a low particle density. The scatteringprofiles of these clouds look like figure 18. These profiles where unexpected because the inten-

Figure 18: An asymmetrical scattering profile where the intensity is plotted to the scattering angle

sity of the signal was not symmetrical in the point zero which is what is expected from Mietheory figure 6. This profile indicates that the amount of light scattered towards the positiveangles is bigger than to negative angles. Or one side of the cloud scatters more light thanthe other. This means that the density of the cloud is of influence on the amount of lightscattered. Thus it is of importance that the light beam is incident on the centre of the dustcloud, which means that the density of the dust cloud is the same at both sides.In order to obtain a symmetrical signal the vacuum vessel was opened and it was discoveredthat the conducting ring, which creates the potential bucket, was not in the center of thesetup. When this was realigned the spectrum became more symmetric. Another geometri-cal property of the setup is that it is obliged that the conducting ring is completely horizontal.

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(a) A symmetrical scatter profile of a cloud of dust particles

(b) A scattering profile of a bigger dust cloud

5.3 Measurements on dust clouds

Measurements are performed on dust clouds. First the scattering profile of dust cloud withsingle scattering properties is discussed. Then a comparison is made with the another cloudwith a higher particle density. Also a theoretical indication is provided of how multiplescattering scatter profiles would look like.

Graph 19a indicates a good symmetrical signal. The angular resolution is also of goodquality. The fact that a clear Mie profile is visible is indicating that there is single scatteringin this case. The expectation is that the Mie profile becomes less and less clear when theamount of multiple scattering is increased. A Theoretical expectation of what happens whenevery light beam scatters two times is provided in the bachelor thesis of M.Bertens [6]. Itstates that the periodic bumps so characteristic for Mie scattering are almost gone. In thismodel however it is assumed that all light beams will scatter two times. In reality somelight in the first measurement may be scattered two times already. Since there is a Mieprofile visible in 19a the hypothesis is that single scattering is dominant here. In a secondmeasurement the scattering profile of a bigger dust cloud was measured, see graph 19b. Herethe periodic bumps of the Mie profile are still visible. Yet the amplitude of the periodicbumps has become less. This implies that the bigger dust cloud that was measured shows

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some signs of a transition phase between single and multiple scattering. Physically it is veryunderstandable that this transition is gradually.Some proposals can be done on where to continue the examining of dust clouds:

1. Is a dust cloud still a point source in the setup that is used?

2. Measure the scatter profiles of several dust clouds with variable cloud densities determineat what time multiple scattering becomes dominant.

3. add a camera to the setup to make sure the volume of the dust cloud is kept constant

4. estimate the amount of particles in the dust cloud

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6 Conclusion and outlook

In this thesis plasma is used as a tool to measure the scattering profile on dust particles.There is provided a procedure to measure scattering profiles on particles that are levitatedin a plasma. In the process of obtaining this procedure a lot of experimental collectiveknowledge about the setup is gained. There are measurements performed where the lightscattering profiles of a cloud of dust particles have been measured successfully. They show aclear indication of a Mie scattering profile, which is the theoretical expectation for the caseof single scattering model. When the density of the dust cloud is increased it becomes visiblethat the periodicity in the Mie profile will be averaged out bit by bit. Thus the amplitude ofthe oscillations will decrease. During these measurement no quantitative information aboutthe density of the dust cloud was gathered. This something that should be done in a followup research. To determine where the single scattering or multiple scattering is dominant.This investigation only shows that the scattering gradually goes from the single to multiplescattering profile as the density of the dust cloud is increased.To discover more about the scattering on dust clouds it is essential that light scattering ona single dust particles is understood. Measurements have been done on scattering profiles ofthese single dust particles. These profiles where compared to the theoretical expected Miescattering profiles. Successful measurements have been done with the new setup. Yet whenthose profiles where compared to each other there was a great contrast. The only differencein the two measurements was that the scattering profile was performed with different sizeparticles. Yet from outside the setup there are no indication of this being the case. There isonly the possibility that the particles cluster together. Another cause of the different signalscould be that one of the two particles was already a night inside the plasma which couldhave an effect on the particle (etching). Some further research is done on this and it appearsthat a particle inside the plasma changes in size over time. The hypothesis is that this isbecause etching occurs inside the plasma on the particle whereby the size of the particle isdecreased. To find out if this is true the setup could use a good imaging section added toit. Also some measurements could be done with other gasses which could accelerate or slowdown the etching process.

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References

[1] ”EFFICIENT BLUE LIGHT-EMITTING DIODES LEADING TO BRIGHTAND ENERGY-SAVING WHITE LIGHT SOURCES.”. www.nobelprize.org/nobel-prizes/physics/laureates/2014/October 13, 2014. Accessed July 12, 2015.

[2] Lougheed T. 2014. Hidden blue hazard? LED lighting and retinal damage in rats. EnvironHealth Perspect 122:A81; http://dx.doi.org/10.1289/ehp.122-A81

[3] Mendis, D. A. 2002. Progress in the study of dusty plasmas. Plasma Sources Science andTechnology 11, (3A): A219-A228

[4] Beckers, J. (2011). Dust Particle(s) (as) Diagnostics in Plasmas. Phd thesis. EindhovenUniversity of Technologie. 1-36.

[5] Bohren, Craig F., and Donald R. Huffman. 1983. Absorption and scattering of light bysmall particlesWiley-Interscience. 94,100,103,112

[6] Bertens, M. (2015). Numerical Models of Light Scattering in Dusty Plasma. BSc-thesis.Eindhoven University of Technologie.

[7] Ishimaru, A. (1978). Wave propagation and scattering in random media. New York:Academic Press.160-163.

[8] Lieberman, M., Lichtenberg, A. (1994). Principles of plasma discharges and materialsprocessing. New York: Wiley.

[9] Langmuir, Irving. (1928). Oscillations in ionized gases. Proceedings of the NationalAcademy of Sciences of the United States of America 14, (8): 627-637

[10] T. Sheridan and J.Goree,(1991) ”Collisional plasma sheath model,” Phys.Fluids B,vol.3,pp. 2796-2804.

[11] G.Paeva,(2005), Sheath phenomena in dusty plasmas. Phd thesis, Eindhoven Universityof Technology.

[12] Mott-Smith, H. M., and Irving Langmuir. 1926. The theory of collectors in gaseousdischarges. Physical Review 28, (4): 727-763

[13] J.G.Laframboise, (1996) ”Theory of spherical and cylindrical langmuir probes in colli-sionless, maxwellian plasma, at rest.,”PhD thesis, university of Toronto.

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A Matlab source codes

rawdata.mat is the file responsible for reading out all separate files written by SetupControl.viwhich is the LabView programme that will save each measured scattering spectrum for eachangle. The programme rawdata.mat will read each of these spectrum files and subtract thewavelengths λ = 530 t/m 534nm and add them. This is the range where the laser light isvisible. Also other critical parameters as the angle at witch the spectrum was taken and theintegration time are subtracted.

1 %popup to select folder containing measurements2 folder = uigetdir('Z:\Dusty Plasmas\Light Scattering','measurement');3 %popup to select folder containing measurements4 bfolder = uigetdir('Z:\Dusty Plasmas\Light Scattering',['background' folder]);5

6 %load data into matlab7 [time, angles, average, inttimes, diode1, diode2, pressure1, pressure2,8 spectrum2]=Loadfiles(folder);9 [btime, bangles, baverage, binttimes, bdiode1, bdiode2, bpressure1, bpressure2,

10 bspectrum2]=Loadfiles(bfolder);11

12 %remove wavelength row13 spectrum=spectrum2(2:length(spectrum2(:,1)),:);14 bspectrum=bspectrum2(2:length(bspectrum2(:,1)),:);15

16 [path, name]=fileparts(folder);17

18 %all angle dependent data in one array19 %row gives the wanted variable, column gives the angle20 data= [angles; inttimes; binttimes; diode1; bdiode1; diode2; bdiode2; pressure1;21 bpressure1; pressure2; bpressure2];22

23 %spectrum and background24 %each row is one spectrum at a different angle each colum is one25 %wavelength.26 spectra(:,:,1)=spectrum; %raw27 % spectrum28 spectra(:,:,2)=bspectrum; %raw29 % background30 spectra(:,:,3)=bsxfun(@rdivide,spectrum,inttimes'/1000); %spectrum31 % per second32 spectra(:,:,4)=bsxfun(@rdivide,bspectrum,binttimes'/1000); %background33 % per second34 spectra(:,:,5)=spectra(:,:,3)-spectra(:,:,4); %spectrum -35 % background36 spectra(:,:,6)=bsxfun(@rdivide,spectra(:,:,3),diode2'/diode2(1)); %spectrum37 % per second normalised to diode38 spectra(:,:,7)=bsxfun(@rdivide,spectra(:,:,4),bdiode2'/diode2(1)); %background39 % per second normalised to diode40 spectra(:,:,8)=spectra(:,:,6)-spectra(:,:,7); %spectrum -41 % background normalised to diode42

43 %extract desired wavelength. (530 - 534 nm)44 spectra2=spectra(:,623:637,:);45 scattered=sum(spectra2,2);

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46

47 %place scattered in the data array48 data(12,:)=scattered(:,1,1); %raw spectrum49 data(13,:)=scattered(:,1,2); %raw background50 data(14,:)=scattered(:,1,3); %spectrum per second51 data(15,:)=scattered(:,1,4); %background per second52 data(16,:)=scattered(:,1,5); %spectrum - background53 data(17,:)=scattered(:,1,6); %spectrum per second normalised to diode54 data(18,:)=scattered(:,1,7); %background per second normalised to diode55 data(19,:)=scattered(:,1,8); %spectrum - background normalised to diode56

57 %save data58 save(fullfile(folder,strcat(name,' data')),'data');59 %save(fullfile(folder,strcat(name,' spectra')),'spectra');%relatively large60 %file. use only when necesary.61

62 %make and save figure.63 semilogy(data(1,:),data(16,:));64 title('Scattered light intensity');65 xlabel(' Scattering angle');66 ylabel(' Intensity' );67 savefig(fullfile(folder,'scatterprofileraw.fig'));68 saveas(gcf,fullfile(folder,'scatterprofileraw.jpg'))

The programme SelectData.mat is used to add a specific matrix of several measured profilesto the workspace in MATLAB. This makes it easier to plot the measured signals of severalstand-alone measurements into a single graph and compare them.

1 function varargout = SelectData(varargin)2 % SELECTDATA MATLAB code for SelectData.fig3 % SELECTDATA, by itself, creates a new SELECTDATA or raises the existing4 % singleton*.5 %6 % H = SELECTDATA returns the handle to a new SELECTDATA or the handle to7 % the existing singleton*.8 %9 % SELECTDATA('CALLBACK',hObject,eventData,handles,...) calls the local

10 % function named CALLBACK in SELECTDATA.M with the given input arguments.11 %12 % SELECTDATA('Property','Value',...) creates a new SELECTDATA or raises the13 % existing singleton*. Starting from the left, property value pairs are14 % applied to the GUI before SelectData OpeningFcn gets called. An15 % unrecognized property name or invalid value makes property application16 % stop. All inputs are passed to SelectData OpeningFcn via varargin.17 %18 % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one19 % instance to run (singleton)".20 %21 % See also: GUIDE, GUIDATA, GUIHANDLES22

23 % Edit the above text to modify the response to help SelectData24

25 % Last Modified by GUIDE v2.5 05-Jun-2015 14:42:2026

27 % Begin initialization code - DO NOT EDIT28 gui Singleton = 1;

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29 gui State = struct('gui Name', mfilename, ...30 'gui Singleton', gui Singleton, ...31 'gui OpeningFcn', @SelectData OpeningFcn, ...32 'gui OutputFcn', @SelectData OutputFcn, ...33 'gui LayoutFcn', [] , ...34 'gui Callback', []);35 if nargin && ischar(varargin{1})36 gui State.gui Callback = str2func(varargin{1});37 end38

39 if nargout40 [varargout{1:nargout}] = gui mainfcn(gui State, varargin{:});41 else42 gui mainfcn(gui State, varargin{:});43 end44 % End initialization code - DO NOT EDIT45

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47 % --- Executes just before SelectData is made visible.48 function SelectData OpeningFcn(hObject, eventdata, handles, varargin)49 % This function has no output args, see OutputFcn.50 % hObject handle to figure51 % eventdata reserved - to be defined in a future version of MATLAB52 % handles structure with handles and user data (see GUIDATA)53 % varargin command line arguments to SelectData (see VARARGIN)54 handles.filelist=[];55 guidata(hObject,handles);56

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58 % Choose default command line output for SelectData59 handles.output = hObject;60

61 % Update handles structure62 guidata(hObject, handles);63

64 % UIWAIT makes SelectData wait for user response (see UIRESUME)65 % uiwait(handles.figure1);66

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68 % --- Outputs from this function are returned to the command line.69 function varargout = SelectData OutputFcn(hObject, eventdata, handles)70 % varargout cell array for returning output args (see VARARGOUT);71 % hObject handle to figure72 % eventdata reserved - to be defined in a future version of MATLAB73 % handles structure with handles and user data (see GUIDATA)74

75 % Get default command line output from handles structure76 varargout{1} = handles.output;77

78

79 % --- Executes on button press in Load.80 function Load Callback(hObject, eventdata, handles)81 % hObject handle to Load (see GCBO)82 % eventdata reserved - to be defined in a future version of MATLAB83 % handles structure with handles and user data (see GUIDATA)84

85

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86 %check checkboxes87 check=zeros(1,19);88 check(1)=get(handles.angles,'value');89 check(2)=get(handles.IntegrationTimes,'value');90 check(3)=get(handles.BIntegrationTimes,'value');91 check(4)=get(handles.Diode1,'value');92 check(5)=get(handles.Bdiode1,'value');93 check(6)=get(handles.Diode2,'value');94 check(7)=get(handles.Bdiode2,'value');95 check(8)=get(handles.Pressure1,'value');96 check(9)=get(handles.Bpressure1,'value');97 check(10)=get(handles.Pressure2,'value');98 check(11)=get(handles.Bpressure2,'value');99 check(12)=get(handles.Measured,'value');

100 check(13)=get(handles.Background,'value');101 check(14)=get(handles.MeasuredPerSecond,'value');102 check(15)=get(handles.BackgroundPerSecond,'value');103 check(16)=get(handles.MeasuredB,'value');104 check(17)=get(handles.MeasuredDiode,'value');105 check(18)=get(handles.BackgroundDiode,'value');106 check(19)=get(handles.MeasuredBDiode,'value');107

108

109 %load in data from .mat files110 for i=1:length(handles.filelist)111 load(handles.filelist{i});112 angles(i,:)=data(1,:);113 IntegrationTimes(i,:)=data(2,:);114 BIntegrationTimes(i,:)=data(3,:);115 Diode1(i,:)=data(4,:);116 Bdiode1(i,:)=data(5,:);117 Diode2(i,:)=data(6,:);118 Bdiode2(i,:)=data(7,:);119 Pressure1(i,:)=data(8,:);120 Bpressure1(i,:)=data(9,:);121 Pressure2(i,:)=data(10,:);122 Bpressure2(i,:)=data(11,:);123 Measured(i,:)=data(12,:);124 Background(i,:)=data(13,:);125 MeasuredPerSecond(i,:)=data(14,:);126 BackgroundPerSecond(i,:)=data(15,:);127 MeasuredB(i,:)=data(16,:);128 MeasuredDiode(i,:)=data(17,:);129 BackgroundDiode(i,:)=data(18,:);130 MeasuredBDiode(i,:)=data(19,:);131 end132

133 %load data to workspace dependent on checked boxes134 if check(1)==1;135 assignin('base','angles',angles);136 end137 if check(2)==1;138 assignin('base','IntegrationTimes',IntegrationTimes);139 end140 if check(3)==1;141 assignin('base','BIntegrationTimes',BIntegrationTimes);142 end

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143 if check(4)==1;144 assignin('base','Diode1',Diode1);145 end146 if check(5)==1;147 assignin('base','Bdiode1',Bdiode1);148 end149 if check(6)==1;150 assignin('base','Diode2',Diode2);151 end152 if check(7)==1;153 assignin('base','Bdiode2',Bdiode2);154 end155 if check(8)==1;156 assignin('base','Pressure1',Pressure1);157 end158 if check(9)==1;159 assignin('base','Bpressure1',Bpressure1);160 end161 if check(10)==1;162 assignin('base','Pressure2',Pressure2);163 end164 if check(11)==1;165 assignin('base','Bpressure2',Bpressure2);166 end167 if check(12)==1;168 assignin('base','Measured',Measured);169 end170 if check(13)==1;171 assignin('base','Background',Background);172 end173 if check(14)==1;174 assignin('base','MeasuredPerSecond',MeasuredPerSecond);175 end176 if check(15)==1;177 assignin('base','BackgroundPerSecond',BackgroundPerSecond);178 end179 if check(16)==1;180 assignin('base','MeasuredB',MeasuredB);181 end182 if check(17)==1;183 assignin('base','MeasuredDiode',MeasuredDiode);184 end185 if check(18)==1;186 assignin('base','BackgroundDiode',BackgroundDiode);187 end188 if check(19)==1;189 assignin('base','MeasuredBDiode',MeasuredBDiode);190 end191

192 %load list of filelist to workspace.193 assignin('base','Files',handles.filenames);194

195 guidata(hObject,handles);196 %close GUI197 close(SelectData)198

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207 % --- Executes on selection change in Files.208 function Files Callback(hObject, eventdata, handles)209 % hObject handle to Files (see GCBO)210 % eventdata reserved - to be defined in a future version of MATLAB211 % handles structure with handles and user data (see GUIDATA)212

213 % Hints: contents = cellstr(get(hObject,'String')) returns Files contents as214 % cell array215 % contents{get(hObject,'Value')} returns selected item from Files216

217

218 % --- Executes during object creation, after setting all properties.219 function Files CreateFcn(hObject, eventdata, handles)220 % hObject handle to Files (see GCBO)221 % eventdata reserved - to be defined in a future version of MATLAB222 % handles empty - handles not created until after all CreateFcns called223

224 % Hint: listbox controls usually have a white background on Windows.225 % See ISPC and COMPUTER.226 if ispc && isequal(get(hObject,'BackgroundColor'),227 get(0,'defaultUicontrolBackgroundColor'))228 set(hObject,'BackgroundColor','white');229 end230

231

232 % --- Executes on button press in add.233 function add Callback(hObject, eventdata, handles)234 % hObject handle to add (see GCBO)235 % eventdata reserved - to be defined in a future version of MATLAB236 % handles structure with handles and user data (see GUIDATA)237

238

239 % --- Executes on selection change in FilesToLoad.240 function FilesToLoad Callback(hObject, eventdata, handles)241 % hObject handle to FilesToLoad (see GCBO)242 % eventdata reserved - to be defined in a future version of MATLAB243 % handles structure with handles and user data (see GUIDATA)244

245 % Hints: contents = cellstr(get(hObject,'String')) returns FilesToLoad contents246 % as cell array247 % contents{get(hObject,'Value')} returns selected item from FilesToLoad248

249

250 % --- Executes during object creation, after setting all properties.251 function FilesToLoad CreateFcn(hObject, eventdata, handles)252 % hObject handle to FilesToLoad (see GCBO)253 % eventdata reserved - to be defined in a future version of MATLAB254 % handles empty - handles not created until after all CreateFcns called255

256 % Hint: listbox controls usually have a white background on Windows.

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257 % See ISPC and COMPUTER.258 if ispc && isequal(259 get(hObject,'BackgroundColor'),260 get(0,'defaultUicontrolBackgroundColor'))261 set(hObject,'BackgroundColor','white');262 end263

264

265 % --- Executes on button press in Remove.266 function Remove Callback(hObject, eventdata, handles)267 % hObject handle to Remove (see GCBO)268 % eventdata reserved - to be defined in a future version of MATLAB269 % handles structure with handles and user data (see GUIDATA)270

271

272 % --- Executes on button press in Select.273 function Select Callback(hObject, eventdata, handles)274 % hObject handle to Select (see GCBO)275 % eventdata reserved - to be defined in a future version of MATLAB276 % handles structure with handles and user data (see GUIDATA)277

278 %select files to load in.279 file=uipickfiles('FilterSpec','Z:/Dusty Plasmas/Light Scattering/280 * data.mat','prompt','Select folder to search for data');281 handles.filelist=[handles.filelist file];282 %show file names not full path283 handles.filenames=[];284 for i = 1: length(handles.filelist)285 a=handles.filelist{i};286 b=find(a=='\');287 c=a(b(length(b))+1:length(a));288 handles.filenames= [handles.filenames; {c}];289 end290 %show file names in listbox291 set(handles.Files,'string',handles.filenames);292

293 guidata(hObject, handles);294

295

296

297 % --- Executes on button press in angles.298 function angles Callback(hObject, eventdata, handles)299 % hObject handle to angles (see GCBO)300 % eventdata reserved - to be defined in a future version of MATLAB301 % handles structure with handles and user data (see GUIDATA)302

303 % Hint: get(hObject,'Value') returns toggle state of angles304

305

306 % --- Executes on button press in IntegrationTimes.307 function IntegrationTimes Callback(hObject, eventdata, handles)308 % hObject handle to IntegrationTimes (see GCBO)309 % eventdata reserved - to be defined in a future version of MATLAB310 % handles structure with handles and user data (see GUIDATA)311

312 % Hint: get(hObject,'Value') returns toggle state of IntegrationTimes313

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314

315 % --- Executes on button press in Diode1.316 function Diode1 Callback(hObject, eventdata, handles)317 % hObject handle to Diode1 (see GCBO)318 % eventdata reserved - to be defined in a future version of MATLAB319 % handles structure with handles and user data (see GUIDATA)320

321 % Hint: get(hObject,'Value') returns toggle state of Diode1322

323

324 % --- Executes on button press in Diode2.325 function Diode2 Callback(hObject, eventdata, handles)326 % hObject handle to Diode2 (see GCBO)327 % eventdata reserved - to be defined in a future version of MATLAB328 % handles structure with handles and user data (see GUIDATA)329

330 % Hint: get(hObject,'Value') returns toggle state of Diode2331

332

333 % --- Executes on button press in Pressure1.334 function Pressure1 Callback(hObject, eventdata, handles)335 % hObject handle to Pressure1 (see GCBO)336 % eventdata reserved - to be defined in a future version of MATLAB337 % handles structure with handles and user data (see GUIDATA)338

339 % Hint: get(hObject,'Value') returns toggle state of Pressure1340

341

342 % --- Executes on button press in Pressure2.343 function Pressure2 Callback(hObject, eventdata, handles)344 % hObject handle to Pressure2 (see GCBO)345 % eventdata reserved - to be defined in a future version of MATLAB346 % handles structure with handles and user data (see GUIDATA)347

348 % Hint: get(hObject,'Value') returns toggle state of Pressure2349

350

351 % --- Executes on button press in Measured.352 function Measured Callback(hObject, eventdata, handles)353 % hObject handle to Measured (see GCBO)354 % eventdata reserved - to be defined in a future version of MATLAB355 % handles structure with handles and user data (see GUIDATA)356

357 % Hint: get(hObject,'Value') returns toggle state of Measured358

359

360 % --- Executes on button press in MeasuredPerSecond.361 function MeasuredPerSecond Callback(hObject, eventdata, handles)362 % hObject handle to MeasuredPerSecond (see GCBO)363 % eventdata reserved - to be defined in a future version of MATLAB364 % handles structure with handles and user data (see GUIDATA)365

366 % Hint: get(hObject,'Value') returns toggle state of MeasuredPerSecond367

368

369 % --- Executes on button press in MeasuredDiode.370 function MeasuredDiode Callback(hObject, eventdata, handles)

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371 % hObject handle to MeasuredDiode (see GCBO)372 % eventdata reserved - to be defined in a future version of MATLAB373 % handles structure with handles and user data (see GUIDATA)374

375 % Hint: get(hObject,'Value') returns toggle state of MeasuredDiode376

377

378 % --- Executes on button press in MeasuredB.379 function MeasuredB Callback(hObject, eventdata, handles)380 % hObject handle to MeasuredB (see GCBO)381 % eventdata reserved - to be defined in a future version of MATLAB382 % handles structure with handles and user data (see GUIDATA)383

384 % Hint: get(hObject,'Value') returns toggle state of MeasuredB385

386

387 % --- Executes on button press in BIntegrationTimes.388 function BIntegrationTimes Callback(hObject, eventdata, handles)389 % hObject handle to BIntegrationTimes (see GCBO)390 % eventdata reserved - to be defined in a future version of MATLAB391 % handles structure with handles and user data (see GUIDATA)392

393 % Hint: get(hObject,'Value') returns toggle state of BIntegrationTimes394

395

396 % --- Executes on button press in Bdiode1.397 function Bdiode1 Callback(hObject, eventdata, handles)398 % hObject handle to Bdiode1 (see GCBO)399 % eventdata reserved - to be defined in a future version of MATLAB400 % handles structure with handles and user data (see GUIDATA)401

402 % Hint: get(hObject,'Value') returns toggle state of Bdiode1403

404

405 % --- Executes on button press in Bdiode2.406 function Bdiode2 Callback(hObject, eventdata, handles)407 % hObject handle to Bdiode2 (see GCBO)408 % eventdata reserved - to be defined in a future version of MATLAB409 % handles structure with handles and user data (see GUIDATA)410

411 % Hint: get(hObject,'Value') returns toggle state of Bdiode2412

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414 % --- Executes on button press in Bpressure2.415 function Bpressure2 Callback(hObject, eventdata, handles)416 % hObject handle to Bpressure2 (see GCBO)417 % eventdata reserved - to be defined in a future version of MATLAB418 % handles structure with handles and user data (see GUIDATA)419

420 % Hint: get(hObject,'Value') returns toggle state of Bpressure2421

422

423 % --- Executes on button press in Background.424 function Background Callback(hObject, eventdata, handles)425 % hObject handle to Background (see GCBO)426 % eventdata reserved - to be defined in a future version of MATLAB427 % handles structure with handles and user data (see GUIDATA)

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428

429 % Hint: get(hObject,'Value') returns toggle state of Background430

431

432 % --- Executes on button press in BackgroundPerSecond.433 function BackgroundPerSecond Callback(hObject, eventdata, handles)434 % hObject handle to BackgroundPerSecond (see GCBO)435 % eventdata reserved - to be defined in a future version of MATLAB436 % handles structure with handles and user data (see GUIDATA)437

438 % Hint: get(hObject,'Value') returns toggle state of BackgroundPerSecond439

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441 % --- Executes on button press in MeasuredBDiode.442 function MeasuredBDiode Callback(hObject, eventdata, handles)443 % hObject handle to MeasuredBDiode (see GCBO)444 % eventdata reserved - to be defined in a future version of MATLAB445 % handles structure with handles and user data (see GUIDATA)446

447 % Hint: get(hObject,'Value') returns toggle state of MeasuredBDiode448

449

450 % --- Executes on button press in BackgroundDiode.451 function BackgroundDiode Callback(hObject, eventdata, handles)452 % hObject handle to BackgroundDiode (see GCBO)453 % eventdata reserved - to be defined in a future version of MATLAB454 % handles structure with handles and user data (see GUIDATA)455

456 % Hint: get(hObject,'Value') returns toggle state of BackgroundDiode457

458

459 % --- Executes on button press in Bpressure1.460 function Bpressure1 Callback(hObject, eventdata, handles)461 % hObject handle to Bpressure1 (see GCBO)462 % eventdata reserved - to be defined in a future version of MATLAB463 % handles structure with handles and user data (see GUIDATA)464

465 % Hint: get(hObject,'Value') returns toggle state of Bpressure1

B Matlab Scattermatrix script

This Matlab script will calculate the scatter matrix S1 based on equation 16. From this aplot can be created which shows the theoretical expected intensity for a well defined particlesradius.

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3 %input4 theta=transpose(0:pi/320:pi);5 theta1=(-(16/18)*pi:(32/18)*pi/640:(16/18)*pi);6 m=1.68+0.00000002i;7 a=2.4e-6;8 r=a;

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9 labda=532e-9;10 k=2*pi/labda;11 x=a*2*pi/labda;12 %factor van bolgolf13 bol=exp(1j*k*r)/(-1j*k*r);14

15 %determine stopcreterion according to Bohren and Huffman16 n=round(x + 4*xˆ(1/3)+2);17

18 %calculate scatter coefficients19 [an, bn]=scattercoefficients(x,m,n);20

21 [l, w] = size(theta);22

23 %calculate angle dependent functions24 [pin, taun]=pitau(theta,n);25

26 %Calculate factors27 fac=(2*(1:n)+1)./((1:n).*((1:n)+1));28

29 %expand vectors as arrays to allow multiplication with angledependent30 %functions31 an=repmat(an',1,l);32 bn=repmat(bn',1,l);33 fac=repmat(fac',1,l);34

35 %calculate full sum36 S1n=fac.*(an.*pin+bn.*taun);37 S2n=fac.*(bn.*pin+an.*taun);38

39 S1=sum(S1n)';40 S2=sum(S2n)';41

42 %cross sections43 Csca=2*pi/(2*pi/532e-9)ˆ2*sum((2*(1:n)+1)'.*(abs(an(:,1)).ˆ2+abs(bn(:,1)).ˆ2))44 Cext=2*pi/(2*pi/532e-9)ˆ2*sum((2*(1:n)+1)'.*real(an(:,1)+bn(:,1)))45

46 %intensity plot47 figure, semilogy(theta*180/pi,abs(S1).ˆ2)48

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50 Cabs=Cext-Csca51

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53 %-180tm18054

55 w=transpose(S1);56 w1=fliplr(w);57 w11=w1(:,1:320);58 W=[w11 w];59 figure, semilogy(theta1*180/pi,abs(W).ˆ2)

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