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Particulate Matter Counter

Alankar Gupta

B.TECH. – 4th year, Engineering Physics

IIT Guwahati

Arul Goutham

B.TECH. – 4th

year, Electricals and Electronics Engineering

NIT Tiruchirapalli

Project Mentor:

Prof. Navakant Bhat

Department of Electronics and Communication Engineering

Indian Institute of Science, Bangalore July - 2011

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ACKNOWLEDGEMENT

We wish to express our deep gratitude to our project mentor, Prof. Navakant Bhat for

providing us an opportunity to work under his expert guidance. We would also like to thank

Mr. Amit Kumar Gupta for guiding and directing us throughout the project work at each

and every possible step.

A debt of gratitude to Mr.Dwarkanath and Mrs. Subhashini for their assistance and support

during the course of our project.

The work mentioned in this report was carried out at Characterization Lab - II,

Microelectronics and Photonics Building, Department of Electronics and Communication

(ECE), IISc- Bangalore.

- Alankar and Arul

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Contents

List of figures 4

Particulate Matter 5

Scattering Theories 6

Proposition on how to count particulate matter 11

Experimental Setup 12

Opacity experiment: 13

90 deg scattering: 14

Details of Photodiode and Laser diode used 18

Numerical Method: 19

Observations and Inferences 23

Proposed calibration method: 26

Conclusions 27

References 28

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List of figures

1. Light scattering by an induced dipole moment due to an incident EM wave

2. Schematic showing scattering angle w.r.t incident beam

3. Normalized scattering pattern of particles of various sizes in Log scale

4. Setup showing Laser Diode (bottom), sampling tube (center) and Photodiode (left).

5. Setup while calibrating the size of laser beam falling on the sampling area.

6. Rough Schematic of opacity experiment

7. Rough schematic of 90 deg scattering experiment

8. Voltage (v) of PD Vs Samples taken in the absence of blower at 90deg to sample area.

9. Setup with the new Exhaust mechanism – consists of a funnel arrangement and

blower.

10. Voltage of PD Vs samples taken in presence of blower run at lower speed.

11. Voltage of PD Vs samples taken in presence of blower run at higher speed.

12. APC LD ADL-65075TA2 circuit with POT attached to terminal 3.

13. PD OPT101 circuit used to detect scattering.

14. Chi-square method to determine particle size

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Particulate Matter

Particulates – also known as particulate matter (PM), fine particles, and soot – are tiny

subdivisions of solid matter suspended in a gas or liquid. In contrast, aerosol refers to

particles and/or liquid droplets and the gas together. Sources of particulate matter can be

manmade or natural. Air pollution and water pollution can take the form of solid particulate

matter, or be dissolved [1].Salt is an example of a dissolved contaminant in water, while sand

is generally a solid particulate.

Classification and Composition

PM is classified according to the aerodynamic diameter, which is a physical property of a

particle in a viscous fluid such as air. In general, particles have irregular shapes with actual

geometric diameters that are difficult to measure. Aerodynamic diameter is an expression

of a particle's aerodynamic behaviour as if it were a perfect sphere with unit-density and

diameter equal to the aerodynamic diameter. Such a model has the same terminal settling

velocity.

Fraction Size range

PM10 (thoracic fraction) <=10 μm

PM2.5 (respirable fraction) <=2.5 μm

PM1 <=1 μm

Ultrafine (UFP or UP) <=0.1 μm

PM10-PM2.5 (coarse fraction) 2.5 μm – 10 μm

Table. 1 Particulate Matter classification

Coarse particles (PM10) have an aerodynamic diameter between 2.5µ m and 10µ m. They are

formed by mechanical disruption (e.g. crushing, grinding, abrasion of surfaces); evaporation

of sprays, and suspension of dust. PM10 is composed of aluminosilicate and other oxides of

crustal elements, and major sources including fugitive dust from roads, industry, agriculture,

construction and demolition, and fly ash from fossil fuel combustion. The lifetime of PM10 is

from minutes to hours, and its travel distance varies from <1km to 10 km.

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Fine particles have an aerodynamic diameter less than 2.5µ m (PM2.5). They differ from

PM10 in origin and chemistry. These particles are formed from gas and condensation of high-

temperature vapours during combustion, and they are composed of various combinations of

sulfate compounds, nitrate compounds, carbon compounds, ammonium, hydrogen ion,

organic compounds, metals (Pb, Cd, V, Ni, Cu, Zn, Mn, and Fe), and particle bound water.

The major sources of PM2.5 are fossil fuel combustion, vegetation burning, and the smelting

and processing of metals. Their lifetime is from days to weeks and travel distance ranges

from 100s to >1000s km. In addition, fine particles are associated with decreased visibility

(haze) impairment in many cities of the U.S.

Physical properties and physiological effects

The capacity of particulate matter to produce adverse health effects in humans depends on its

deposition in the respiratory tract. Particle size, shape, and density affect deposition rates.

The most important characteristics influencing the deposition of particles in the respiratory

system are size and aerodynamic properties. Particles between 2.5 and 10µ m in aerodynamic

diameter correspond to the inhalable particles capable to be deposited in the upper respiratory

tract. Particles with aerodynamic diameter smaller than 2.5µ m (PM2.5) correspond to the

respirable particle fraction capable of penetrating the alveolar region of the lung. Inhaled

particles come in contact with surface of the respiratory system. These particles pass the

proximal airway (throat and larynx) of the respiratory tract, and deposit in the

tracheobronchial conductive airway of the lungs (bronchial and bronchiolar airway) or in the

gas exchange region (respiratory bronchioles, alveolar ducts, and alveoli of the lung

parenchyma).

Scattering theories

The scattering of light may be thought of as the redirection of light that takes place when an

electromagnetic (EM) wave (i.e. an incident light ray) encounters an obstacle or non-

homogeneity, in our case the scattering particle. As the EM wave interacts with the discrete

particle, the electron orbits within the particle’s constituent molecules are perturbed

periodically with the same frequency (νo) as the electric field of the incident wave. The

oscillation or perturbation of the electron cloud results in a periodic separation of charge

within the molecule, which is called an induced dipole moment. The oscillating induced

dipole moment is manifest as a source of EM radiation, thereby resulting in scattered light.

The majority of light scattered by the particle is emitted at the identical frequency (νo) of the

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incident light, a process referred to as elastic scattering. In summary, the above comments

describe the process of light scattering as a complex interaction between the incident EM

wave and the molecular/atomic structure of the scattering object; hence light scattering is not

simply a matter of incident photons or EM waves “bouncing” off the surface of an

encountered object.

Fig. 1 Light scattering by an induced dipole moment due to an incident EM wave

Formal light scattering theory may be categorized in terms of two theoretical frameworks.

One is the theory of Rayleigh scattering (after Lord Rayleigh) that is, strictly speaking as

originally formulated, applicable to small, dielectric (non-absorbing), spherical particles. The

second is the theory of Mie scattering (after Gustav Mie) that encompasses the general

spherical scattering solution (absorbing or non-absorbing) without a particular bound

onparticle size. Accordingly, Mie scattering theory has no size limitations and converges to

the limit of geometric optics for large particles. Mie theory, therefore, may be used for

describing most spherical particle scattering systems, including Rayleigh scattering.

However, Rayleigh scattering theory is generally preferred if applicable, due to the

complexity of the Mie scatteringformulation [3]. The criteria for Rayleigh scattering is that

α<<1 and |m|<<1, where α is the dimensionless size parameter given by the expression

where a is the spherical particle radius, and λ is the relative scattering wavelength defined as

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where λo is the incident wavelength with respect to vacuum, and mo represents the refractive

index of the surrounding medium. Finally, m is the refractive index of the scattering particle,

and is commonly represented by the complex notation defined as

In this notation, n indicates the refraction of light (i.e. n equals the speed of light in vacuum

divided by the speed of light in the material), while the complex term is related to absorption.

The commonly used absorption coefficient of the material (cm-1

) is related to the complex

part of the refractive index via the relation

It is noted that the value of k is never exactly zero for any material, but materials with a

value approaching zero are termed dielectrics. The magnitude of the refractive index, |m| , as

needed for the Rayleigh criteria, is given by the expression

The Rayleigh criteria as related above, namely α<<1 and lml<<1, correspond physically to

the assumptions that the particle is sufficiently small such that the particle encounters a

uniform electric field at any moment, accordingly the time for penetration of the electric field

is much less than the period of oscillation of the EM wave. In our case mo = 1 (air)

For our Particle size calculation the size parameter ranges from 48- 12 (for PM10 and PM2.5 ).

Hence Rayleigh criteria is not applicable and we are bound to use the complete MIE theory.

MIE Theory is a pretty complex mathematical theory describing the complete profile of

scattering but has some essential condition which needs to be fulfilled –

Incident light of only a single wavelength is considered.

No dynamic scattering effects are considered.

The scattering particle is isotropic.

There is no multiple scattering.

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All particles are spheres.

All particles have the same optical properties.

Light energy may be lost to absorption by the particles.

For developing the algorithm for our particle size calculation we will be only touching the

essential parts of the Mie theory which is helpful in serving our purpose. We will not go into

details of calculation of scattering cross sections and many more unnecessary things.

1. Calculation of the complex Mie coefficients -

The Ricatti-Bessel functions Ψ and ξ are defined in terms of the half-integer-order Bessel

function of the first kind (Jn+1/2 (z)), where

The parameter ξn is given by the expression,

where Hn+1/2(z) is the half-integer-order Hankel function of the second kind, where the

parameter Xn is defined in terms of the half-integer-order Bessel function of the second kind,

Yn+1/2(z), Namely

2. With the help of Mie coefficients calculated above we can further calculate Mietheory

scattering amplitudes,

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Where Ɵ is the angle between the incident ray and the scattered ray called the scattering

angle.

Fig. 2 Schematic showing scattering angle w.r.t incident beam

The values of an and bn are same as defined earlier and the angular dependent functions πn and

τn are expressed in terms of the Legendre polynomials by

Now For a randomly polarized light source, the total scattered light intensity is given by the

term S11:

So now in the end we got S11 as a function of Ɵ (scattering angle). In this derivation of S11 we

are not bothered about the exact magnitude rather we are more concerned about the relative

distribution across the various Ɵ values. So we can just normalize the scattering profile with

some known value and then compare the scattering pattern for various particle size.

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Proposition on how to count particulate matter

In order to determine the concentration of PM in air sample, we first need to determine the

size of particle. From the scattering theories, it is clear that scattering pattern of light largely

depends on shape, size and optical properties of the particle scattering light. We could very

well assume PM in air (like smoke) to be a sphere of fixed refractive index [2]. With this

assumption, the parameter affecting light scattering is the size of the particle. As explained

earlier, we can obtain Mie pattern for various particle sizes theoretically by employing the

rigorous mathematical equations developed above.

Diameter 1µm Diameter 2.5µm

Diameter 10µm Diameter 20µm

Fig. 3 Normalized scattering pattern of particles of various sizes in Log scale

We can also obtain scattering pattern experimentally by measuring intensity at various angles

around the sampling area. This intensity pattern needs to be normalised for comparison with

the theoretical pattern. We then compare both the patterns for resemblance and hence

establish the particle size from it. This would require some kind of arrangement for

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measuring intensity at multiple angles but later in this report we have proposed a way to

eliminate this need.

Once we have determined the particle size, we can proceed to find the concentration of the

same. For this we propose to use a constant volume pump which delivers quite stable flow

rate of air. The density of PM in air is usually less and we can obtain single particle scattering

all the time. We get pulses of light and we can categorise them by proper matching. With the

fixed flow rate, we can also get the volume of air flowing or which is being sampled. With

these two data in hand, we can easily obtain the type of particle and its concentration in air.

The variations in intensity are very close to each other for angles close to each other. Even a

slight error in our setup or misalignment in detector optics can make our result totally wrong.

This drawback can be overcome by the use of mirror. The idea is to place our light sensor at

a fixed angle and then use an elliptical mirror which will collect scattered light over an angle

range and focus it to our sensor hence giving us a sum of amplitudes within that angle range.

We can calibrate this setup for various reference particle sizes and hence obtain the count as

well as its size.

Experimental Setup

A rudimentary experimental setup was designed to test our proposition on determining

particle size. To test our proposition we first needed to establish two points – 1. We should be

able to detect light scattering using the equipments we had in hand. 2. We should be able to

detect various densities of smoke using them. On establishing these two points, we can

proceed to determine particle size by our proposition using a better design.

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Fig. 4 Setup showing Laser Diode (bottom), sampling tube (center) and Photodiode (left).

Fig. 5 Setup while calibrating the size of laser beam falling on the sampling area.

Opacity experiment:

The Photodiode (PD) was placed in line with the collimating lens and Laser diode (LD).

Without the absence of sample, the PD reads high voltage. On introduction of sample

(Incense smoke), the particle scatters light in all directions thus reducing the intensity of light

falling on photodiode.

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Fig. 6 Rough Schematic of opacity experiment

We used photodiode OPT101 and APC laser diode ADL-65075TA2. We met with success in

this experiment. The major problem in this experimental setup is that the PD quickly reaches

saturation and changes in voltage with scattering are difficult to observe. We needed to

constantly tune the power output of LD to obtain observable changes in PD voltage.

90 deg scattering:

Fig. 7 Rough schematic of 90 deg scattering experiment

We next placed the PD 90 deg to the sampling area. This avoids several problems with the

initial experiment- 1. PD doesn’t reach saturation. 2. LD can be operated at high power

(intense beam). 3. Multiple interactions of smoke particles with the light beam is avoided.

Without the absence of sample, the PD read a low voltage. This could be attributed to the

stray light falling on PD. It can also be observed from fig.2 on the left and right wall of the

cardboard box some reflections of laser beam. This can only be avoided by using a

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slit/cylinder kind of arrangement in front of the collimating lens. On introducing sample, the

PM scatters light in all directions and we could observe a rise in voltage of PD.

Fig. 8 Voltage (v) of PD Vs Samples taken in the absence of blower at 90deg to sample area.

From the plot we could infer that,

1. There are too many oscillations in the voltage of PD (sampled every 0.5 sec) due to

the unsteady flow of smoke through the sample area.

2. We can clearly differentiate between the absence and presence of smoke with proper

sampling mechanism.

3. We might also need to sample the voltage of PD at a faster rate. It would be better to

use an oscilloscope than a multimeter.

4. We needed to reduce oscillations in voltage before measuring intensities at various

positions for particle size measurement.

We next fitted a exhaust mechanism to our present setup to have a steady smoke flow through

the sample area.

0 10 20 30 40 50 60 70 80 90 1000.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

samples

Voltage v

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Fig. 9 Setup with the new Exhaust mechanism – consists of a funnel arrangement and blower.

The blower used had only two levels of speed. Repeating the experiment at the two speed ,

we were able to get improved results, lesser oscillations in voltage.

Fig. 10 Voltage of PD Vs samples taken in presence of blower run at lower speed.

0 10 20 30 40 50 60 70 80 90 100

0.16

0.18

0.2

0.22

0.24

0.26

0.28

samples

Voltage (

V)

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Fig. 11 Voltage of PD Vs samples taken in presence of blower run at higher speed.

From these plots,

1. We could see the reduction in oscillations of PD voltage. From fig.6 the oscillation is

about 0.04-0.06 V whereas in fig.7 oscillations were around 0.4 V.

2. We could clearly differentiate between the presence and absence of smoke at all

instants except for few when the voltage drops to base value.

We used photodiode OPT101 and APC laser diode ADL-65075TA2 to obtain these plots.

0 10 20 30 40 50 60 70 80 90 100

0.35

0.4

0.45

0.5

0.55

0.6

samples

Voltage (

v)

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Details of Photodiode and Laser diode used

Laser diode ADL-65075TA2 comes with automatic power control. By varying the resistance

of TrimPot attached to terminal 3 of LD we can get various output power from LD.

Fig. 12 APC LD ADL-65075TA2 circuit with POT attached to terminal 3.

We used a 10 K ohm POT. Usually operated at 4-5 K ohm. The maximum output power with

this LD is 10 mW. For more intense (power) beam we used Sanyo red laser diode DL-6147-

040 with Edmund optics laser driver demo module #56-805 and Edmund optics driver chip

#56-804. We could achieve a power output of 40 mW with this setup.

Photodiode we used in all our experiments were OPT101 Ic. We occasionally used

Hamamatsu Photodiode which has more sensitivity (in the nW range) as compared to

OPT101 (in the micro watt range). This was due to fact that the oscillations we initially

obtained with the setup was too high to use a more sensitive PD (it would just give more

voltage fluctuation).

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Fig. 13 PD OPT101 circuit used to detect scattering.

We tried with different Rext and Cext values to improve the responsivity of PD once the

oscillations have been reduced.

We also carried out the experiment with different beam widths at sample area.

Numerical Method:

As explained in our proposition, we need to match the theoretical and experimental graphs in

order to determine the particle size. The necessity to measure at different angles before going

for single angle measurement has already been explained in the calibration topic (page: ).

There are various numerical techniques to measure the degree of closeness of a curve with a

set of standard curves. The method we have used is Chi-square method [4]. By this method,

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we generate the theoretical values t various angles. We also feed the experimental values

measured at the same angles. The program compares the two values using the formula,

(16)

The minimum value of x2 gives the best fit theoretical curve for the experimental data and

hence the particle size. The transfer function for converting the voltage output of PD to

intensity of light is a linear and can be obtained from the plots provided in the corresponding

PD datasheets.

In order to calculate theoretical Mie plot, we need Mie coefficients an and bn values. We do

so by using equations (1) - (7). We used in-built Bessel functions available in matlab. The

initial conditions n=0 has been taken care [5]. We calculated it using recursive functions.

function coeff=zerocool_anbn(x,m) % to calculate coefficients an,bn

inputs: x- size parameter & m- complex refractive index

nmax=round(x+2+(4*(x)^(1/3))); % calculates max. n req for an &

bn n=1:1:nmax;frac=(n+0.5);c=m*x; sqx=sqrt(pi*0.5/x);sqc=sqrt(pi*0.5/c);

bessjx=besselj(frac,x).*sqx; %calculates spherical bessel

functions of first kind & second kind bessjc=besselj(frac,c).*sqc; bessyx=bessely(frac,x).*sqx;

hx=bessjx+i*(bessyx); %defines hankel functions

bessjxl=[(sin(x))/x,bessjx(1:nmax-1)]; % bessel functions for

order=0 to order=nmax-1 bessjcl=[(sin(c))/c,bessjc(1:nmax-1)]; bessyxl=[(-cos(x))/x,bessyx(1:nmax-1)];

derx=x.*bessjxl-n.*bessjx; %derivative of bessel

functions expanded using recursive formula derc=c.*bessjcl-n.*bessjc;

hxd=bessjxl+i*(bessyxl); derh=x.*hxd-n.*hx;

m2=m*m;

an=(m2.*bessjc.*derx-bessjx.*derc)./(m2.*bessjc.*derh-hx.*derc); %

an bn=(bessjc.*derx-bessjx.*derc)./(bessjc.*derh-hx.*derc);

%bn

coeff=[an;bn];

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We next calculated angular dependent functions πn and τn are using Legendre polynomials.

function angular=zerocool_pitau(u,nmax) %calculates angular

dependent functions pi n and tau n inputs: u= cos(theta) and nmax

%p and t are for pi n and tau n respectively. p(1)=1; p(2)=3*u;t(1)=u;t(2)=6*u*u-3; %defines the initial

conditions for pi n and tau n for n=3:1:nmax pn1=((2*n-1)/(n-1)).*p(n-1); pn2=(n/(n-1)).*p(n-2); p(n)=pn1.*u-pn2; % pi n calculated

using recursive formula

tn1=n.*p(n); tn2=(n+1).*p(n-1); t(n)=tn1.*u-tn2; %tau n calculated

using recursive formula end angular=[p;t];

We use the above two functions to obtain scattering amplitudes S1 and S2.

function s=zerocool_s1s2(m,x,u) % calculates scattering

amplitudes s1 & s2 inputs: complex refractive index % size parameter and

u=cos(theta) theta- scattering angle temp=zerocool_anbn(x,m); % calls an & bn a=temp(1,:); b=temp(2,:);

nmax=round(x+2+(4*(x)^(1/3))); temp1=zerocool_pitau(u,nmax); % calls pi n &

tau n p=temp1(1,:); t=temp1(2,:);

s1=0; s2=0; for n=1:1:nmax s1=s1+((2*n+1)/(n*(n+1)))*(a(n).*p(n)+b(n).*t(n)); %

calculates scattering amplitude - perpendicular s2=s2+((2*n+1)/(n*(n+1)))*(a(n).*t(n)+b(n).*p(n)); %

calculates scattering amplitude - parallel

end s=[s1;s2];

We then obtained the intensity at various angles.

function raiden=zerocool_main(m,x,angledata)

%calculates intensity function and plots intensity versus scattering angle %inputs: complex

refractive index x- scattering parameter step- step size

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n=0;

for i=1:1:length(angledata) n=n+1; temp=zerocool_s1s2(m,x,cos(angledata(i)*pi/180)); s1=temp(1,:); s2=temp(2,:); s12=s1*s1'; s22=s2*s2'; I1(n)=s12; % calculates magnitude of

s1 square I2(n)=s22; % calculates

magnitude of s2 square end I1=I1./max(I1); %theta=0:stepsize:pi; %sum=0; %for n=390:1:612 % sum=sum+(I1(n)+I2(n))./2; %end %plot(theta*(180/pi),I1); % plots I1 versus

theta %sum %polar(theta,I1); %plot(theta*(180/pi),I2); raiden=[I1];

We then employ our Chi-square method to obtain the best fit curve.

function raiden=zerocool_main(m,x,angledata)

%calculates intensity function and plots intensity versus scattering angle %inputs: complex

refractive index x- scattering parameter step- step size

n=0;

for i=1:1:length(angledata) n=n+1; temp=zerocool_s1s2(m,x,cos(angledata(i)*pi/180)); s1=temp(1,:); s2=temp(2,:); s12=s1*s1'; s22=s2*s2'; I1(n)=s12; % calculates magnitude of

s1 square I2(n)=s22; % calculates

magnitude of s2 square end I1=I1./max(I1); %theta=0:stepsize:pi; %sum=0; %for n=390:1:612 % sum=sum+(I1(n)+I2(n))./2; %end %plot(theta*(180/pi),I1); % plots I1 versus

theta

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%sum %polar(theta,I1); %plot(theta*(180/pi),I2); raiden=[I1];

We tested this program by feeding data generated (by means of another program) for various

particle sizes (approx) and checked if the program is able to return a close value.

Fig. 14 Chi-square method to determine particle size

The program was quite accurate and its accuracy greatly dependent on the step size entered

for the size parameter in the program. The smaller the step size, the greater is the accuracy

but more run-time required.

Observations and Inferences

Mie scattering:

Mie scattering assumes single particle scattering i.e. incident light is scattered

by a single sphere and detected. No multiple scatterings are allowed.

Experimentally this can be achieved by having thin volume of air in the path of

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beam. In lab, as we are using incense sticks (which produces dense smoke) we

have to use a variable speed pump to draw it slowly. Practically in the field,

particle concentration is going to be low and it can be fairly assumed to be

single particle scattering. This precaution ensures that the scattering curve we

get is just a multiple of the actual Mie curve.

For size parameter between 0.1<x<100 we use Mie scattering for experiments.

Photodiode:

Keeping a mirror to collect light around 70 to 90 degrees (or in the higher

ranges) could help differentiate particles of 10µm and 2.5 µm. This is due to the

fact that 2.5 µm scatters light in the higher degrees too. The comparison can be

made only upon normalisation if the highest intensities (intensity of incident

beam) are different (usually at 0 deg). The mention of angles here are just to

give an idea. Actual angle needs to be determined. GRIMM also claims that by

proper placing of this mirror any undulations in Mie scattering can be

eliminated to some degree.

It is better to have the window of the photodiode as small as possible. This

ensures high resolution. Hamamatsu photodiode has a smaller window than the

IC version. Further improvement in resolution can also be achieved by closing

the aperture of the diode.

The photodiode can be placed further (not too far) from the point where beam of

light incidents on the particle. This can ensure that laser beam which tends to

diverge (from the datasheet) doesn’t fall on the detector and we observe only the

scattered light. A second collimating lens could also be used for focusing the

beam.

Filters can be used along with photo detectors to remove stray light. It can also

prevent the change in colour (or wavelength) due to motion of the smoke

particles (dynamic light scattering).

The Photo diode should be fast enough to detect pulse of light as it happens. It

is advisable to use an oscilloscope in the measurement of pulses of voltage by

diode as it has a high sampling frequency. In the actual product, we might need

a fast ADC to sample the voltage and provide for further processing.

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A sensitive photodiode should be used. This is necessary as practically the no

of particles in air would be very less and hence the intensity of scattered light.

This again entails use of amplifiers for significant voltage output.

An array of photodiodes may be used for detecting the scattering pattern.

Charge coupled device may be used in place of normal photodiode.

We faced problem of saturation of photodiode on exposure to unscattered

beam. This might occur even if the photodiode is in region of maxima of the

Mie pattern. Two adjustments can be done regarding this: 1. Adjust the

sensitivity of the diode by adding resistors and capacitors (refer datasheet), 2.

The laser diode light can be attenuated.

o It could also be caused by reflection of laser beam from the walls of the

container. Hence a slit kind of arrangement can be placed in front of the

collimating lens of laser diode to prevent any reflection.

Laser diode:

We placed problem of saturation of photodiode on exposure to unscattered

beam. This might occur even if the photodiode is in region of maxima of the

Mie pattern. Two adjustments can be done regarding this: 1. Adjust the

sensitivity of the diode by adding resistors and capacitors (refer datasheet), 2.

The laser diode light can be attenuated.

Constant power of the laser diode can be ensured by using the driver demo

module. Multiplexing of laser diode with two power levels might be required

depending on the size of the particle to be measured.

Polarisers can be used for perpendicular and parallel polarisations.

Sampling:

A fairly wide beam (wide here means some small multiple of actual particle

size) of light can be made to incident on the sample. This ensures parallel rays

of light are incident on each particle.

Steady flow of smoke would be preferable. This in turn could help in

calculating no of particles in certain sample of air using no of pulses.

Stray light needs to be prevented. Cover the entire setup. Even optical fibre

could be used to introduce light on the sample keeping the laser diode out.

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We need not consider the bright spot formed at 0 deg for particles of all size.

Our region of interest should be around the region where light intensity

decreases rapidly. (90 deg). This is the region which shows considerable

changes (oscillations) depending on particle size.

Humidity should be low. Preheating of the sampling air can improve accuracy.

Numerical Methods:

Advanced methods such as Monte Carlo and genetic algorithms are used for

solving the scattering pattern. The method we have used is a simple one and

hence introduces some amount of error in the theoretical calculation of

intensity.

There might be light reflected from the interior of the particle. This might

undergo a change in angle while being received at the detector due to change in

refractive index. This might require correction to be made for theoretical Mie

plot. This is not considered in our program.

Proposed calibration method:

o With the initial setup measurements of intensity can be taken at various

angles and fitted with the Mie curve to determine particle size. This requires

setup of the pump system for steady flow, distance of detector from sample,

lens in front of detector, adjustment of collimating lens for proper size of

beam, adjustment of intensity of laser diode, filters (if necessary) and

attenuation (if necessary). This will ensure that our setup is capable of

producing Mie pattern.

o Later the detector can be fixed at particular angle (90 deg) and calibrated

using test particles and thresholds can be set for each particle. These

thresholds can then be programmed in microprocessor of the actual device.

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o Why this can’t be done at the first place?

It needs to be ensured that the setup (here I mean the various

parameters mentioned above) are right for Mie scattering detection.

It should be made sure that the detector detects only the scattered

light from the sample and not something else.

Conclusions

In future we can follow the suggestions we have mentioned above to obtain an accurate Mie

plot and hence determine the particle size. By replacing the exhaust mechanism with a

constant volume pump, we can eliminate oscillations in PD voltage and also determine the

concentration of PM in air.

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References:

1. Light Scattering Theory – David W.Hahn – Department of Mechanical and

Aerospace,

University of Florida. (dwhahn@ufl.edu)

2. George W. Mulholland, Raymond L. McKenzie, Egon Marx, and

Robert A. Fletcher - Refractive Index and Evaporation Rate of Individual Smoke

Droplet. Langmuir Vol. I, No. 3, 1985 .

3. Lorenz-Mie Scattering

4. Particle size determination: An undergraduate lab in Mie scattering

Weiner, M. Rust, and T. D. Donnell Harvey Mudd College, Department of Physics,

Claremont, California 91711

5. Bohren_C.F.,_Huffman D.R. Absorption and Scattering of Light by

Small_Particles(1983)