Candidate Number: 446163Word Count: 5537

AO09: Retrieving the complex refractive index of volcanic ashfor wavelengths in the visible spectrum

Supervisors: Dr R. G. Grainger & B. E. Reed

To fully exploit the remote sensing technologies that are used to monitor a volcanic eruptionand return information on its plume, the complex refractive index of the ingredient volcanicash is required. This report presents how the complex refractive index was determined for aset of volcanic ash samples taken from various sources, for light at three visible wavelengths(450.0 nm, 546.7 nm and 650.0 nm). With the use of an optical microscope, the Beckeline method was employed to acquire the real part of the refractive index of ash samplestaken from eruptions at Grímsvötn (Iceland), Chaitén (Chile), Etna (Italy), Eyjafjallajökull(Iceland), Tongariro (New Zealand), Askja (Iceland), Nisyros (Greece), Okmok (Alaska),Augustine (Alaska) and Spurr (Alaska). An original method involving the digital analysisof microscopic images of the constituent ash particles was used to derive the imaginarypart of the refractive index of ash samples taken from Grímsvötn, Chaitén, Eyjafjallajökull,Tongariro, Nisyros and Okmok.

1 Introduction

A volcanic eruption has the potential to pose avariety of severe and widespread threats to humanwell-being. Beyond the obvious calamitous effectsto anyone in the immediate vicinity, eruptions arealso known to cause acute respiratory difficulties topeople unfortunate enough to be caught in an ashfall [1]. Furthermore, it is well documented thatthe resulting injection of aerosols into the atmo-sphere is a hazard to civil aviation [2], as well asthe cause of dramatic climatic events [3]. It is im-perative therefore, that we can effectively monitorthese imposing and destructive events.

One way to acquire information on an eruptionis through remote sensing, particularly satellite ob-servation. Images taken from space can cover vastareas and so are able to provide a complete view ofan ash cloud. However, an unfortunate fact of re-mote sensing is that properties of the target are of-ten required before accurate measurements can betaken. To acquire detailed information on a plume,a priori information on the size, shape and opticalproperties of the constituent matter is needed [4].

Volcanic ash is defined as being pyroclasts witha diameter of less than 2 mm. The content of vol-

canic ash depends entirely upon the eruptive pro-cesses in engagement at the time of production, butgenerally it can be said to be made up of a mix-ture of vitric (glass), crystalline and lithic (rock)particles [5]. Volcanic glass is formed from frag-ments of magma which have cooled and solidifiedduring the progression of an eruption. Crystallinematerial grows in the magma beneath the Earth be-fore it is expelled. The rock fragments are presentas a result of being broken off the walls of themagma conduit by the force of the eruptive flow[6]. The myriad of different particles means thatunderstanding the overall optical effect of volcanicash is particularly challenging.

The complex refractive index (m = n+ ik) of asubstance provides information on how it scattersand absorbs radiation but existing measurements ofthis parameter for volcanic ash are very limited.Papers by Patterson give only values of the ima-ginary part of ash from eruptions at Mt. St. Helens[7], El Chichón [8] (both in the spectral range 0.3-0.7 µm) and Mayon [9] (in the spectral range 1-16µm). Krotkov et al. (1999) were able to determineboth the real and imaginary parts for ash from Mt.Spurr at three frequencies in the ultraviolet spec-

1

tral region [10]. Recent progress has been made byGrainger et al. (2013) who were able to retrievethe real and imaginary parts for ash from the 1993eruption of Mt. Aso in the spectral range 1-20 µm[4]. More values of the refractive indices of vol-canic material including basalt [11, 12], andesite[11, 12], pumice [13], obsidian [11] and granite[14] are available. However, these can only everprovide an approximation to real ash. To be able tomake maximum use of satellite imagery and mod-ern precision instruments, the refractive indices ofa range of ashes needs to be determined.

Observing a volcanic plume via satellite is pos-sible as it perturbs the Earth’s radiation fieldthrough absorption and scattering of radiation.Transmission through an optically active mediumis related to its physical properties via Bourguer’sLaw [15]:

T (λ) = e−βext(λ)x (1)

where βext is the volume extinction coefficient.According to Mie theory, it is given by [16]:

βext =

ˆ∞

0Qext (r,m(λ),λ)πr2n(r)dr (2)

where Qext is the extinction efficiency, which canbe calculated with Mie theory from values for theparticle radius, wavelength of light and the com-plex refractive index. The variable n(r) is the num-ber of particles with a given radius and is often as-sumed to conform to a log-normal distribution inthe case of volcanic ash [4]. With knowledge ofthe complex refractive index of ash we gain theability to calculate the extinction coefficient andtherefore an understanding of how radiation is at-tenuated as it passes up from the Earth, through anash cloud and up to a satellite. For visible light,the relative levels of back scattered light can alsobe important. Instruments on board a satellite canmeasure such perturbations in intensity, so by com-paring this to the Earth’s unperturbed field, defin-ing features of the volcanic plume can be determ-ined. One such feature is mass loading (concentra-tion of ash) which is important when determiningwhether a region is safe for a plane to fly through.Francis, Cook and Sanders (2012) describe howthey retrieved the physical properties of ash fromthe 2010 Eyjafjallajökull eruption using data fromthe Meteosat weather satellite, noting their resultswere very sensitive to the choice of the assumed

refractive indices [17]. Without the availability ofa refractive index specific to the ash, they settledon the very general values of andesite [11], a factwhich highlights the relevance and importance ofthis project.

In the following report, an account of the meth-ods used to retrieve the complex refractive indexfor a set of volcanic ash samples is presented. Anapplication of the Becke line method was used toretrieve an overall value of the real part of the re-fractive index for ten ash samples. This method re-quired an optical microscope to inspect the signa-ture movements of light, caused by refraction andinternal reflection, produced when the ash particleswere immersed in a medium of a known refract-ive index and illuminated from below. An originalmethod, involving the measurement and combina-tion of the imaginary part for individual particleswithin a sample, was used to calculate an overallvalue of the imaginary part of the refractive in-dex for six of the ash samples. This method in-volved taking microscopic photographs of the ashsamples, and digitally analysing them to determ-ine the levels of light absorption occurring in theindividual particles. The overall value of the ima-ginary part of the refractive index of a sample wasfound from the absorptive effects of the constituentparticles by volume-averaging. A list of the ashesinvestigated is provided in Table 1, along with thereference numbers by which the samples will bereferred to throughout.

Table 1: Reference table showing the referencenumbers, eruption sources and dates of the vol-canic ash specimens which were examined.

2

2 Background

2.1 The complex refractive index

The complex refractive index, m, describes howlight propagates in a medium and can be expressedas:

m = n+ ik (3)

A plane wave travelling in an homogeneous me-dium with this refractive index may be describedin the form [15]:

E = E0 exp(−2πkz

λ

)exp(

i2πnzλ− iωt

)(4)

where E is the electric field, E0 is the electricfield at z = 0, λ is the wavelength of light in vacuoand ω is the angular frequency of the light. Fromthis, it follows that k, the imaginary part of the re-fractive index, determines the attenuation of waveas it travels through the medium. The real part ofthe refractive index determines the phase velocity,v = c/n, therefore describing how light is refractedwhen entering the medium. From this, the Poynt-ing vector, S = E×H, can be shown to be [15]:

S =12

Re{√

ε

µ

}|E0|2 exp

(−4πkz

λ

)e (5)

where e is the unit vector in the direction of wavepropagation. The magnitude of S is called the irra-diance, I. As the wave progresses through the me-dium without scattering, the irradiance is exponen-tially diminished as described by the Beer-Lambertlaw [15]:

I = I0e−βabsz (6)

where the absorption coefficient is given by:

βabs =4πkλ

(7)

2.2 Absorption & scattering

When considering the absorption and scattering oflight by a particle, the size of the particle relative tothe wavelength of light is of fundamental signific-ance. The regime in which an interaction is takingplace is commonly expressed numerically as a di-mensionless value called the size parameter, x:

x =2πaλ1

(8)

where a is the particle radius (for non-sphericalparticles the radius of a surface-equivalent spherecan be used) and λ is the wavelength of light in thesurrounding medium [18].

Rigorous treatment of the scattering of electro-magnetic radiation by particles can be providedby Mie theory (for spherical particles) or the T-matrix method (for non-spherical particles). How-ever, these techniques are mathematically labori-ous and require forward modelling of the systemand so should be avoided where possible. In thelimit where x→ 0, scattering becomes negligibleand extinction can be said to be due entirely to ab-sorption. This is known as the Raleigh regime. Onthe other hand, as x→∞, geometric optics (ray tra-cing) becomes applicable [18].

Exactly how large or small the particles haveto be in comparison to the incoming light for theabove regimes to become good approximations isnot entirely clear. In section 3.2, the method relieson the validity of the ray tracing approximation.Mishchenko, Travis and Lacis (2008) demonstratethat a reasonable match to Mie and T-matrix meth-ods is achieved by the geometric optics approxim-ation for size parameters of around 120 [18].

3 Project

3.1 Becke line method

The method used to retrieve the real part of refract-ive index was the Becke line test, which is basedon the comparison of the mineral being studied toa mounting medium of a known refractive index.

3.1.1 Method outline

When a fragment of a mineral is immersed in a li-quid of a different refractive index and illuminatedfrom below, the effects of refraction and total in-ternal reflection cause a concentrated band of light(known as the Becke line) to form close to thefragment-liquid interface. This rim of light is ob-servable when such a fragment is viewed, slightlyout of focus, under a microscope. If one were tostart by viewing an immersed grain slightly abovethe focal point of the microscope’s objective lens,and the stage were to be lowered (or equivalently,the focus raised) the Becke line would appear to

3

Figure 1: Ash fragment from the May 2011 eruption of Grímsvötn, Iceland immersed in liquid ofrefractive index n = 1.55 viewed at 546.7 nm. As the stage was lowered (left to right) the Becke linecould be seen entering the fragment, demonstrating that the ash had a higher refractive index than theliquid at this wavelength.

move into the material with the higher refractive in-dex. Nesse (1991) provides a detailed explanationas to why this happens [19]. Therefore, by immers-ing aerosol particles in a series liquids of knownrefractive index and observing in which directionthe Becke line moves when the sample is broughtthrough the focus, it is possible to deduce the re-fractive index of the aerosol particles themselves.

3.1.2 Experimental set-up

The ashes under investigation were compared toa set of Cargille Refractive Index Liquids. Theset of nineteen liquids had a range of n=1.4600to n=1.6400, separated by increments of 0.0100(all with a standard error of ± 0.0002). Thequoted refractive indices were for light of 589.3 nmwavelength at a temperature of 25oC. The Cauchyequations of the liquids were supplied by Cargilleso their refractive indices could be calculated fordifferent frequencies of light. The test was per-formed at three wavelengths: 450.0 nm, 546.7 nmand 650.0 nm. This was accomplished by placingoptical filters, with a bandpass of ±10 nm about thepeak radiance, just above the objective lens of themicroscope. About 3 mg of the ash was immersedin 50 µl of the n = 1.50 liquid and shaken up todisperse the fragments uniformly. This ratio en-sured the fragments were well separated by the li-quid, providing a clear view of the liquid-fragmentboundaries. A couple of drops of the mixture wereplaced on a microscope slide and covered with a

cover slip. The slide was then placed on the micro-scope stage and illuminated from below by whitelight produced by a halogen lamp. One of theabove listed filters was put in place. The samplewas observed with a 20X objective through the mi-croscope eyepiece as well as via a CCD digitalcamera linked up to a computer monitor. To max-imise the contrast and depth of field, and thus pro-duce the most well-defined Becke line possible,the aperture diaphragm was stopped down as muchwould still allow enough illumination for a clearimage of the sample to be seen through the eye-piece [19].

The stage was repeatedly raised and lowered,moving the immersed ash particles through themicroscope’s focus. If the Becke lines movedfrom the fragments into the liquid as the stage waslowered, the ash was noted to have a refractive in-dex lower than 1.50. In this case, a fresh batch ofthe ash would have been immersed in a liquid of alower refractive index and the above process wouldhave been repeated. If the Becke line moved fromthe liquid into the fragments, the ash was noted tohave a higher refractive index than 1.50. In thiscase, a fresh batch of the ash would have beenplaced in a liquid of higher refractive index andthe process would have been repeated. By repeat-ing the process for successive liquids and recordingwhether the ash was of a refractive index whichwas higher or lower than the liquids it had beenplaced in, it was possible to hone in on a value for

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the refractive index of the ash.As the refractive index of the mount became

more closely matched to the ash, the Becke linesbecame fainter. If an almost exact match wasfound, the Becke line would have been be barelyvisible and the fragments would have appeared toblend with the surrounding mixture. If this was thecase for all the particles in view, the ash would beassigned the same refractive index as that of theliquid. If all the Becke lines passed from the frag-ment into the liquid as the stage was lowered forone liquid, but passed from the liquid into the frag-ment when placed in the the incrementally higherliquid, the ash was assigned the refractive indexhalf way between the two liquids.

It was common to see Becke lines passing inopposite directions over the boundary, as well assome blending in for an ash in a specific liquid,indicating the presence of particles of varying re-fractive index. If this was the case a survey of 30particles was taken and the number of particles go-ing in each direction was counted and an averagevalue was calculated. An example distribution isgiven in Table 2.

Table 2: The directions of the Becke line as thestage is lowered in an example ash sample im-mersed in liquids of refractive index 1.59-1.60.

For this example ash, it would be concludedthat 7 particles have a refractive index of 1.595,5 particles have a refractive index of 1.60 and18 particles have a refractive index of 1.605. Aweighted average of these would have been taken,and the ash would have been assigned a refractiveindex of 1.602. Of course, this value would havebeen corrected for the wavelength of light using theCauchy equations of the liquids.

This method returned a value for the real part ofthe refractive index for all ten ash samples.

3.2 Particle absorption method

An original method to combine the individual ab-sorption effects of the particles within the ash

samples to find an overall imaginary part of the re-fractive index was developed and implemented.

Prior knowledge of the value of the real partof the refractive index of each of the ash samplesfor 450.0 nm, 546.7 nm and 650.0 nm light wasrequired for this method, hence why it was per-formed subsequent to the Becke line tests. Again,a wavelength to be studied was selected and thecorresponding filter was placed above the object-ive lens of the microscope.

3.2.1 Method outline

The particles examined with this method had a typ-ical surface-equivalent-sphere radius, rs, between15 µm and 35 µm. The wavelength of light in themedium, λ1 = λ0/n, ranged from 0.26 µm to 0.43µm. Using Equation 8, the size parameter, x, wasbetween 220 and 850. This meant that, accordingto the condition stated in Section 2.2, x was alwayslarge enough for the system to be adequately de-scribed in the geometric optics limit.

In the geometric optics approximation, the pathof a ray between two mediums of different refract-ive index is governed by Snell’s law:

n2 sinθi = n1 sinθt (9)

where n2 is the refractive index of the startingmedium and n1 is the refractive index of the me-dium to which the light is transmitted [15].

The refractive index of the liquid was approx-imately equal to the refractive index of the ashparticles (n2 ' n1) meaning the angle of incidenceand transmission were approximately equal andlight was said to pass straight through the particle,without changing direction due to refraction. Bythis assumption, the intensity of light was not di-minished due to scattering by the ash particles.

In geometric optics, the reflectance and trans-mittance at a plane boundary is governed by theFresnel formulas. The formulas for the reflectioncoefficients of light where the electric vectors areparallel and perpendicular to the plane boundaryare :

r‖ =cosθt −M cosθi

cosθt +M cosθi(10)

r⊥ =cosθi−M cosθt

cosθi +M cosθt(11)

where M = m1/m2 is the relative refractiveindex[15].

5

In the case of normally incident light travellingfrom a non-absorbing medium of m2 = n2 into anabsorbing medium of m1 = n1 + ik1 equations (10)and (11) can be reduced to the equation for the re-flectance R for normally incident light:

R = |r|2 = (n−1)2 + k2

(n+1)2 + k2 (12)

where M = n+ ik [15]. There are two importantobservations to be made using equation (12):

i. The reflectance at the slide-particle boundarywas approximately equal to that of the slide-liquidboundary. This was because for light entering theparticle or the liquid, n1 was approximately equaland for the transparent mounting liquid k1 = 0 andaccording to previous studies of volcanic ash at vis-ible wavelengths, it should be possible to say thatin the case of an ash particle k1 < 0.02 [7, 8].

ii. The reflectance at the particle-liquid bound-ary was negligible as n1 ' n2.

Therefore, the path of light which travelledthrough the particle was essentially the same asthe path of light travelling past the particles, apartfrom the absorption felt by the light which travelledthrough (as illustrated in Figure 2). This meant thatthe intensity of light leaving the particle had an in-tensity which had been reduced according to theBeer-Lambert law (Equation 6) relative to the lighttravelling past the particle.

By combining equations (6) and (7), an equationgiving the imaginary part of the refractive index ofthe particle in terms of the intensity of light en-tering (I0) and leaving (I1) the particle was formu-lated:

k =λ

4πdln(

I0

I1

)(13)

where d is the path length of the light in theparticle.

As no light was absorbed by the mounting me-dium, the intensity of light entering the particlewas equated to the the intensity of the light passingthrough the slide unobstructed by ash particles.

3.2.2 Calibration of camera

The photographs taken from the CCD digital cam-era were stored as bitmap images, for which eachpixel had an R, G and B (red, green and blue) co-ordinate, ranging from 0 to 255. These pixels val-ues, as well as averages of the values over a spe-cified region within an image, could be extracted

Figure 2: Diagram of two beams of light passingthrough the ash/liquid mixture. The beam labelledI0 passes through unattenuated while the beamlabelled I1 is partially absorbed whilst travellingthrough the ash particle. The length d indicates thepath length of the light in the particle.

from the image file using NI Vision Assistant soft-ware. To find out how transmittance could be re-lated to the pixel parameters, neutral density filtersof optical density d = 0.3 and d = 0.6 were usedto provide known readings for of transmittance.The gamma correction and saturation of the cam-era were set to one1. For each wavelength of light(again using the 450.0 nm, 546.7 nm and 650.0nm filters), a set of 4 images was taken: one forthe unobstructed stage (100% transmittance), onefor each of the neutral density filters placed on thestage and one of the stage completely obstructedby a thick, opaque medium (0% transmittance).

The average RGB coordinates for a square re-gion at the centre of these images was retrieved.For the images with the 650.0 nm filter in place,the average R coordinate was shown to have a lin-ear relationship with fractional transmittance, withthe intercept passing through the origin. The G andB coordinates did not register any significant value.Similarly, for 546.7 nm light, the G coordinate hada linear relationship with intensity, with the inter-cept passing through the origin without R or B re-gistering, and for 450.0 nm light the B coordinatehad a linear relationship with intensity, with the in-tercept passing through the origin. These calibra-tion lines are shown in Appendix A.

Relative intensity could therefore be related tothe relative pixel values by:

1Gamma correction is a nonlinear operation applied to im-ages to compensate for how humans perceive light intensity.Saturation describes the intensity of colour in an image. Set-ting these to 1 when taking photographs ensures the intensitydependent corrections to an image are minimised.

6

I1

I0=

X1

X0(14)

where X0 and X1 are the pixel coordinates forthe unobstructed and attenuated light respectively.Substituting this into Equation 4 we get an equa-tion for k in terms of the relevant pixel coordinates:

k =λ

4πdln(

X0

X1

)(15)

where X = R when 650.0 nm light was being ob-served, X = G when 546.7 nm light was being ob-served, and X = B when 450.0 nm light was beingobserved.

3.2.3 Measurements

Figure 3: Illustration of the parameters extractedfrom the image of an ash particle. In this case,where λ = 546.7nm, the average G coordinate wasextracted for a region at the centre of the particle aswell as for four unobstructed regions surroundingthe particle. The perpendicular width and breadthmeasurements are also shown.

Approximately 3 mg of ash was immersed in 60µl of the mounting liquid with the closest matchingrefractive index at that wavelength. The mixturewas shaken vigorously to disperse the ash and afew drops were placed on a microscope slide andcovered with a cover slip. The sample was placedon the microscope stage and illuminated from be-low. An individual particle was selected and thestage was positioned so that it was at the focal pointmicroscope’s 20X objective lens.

Photographs were taken of the ash particle inthe matched medium. For each fragment invest-igated, the average colour coordinate for an area atthe centre of the ash fragment was measured andassigned to the variable X1. The average colour

coordinate for three or four unobstructed areas sur-rounding the fragment was also taken, then aver-aged and assigned to variable X0. By taking anaverage of multiple areas around the particle it re-duced the chance of error caused by fluctuations inthe illuminating field. The length (x1) and breadth(x2) of the particle were also extracted. A conver-sion between image pixels and microns was de-duced by taking a photograph of a micro-ruler.An example of the extraction of these variables isshown in Figure 3.

The final value required to calculate k for theparticle was the path length of the light as it trav-elled through the fragment. The relative verticalposition of the base of the fragment was found bypositioning the stage so that the microscope wasfocused on the upper surface of the glass slide.This position of the stage was read from the stagedial, which read to the nearest micron. The stagewas then adjusted to focus on the upper surface atthe centre of the fragment, visible due to the tinyimperfections which existed on the fragment’s sur-face. The new position was read from the dial andits difference from the initial stage position wassaid to be the path length, d. The value of k wascalculated and recorded for the particle. Lastly, theparticle was assigned to a category of either clear(crystal or vitric), lithic (dark) or mixed. This pro-cess was repeated for 30 particles in each sample,at each wavelength of light.

3.2.4 Overall value from individual particles

To find a value for the imaginary part of the refract-ive index which is representative of the ash sampleas a whole, an appropriate method of averaging thek values of the particles was needed. Due to ef-fects such as fragmentation of the erupted particles,there was no guarantee that chemical compositionand therefore k was independent of particle size[20].

According to Bohren and Huffman (1983), thefactor 2aβabs determines whether absorption isproportional to volume (2aβabs � 1) or to area(2aβabs � 1) [15]. In the case of the ashes understudy, 2aβabs ∼ 1 meaning that they were betweenthe two regimes. However, in a similar study whereEbert et al. (2002) were aiming retrieving theoverall complex refractive index from an ensembleof individual aerosol particles, it was found thatvolume-averaging the components of refractive in-dex for the individual particles was in good agree-

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Figure 4: Chart showing the real part of refractive index at 650nm, 546.7nm and 450nm for 10 ashsamples.

ment with overall photometer measurements [21].

Therefore, an effective imaginary part of the re-fractive index for the samples was calculated bytaking a volume-weighted average of the k valuesof the individual particles:

kash =∑iViki

∑ j Vj(16)

where Vi is the volume of the individualparticles. The exact morphology of the individualparticles was not know. However, a particle couldbe modelled as an idealised cuboid or an ideal-ised ellipsoid, and in both cases V ∝ x1x2d. Thefact that only the relative volume of the paticlesmattered, the product of the particle dimensionsx1x2d could be taken to be an approximate particlevolume used to calculate the weights.

4 Results

4.1 Real part of the refractive index

A value for the mean real part of the refractive in-dex was successfully retrieved at 450.0 nm, 546.7nm and 650.0 nm for the 10 ash samples to an ac-curacy of ± 0.01, determined by the resolution ofmounting liquids. The values are presented in Fig-ure 4 and quoted exactly in Table 3.

It can be seen in Figure 4 that the expected dis-persion relation at visible wavelengths was evidentin all samples, with the refractive index increasingwith photon energy.

Table 3: Table listing the real part of the refractiveindex for 10 ash samples at wavelengths of 650nm,456.7nm and 450nm.

4.2 Imaginary part of the refractive index

The imaginary part of the refractive index wasmeasured for 30 particles within six of the ash spe-cimens at 450.0 nm, 546.7 nm and 650 nm. Thedistribution of the k values is shown in the form ofhistograms in Figure 5.

These histograms tend to show the k values con-forming to a positively skewed distribution withthe majority clustered around a modal peak and along tail of outlying particles with much higher val-ues of k. This clearly demonstrates the inhomogen-eity in the particles present, with the lithic particlesexhibiting unusually high absorption relative to therest of the sample. Samples VA11, VA19 and VA5even appear to show a secondary mode at substan-tially higher k values than the primary peak.

8

0.0016 0.0028 0.004

650.0nm546.7nm450.0nm

0

2

4

6

8

10

12

0 0.0001 0.0002 0.0003 0.0004

Fre

quen

cyChaitén 2008 (VA11)

0

2

4

6

8

0 0.0006 0.0012 0.0018 0.0024 0.003 0.0036

Fre

quen

cy

Tongariro 2012 (VA16) 650.0nm

546.7nm

450.0nm

0

2

4

6

8

0 0.0001 0.0002 0.0003 0.0004

Fre

quen

cy

Nisyros (VA19)

0.0005 0.0025 0.0045

650.0nm546.7nm450.0nm

0

2

4

6

8

10

0 0.0006 0.0012 0.0018 0.0024

Fre

quen

cy

Grímsvötn 25/5/2011 (VA5)

0.003 0.005 0.007

650.0nm546.7nm450.0nm

0

2

4

6

8

10

0 0.0012 0.0024 0.0036 0.0048 0.006

Fre

quen

cy

Imaginary part of refractive index (k)

Okmok 7/2008 (VA20) 650.0nm546.7nm450.0nm

0

2

4

6

8

10

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Fre

quen

cy

Eyjafjallajökull 15-16/5/2010 (VA15) 650.0nm

546.7nm

450.0nm

Figure 5: Combined histograms showing the distribution of k values amongst the 30 particles sampledfrom each specimen at 650.0 nm, 546.7 nm and 450.0 nm. There is a break in the x-axis showing achange in scale for (a), (b) and (e).

9

Table 4: Table listing the imaginary part of the refractive index at wavelengths of 650nm, 546.7nm and450nm for six ash samples.

The overall imaginary refractive index values,calculated as a volume average of the sampledparticles, are displayed in Figure 6 and quoted ex-actly in Table 4. The standard error was calculatedby combining the weights from the averaging pro-cess with the standard deviations of the k valueswithin the different particle categories, as detailedin Appendix B.

Figure 6: Chart showing the imaginary part of therefractive index at 650nm, 546.7nm and 450nm for6 ash samples.

5 Discussion

The Becke line method is a standard procedure andreturned good results. The resolution could havebeen increased had there been liquids of a finerrefractive index incrementation. Furthermore, theinhomogeneity of particles could have been betteraccounted for. A similar volume-averaging tech-

nique to the one used in the method to find theimaginary part could have been used. However,the variation within a sample was generally smalland embarking on the time consuming process ofrecording the volume and refractive index of eachparticle would not have been justified. The obviousdispersion relation, visible in all samples, providesreassurance and suggests that the errors attached tothese results were in fact too cautious.

The particle absorption method seemed to re-turn good results for all samples other than VA15which had errors comparable to the returned val-ues of k. This was because VA15 showed a higherand less discrete degree of inhomogeneity relativeto the other samples, making it difficult to categor-ise its particles into distinct groups. All samplesappeared to show their particles distributed about amodal k value, with samples VA11, VA19 and VA5appearing to show the development of a secondarymode of more highly absorbing particles. This dis-tribution was due to the varied make-up of particleswithin the sample, with the vitric and crystallineparticles showing substantially less absorption thanthe lithic particles. A better idea of the true distri-butions, as well as a more accurate overall value,would have been gained with a larger sample size.

The variation in the overall real and imaginarypart of the refractive index between the sampleswould have been primarily due to their differingchemical compositions, determined by the type oferuption from which they originate [6]. A key in-gredient of volcanic matter is silica (SiO2). Bothreal and imaginary parts were shown to correlatewith percentage silica content of the ash (see Ap-pendix C).

A substantial limitation of the particle absorp-tion method was that it was unable to test theparticles with a size parameter lower than about120 due to the restrictions mentioned in Section

10

2.2 and the sensitivity of the camera. Theseparticles, although individually small, constitute alarge combined volume within each sample. Fur-thermore, there is evidence that smaller aerosolparticles are more highly absorbing [22], meaningthat the returned overall k values would be smallerthan the true values for the entirety of the samples.

The overall k values were calculated by volume-averaging the values for the individual, constituentparticles which is a commonly employed proced-ure and allowed for the straight forward combina-tion of all the unique, measured particles. How-ever, there has been some debate as to whetherthis is an effective approach when applied to atmo-spheric aerosols [15, 23, 24], and it has been sug-gested that the Bruggeman and Maxwell Garnettmixing rules may map the individual particle’s re-fractive indices to that of the bulk matter more hon-estly [25]. It would be interesting to see how dif-ferent the results would have been had these rulesbeen applied but the lengthy calculations wouldhave been unlikely to have made a significant dif-ference due to the comparatively narrow range of kvalues of the particles that were retrieved.

The averaging procedure required the assump-tion that the ashes were an external mixture ofparticles, each of a uniform consistency. How-ever, fragments were often either fused from a mix-ture of different materials or contained bubbles ofvolcanic gas. These inhomogeneities within theparticles themselves would have produced unac-counted for scattering, which would have been as-sumed to be absorption, and would have led to in-accurately high values for k.

6 Conclusions and suggestions forfurther research

The real part of the refractive index of ten volcanicash samples was successfully determined. A newmethod to determine the imaginary part of the re-fractive index was developed and successfully im-plemented to retrieve the imaginary part of the re-fractive index of six of these samples. This re-port provides a way to extract much needed vol-canic ash optical data, with inexpensive and ac-cessible equipment. The obtained results could beused to better interpret satellite images of the erup-tions form which they come or other eruptions withplumes containing similar ash.

Although apparently effective, the true success

of the particle absorption method cannot be gaugeduntil a calibration material has been tested. Col-oured glass has been suggested as a material whichwould provide a known value of the complex re-fractive index to test the method against.

To test the absorption of small particles, thesamples could be filtered so that only the finestparticles remain. They could then be suspendedin a liquid of a matched refractive index and theextinction could be measured. Providing they aresmall enough, the Raleigh approximation wouldmean that extinction would be entirely due to ab-sorption, and the imaginary part of the refractiveindex could be retrieved and compared to that ofthe larger particles measured in this project.

7 Acknowledgements

My heartfelt thanks go Don Grainger and BenReed for the assistance and advice given through-out the project. Thanks must also go to Karen Ap-lin and Keith Long for their patience during my useof the microscope in the teaching labs.

References

[1] Horwell, C. J. and Baxter, P. J., The respirat-ory health hazards of volcanic ash: a reviewfor volcanic risk mitigation, Bulletin on Vol-canology, v. 69, p. 1-24, 2006.

[2] International Civil Aviation Organisation,Manual on Volcanic Ash, Radioactive Mater-ial and Toxic Chemical Clouds, ICAO Doc9691, 2007.

[3] Robock, A., Volcanic eruptions and climate,Reviews of Geophysics, v. 38.2, p. 191-219.

[4] Grainger, R. G., Peters, D. M., Thomas,G. E., Smith, A. J. A., Siddans, R., Car-boni, E. and Dudhia A., Measuring volcanicplume and ash properties from space, Pyle,D. M., Mather, T. A. and Biggs, J. (eds.), Re-mote Sensing of Volcanoes and Volcanic Pro-cesses: Integrating Observation and Model-ling, Geological Society of London SpecialPublications, v. 380, p. 293-320, 2013.

[5] Schmid, R., Descriptive nomenclature andclassification of pyroclastic deposits and frag-ments: Recommendations of the IUGS Sub-

11

commission on the Systematics of IgneousRocks, Geology, v. 9, p.41-43, 1981.

[6] Heiken, G., Wohletz, K. H., Volcanic ash,University of California Press, 1985

[7] Patterson, E. M., Measurements of the ima-ginary part of the refractive index between300 and 700 nanometers for Mount St.Helens ash, Science, v. 211, p. 836-838, 1981.

[8] Patterson, E. M., Pollard, C. O. and Galindo,I, Optical-properties of the ashes from El-Chichon volcano, Geophysical Research Let-ters, v. 10, p. 317-320, 1983.

[9] Patterson, E. M., Optical absorption coeffi-cients of soil-aerosol particles and volcanicash between 1 and 16 mm, Proceedings ofthe Second Conference on Atmospheric Ra-diation, American Meteorological Society,Washington DC, p. 177–180, 1994.

[10] Krotkov, N. A., Flittner, D. E., Krueger, A.J., Kostinski, A., Riley, C., Rose, W. andTorres, O., Effect of particle non-sphericityon satellite monitoring of drifting volcanicash clouds, Journal of Quantitative Spectro-scopy and Radiative Transfer, v. 63, p. 613-630, 1999.

[11] Pollack, J. B., Toon, O. B. and Khare, B. N.,Optical properties of some terrestrial rocksand glasses, Icarus, v. 19, p. 372-389, 1973.

[12] Egan, W., Hilgeman, T. and Pang, K., Ul-traviolet complex refractive-index of Martiandust – Laboratory measurements of terrestrialanalogs, Icarus, v. 25, p. 344-355, 1975.

[13] Volz, F. E., Infrared optical constants ofammonium sulfate, Sahara dust, volcanicpumice and flyash, Applied Optics, v. 12, p.564-568, 1973.

[14] Toon, O. B., Pollack, J. B. and Sagan, C.,Physical properties of the particles compos-ing the Martian dust storm of 1971–1972,Icarus, v. 30, p. 663-696, 1977.

[15] Bohren, C. F., Huffman, D. R., Absorptionand Scattering of Light by Small Particles,New York, Chichester: Wiley, 1983.

[16] Grainger, R. G., Lucas, J., Thomas, G. E., andGraham B. L. Ewen, G. B. L., Calculation ofMie derivatives, Optical Society of America,2004.

[17] Francis, P. N., Cooke, M. C. and Saunders,R., Retrieval of physical properties of vol-canic ash using Meteosat: A case study fromthe 2010 Eyjafjallajökull eruption, Journalof Geophysical Research, v. 117, i. 20, p.D00U09, 2012.

[18] Mishchenko, M. I., Travis, L. D. and Lacis,A. A., Scattering, absorption, and emissionof light by small particles, Cambridge : Cam-bridge University Press, 2002.

[19] Nesse, W. D., Introduction to optical miner-alogy, New York, Oxford: Oxford UniversityPress, 1991.

[20] Zimanowski, B., Wohletz, K., Dellino, P.,Büttner, R., The volcanic ash problem,Journal of Volcanology and Geothermal Re-search, v. 122, i. 1-2, p. 1-5, 2003.

[21] Ebert, M., Weinbruch, S., Rausch, A., Gorz-awski, G., Hoffmann, P., Wex, H., and Helas,G., Complex refractive index of aerosols dur-ing LACE 98 as derived from the analysis ofindividual particles, Journal of GeophysicalResearch, v. 107, i. 20, p. LAC 3-1–LAC 3-16, 2002.

[22] Lindberg, J. D. and Gillespie, J. B., Relation-ship between particle size and imaginary re-fractive index in atmospheric dust, AppliedOptics, v. 16, i. 10, p. 2628-2630, 1977.

[23] Gillespie, J. B., Jennings, S. G. and Lindberg,J. D., Use of an average complex refract-ive index in atmospheric propagation calcula-tions, Applied Optics, v. 17, i. 7, p. 989-991,1978.

[24] Lindberg, J. D., The composition and opticalabsorption coefficient of atmospheric partic-ulate matter, Optical and Quantum Electron-ics, v. 7, p.131-139, 1975.

[25] Chylek, P., Srivastava, V., Pinnick, R. G.and Wang, R. T., Scattering of electromag-netic waves by composite spherical particles:

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experiment and effective medium approxim-ations, Applied Optics, v. 27, i.12, p2396-2403, 1988.

Appendices

A. Camera calibration graph

The lines show a linear relationship between theRGB coordinates and fractional transmittance, T =10−d , where d is optical density.

B. Determining the errors in the overall kvalues

For n uncorrelated observations with standard de-viations σi and weights wi, the weighted samplemean has standard deviation:

σ(x) =

√n

∑i=1

w2i σ2

i

The 30 particles in were catagorised into threedistinct groups (clear, lithic and mixed) and thestandard deviation within each group was calcu-lated (σc, σl and σm).

The weight of a particle was given by its volumeover the sum of all the volumes of the particles inthe sample:

wi =Vi

∑30n=1Vn

With each particle having a weight set by itsvolume and a standard deviation given by its groupdesignation, the standard deviation of the weightedmean could calculated.

C. Plots of real and imaginary re-fractive index against SiO2 % com-position

(See next page)

13

45 50 55 60 65 70 75SiO2 % w/w

1.50

1.52

1.54

1.56

1.58

1.60

1.62

1.64R

eal p

art o

f re

frac

tive

inde

x

➌ ➊

➊

➋➋

➍

➊➊

➊

➍

➎

➏➏

➍

➊

➐

➑

➒

➌➊

➊

➋

➋

➊ ➊

➊

➍

➎

➏➏

➍

➊

➐

➑➒

➌ ➊

➊

➋ ➋

➊ ➊➊

➍

➎

➏

➏

➍

➊

➐

➑

➒

➌ Aso

➊ Eyjafjallajokull➊ Eyjafjallajokull➋ Grimsvotn➋ Grimsvotn

➍ Etna

➊ Eyjafjallajokull➊ Eyjafjallajokull➊ Eyjafjallajokull

➍ Etna➎ Chaiten➏ Afar Boina➏ Afar Boina

➍ Etna

➊ Eyjafjallajokull

➐ Tongariro➑ Askja➒ Nisyros

The real parts of the refractive indices of some of ashes studied against their measured SiO2 % com-position. Plot: Ben Reed (Atmospheric, Oceanic and Planetary Physics, Oxford) ; Composition data:Gemma Prata (Earth Sciences, Oxford).

45 50 55 60 65 70 75SiO2 % w/w

0.0000

0.0005

0.0010

0.0015

0.0020

Imag

inar

y pa

rt o

f re

frac

tive

inde

x

➋

➎

➊➐

➒

➋

➎

➊➐

➒

➋

➎

➊ ➐

➒

➎ Chaiten´

➊ Eyjafjallajokull¨➋ Grımsvotn´ ¨

➒ Nisyros➐ Tongariro

The imaginary parts of the refractive indices of some of ashes studied against their measured SiO2 %composition. Plot: Ben Reed (Atmospheric, Oceanic and Planetary Physics, Oxford); Composition data:Gemma Prata (Earth Sciences, Oxford).

14