Real Time Particulate Mass Measurement
Based on Laser Scattering
Julia H. Rentz*, David Mansur, Robert Vaillancourt, Elizabeth Schundler, Thomas Evans
OPTRA, Inc. 461 Boston St., Topsfield, MA 01983
Phone: (978) 887-6600, Fax: (978)887-0022
www.optra.com
ABSTRACT
OPTRA has developed a new approach to the determination of particulate size distribution from a
measured, composite, laser angular scatter pattern. Drawing from the field of infrared spectroscopy,
OPTRA has employed a multicomponent analysis technique which uniquely recognizes patterns associated
with each particle size “bin” over a broad range of sizes. The technique is particularly appropriate for
overlapping patterns where large signals are potentially obscuring weak ones. OPTRA has also
investigated a method for accurately training the algorithms without the use of representative particles for
any given application. This streamlined calibration applies a one-time measured “instrument function” to
theoretical Mie patterns to create the training data for the algorithms.
OPTRA has demonstrated this algorithmic technique on a compact, rugged, laser scatter sensor head we
developed for gas turbine engine emissions measurements. The sensor contains a miniature violet solid
state laser and an array of silicon photodiodes , both of which are commercial off the shelf. The algorithmic
technique can also be used with any commercially available laser scatter system.
Key Words: Particulates, Laser, Scattering, Diffraction
1.0 INTRODUCTION
A need has been identified for accurate and rapid determination of particulate matter (PM) present in the
exhaust of a gas turbine engine. Currently, the EPA has recommendations for PM mass measurement for
stationary and mobile sources employing a glass fiber filter to collect the PM and a sensitive gravitational
microbalance to measure the accumulated mass. Such methods require extractive sampling and
conditioning of the exhaust, long integration times, and a low-vibration environment to make the mass
measurement. This type of measurement is generally characterized as impractical and unrepeatable in
regards to the gas turbine application.
Alternatives to this type of method have been demonstrated with some success. Examples include
aerodynamic mobility and laser scattering based particle sizers. Total mass is obtained by integrating over
particle size the measured concentration-volume product and multiplying by the material density. In
general, most of these measurements are faster and reasonably more accurate than the filter based method,
however they still require conditioning of the exhaust. Another issue is that there is still some
inconsistency among measurements between different instruments on the same exhaust. Laser scatter
based sensors in particular employ “first principles” to untangle the size distribution from the measured
scatter pattern without taking into account the effects of the physical instrument on the pattern,i which may
lead to errors.
In light of these issues, OPTRA has been working towards the development of a laser scattering based
particle sizer employing an open path configuration (i.e. non-sampling) and a novel algorithmic approach
to discerning the size distribution and concentration from the measured scatter pattern. In fact, the
technique we have developed is applicable to not only angular scatter measurements but also spectral and
polarization based measurements. This technique can be used with any commercially available laser scatter
based particle sizer in addition to our own. We have also developed a new technique for factory calibrating
the instrument to remove the first principle dependence.
We have demonstrated our concepts with a breadboard system and are in the process of building a
prototype sensor designed specifically for the turbine exhaust application. In particular, the system is
Copyright 2006 Society of Photo-Optical Instrumentation Engineers.
This paper will be published in The Proceedings of Advanced Environmental, Chemical, and Biological Sensing Technologies III
and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use
only. *
Systematic
or multiple
reproduction, distribution to multiple locations via electronic or other means, duplication of any
Contact Author:
[email protected]
material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
intended to quantify particles over the 100 nm to 2 µm size range with a total mass error of better than
10%. The following details our analytical work along with the prototype design.
2.0 LASER SCATTERING BASED PARTICLE SIZING
Angular light scattering by particles is a pretty well understood and modeled phenomenon. Somewhat
analogous to diffraction observed in the far field as light passes through a pin hole, scattering due to
particles has the same inverse tendency where the period of the pattern scales inversely with the diameter of
the particle. In fact for larger particles where the diameter is on the order of 20 to 40 times larger than the
wavelength of light, for a monochromatic source, the far field pattern is the expected Bessel function
indicative of diffraction. For smaller particles which approach the wavelength and below, the far field
pattern still has characteristic features, but the theory which describes it was generated by Gustav Mie
rather than Joseph von Fraunhofer. Mie Theory is actually all encompassing in that it models the
interaction of electromagnetic waves with spherical particles over a range of very small with respect to the
wavelength (i.e. Rayleigh scattering) to very large with respect to the wavelength (Fraunhofer diffraction).
The relationship between particle size and scatter angle is still essentially inverse, but Mie theory also takes
into account both the real and imaginary parts of the refractive indices of the particles and the medium to
give an exact solution based on first principles of physics.ii
Many readily available Mie calculators can predict a scatter pattern based on a particle size or size
distribution and concentration.iii This represents the forward calculation (figure 1). The difficulty lies in
the reverse calculation where we wish to determine the size distribution and concentration from the
measured composite pattern. This is the classic inverse problem to which we typically apply some method
of residuals such as a least squares approach.
Figure 1: Forward and Reverse Mie Calculator
sum
Figure 1. (a) Forward problem: Given a single particle size and using Mie scattering theory, it is
relatively straight-forward to calculate the scattered pattern response (b) Reverse problem: Given
a measured scatter pattern containing the sum of a poly-disperse particle set it is difficult to
determine the size and concentrations of the poly-disperse particle set. A major component of our
effort was to generate an algorithmic recipe for solving the inverse problem.
3.0 INVERSE SOLUTION
Equation 1 describes the resultant scatter pattern from a poly-disperse particle set. I(?,r) represents the
individual scattering effect based on particle size r and scattering angle ? and is modeled by Mie-scattering.
The resultant scatter pattern is then the integral of this kernel over all possible particle sizes with respective
concentration levels (n(r)).
x
I (θ) = ∫ I( θ, r ) n ( r )dr
0
(1)
Methods for solving this equation have been developed utilizing a linear system of equations, integral
transform methods, inversion methods, and various iteration schemes. Commercial instruments based on
measurements of laser scattering patterns are available, for example, from Malvern Instruments Ltd. Much
research continues in this area due to the inability of these commercial instruments to accurately quantify
particulate information for certain particle size ranges and their inconsistency in producing repeatable and
self-consistent results. As a result, there remains a clear interest in improving the methods and algorithms
to invert the light scattering measurements into particulate information.
OPTRA took a fresh approach to the problem and employed our knowledge of infrared (IR) spectroscopic
data processing for organic chemical detection to the particle size and concentration problem. The data
processing problem involved for IR spectra is very similar to that for particle analysis. In organic chemical
detection, a spectrum (absorbance vs optical frequency) is acquired and analyzed in order to determine the
presence or absence of a set of chemical(s) of interest. Each chemical displays a unique spectral signature
as shown in figure 2 much like particles scatter light uniquely for each particle size. Moreover, when
converted to absorbance space (and the equivalent for scattering), the response is linear with concentration.
Given these similarities, we decided to investigate the utility of a “fingerprint” approach to scatter pattern
decomposition.
Our proprietary algorithmic technique is a form of principle component analysis (PCA) which has shown
the best performance with regard to untangling overlapping low-resolution IR spectra, particularly when
strong features are overlapping weaker ones. We employ the same approach of training the algorithm
engine with conditioned theoretical scatter patterns (as opposed to accurate IR reference spectra) which
teaches the algorithms to make accurate future predictions on unknown composite scatter patterns. The
significance of “conditioning” the theoretical patterns is that we take into account the effects of measuring
ideal patterns with a physical
Figure 2: Overlapping IR Spectra
instrument which modifies
the patterns because of
diffraction, aberrations, and
misalignments.
In other
words,
we
train
the
algorithms with data that is
representative of what the
instrument actually measures
(rather than relying on first
principles). The IR spectra
equivalent is convolving the
characteristic
sinc-shaped
instrument function with
accurate, high resolution
reference spectra.
This
conditioning is described in
more detail in section 5.0.
4.0 SIMULATIONS
This section details some simulations of our PCA approach to deciphering size distribution from the
measured scatter patterns. The purpose of these simulations was first to determine the optimal number of
principle components (which are equivalent to size bins) for this application. In addition, we established
the optimal range of angles required to make an accurate measurement along with the minimum number of
detectors required. For this exercise we simulated the training patterns by generating composite patterns
for each size bin with a Gaussian distribution and a concentration between zero and one. We then used one
or both of two different types of composite patterns to challenge the algorithms . Each is shown below
along with the results.
The first challenge pattern was generated from a generic continuum size distribution in the range of interest
for this application. Figure 3a shows the actual and predicted distribution for patterns over the 0 to 180º
angular range using 512 points. The algorithms are able to track the size distribution almost perfectly. We
were also interested in assessing the size resolution and the algorithm’s ability to determine not only when
a specific size particle is present but also when it is not present. For this, we challenged the trained
algorithm with a composite pattern made from the Gaussian distribution of a single bin and found the
results shown in figure 3b. Interestingly enough, the result looks very similar to the sinc function we
measure with the spectrometer in response to a narrow spectral band (such as a laser), which is the typical
spectral resolution test. In fact, we see the same sinc pattern when we challenge over any size bin in the
range (figure 3c).
Figure 3a: Continuum Challenge
Figure 3 b: Size Resolution
1
1.2
0.9
1
0.8
0.8
0.6
PLSPrediction(1=full)
0.6
0.4
0.5
0.4
0.2
0.3
0
0.2
-0.2
0.1
-0.4
0.1
0
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
ParticleDiameter(micron)
Particle Diameter (micron)
Figure 3c: Sinc Responses Across Size Range
2
0.1
0.21875
1.5
0.3375
0.45625
1
0.575
0.69375
0.8125
0.5
0.93125
1.05
1.16875
0
1.2875
1.40625
1.525
-0.5
1.64375
1.7625
-1
1.88125
2
-1.5
0.1
0.3
0.5
0.7
0.9
1.1
1.3
Particle Diameter (micron)
1.5
1.7
1.9
Size of bin centers (µm)
0.1
PLS Prediction (1 = full)
PLSPrediction(1=full)
0.7
1.9
Figure 4: Principle Component Optimal Number
45
40
35
Median Error (%)
With these models in hand, we
used them to first determine the
optimal number of principle
components for this application.
From our IR spectral experience,
we knew that this type of
algorithm requires a certain
number of principle components
to quantify noise; we also knew
that at some point, adding more
principle components causes the
whole algorithm to go unstable
with resulting large prediction
errors. This ultimately limits the
number of compounds than can
be simultaneously quantified.
30
25
Positive Error
Negative Error
20
15
10
5
0
0
5
10
15
20
25
30
Number of Principle Components
35
40
The optimal number for the IR spectral case is nine for noise plus 17 for compounds for a total of 26. In
order to investigate the optimal number for particle sizing, we held the size range constant (in this case 0.1
to 2 µm) and varied the number of Gaussian shaped bins. The goal was to determine how many bins make
the algorithms go unstable with the understanding that we want to use as many bins as possible to minimize
binning errors. Interestingly enough, we found the optimal number of bins was just about 17. In figure 4,
the y-axis is in units of median count error where positive error represents prediction errors when the
particle is present and negative error represents prediction errors when the particle is absent. The principle
component number (x-axis) does not include the nine noise components. As part of this exercise we also
varied the bin spacing and bin width and found that we get the best predictions when they are equal (bin
spacing = bin width).
PLS Prediction (1 = full)
We then investigated how much of the angular range we actually need to measure in order to make an
accurate size prediction. Figure 5a shows the continuum plot for a series of different angular ranges, and
figure 5b through 5e
Figure 5a: Continuum Plot for Different Angle Ranges
shows the resolution plot
2
for the first four angular
ranges. For all of these
we used the previously
1.5
determined
optimal
Actual
principle
component
0-180
1
number of 17. In each
0-90
0-45
case the concentration
10-80
0.5
should go to one at the
20-70
15-35
bin center (or at the
center of the continuum
0
in
figure
5a).
Discrepancies from this
-0.5
value represent count
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
errors.
Particle Diameter (micron)
Figure 5 b: Sinc Plot for 0 to 180º
Range0-180
AngleDetector
Range
2
Figure 5c: Sinc Plot for 0 to 90º
Detector Range 0-90
Angle
Range
0.1
1.5
1.5
0.3375
0.45625
1.25
0.1
0.21875
1
0.575
0.69375
1
0.3375
0.45625
0.75
0.575
0.69375
0.8125
0.93125
0.5
1.05
1.16875
1.2875
0
-0.5
1.40625
1.525
-1
1.64375
1.7625
PLS prediction (1 = full)
PLS Prediction (1 = full)
0.21875
0.8125
0.5
0.93125
1.05
0.25
1.16875
1.2875
0
1.40625
1.525
-0.25
1.64375
1.7625
1.88125
-1.5
0.1
-0.5
0.1
2
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
0.3
0.5
0.7
1.3
1.5
1.7
1.9
1.88125
2
Figure 5e: Sinc Plot for 10 to 80º
DetectorRange10-80
Angle
Range
1.5
1.5
0.1
0.21875
0.3375
1
0.45625
0.575
0.75
0.69375
0.8125
0.93125
0.5
1.05
1.16875
1.2875
0.25
0
1.40625
1.525
1.64375
-0.25
0.3
0.5
0.7
0.9
1.1
1.3
ParticleDiameter(micron)
1.5
1.7
1.9
1.7625
1.88125
2
0.1
0.21875
0.3375
1.25
PLS Prediction (1 = full)
1.25
PLS Prediction (1 = full)
1.1
ParticleDiameter(micron)
ParticleDiameter(micron)
Figure 5 d: Sinc Plot for 0 to 45º
Range 0-45
AngleDetector
Range
-0.5
0.1
0.9
1
0.45625
0.575
0.75
0.69375
0.8125
0.93125
0.5
1.05
1.16875
1.2875
0.25
0
1.40625
1.525
1.64375
-0.25
-0.5
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
1.7625
1.88125
2
ParticleDiameter(micron)
Figure 5a clearly shows degraded prediction capability for angle ranges from 0 to 45º on. Figure 5b and 5c
show an additional degradation between 0 to 180º and 0 to 90º. Figures 5d and 5e show how the
predictions really blow up for increasingly smaller angular ranges. From these simulations we concluded
that the optimal range of angles is the full 0 to 180º.
Having zeroed in on the 0 to 180º range, we then determined how many detector elements are required to
make the accurate measurement. For this we simulated the binning effect in angle space of a series of
lens/detector assemblies spanning the 0 to 180º angle range. For example, 512 detectors spanning 0 to 180º
is equivalent to 0.35º per detector. Figure 6 shows the results.
Figure 6: Detector Number Determination
1.2
1
PLS Prediction (1 = full)
From figure 6 we can
conclude that we can
have as few as 32
receiver elements and
still maintain adequate
prediction performance.
We further refined this
value to 30 receivers
before the performance
falls off.
0.8
Actual
512
0.6
256
128
64
32
26
0.4
0.2
Other
simulations
included investigation of
0
polarization
and
-0.2
misalignment. For this
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
size
range,
we
Particle Diameter (micron)
established that using
one polarization or the
other provides slightly better prediction accuracy than we get when using unpolarized light. We also found
that we can tolerate ±0.4º of random angular error for this size range, angular range, and number of receiver
elements. An interesting and somewhat serendipitous aspect of the PCA and sinc-like response is that the
oscillatory behavior in the size domain, when integrated to convert to total mass, has an averaging effect
where the negative or false positive errors average to zero. The result is low total mass error even when
there is moderate count (as a function of size) error.
5.0 INSTRUMENT FUNCTION
A significant component of our technique in that it allows us to train the algorithms without actually
measuring calibration patterns at every size and refractive index we hope to measure over. This
capability is essential to the versatility of the system to this application where getting an accurately
quantified (by independent means) measurement of turbine emissions is completely prohibitive. When this
type of PCA is used for the IR spectral multicomponent analysis, the training set is generated by
convolving accurate reference spectra (not measured by the instrument under calibration) with the
measured instrument function. In IR spectroscopy, the instrument function is related to the spectral
resolution and is typically quantified as the instrument response to a narrow spectral source such as a laser.
The convolution has the effect of producing a spectrum that is representative of what the instrument
response would have looked like had the instrument been physically presented with the chemical. In the IR
spectroscopy cas e, we therefore have a way to calibrate the algorithms without having to handle and
measure actual chemical vapors. In our case, we have established an analogous technique which applies
independently measured instrument characterization information to, in this case, a theoretical Mie pattern
generated using the OLMC code, to produce a scatter pattern that is representative of what the instrument
response would have looked like had the instrument been physically presented with particulates of that size.
Our technique relies on a simple laboratory measurement of calibrated particles. From a series of two data
sets at two different particle concentrations (measured by independent means), we can extract the two
components of what we’re calling the instrument function, which we define as the effect in amplitude and
offset of measuring the Mie scatter pattern with a physical optical instrument which has inherent (although
minimized) aberrations, misalignments, etc. In our case, the independent measurement consists of NIST
traceability for size distribution and use of a Thermo model pDR-1000 for measuring the mass
concentration. We also assume a small exponent approximation (i.e. e-µsL ˜ µs L which is entirely
appropriate for the concentrations and scatter coefficients expected in this application). Note that the
instrument function in this case has a different definition than that in the IR spectroscopic instance.
Because the scatter pattern measured effectively in the far field can be thought of as Fourier space,
multiplication actually makes sense in comparison to convolution in temporal space. Our method
compensates for all departures from an “ideal” system. To the best of our understanding, commercially
available systems do not account for this in the same way.
The purpose behind measuring the instrument function is such that we can apply it to any theoretical
pattern and use the result to train the algorithm. This means that from the two measurements described
above, we can train the algorithm for any particle size and any refractive index and tailor this specifically
for the application. The instrument function can be thought of as the linear relationship in particulate
concentration between the measured scatter pattern and the theoretical scatter pattern for a given angular
location. We therefore define the instrument function at every angle increment over our measurement
range. The slope component of the instrument function is given by
slope( θ) =
datahigh (θ) − datalow ( θ)
theoryhigh (θ) − theory low (θ)
(2)
where datahigh/low (θ) is the angular scatter pattern measured at independently measured high and low
concentrations respectively and theoryhigh/low (θ) are the corresponding theoretical scatter patterns. The
theoretical patterns are binned in angle space to represent the discrete receiver elements, and each bin is
given a Gaussian weighting within its internal field of view to account for the non uniform far field pattern
of a lens. The intercept component is then given by
int ercept ( θ) = data high ( θ) − slope( θ) ⋅ theory high( θ)
(3)
Of course, the low concentration data and theory patterns may also be used to calculate the intercept.
Training set data are then calculated by applying the slope and intercept to a theoretical pattern.
datatraining(θ) = slope(θ) ⋅ theory(θ) + int ercept(θ)
(4)
Figure 7a shows the calculated slope and offset curves generated from two different concentrations of NIST
traceable 7 µm particles with a 0.7 µm standard deviation. Figure 7b shows the measured scatter pattern
from NIST traceable 10 µm particles with a 0.9 µm standard deviation overlayed with a theoretical pattern
for the same particle size, standard deviation, and concentration with the slope and intercept applied.
Figure 7a: Slope and Intercept
Figure 7 b: Data Overlayed with Theory with
Instrument Function Applied
Theory
Theory x slope - intercept
Data
Slope
Intercept
Data
We present these plots to show that we are able to produce a representative training pattern from theory
alone at a different particle size range from where we measured the instrument function slope and intercept.
6.0 THE HARDWARE
The following section details the hardware we developed in response to the requirement derived from our
simulations. To summarize, the system specifications are listed below.
QUANTITY
Particle size range
Concentration*
Number of size bins
Species
Update rate
Mass error
VALUE
0.1 to 2
105 – 106
17
carbon
10
< 10%
UNITS
µm
particles/cm3
Hz
-
* concentration will depend on dilution of sampled exhaust and engine parameters
The corresponding opto-mechanical specifications fall out of the system specifications.
QUANTITY
Angular range
Number receiver elements
Angular error
Laser power*
Laser wavelength*
Polarization
Lens diameter*
Spectral filter width*
Detector NEP *
VALUE
0 to 180
30
0.4
25
405
None
πD/(2N)**
10
10-14
UNITS
º
º
mW
nm
cm
nm
W/vHz
* While we do not present our radiometric analysis here in an attempts to constrict
the scope, the lens diameter, laser power, wavelength, filter width, and detector
characteristics support a shot noise limit at the specified bandwidth for the
expected particle size range and concentration.
** D is the ring diameter and N is the number of receiver elements.
Figure 8a: Open-path Particle Analyzer
Figure 8b: Receiver Location designation
Fiber optic
laser feed
Beam
dump
Figure 8a shows the exterior of our design. We have developed a six-inch open-path ring sensor which
employs a 25 mW 405 nm fiber coupled solid state laser and 30 receiver modules spaced along the
circumference. Based on our findings that the use of polarized light offers only a small improvement over
unpolarized light and given the convenience of the fiber coupling, we opted for this approach and the
resulting unpolarized fiber output. The laser head and driver are located below in the ring stand (not
shown). The fiber optic coupled laser is collimated and reflected off a total internal reflection (TIR) prism
which points the beam across the interior of the ring towards another TIR prism which direct the light onto
a “beam dump” detector. We use this measurement for auto shut off purposes (i.e. we can tell if the beam
is being blocked completely and can immediately shut off the laser). The receiver elements are staggered
around the circumference to provide continuous coverage from 1.38 to 178.62º in roughly 5.9º increments.
Figure 8c: Laser Collimator
Figure 8d: Beam Dump
Note the small discrepancy
from 0 to 180º does not
measurably
impact
the
prediction performance and
allows for the physical space
of the fiber collimator and
beam dump prisms. Each
receiver
module
is
composed of a narrow band
filter centered at 405 nm, a
BK7, 9 mm focal length f/1
plano-convex lens, and a 1
mm silicon photodiode.
We have also developed a means for sealing off the ring as we pass exhaust through (and evacuate from the
other side). We have added this feature because most test facilities are indoor and do not allow open flow
exhaust. While the test plans will adopt the closed off, sealed configuration, we do not require this, nor do
we require dilution and conditioning of the exhaust owing to our non-contact approach. One of the
potential benefits of our approach over sampling systems is the ability to measure hot (T ˜ 150°C) exhaust
which requires no dilution to mitigate water condensation. We have a potentially more direct measurement
capability.
Enclosed in the sensor head are four preamplifier boards which handle the 31 detector outputs (30 scattered
light receivers and one beam dump detector). The system also has a separate electronics module which
hosts the terminal board for a 64 channel National Instruments data acquisition card and the laser and
preamp power supplies. The scatter patterns are collected through a National Instruments I/O PCI card
onto a portable suitcase PC. The PC hosts the graphical user interface and processing algorithms which
together yield a display of size distribution and concentration as well as total mass at the 10 Hz update rate.
7.0 FUTURE PLANS
We are presently in the build and integration phase of our program. Upon full integration, we will measure
the instrument function as described in section 5.0. We will then complete a series of laboratory
measurements using calibrated samples and the Thermo sensor for our reference measurement. These
samples will include NIST traceable diesel particulates, which are reasonably similar to the expected
turbine emissions. The goal is to demonstrate accurate prediction without additional calibration beyond
the instrument function. Our work will commence with a final testing session at United Technologies
Research Center in East Hartford, CT on a combustor rig. During this session the OPTRA system will be
connected to a sample line of the combustor under test. We will be able to compare our size distribution
and concentration predictions with that of a parallel aerodynamic particle sizer and the total mass result to
that measured by the standard filter based method. Results will be analyzed and presented in the final
report at the end of the contract (January 2006). Follow on plans include a measurement on diesel exhaust.
ACKNOWLEDGEMENTS
This research is being conducted under an SBIR Phase II contract funded by the U.S. Navy. Technical
Monitor: Steve Hartle, NAVAIR. This SBIR was funded to support the Joint Strike Fighter program.
i
Rawle, Alan, “Basic Principles of Particulate Size Analysis,” <http://www.malvern.co.uk>
van de Hulst, H.C., Light Scattering by Small Particles, ch.1, Dover Publications, Inc., New York, 1987.
iii
World Wide Web < http://omlc.ogi.edu/calc/mie_calc.html>
ii