# Presentation: 064596

## Determination of Aerosol Refractive Index using Genetic Algorithms on Polar Nephelometer Data

- Suzanne Paulson
- Brian Barkey
- Albert Chung
- Sheldon Friedlander
- Kuo-Nan Liou
- Antonio Miguel
- Departments of Atmospheric & Oceanic Sciences, Chemical Engineering, and Institute of the Environment, UCLA

**Notes:**
Introduction

## Goals

- Develop a Genetic Algorithm method to retrieve the real and imaginary refractive indices from polar nephelometer measurements
- Determine the effect of particle non-sphericity on aerosol optical properties
- Measure the effect of aerosols on the polarization state of scattered light
- Study the scattering properties (absorption, scattering, etc) of aerosols of various mixing states (internal, external) and composition.

## Polar Nephelometer

**Notes:**
This instrument was originally developed to measure scattering properties from ice crystals on a balloon borne platform

The light from the 780 nm laser is directed across the 2-dimensional sensing plane.

Particles, isolated by a sheath flow intercept the laser beam at the center.  The scattered light intensities are directed to the photodiode detectors via fiber optics.  An onboard PC computer and high speed data acquisition card processes theses signals.

The instrument is about 20 inches long, 20 inches wide and 7 inches tall.  The 

## Genetic Algorithms

- Population of possible answers
- (mr, mi)1
- (mr, mi)2
- (mr, mi)3
- .
- .
- .
- (mr, mi)N

- Mating (binary mapping)
- Parent 1: (mr, mi)1 _**010101**__ _01010100
- Parent 2: (mr, mi)2 000111 _**01110101**_
- Child:      (mr,mi)  010101 01110101

- Mutation
-  10101010111
-  10101011111

**Notes:**
A brief descriptions about genetic algorithms
GA is based on  the way in which biological organisms (animals) evolve to produce the best solution for their environmental niche, hence the origin of many of the terminology.
First, a population of possible solutions is developed randomly, in this case each member of the population is a possible real and refractive index pair.
Then, each member is tested to determine the best member.  In this case the scattering properties of each refractive index is compared to the experimentally measured result.  A fitness value is assigned to each population, in this case, the refractive index that fits the measured results the best has the highest fitness score. 
Then the ‘best’ results are combined.  Here I show how the binary representation of two ‘parents’ form the child result by a simple swapping of ‘genetic’ information.
Also, to ensure that we are not stuck at a local maximum in the solution space, we periodically apply a ‘mutation’ to members of the population.
Thus, each of these cycles, or generations is repeated until we have the ‘right’ answer or desired fitness level. 

## Advantages of GA

- Not an analytical solution, therefore not limited to Mie Scattering. FDTD, Discrete Dipole, Spheriods, infinite Cylinders
- Easy to add other parameters
- Relatively fast

## Simulated experimental results

- detector

- laser beam

- 

- refractive index = 	1.33 - i2.18  10-8
- n(r) = log-normal size distribution,  = 0.1 m,  = 0.1
- R(i)=instrument response function

**Notes:**
Some details

The method is tested using the scattering expectations from Mie-Lorentz calculations adjusted to fit the physical parameters of our polar nephelometer.

The scattering properties are determined for a log-normal population of particles with and average size of 0.1 micron and a standard deviation of 0.1.

These particles have an index of refraction of 1.33 and very small, negligible absorption

The light scattered from these particles are adjusted to the physical parameters of the nephelometer, including the scattering angle and the response function of each detector which includes the shape and width of the sample volume and the angular width of the sensing area.

Thus I have an expected intensity at each of the 34 nephelometer channels.

## Simulated Experimental Results Non-absorbing particles

- Simulated Experimental Results Non-absorbing particles

- Result: 1.30 - i3.0510-16

- Expected: 1.33 - i2.1810-8

**Notes:**
Shown on the left here is an example of how the GA routine searches for the solution, in this case the refractive index of a “simulated” experimental result.

On the right is the best solution produced from a GA run of 10 generations and a population of 10.  

As you can see, the real refractive index (1.3) is close to the expected result of 1.33,  but the imaginary part is quite different.  I found through several similar tests, that retrieval of the imaginary part is not possible.  This has also been found from another study in which a direct inversion of the Mie-Lorentz solution for scattering from a sphere was used. (Jones et al., 1994)

## Simulated Experimental Results Absorbing particles

- Simulated Experimental Results Absorbing particles

- Result:
- real: 1.7 to 1.9
- imaginary: 0.04 to 0.9

- Expected: 1.67 - i0.26

**Notes:**
This is similar to the previous slide, but now I’m trying to see how well GA’s find the refractive index of absorbing particles.

The model is nigrosin particles, which are spherical and have an index of refraction of 1.67 - i0.26.  Again a log-normal distribution is assumed with an average of 20 m and a variance of 10.

Shown on the left are the results of several different GA searches in which I varied several GA parameters such as population size and number of generations.

The best result is shown on the right which has a retrieved index of 1.7 and an imaginary index of 0.22.  Very close to the expected, but this is not generally true.

## Theoretical results: Summary(one polarization component)

- Theoretical results: Summary(one polarization component)

- Non-absorbing

- Absorbing

**Notes:**
Summarized, I show that for the non-absorbing particles the GA retrievals are quite consistent in the real part, but not in the imaginary part.  As I already mentioned, this has been found before, and would most likely be due to the incompleteness of the problem, i.e., I need more input parameters as the scattering properties of these particles vary very little for particles with very little absorption.

There is a significant spread in both the real and imaginative parts of the refractive index for the absorbing case.  In this case it looks like the absorption is damping out variations due to the real part of the refractive index, hence a more uncertain retrieval.  Again, we need to include more parameters toour problem.

## Two Polarization Components

- u

- Expected:  1.67 - i0.26
- GA result: 1.6 to 1.7 (real)      0.5 to 0.6 (imaginary)

## Experimental results, Non Absorbing particles

- Polar nephelometer

- nebulizer

- filtered dry air

- Drying volume

- SMPS

- Polystyrene latex spheres
- I.R. = 1.58 - i0.0
- log-normal distribution, = 0.372 m, =0.0054

**Notes:**
The previous results are from theoretical studies, therefore they do not include any effects due to instrument noise, calibration, laser beam misalignment, multiple internal reflections and other real world experimental factors.

Hence we decided to do some preliminary tests.

We selected some standardized polystyrene latex particles with an average diameter of 0.372 m, and a standard deviation of 0.00545 (this is very narrow)

PSL particles have an index or refraction of 1.58 and negligible absorption.

These particles are diluted in de-ionized water and nebulized in a small spray.  After drying out, the particles are sent to the nephelometer and a scanning mobility particle sizer

## Experimental results, Non Absorbing particles

- Expected : 1.58     GA result : 1.59 to 1.6

- Log-normal
-  = 0.372 m
- = 0.0054

**Notes:**
(Data from fit psl,9-29)
Here is a representative scattering measurement along with the GA fit.  
In the forward direction, the two diverge.  This is most likely due to dust in the laser path or on the mirror, or laser beam drift.  Note also that there is some variation in the signal at about 60o ,  Which is caused by calibration errors because the signal is very low.  We are in the process of installing a larger laser so that the scattered intensities are in the range where the instrument is better calibrated. And in the reverse direction, we see some indication of back scatter from the forward intensities, which are several decades above those in the reverse directions and difficult to eliminate. 

Thus, we do not use the far forward and reverse results in the GA retrieval.

The real refractive index is close to the expectation.  

## Experimental results Absorbing particles

- Experimental results Absorbing particles

- Expected:  1.67 - i0.26
- GA result: 1.1 to 1.9 (real)      10-12 to 0.23 (imaginary)

- Log-normal
-  = 19.7m
- = 9.9

**Notes:**
Absorbing Nigrosin particles.

Size distribution is from direct measurement of scanning electron microscope.

Note that as in the theoretical experiment, there is a wide range in the retrieved refractive index.

## Summary

- GA retrieval of the real part of the refractive index has been shown both theoretically and experimentally.
- GA algorithm retrieval of the imaginary part of the refractive index is problematic at best.
- Preliminary experimental and theoretical measurements of the refractive index of absorbing particles is so far unsuccessful.

## Future Plans

- Investigate ways to implement other parameters into the retrieval scheme including, polarization properties of scattered light and inclusion of simultaneous extinction properties.
- Sensitivity studies.
- Investigation of the effects of non-sphericity on the retrieval of refractive indices.