Image processing App in Mathematica™: measuring complex shaped metal nanoparticles in noisy micrographs
(preliminary version)

Filip Novotný

Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering

Outline

1 Introduction to noble metal nanoparticle and their technological applications

Unique optical properties

Compresison of light energy

Modern colloidal chemistry methods for shape control

Shape governs the optical properties

2 Mathematica approach to plasmonic particle analysis

Mathematica allows to implement both the initial filtering of the microscopic images and also the segmentation and the particle parameter analysis.

Determining the right parameters and methods for microscopic image is often laborous and based on experience

Mathematica dynamic functionality allows for interative visualization of the effect of filters dering changin of the parameters, this results in much more streamlined workflow.

3 Image Explorer - micrograph browser

Basic App used for browsing through microscopic images together with the functionality of hand measurements with scale imported from the microscopic image format.

App-like interface allows any user to work with the notebook without any knowledge of Wolfram Language

Allows editing of the already measured lines and utilizes localization of the variables in the notebook, so the work can be saved and reopened later for continuation.

Allows exporting the data in universal tabular format for further analysis in Methematica or elsewhere.

4 Complex metal nanoparticle analysis

Common practice

Technology needs

5 Mathematica Particle Analysis App

A multipaneled interactive app allowing interactive filtering of image and then segmentation

GUI interface for utilization of Mathematica build in image filters, together with layering of multiple effects

Working on a limited subimage to allow responsive dynamic action

Interactive selection of segmented particle properties using custom dynamic controls

Programatic selection of differing particle shapes

6 Mathematica Particle Analysis App workflow

Basic image tresholding and leveling

Image filtering and binarization using several layers of effects

Selection of the properties of particles during component analysis

Interactive determination of multiple shapes in image and the identification of clusters and badly segmented particles

7 Utilization: noisy scanning electron microscope images

Although moder transmission electron microscopes provide superior image quality, which need no filtering before binarization of edge detect, the need a specially prepared ultrathin samples.

Many modern technological application of gold nanoparticles use a depostiion of such particles on arbitrary substrates. Many of them are not conductive (such as transparent glass).

The described Mathematica App allows to analyze the particle orientation and size distribution even in micrographs with a high level of noise.

8 Mathematica notebook as an App

Wolfram Language code demosntration for creation of App-like notebook (interactive zoomable plot of solar irradiance spectrum)

9 Summary

Introduction to plasmonic nanoparticles

Noble metal nanoparticles are known for their intriquing deep colors which inspired people since the ancient times.

In last three decades, new methods of colloidal chemistry allowed for cost-effective preparation of noble metal nanoparticles. This turned them into nanotechnolgy workhorse, exploiting their unique optical behaviour (localized surface plasmon resonance).

The localised surface plasmon resonance is, in fact, a strong compression of the visible light energy into collective oscillations of conductive electrons of the noble metal nanoparticle.

Introduction to plasmonic nanoparticles - Shape matters

The moder methods of colloidal chemistry not only optimized the process of gold nanoparticle synthesis, but also allowed for preparation of colloidal solutions consisting of variously shaped gold nanoparticles.

As the shape of the particle changes so changes the condition for the plasmon resonance - therefore, by controlling the shape of the particle, one can control the optical properties.

The final noble metal nanoprticle colloidal solution color is the sum of the scattering and absorption of individual particles. A method for quantitative analysis of the franctions of different particle shapes and sizes in the solution is needed.

Mathematica approach to plasmonic particle analysis

Typically, colloidal solution is visualized under electron microscope and statistical amount of the visuazed particles are counted and analysed. This can be then correlated to their optical extinction spectra for full characterisation.

Mathematica allows to implement both the initial filtering of the microscopic images and also the segmentation and the particle parameter analysis.

Determining the right parameters and methods for microscopic image is often laborous and based on experience.

Mathematica dynamic functionality allows for interative visualization of the effect of filters dering changin of the parameters, this results in much more streamlined workflow.

Image Explorer - micrograph browser

Basic App used for browsing through microscopic images together with the functionality of hand measurements with scale imported from the microscopic image format.

App-like interface allows any user to work with the notebook without any knowledge of Wolfram Language

Allows editing of the already measured lines and utilizes localization of the variables in the notebook, so the work can be saved and reopened later for continuation.

Allows exporting the data in universal tabular format for further analysis in Mathematica or elsewhere.

Basic browsing and annotating

Auto-scale calibration and hand measurement

Options for measuring marks modification

Data Export

Complex metal nanoparticle analysis

Common practice

Detecting oinly the equvivalent sphere radius

Technology needs

Resolving both the targeted shapes and their dimensions but also other shapes to asses the statistics of impurities in the solution

Particle Analysis App

A multipaneled interactive app allowing interactive filtering of image and then segmentation

GUI interface for utilization of Mathematica build in image filters, together with layering of multiple effects

Working on a limited subimage to allow responsive dynamic action

Interactive selection of segmented particle properties using custom dynamic controls

Programatic selection of differing particle shapes

⟶

Particle Analysis App workflow

1 Basic image preparation and leveling

2 Image filtering and binarization - advanced custom dynamic controls

Edge detection

If the apllied layers of filter start to cause the dynamic control unresponsive, some of the layers could be “frozen” (computed in advance) and create a static filtered image upon which next filter could be applied with responsive dynamic controls.

3 Selection of the elements to compute during the segmentation alalysis

4 Segmentation analysis and setup - the ability to programmaticaly divide differing shapes

Particle fractions can be programatically resolved by determinig intervals in the histograms of their respective properties (right)

Custom dynamic control allows to interactively select multiple intervals in one histogram - thus allowing to select the differing shape fractions

Individual selection and override can be done for each displayed particle by a simple click of a mouse either in the image explorer or in the ListPlot view.

Application: noisy scanning electron microscope images

Although moder transmission electron microscopes provide superior image quality, which need no filtering before binarization of edge detect, the need a specially prepared ultrathin samples.

Many modern technological application of gold nanoparticles use a depostiion of such particles on arbitrary substrates. Many of them are not conductive (such as transparent glass).

The described Mathematica App allows to analyze the particle orientation and size distribution even in micrographs with a high level of noise.

Result

Mathematica notebook as an App

With a special settings, notebook can be made to appear as a standard application window with all the functions as saving or opening. Such notebook applications are convenient for user not familiar with the Wolfram language, or just starting to learing it.

An App based in a notebook in a DynamicModule or Manipulate construct can store all the values and definitions and upon opening restore the variables and definitions. This make the notebook App interface an practical application of quine, a self-contanied app in one file, able to clone itself (trough saving the notebook with different filename).

An example of such notebook construct follows - a interactive modification of ListPlot of solar irradiance spectra:

ListLinePlot[solarIrradianceSpectrum]

Plot with Zoom Selection Box

Zoom box for ListPlot create using EventHandler[]

The whole functionality uses the DynamicModule[] to localize the variables. SetterBar[] allows for control over default Graphics[] editing and the new functionality.

DynamicModule[
{
plotRange=All
,rangeTemp={}
,selectionBox={}
,selectionMode=True
},
Column[{

Row[{
SetterBar[Dynamic[selectionMode],{False->pointerIcon,True->zoomInIcon}]
,Button[zoomOutIcon,plotRange=All]
}],

Dynamic[
EventHandler[
Show[
ListLinePlot[
solarIrradianceSpectrum
,plotStyle
,ImageSize->600
,PlotRange->plotRange
]
,selectionBox
],

If[selectionMode,
{{"MouseDown":>(
rangeTemp=MousePosition["Graphics"];
selectionBox=Graphics[
{EdgeForm[Directive[Thin,Dashed]],Transparent,Rectangle[rangeTemp,Dynamic[MousePosition["Graphics"]]]}
];
)},

{"MouseUp":>(
plotRange=Transpose[{rangeTemp,MousePosition["Graphics"]}];
selectionBox={}
)}}
]
]]
},Frame->True]
]

Auto-Resizing App-like window

One can easily convert such dynamic cell into a notebookk behaving like a standard system App by using CreateDocument[] and dynamicaly reading the actual parameters of the notebook such as window size Dynamic[CurrentValue[WindowSize]].

CreateDocument[
DynamicModule[
{
plotRange=All
,rangeTemp={}
,selectionBox={}
,selectionMode=True
},
Column[{

Row[{
SetterBar[Dynamic[selectionMode],{False->pointerIcon,True->zoomInIcon}]
,Button[zoomOutIcon,plotRange=All]
}],

Dynamic[
EventHandler[
Show[
ListLinePlot[
solarIrradianceSpectrum
,plotStyle
(*Zde vlozim dynamicky updatovany parametr CurrentValue[WindowSize] - tim se dosahne skalovani obsahu podle velikosti notebooku*)
,ImageSize->Dynamic[CurrentValue[WindowSize]-{20,40}]
,PlotRange->plotRange
]
,selectionBox
],

If[selectionMode,
{{"MouseDown":>(
rangeTemp=MousePosition["Graphics"];
selectionBox=Graphics[
{EdgeForm[Directive[Thin,Dashed]],Transparent,Rectangle[rangeTemp,Dynamic[MousePosition["Graphics"]]]}
];
)},

{"MouseUp":>(
plotRange=Transpose[{rangeTemp,MousePosition["Graphics"]}];
selectionBox={}
)}}
]
]]
},Frame->False],
Initialization:>{
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zoomInIcon=;
zoomOutIcon=;
pointerIcon= ;
plotStyle={
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,FrameLabel->{"λ [nm]","Irradiance at sea level"}
,PlotLabel->Style["Solar Irradiance Spectrum",18,Bold]
,ColorFunction->(ColorData["VisibleSpectrum"][#]&)
,ColorFunctionScaling->False
,LabelStyle->Directive[Bold,White,14]
,FrameStyle->White
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,InterpolationOrder->3
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}
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,WindowSize->{800,600}
,WindowFrame->"Normal"
,WindowElements->{}
,WindowTitle->"Solar Irradiance Spectrum"
,CellFrame->False
,CellMargins->0
,CellFrameMargins->0]

Thank you for attention...

Initialization

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