# Extinction Suite Macro (v3.2.4.7) for ImageJ (2011-2015)

## Written by Lukas Payne (LP)

Acknowledgements:

• David Coffin for the DCRAW reader plugin, and any contributors to ImageJ's original batch converter plugin.
• Wolfgang Langbein and Paola Borri for supervision and advice.

The extinction technique is described in the publication

Polarization-resolved extinction and scattering cross-sections of individual gold nanoparticles measured by wide-field microscopy on a large ensemble
Lukas M. Payne, Wolfgang Langbein, and Paola Borri
Appl. Phys. Lett. 102, 131107 (2013) DOI 10.1063/1.4800564

Please cite this work when using the suite.

Plugin File: Extinction_Suite_v3p2p4p7.jar

### Outline

The Extinction Suite Macro was developed with the specific intention of analyzing images of nanoparticles fixed in a field of view.  It currently supports recognition of gold and silver metallic nanoparticles via their color, as well as non-metallic nanoparticles.  It can also recognize two different particle size ranges via the related extinction crossection range.  The Macro requires an installation of ImageJ or Fiji. To use this program with Canon RAW files the DCRaw Reader plugin has to be installed.  The program has both unpolarized and polarized processing modes.  There are four processing modules of the macro and a mapping module which creates the required folder mapping.

### Installation

Please install ImageJ or Fiji following the instructions for your system found here (ImageJ) or here (Fiji).
DCRAW plugin can be found here along with instructions, information etc.

• In version 3.2.3.6, the DCRAW call command has been updated to use the v1.5.0 ij-dcraw plugin.  PLEASE update DCRAW.
• Windows users: v1.5.0 DCRAW is available here
• Critical Note for Mac OSX users:  I have not found an updated binary file for this plugin for Mac OSX, and so have compiled the dcraw.c file myself.  I make it available along with the ij-dcraw.jar file here.
• For both platforms, simply unzip the folder and then drag the dcraw folder and ij-dcraw.jar file into the plugins folder of ImageJ/Fiji.
• Other dcraw builds are available from the link in the installation instructions further down this page.

The simplest way to install the plugin is to open ImageJ or Fiji, click the "Plugins" drop-down menu and select "Install Plugin."  You will be prompted to find/select the plugin on your computer to install.  Once installed it will be available directly from the Plugins drop-down menu.  However, I have encountered problems with this, where it does not remain permanently installed.  If you find that happens then proceed with the following:

ImageJ: find the "plugins" folder inside the ImageJ application folder (mac: in "Applications" folder, PC: in "Program Files").  Simply place the plugin in this folder.  Or if you prefer it be within the "Macros" portion of the Plugins drop-down menu, then within the plugins folder is a "Macros" folder.  Simply copy the Extinction macro to this folder.  It will then appear in the drop-down menu via Plugins->Macros->Extinction Suite vx.x.x.

Fiji: the operation is similar, however you will need to add an underscore "_" to the end of the "Macros" folder if you wish to use it instead of the Plugins folder.  The "Macros" folder contents will then be available through the plugins drop-down menu.  A note on Mac with Fiji:  if you browse to the Application folder in search of the Fiji application folder and you only find an icon, simply control-click or two-finger click Fiji and select "Show Package Contents."  You will then find the Fiji application contents.

### Initialization

After starting the Macro in ImageJ it prompts the user to close any images in ImageJ previously opened. Close any open images and click "ok". It then prompts the user to select the processing mode, as unpolarized or polarized (see panel shown to the right), and to select the desired operation to execute.  There are two operations available: run the Extinction Suite, or run the folder mapping module.

### Mapping Module: Extinction Suite Folder Tree

The mapping module creates the folder structure required by the main Extinction Suite modules.  It will ask the user for a name (e.g. the date "2015_01_01", see image at right), and create a folder of this name, which will serve as base folder for the experiment and analysis.  The mapping of folders within the base folder differs for unpolarized or polarized processing, whether or not darkfield images are included, and whether or not the converter and averaging modules will need to be run.  In the unpolarized case, the program will create focus (F), defocus (D), background (BG),  dark-field (DF), and dark-field background (DFBG) (if you chose to include darkfield and darkfield BG) folders, in the base folder.  These folders have to contain the respective images from your camera, regardless of image type.
After acquiring images, saving them to the appropriate folders, and running the main Extinction Modules, a new folder, named "RAW," will be added to each of the afore-mentioned folders.  The images in each folder will be moved into these new "RAW" folders.  This process is the same whether or not you are capturing color, or black/white (BW), images, with one exception:  the capture of color data, i.e. via separate color filters, using a grayscale camera.  Rather than an input of single images containing three channels of color information, an input of three separate images each containing different color information is required.  Frequently, grayscale cameras output data in suitable formats, such as "Tiff" so that conversion is unnecessary.  Hence, by UNchecking the "Will you need to convert images?" option and selecting the "Color" option, you are indicating that you have captured "color" data with a grayscale camera.  This will prompt the mapping module to provide three folders, named "R," "G," and "B," in each of the F, D, and BG (and optionally DF and DFBG) folders.  "RAW" folders will not be created during any subsequent run of the main Extinction Modules.
In the case of polarized processing, the mapping is based upon the polarization range of captured images (e.g. 0˚-180˚), and the step size, in degrees.  You will be prompted for the intial angle, final angle and angle step size in integer values.  If, for example, 0˚, 180˚, and 10˚ steps are entered, 19 sub-folders would be created by the program in the base folder, each named with their respective polarization angle, i.e. 0, 10, 20, etc, which contain the F, D, and DF folders.  The BG folder stays in the base folder as the background is independent of polarization.  Again, R, G, and B folders will be created in each of the F, D, DF, BG, and DFBG folders, if the user reqyures the color option, and that image conversion will be unnecessary.  The mapping module should be used prior to acquiring the images, so that you can save images from the camera in the appropriate folders.

The folder structure is summarized in the table below

#### Polarized Analysis

• Base Folder
• F
• R (if using color data w/out conversion)
• G (...)
• B (...)
• D
• ...
• DF (if selected)
• ...
• BG
• ...
• DFBG (if selected)
• ...
• Base Folder
• 0
• F
• R (if using color data w/out conversion)
• G (...)
• B (...)
• D
• ...
• DF (if selected)
• ...
• 10
• ...
• ...
• ...
• BG
• ...
• DFBG (if selected)
• ...
To run the module,  choose "Run Folder Mapping Module" from the operating mode drop-down menu (see Extinction Suite panel).

### Main Extinction Suite Modules:

By choosing "Run Extinction Suite" from the operating mode drop-down menu (see Extinction Suite Panel), you will move onto the main modules of Extinction suite.  These modules are to be run once you have captured all data required for analysis (see Summary of Images to be taken).
Upon choosing "Run Extinction Suite," the user will be prompted to select which modules may be run, see the panel at the right.  The modules can all be run individually, or in various combinations, however, some require a folder structure developed by the previous module.  For instance, the Particle Analysis can be run alone, but at some point previously, the Extinction Analysis module must also have been run.  Details about how each module runs can be found in the next sections, so the user can decide his/her preferred usage of the suite.

Following the user's choice of modules, he/she will be presented with a panel prompting input of the main characteristics of the data to be analysed.  The panel will change depending on what modules the user has chosen to run.  The example panel, seen at right, assumes all modules have been chosen.  The first option asks the user to specify the format of the captured images.  This input allows that the folders may contain files other than those to be analyzed, for instance ".rec" or ".txt" files containing camera and image information recorded along with the image.  It will recognize any of the native formats of ImageJ, and any of the consumer RAW formats listed on the Wikipedia Raw Image Formats page.  The second input is simply a choice of whether or not the data is color or BW.  Instructions for the next two options are given, in detail, directly in the panel.  Briefly, you can choose between two types of image, namely, standard single image files, or multi-image stack files.  The final option is to specify whether or not darkfield images were captured, and if so, how the darkfield background will be dealt with.  The options are (A) no darkfield images were taken (B) no darkfield background reduction (C) subtraction of DFBG images (D) subtraction of a numerical offset.  By choosing any of the methods of darkfield background management, you are, by default, indicating that you have acquired darkfield images.

### Converter Module: Conversion and RGB image channel splitting

This module is intended to convert RAW files, such as Canon .CR2, to files usable by ImageJ, such as TIFF or JPEG. It can more generally be used also as a batch converter between image formats.  The RAW files are opened with the DCRAW reader plugin into 16-bit linear format for quantitative analysis.  For a detailed list of the image formats, which can be opened using DCRAW reader, please see the DCRAW homepage (toward the bottom).
The user selects which of the F, D, BG, etc. folders will be considered for conversion (see panel to the right). ImageJ will determine the number of files in the folder, and collect filenames from the folder in alphabetic order.  By default the background set is not selected, because the background during one imaging session is typically stable and needs to be converted only once. In this case move the BG folder (converted/averaged during a previous macro  run) into the new base folder.  Immediately after this panel, a similar one will be seen for the averaging (next) module, if selected.

Next, if you are running only the converter module and using colour images, you will be asked if you want to split the colour channels. If yes, the split images will be created in subfolders called "R","G", and "B" in each of the parent folders. The Averager module requires this splitting into single channel images, thus you will not be prompted for this choice, if you run both the converter and averager.

Next you will be asked if you used the mapping module to create your folder tree.  If yes, the program will use the related folder names.  If not, you will be asked to provide the title of the base folder and the sub-folders manually (panel to the right).

Next you will be asked for the destination format and the number range of images to convert, defined by the starting image number, and number of  images to convert. By default the range is set to use all images in the folders.  The starting image and number of images to convert can be different between the different kinds of images, i.e. Focus, Defocus, etc.  However, in polarized mode, the starting image and number of images must be the same through ALL polarizations of the same image type, i.e. focus, defocus etc. may still be different, but focus(0) and focus(10) ...focus(180) must have the same number of images.  The panel to the right will be seen once for each of the image types.  A similar panel will be seen for the averaging (next module), also once for each image type.

After this selection, the conversion process will start.  The original images will be moved into a RAW subfolder.  If RGB splitting is chosen, the split images are stored in the R, G, and B subfolders.  If splitting is not chosen, or not possible, the converted images will be created in a new folder name, "converted."

### Averager Module: Image averaging

This module produces averaged images of all image files in each subfolder.  You are also given the option to create an RGB merged average image, from the images in the R,G,B sub-folders. The averaged images are stored in a subfolder "Averages", with a identical R G B folder structure, assuming a color image as input.  If BW images are averaged, then the averaged F, D, BG, etc. images are created in an "Averages" folder in the main directory.

Note: In the option panels for the averaging modules (similar to the one seen above for the conversion options), you will find a checkbox option for deletion of individual converted channel files.  Check this if you want to delete the converted files, hence saving space by keeping only the averaged, and original, images.

You may use this module individually, in which case you will be prompted to provide the folder names and the image format, as in the converter module.

### Extinction Module: Calculation of Extinction Image and Dark-Field Image Preparation

This module assumes a folder structure as created by averaging module. It creates a folder in the base folder called "Extinction" into which the resulting images are saved.

The extinction images are calculated as (1-(Focus-BG)/(Defocus-BG)), and are saved as 32bit float TIFF files.

The dark-field images, if selected, will be background-subtracted only, DF-BG, and saved as 16bit TIFF files.

You can run this module separately.  In B/W mode you will be prompted to choose the files directly rather than the containing folder, i.e. one for each of the image sets, unless running the polarized procedure.  In RGB mode you will be prompted for the containing folder.

#### Application note

While the plugin was written to analyze nanoparticles within an image, the development of the extinction image applies to many cases where you may wish to inspect the absorption/scattering of a sample.  As such, depending on what you are using the program to observe, you may not wish to average any images.  The converter module can be used seamlessly with the extinction module, bypassing the averager module, in order to develop an extinction image from only one captured image.  If you choose to do this, in the RGB case, the converter will create the "R", "G", and "B" folders, convert and split the single file, and place each of the appropriate channels into the folders (one file per folder).  Hence, the extinction module will no longer look in the averages folder, but will take files from each of the R, G, and B folders in each of the F, D, BG, etc., sets.  In the B/W case, you will be asked to simply select the individual F, D, BG, etc.,  images.

### Analysis Module: Particle analysis from Extinction Images and Dark-Field Images

#### (A) Preliminary Options and Image Registration

This is a section with more significant input from the user.  The macro uses ImageJ's built-in "Find Maxima" function to locate the positions of the nanoparticles in the images.  In order to do this it must be thresholded above the image noise.  You will be  prompted to choose the analysis options.  If you run only the analysis module (having perhaps previously prepared the extinction images), you will have to specify the image type as RGB or B/W.  The other options include three methods of cross-section calculation, i.e. single radius, double radius, or regional methods, one or two nanoparticle sizes, and the material to be analyzed, i.e. gold, silver, or non-metallic.  The choice of material is relevant only to color images.  The material choice allows us to place a filter on the data to collect information only for particles having a cross-section which is largest in the color channel corresponding to the plasmon resonance of the material, i.e. for single spherical particles, the blue channel for silver, or the green channel for gold.  Choosing non-metallic particles no such filter is used.  In the case of the polarized analysis, selecting the material allows us to again choose those particles which we believe to be single/mostly spherical, based upon the color of those particles whose mean cross-sections (across all polarizer angles, i.e. as if unpolarized) are largest in the channel corresponding to the plasmon resonance.  If you wish to measure the ellipticities of all particles even those of extreme ellipticity or aggregation, i.e. those whose mean cross-section is no longer largest in the channel corresponding to the plasmon, then select "Non-Metallic."  Finally, there are two options available for one-time processes to calibrate the optimum measurement radius (Ri) for your setup, as well as the η factor (see paper for explanation).  The η factor is used for the absolute scaling of the scattering cross-section from dark-field images, which depends only upon the condenser / objective / camera combination.  These two calibrations should be done in unpolarized mode.

You can also choose between two analysis modes, namely, the defocus and shifted reference methods, from a drop-down icon in the panel at right.  The selection is based on your choice of experimental acquisition of the reference image.  In the publication, we use only the 'defocus' reference method.  However, for high-sensitivity experiments, it may be more suitable to use a 'shifted' reference method.  In this case, the reference images are stored, named, and used exactly as the 'defocus' images would be by the program.  The difference is in acquisition during the measurement period.  If you choose to use the shifted reference method, rather than defocussing of the sample, please shift the sample laterally, via stage controls, by a known amount of pixels.  The shift can be in the x or  y directions, or in a combination of the x and y directions.

In the Nikon Ti-U microscope stand with the Canon D-40 camera on the left port with the sensor in the intermediate image plane, the optimum measurement radius is given by Ri=0.135 pixels*magnification*tube multiplier/numerical aperture. For 0.95NA 40x magnification with a 1.5x tube multiplier we find Ri=8.5 pixels.  If you do not know your optimum Ri, run the one-time calibration.  The extinction image most relevant to your chosen material will be displayed. You will be prompted to locate a well isolated particle, and zoom in using the ImageJ toolbar.  Place the cursor as best you can over the center of the particle and then note the X & Y coordinates shown in the ImageJ toolbar.  Click "Ok" to close the prompt.  You will be instructed to enter the X&Y values in another prompt.  Do so, and the program will construct a plot of extinction cross-section versus measurement radius, Ri.  It uses the double radius method, with the second radius give by 2Ri.  Inspect the plot.  Record the radius at which the extinction cross-section saturates.  This is your optimum Ri.  Close the plot.

##### Darkfield / Brightfield scaling factor η

The η factor calibration does not need a manual selection of a particle.  However, it requires a "purely" scattering sample of nanoparticles smaller than the optical resolution, creating an approximately isotropic scattering.  If you run this calibration you will not be prompted for the η factor later in the same run of the module.  Instead the η factor will be calculated (see paper), written to the log, and automatically used to scale your scattering values.  Keep the value of η for your records, so that you will be able to use it afterwards in this module for the same condenser/objectives/camera.configuration. A suited scatterer material are nanodiamonds of 100nm size, which should show a white powder color in dry form..

For a correct scaling of darkfield and brightfield, the lamp intensity has to be constant. The different signal strength can be compensated using the camera exposure time.To allow for alignment under dark-field, one can remove a neutral density filter and replace it for the measurements. For the Canon D-40, short camera exposure times (<10ms) lead to shutter induced artifacts in the measured intensity.

##### Background methods
• Double radius method: this is now the preferred method for deduction of the local background from the particle's calculated extinction cross-section for all cases.  The methods given below should be considered obsolete.  For further discussion look toward the bottom of the Analysis Calibration section.
• Single radius method: Allows for higher densities of particles. It uses the randomized background calibration mentioned previously which provides a mean background value which is subtracted from the particle values.
• Regional method: a modification of the single radius method.  The single radius method takes background points randomly throughout the region of interest (see below).  However, background gradients over large regions of interest can lead to systematic errors. The regional method applies the single radius method on a region defined by a user-specified radius around each maximum. This is the preferred method for higher particale densities and large regions of interest.

If you analyze dark-field images as well as extinction images, or if you analyze polarized images, it is common to see small transverse shifts in the field of view due to drift or movement during switching from brightfield to darkfield, or during the polarization experiment.  An image registration (2D shift) can be applied match the positions of the maxima of the darkfield to the extinction, or the extinction/darkfield images of different angles.  If you are running in unpolarized mode and want darkfield analysis you will only perform one image registration.  However, if you are running in polarized mode you will perform one registration for brightfield only, or three registrations for brightfield and darkfield.  Three sets of registrations are needed for the polarized extinction/darkfield analysis, because we must register the extinction images of different polarizations, the darkfield images of different polarizations, and the first extinction image to the first darkfield image.

You will be given explicit instructions in a prompt and asked to use "Find Maxima" on the extinction image to preview the noise tolerance (do NOT run the protocol, simply "preview point selection" followed after inspection by "Cancel"). The image registration looks for patterns of points within a certain ROI.  The procedure works well if you choose a noise tolerance that results in about 10 points, especially if the ROI is small. You will be prompted to provide the noise tolerance and the "Pattern Recogniton Tolerance" (PRT). The PRT allows for slight changes in particle maxima within a pattern. The pattern should be fixed, as the nanoparticles are fixed relative to each other, however very small (1-2 pixels) shifts in the particle positions in the pattern (i.e. relative to each other) may occur due to noise and pixelation. The default PRT is 3 pixels, which should  be sufficient.  If you have many points, appearing to threshold above the same value, simply resize the selection oval (seen in the image below) around fewer points, then press "Ok."

You will then need to preview the Find Maxima for the darkfield image, which will open after reformatting of the selection oval.  Since this image is not normalized, expect  mean values over the particles, e.g. we see about 2000 counts (see right panel). Again, click cancel and input this number in the following prompt.

You can see in this darkfield image (right, below) the reformatted size of the selection oval chosen for the extinction image above, when prompted.  Input the noise tolerance (2000) and press "ok."

The next screen will prompt you to check the log for abnormalities.  The bottom two numbers of the log window,  show the mean shift of the particles' x (upper row) and y (lower row) positions, from the extinction image to the darkfield image.

In the above example, mean shifts in the x and y positions of the maxima of 0.5 pixels are seen.  The value is expected to be below a few pixels for a stable microscope. So we can press "Ok" here and say "No" to the next prompt, which asks whether to re-register.  Sometimes re-registration is necessary. If, for instance, the numbers are extremely large (positive or negative) or NaN (not a number), you will need to re-register.  Perhaps there was not enough pattern overlap, or the maxima density was too high, etc.  If this occurs, simply confirm you would like to repeat the registration and reformat the selection oval, or choose more appropriate thresholds for the Find Maxima  protocols.

The above case is applicable for brightfield to darkfield in either polarized or unpolarized mode.  However, in polarized mode, you will register extinction images across different angles, and this is a one-step procedure, i.e. you will be prompted to input a noise tolerance as you did above for the extinction, but not for dark field.  It is the same for darkfield across the polarizations.  Of course, you will likely use the same values you noted for brightfield to darkfield, however, the three registrations are distinct to allow you to check the Log each time and potentially rerun each if there are problems in any of the three.  Across the polarizations the shifts will appear as a row of comma-separated values (1st row is x, 2nd is y), as opposed to the one value in the bright/dark-field registration.  Check the entire row for abnormalities.  When this is finished you can proceed to the calibration.

#### (B) Calibration

A screenshot after running module 3, confirming the analysis options, and performing image registration (if necessary) is shown on the right.  The prompt provides explicit instructions.  You start the "Find Maxima" protocol found in the ImageJ Menu Bar->Process->Find Maxima.  Since the extinction images are normalized images, the threshold should correspond to the relative intensity noise in the image, so in this example 0.0165.  You can preview the number of maxima without running the protocol (seen below). Do NOT actually run the protocol, and do NOT press 'ok' on the above prompt until you have completed its instructions. Brightness/contrast adjustment might be necessary to evaluate the maxima which were found.

A small fraction of maxima which do not correspond to nanoparticles is acceptable.  It is important to choose the threshold close to the noise since the background in the single radius method is taken from points outside the disks of a given radius around the maxima. These regions should not be influenced significantly by any relevant particles.  After making notation of the required noise tolerance, close the prompt, leaving the extinction images as they are.

Next, the module will filter the maxima which have an average value (measured over the disk of a user-defined radius) within a range you will calibrate, as well as by the color of the average value if RGB data is available (see nanoparticle material options above).

You may manually determine reasonable numbers for the lowest or highest allowable mean values of the particles using a point & click scheme whose instructions are given explicitly in a prompt (1st image down).  Prior to this you will be prompted for the measurement radii for the single or double radius methods.  If you choose to attempt to recognize two different particle size ranges, you will be prompted to give an upper mean value bound for the smaller particle size and a lower mean value bound for the larger particle size (four values in total for two particle sizes). One should choose particles which are representative of the largest and smallest particles (either for one or for both sizes) by measuring the means of the brightest and dimmest particles, respectively. A screenshot of this procedure is shown to the right, where the results appear in a new panel. Instructions are explicit, however you must close the prompt this time, before you will be able to use the Point & Click procedure.

One should be able to see the yellow outline of the hand-drawn region of interest around the bottom right particle (see third image down).   Importantly, this example represents the situation where I wish to analyze gold, hence the green channel extinction image has been selected for the user, as gold has it's plasmon resonance in the green. If I were interested in silver, the blue channel would have been selected.

After taking note of the required upper and lower mean limits (and intermediates if necessary), simply close the results , choose "don't save," and leave the extinction images as they are.  Follow the instructions and close the "Test" image to end the Point & Click process.

You are then asked to enter values into several fields. The desired number of BG datapoints represents how many background datapoints will be sampled to produce a BG mean and standard deviation. If you chose to run the regional reduction method, the BG datapoints represents how many datapoints will be sampled per particle, and hence, per region. You will also be asked to submit a radius for the region around each particle which will be sampled for background data.  The smaller the region, the closer the mean and standard deviation to the double radius method.  Be careful, though, in a very dense sample, you have to make the region large enough so that the BG datapoints will have a probability of finding  space free from particles.  The scale value in pixels per micron is dependent on your objective and camera.  The desired radius of the region of interest (ROI) is for us 8.5 pixels. We use twice this radius for the second radius, giving us a shot noise of the background value a factor of 2 lower than the average value over the inner disk. Furthermore, one sets the range values and pixel size values from manual calibration.  You will be asked to specify the noise tolerance (threshold) you determined via the mock-Find Maxima performed, previously.  At this point, you will also enter the dark-field and bright-field exposure times (in decimal format), as well as the η factor.  If you chose the shifted reference method in the first analysis option panel, then you will be required to enter the shift, in pixels, in the x and y direction.  Relating the reference image to the focused image, a shift to the left is negative in the x direction, and upwards is negative in the y direction.  The next option is not a numeric input, but an optional field.  The user can choose whether or not to use a Gaussian fit to the particle's intensity profile for improved centering of the ROI.  A Gaussian fit to the particle's intensity is made along the x-axis, y-axis, and both of the main diagonals, all having their origin at the peak pixel of the particle's ROI.  The mean peak position (in x and y pixel coordinates) of the fitted Gaussian is then taken as the new center of the particle's ROI.  It is useful in lower resolution images, or images with a high level of noise, such that the peak pixel does not define well the "center" of the airy function of the particle.  The next, and final, input requested has some information given directly in the panel.  More explicitly, though, using the double radius method, a particle must be spaced at least 3 Ri from any other particle or debris, in order to avoid contamination of the particle's local BG measurement in the outer radius.  We can get around this limitation, however.  Let's call the mean pixel value of the outer radius, $\mathrm{\Sigma , and}$ the standard deviation of the pixel values in the outer radius, $\sigma$ (called "sigma" in the user prompt).  We first measure the mean of the pixels in the outer radius.  Next, we exclude any pixel, P, for$\text\left\{P\right\}\ni\left[\Sigma-N\,\sigma,\Sigma+N\,\sigma\right]$, and then remeasure the mean, performing this recursively, until the value converges.  N is a simple factor indicating the number of standard deviations to be accepted, and is the value requested in the user prompt.  By default, N is 2.  In this way, we can exclude points in the outer radius, attributable to nearby particles/debris.  The spacing limit is now reduced to 2 Ri, allowing for increased particle density in the image.  Any particle who loses more than 50% of the datapoints in its outer radius via the $\sigma$-recursion loop is not accepted however.

#### (C) Output Data

##### General

Analysis Metadata is printed in the ImageJ Output Log and contains all user inputs to the particle analysis.

The final data will be saved in the form of excel files and histograms, produced by custom scripting of ImageJ's plotting capabilities.  These histograms are saved as .png images.  I include a screenshot of a portion of the BG dataset that would be output using the double radius method (specified at the top of each column as DR-...).  The actual particle data is similarly presented.  The x&y coordinates of the BG points where the measurements were taken are given in the 2nd and 3rd columns, and the data-type is given in the 1st column.  The data-type specifies whether or not the row is for a particle, mean, or standard deviation.  Notice that the BG measurements are given in the form of a cross section and were measured with the same radius, Ri, as the particles were.  To the right of the viewable region of that dataset is the scattering and absorption data (extinction minus scattering), similarly arranged.  The regional BG dataset is similarly constructed however columns will have row-breaks due to each region having a specified number of datapoints, its own mean, and standard deviation.  The mean and standard deviation shown at the bottom represent that of all BG datapoints collected across all individual regions.  Intra-regional means and standard deviations converge to those of the double radius technique.  Inter-regional means and standard deviations converge to those of the single radius technique.  Note: a user may run all three background methods. The amount of resulting data will be accordingly large, particularly in the polarized case.  Histograms are provided for each color channel (one channel if B/W).  They show the distribution of cross-sections of the BG and of the nanoparticles.  Lastly, an extinction image is saved, where each particle is labeled with its corresponding number on the excel spreadsheet, making it easy to cross-reference the data with the actual image.

##### Polarized

The output data discussed in the general case above is created for every polarization's "Extinction" folder.  Furthermore, a folder called "Polarization Data" in the base folder will contain: histograms of the mean particle cross sections (cross-sections as if unpolarized), histograms of the experimental ellipticity parameter, plots of cross-section versus polarization for each particle, distribution (histogram) of individual particles' ellipticity parameter given simulated noise, and finally a histogram using all of the particles' ellipticity distributions. More precisely, each particle's extinction cross-section and scattering cross-section is recorded versus polarization: see excel file in "Polarization Data".  Each particle will have it's data plotted for each color channel (custom scripting with ImageJ's native plotting scheme) and stored in the, "B", "G", or "R" folders within a new folder called Polarization Data->"Polarization Curves".  Each particle's cross-sectional data across the polarizations will also be fitted in order to deduce the relative amplitude parameter, mean cross-section (as if the particle were unpolarized), and orientation with respect to the polarizer (see paper for fitting function): see excel file in "Polarization Data".  The fitted function will be added to each particle's plot (in all three channels).  The user will also be provided with histograms of the mean cross-sections and relative amplitude parameters across the color channels: see "Polarization Data"->"Histograms".  Finally, the noise associated with each particle's relative amplitude parameter will be measured via a simulated noise procedure (see paper), and presented in the form of histograms of the possible relative amplitude parameters for that particle, given the noise: see "Polarization Data"->"Sim Noise Hist".  These fit-distributions are collectively represented in another histogram found in the same location.

### Summary of Images to be taken

The following images need to be taken to determine extinction and scattering of a nanoparticle sample

• Bright-field with an exposure time providing about 70% of the saturation counts of the camera
• in-focus
• out-of-focus, displacement about 10um (see paper), or alternatively for high sensitivity measurements
• a shifted reference image - an image of the laterally shifted sample, with best results coming from a shift of ~2 Ri
• Dark-field images with suited exposure times. Dark field intensities scale with the sixth power of the particle radius in the dipole limit. A dynamic range of 1000 therefore corresponds only to a factor 3 in radius. To increase the dynamic range you can take two images with a factor of ~100 different exposure times.

Created by Lukas Payne & WL 05/02/2015