Phasor Plot

The Phasor Plot panel represents the phasors of all pixels as a color-coded map (a 2-dimensional histogram):

Not shown in the picture above is the Phasor Frequency control, located below the Phasor Plot, which allows selecting which Phasor Frequency is used when computing the Phasor Plot. This value can be also set on the Phasor Graph panel or in the Settings window. The right-click menu for this control allows choosing a "natural" phasor frequency (or harmonic) based on the laser period T:

The first item using the base frequency f = 1/T, while the second allows selecting a different harmonic via a dialog window.

The Phasor Plot is calculated from the loaded dataset and is controlled by a number of dataset-independent parameters (described below), some of which are found in the Settings>>Phasor Plot tab, but some others in the Settings>>Fluorescence Decay>>Basic Analysis tab or the Settings>>Phasor Graph tab.

Each time a new dataset is loaded, or the same dataset is reloaded with different settings, or a parameter is modified that would affect the Phasor Plot, the Phasor Plot Update Needed red LED at the bottom right of AlliGator's main window lights up. If the parameters are restored to their original values used to compute the Phasor Plot (or if the Phasor Plot has just been computed), this :LED will turn off.

1. Phasor Plot Image Size, Aspect Ratio and Binning

The Phasor Plot Image features the g and s axis of a standard phasor plot, as well as the universal semicircle (UC, in blue in the image above).

It is possible to specify its size (H and V in pixels) in the Phasor Plot tab of the Settings window (see the corresponding manual page) as well as the extra space represented on the left and right of the UC (Margin).

Changing these parameters will require refreshing the plot using the Refresh Phasor Plot button on the top left of the Phasor Plot:

Finally, it is also possible to compute a smoothed Phasor Plot by defining a Phasor Plot Bin value different from 1 in the Settings>>Phasor Plot window: in the case of noisy images (low sum pixel values), it can be useful to compute phasor values by grouping neighboring pixels together. This is done by setting the Phasor Plot Bin parameter (b) to a value larger than 1 (and odd) and selecting a Kernel Type (Uniform, Bilinear or Gaussian).

Each pixel's phasor is replaced by the average phasor obtained using b x b pixels centered around that pixel, using weights defined by the kernel type.

- Uniform kernel: the weight of all pixels is equal to 1.

Bilinear kernel: the weight of each pixel decreases linearly from 1 at the center down to zero for pixels outside the kernel, proportionally to its distance from the center.
Gaussian kernel: the weight of each pixels is proportional to a normal distribution with standard deviation = b/3.

Smoothing the Phasor Plot is not recommended for data sets with good signal-to-noise ratio or for in vivo datasets, as this operation artificially couples regions with potentially different lifetime characteristics and therefore creates artifacts ("bridges") in the Phasor Plot.

For instance, the phasor plot represented above will look as shown below when using a Phasor Plot Bin value of 3 (and a bilinear kernel).

Remember to press the Refresh Phasor Plot button (top left corner of the image) to apply this new setting.

Note that the Phasor Plot Image calculation takes some computational time and might not be useful during time-series analysis. In order to speed up analysis, it is therefore possible to skip this process by unchecking the box at the top left corner of the panel (not shown in the figure above).

2. Phasor Plot Settings and Controls

The Phasor Plot Image uses the same settings used by the Phasor Plot Graph (Phasor Graph panel).

In particular, phasors are corrected by the same calibration phasor (or calibration phasor map), if one is defined and selected (Use Single Phasor Calibration/Phasor Calibration Series/Phasor Calibration Map checkboxes in the Phasor Graph panel).

For time series analysis, each image's Phasor Plot Image uses the corresponding calibration point of the calibration curve, if one has been defined and selected (Use Phasor Calibration Series checkbox in the Phasor Graph panel).

The controls on the right-hand side of the panel (Phasor Plot Color Scale, Phasor Plot Display Range) are used to control the appearance of the Phasor Plot Image. The actual palette used for the Phasor Plot is selected via the right-click menu, as explained in the Image Palette section of the manual (*). Pixels with value outside the indicated range will be displayed with the Low or High colors shown at the bottom and top of the color scale, respectively. When changing the Low or High color value, use the Palette>>Refresh Image context menu item for these changes to take effect.

The Refresh Phasor Plot button (recycle icon) at the top left corner of the image is used to refresh the Phasor Plot if one of the controlling parameters mentioned above have been modified.

Note that the phasor plot will not be recalculated if none of the parameters influencing it have been modified.

Finally, the Cumulative Phasor Plot checkbox allows summing up all phasor plots during a time series analysis.

3. Phasor Indicator

When the cursor is located in the image part of the Phasor Plot, a Phasor at Cursor indicator is shown, indicating the phasor components at this location. This indicator is hidden when the cursor is not within the image display area.

4. Highlighting Phasor ROIs in the Source Image

The Highlight ROI button on the left (pencil icon) is used in conjunction with the Overlay Color box below it to highlight pixels in the original image corresponding to the selected region in the Phasor Plot. To select a ROI in the Phasor Plot, use one of selection tools on the left hand side palette. The ROI will be overlayed in the selected color on the Phasor Plot and the corresponding pixels will be overlayed (painted) with the same color on the original image. Choosing a Transparent color (T) will result in no overlay being added to the source image.

The image below shows an example where two different ROIs were selected successively and highlighted with different colors (pink and blue):

Note: The picture above corresponds to an older version of AlliGator.

Note that for the best contrast, it is recommended to choose a Grayscale or Temperature palette for the original image. The overlay(s) can also be applied to the White Light Image if one has been loaded and is displayed in the Source Image.

Pressing the Refresh Phasor Plot or the Clear Overlay buttons clears these overlays in the respective images.

5. Phasor Plot Context Menu

The context menu of the Phasor Plot image is shown below:

This menu functions in the same manner as that of the Source Image, to whose manual page the reader is referred for further details.

Some functions are specific to the Phasor Plot and are described below.

5.1. Saving the Phasor Plot Image

- Save Phasor Plot Data as TIFF

This will save the 2-dimensional histogram shown in the Phasor Plot Image as a TIFF image in the same way as the Source Image context menu function does. Options involved in saving this image are discussed in the Saving a Dataset as Gate Images page of the manual.

- Save Phasor Image with Overlay

While it is possible to right-click on the Phasor Plot and use the "Copy Data" menu item to copy the Phasor Plot Image Object to the clipboard, this includes the object's frame and tool palette, which are of little use. The context menu offers an alternative in the form of the Save Phasor Image with Overlay function. This function saves the visible part of the Phasor Plot, including overlays, as a file with format specified by the Saved Image File Format control in the Options page. The file can be of type PNG, JPEG or BMP.

The name of the file is Phasor Plot Name.XXX where XXX is the file format and Name is the folder containing the current data set folder (for Gate Image Folder) or current data set name.

In addition, it is possible to automatically save the Phasor Plot image after it has been computed, by checking the Save Phasor Plot checkbox. This is particularly useful during a time series analysis, and an animated sequence needs to be created for presentation purposes.

5.2. Export Complex Phasor Data

The complex phasor data calculated to form the Phasor Plot can be saved using the right-click menu (see below) Export Complex Phasor Data.

This will save an ASCII file (comma separated values) with Nx columns and Ny lines of complex g + is phasor values, where Nx x Ny is the image dimension.

Phasors that were not computed (due the various settings selected in the Phasor Plot tab of the Settings window, or other reasons) are replaced by NaN + iNaN.

5.3. Analysis

Once the phasor plot has been calculated, the complex phasor data can be analyzed using the following functions, which output a single plot:

- Phase Lifetime Histogram: computes the phase lifetime of all phasors and histograms them following the options defined by the user in the dialog window opening at the beginning of the analysis. The resulting plot is output in the Lifetime Graph of the Lifetime Analysis panel.

Phasor Ratio Histogram: computes the phasor ratio (or amplitude ratio if that option is selected in the Phasor Ratio Analysis panel) of all phasors and histograms them following the options defined by the user in the dialog window opening at the beginning of the analysis. The resulting plot is output in the Phasor Ratio Graph of the Phasor Ratio Analysis panel. Phasor references need to have been defined for this analysis to work.
Phase Lifetime vs Intensity Scatter Plot: computes the phase lifetime of all phasors and plots them versus the corresponding total intensity of the pixel, as shown in the Source Image. The resulting plot is output in the Lifetime Graph of the Lifetime Analysis panel.

5.4. Representing Phasor Ratio Values as a Color Map in the Source Image

It is possible to use the Phasor Graph and Phasor Plot to define two phasor ratio references and assign colors to them, which will be used to color-code pixels in the Source Image having phasors close enough to these references. See the Phasor Ratio Map page of the manual for details on this representation.

Instead of using the Phasor Graph to define the phasor ratio references, it is possible to define them directly in the Phasor Plot in the following two different possible manners:

- Using the Phasor Ratio Reference n button: The two buttons at the bottom left of the Phasor Plot can be toggled on or off (they turn orange when pressed). Once pressed, clicking in the Phasor Plot and moving the mouse while clicked continuously updates the location of the corresponding reference.
- Using the Line Tool: Selecting the Line tool in the toolbox located on the left side of the Phasor Plot, draw a line and use the following right-click menu item to set the two references to its extremities:

Either way, the newly defined phasor ratio references will be used (and displayed) in the Phasor Graph as well.

Note: to see the references (and the bounding box indicating the range of the phasor ratio calculation), make sure that you have selected Show References in the Phasor Ratio References menu.

5.5. Color-coding Phasors with a user-defined Color Map

This topic is discussed in more details in the Phasor Color Map page of the manual.

The tool used to define this map is show by selecting the Phasor Map Color Picker function.

When such a map has been defined, it is possible to show or hide its vertices and edges by checking the Show Phasor Color Map Vertices menu item.

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