Time-Gated Phasor Shot Noise Simulations

This software performs Monte Carlo simulations of a finite number of photon detections by a time-gated photon-counting detector, followed by phasor analysis of the resulting signal, as describe in ref. [2] of the Bibliography.

Two types of simulations series can be performed:

• • Photon Number Series

  • Gate Width Series

In both cases, the assumption is that the detector opens up one square gate of duration W per laser period T, and that detected photons are emitted by a species with lifetime tau. Because of the periodicity of excitation, the probability distribution of photon arrival times "wraps around" at the end of the period. Arrival times are picked up randomly according to this distribution, and assigned to a random gate.

The detector is assumed to be used with a finite number G of gates, each separated from the next by a step d (expressed in ns, as all times in this software). Note that G and d are linked: depending on the Parameter to Adjust option, changing one will update the other, in order for the G  gate steps to cover the full laser period.

This process is repeated a fixed number of times (# Simulations parameter), before phasor analysis of the data is performed.

Phasor analysis is defined by the harmonic frequency (Phasor Frequency paramater) and Calibration Lifetime.

Implementation details can be found on the Shot Noise Simulation Details page.

1. Photon Number Series

This type of simulations is visualized in the Phase Lifetime vs N panel and started with the Analysis>>N Ramp as shown below.

In this mode, the user selects the range of number of photons to be simulated: [N_min, N_max} by setting the # Photons axis range and the # Bins/Decade parameter at the bottom left of the graph. A geometric progression of photon number will be generated accordingly and simulations performed for each value of N.

The number of simulations for each value of N is defined by the # Simulations parameter on the top right corner of the panel. The larger this number, the better the accuracy of the result, but the longer the computation time.

Tip: Try a small number first (say 100) to get an idea of the result and repeat with a larger value when deemed worthwhile.

Note that during the simulation, a progress bar appears at the bottom of the graph, and an Abort button at the bottom of the window. The Abort button can be used to interrupt the simulation if it takes longer than anticipated. All data from the current series will be discarded.

Two curves are generated for each series:

• • tau (N) Plot: reports the average phase lifetime for each value of N

  • SDV tau (N) Plot: reports the standard deviation of the phase lifetimes calculated for each value of N

Right-clicking on a plot name in the legend gives access to a variety of functions to manipulate these plots (and save them in ASCII format).

The parameters used for the series simulations are output in the Notebook, which can be opened using the Windows>>Notebook (Ctrl+N) menu item.

2. Gate Width Series

This type of simulations is visualized in the Phase Lifetime vs W panel and started with the Analysis>>W Ramp as shown below.

In this mode, the user selects the range of gate width to be simulated: [W_min, W_max} by setting the W axis range and the # Bins parameter at the bottom left of the graph. A linear progression of gate width will be generated accordingly and simulations performed for each value of W. The number of photons generated in each simulation can be defined in different ways, discussed later.

The number of simulations for each value of N is defined by the # Simulations parameter on the top right corner of the panel. The larger this number, the better the accuracy of the result, but the longer the computation time.

Number of simulated photons:

• • simulations can be performed with a constant number of photons no matter what the gate width is. To do so, uncheck the # Photons Scales with W checkbox and set the desired number of photons: # Photons.

  • simulations can also be performed with a number of photons depending on the gate width. This would correspond to a situation where the same sample is acquired successively with increasingly larger gates, but using the same excitation intensity. There are two different ways to use this mode, both selected first by checking the Photons Scales with W checkbox:

    • Use Offset/Slope: checking this box reveals two parameters: Offset and Slope, which define how the number of photons N varies as a function of W:

N = Offset + Slope x W

• • do not Use Offset/Slope: in this case, the number of photons, N_min, for the first gate width value, W_min, needs to be entered in # Photons, and subsequent numbers are calculated according to:

N = N_min x W/W_min

This first scenario is encountered when the measured signal level (N) does not verify the last equation and the linear relationship between N and W is affected by an offset (positive or negative).

Note that during the simulation, a progress bar appears at the bottom of the graph, and an Abort button at the bottom of the window. The Abort button can be used to interrupt the simulation if it takes longer than anticipated. All data from the current series will be discarded.

Two curves are generated for each series:

• • tau (N) Plot: reports the average phase lifetime for each value of N

  • SDV tau (N) Plot: reports the standard deviation of the phase lifetimes calculated for each value of N

Right-clicking on a plot name in the legend gives access to a variety of functions to manipulate these plots (and save them in ASCII format).

The parameters used for the series simulations are output in the Notebook, which can be opened using the Windows>>Notebook (Ctrl+N) menu item. The Notebook can be saved as a Rich Text Format (rtf) file and additional comments can be typed in and graph bitmaps copied in (right-click in a Graph plot area and choose Copy Data to copy the Graph's bitmap to the clipboard, and go to the Notebook window to paste it in),

Notes

1. To perform simulation for a single set of parameters, simply set the number of bins to 1.

2. Since the software is using parallel threads to perform each set of simulations, it is advantageous to use a multicore PC.

3. Each new series of simulations adds a complete set of plots. To delete the plots from one series to the next, use the the right-click command Clear Graph or select the plots to be deleted (check the box next to their name in the legend and use Delete Selected Plots).