Video parameters

Video parameters is the first panel of module Simulation. Access the panel content by pressing Bottom arrow . The panel closes automatically after other panels open or after pressing Top arrow .

Use this panel to define the settings of data acquisition like camera noise and video characteristics.

Video length

Defines the total number of image frames in the video.

It is usually noted L

default: L = 4000 frames

Frame rate

Defines the acquisition rate of the video in frames per second (fps).

It is usually noted f and is linked to the acquisition time t_exp by the relation:

$f = \frac{1}{t_{\textup{exp}}}$

with t_exp in seconds

default: f = 10 fps

Pixel size

Defines the square dimensions of a pixel in micrometers.

It is used in the conversion of PSF widths from micrometers to pixels.

default: 0.53 μm

Bit rate

Defines the camera digitization bit depth in bit/pixel and defines the range of pixel values.

It is used to calculate the saturation pixel value in the video.

default: 14 bit/pixel

Video dimensions

Define the dimensions of video frames in pixels , following the x- (a) and y- (b) directions.

default: 256-by-256 pixels

Camera SNR characteristics

Use this interface to define the camera noise distribution and the conversion of photon counts to images counts.

Select the camera noise model in (a) and set the corresponding parameters in (b).

Available camera noise models are:

Offset only
P- or Poisson
N- or Gaussian
NExpN- or Gaussian + exponential tail which is relatively time consuming; expect spending around 20 minutes to simulate a 256-by-256-wide and 4000 frame-long video
PGN- or Hirsch

Refer to table Model parameters for an exhaustive list of model parameters.

Offset only

Photon counts μ_pc are ideally converted to image counts μ_ic such as:

$\mu_{\textup{ic}} = \mu_{\textup{pc}}$

A constant camera dark count μ_ic,d is then added.

default: μ_ic,d = 113 ic

P- or Poisson

Photon counts μ_pc are converted to electron counts μ_ec with a detection efficiency η such as:

$\mu_{\textup{ec}} = \mu_{\textup{pc}} \times \eta$

Electron counts are distributed following a Poisson distribution and are ideally converted to image counts μ_ic such as:

$\mu_{\textup{ic}} = \mu_{\textup{ec}}$

A constant camera dark count μ_ic,d is then added.

default:

μ_ic,d = 113 ic
η = 0.95 ec/pc

N- or Gaussian

Photon counts μ_pc are converted to electron counts μ_ec with a detection efficiency η such as:

$\mu_{\textup{ec}} = \mu_{\textup{pc}} \times \eta$

Electron counts are converted to image counts μ_ic with an overall gain K such as:

$\mu_{\textup{ic}} = \mu_{\textup{ec}} \times K$

A constant camera dark count μ_ic,d is added and image counts are distributed following a Gaussian distribution of mean μ_ic and standard deviation σ_ic.

σ_ic depends on μ_ic, the readout noise standard deviation σ_d and the analog-to-digital noise standard deviation σ_q such as:

$\sigma_{\textup{ic}} = \sqrt{\mu_{\textup{ic}} + ( K × \sigma_{\textup{d}} )^{2} + \sigma_{\textup{q}}^{2}}$

default: values taken from the literature (reference here):

μ_ic,d = 113 ic
η = 0.95 ec/pc
K = 57.8 ic/ec
σ_d = 0.067 ec
σ_q = 0 ic

NExpN- or Gaussian + exponential tail

Photon counts μ_pc are converted to electron counts μ_ec with a detection efficiency η such as:

$\mu_{\textup{ec}} = \mu_{\textup{pc}} \times \eta$

Electron counts are converted to image counts μ_ic with an overall gain K such as:

$\mu_{\textup{ic}} = \mu_{\textup{ec}} \times K$

A constant camera dark count μ_ic,d is added and image counts are distributed following an exponential-tailed Gaussian distribution with mean μ_ic, standard deviation σ_ic, tail contribution A_CIC and exponential decay constant τ_CIC.

This model is purely empirical: model parameters are obtained by fitting the distribution P of image counts obtain from a camera with closed shutter μ_ic,0 with the function:

$\textup{P}(\mu_{\textup{ic,0}}) = ( 1-A_{\textup{CIC}} )\textup{exp}\left [ -\frac{( \mu_{\textup{ic,0}} - \mu_{\textup{ic,d}} )^{2}}{2\sigma_{\textup{ic}}^{2}} \right ] + A_{\textup{CIC}}\textup{exp}\left ( - \frac{\mu_{\textup{ic,0}}}{\tau_{\textup{CIC}}} \right )$

To fit dark count distribution with the NExpN model, you can use our home-written script located at:

MASH-FRET/tools/fit_NExpN.m

default: values taken from the literature (reference here):

μ_ic,d = 106.9 ic
A_CIC = 0.02
σ_ic = 4.9 ic
τ_CIC = 20.5 ic
η = 0.95 ec/pc
K = 57.8 ic/ec

PGN- or Hirsch

Photon counts μ_pc are converted to electron counts μ_ec with a detection efficiency η and a contribution of clock-induced charges CIC such as:

$\mu_{\textup{ec}} = \mu_{\textup{pc}} \times \eta + CIC$

Electron counts are distributed following a Poisson distribution of mean μ_ec and are then multiplied in the electron-multiplier (EM) register following a gamma distribution with shape parameter μ_ec and the EM gain g, for scale parameter.

Multiplied electron counts are converted to image counts μ_ic with an analog-to-digital factor s such as:

$\mu_{\textup{ic}} = \frac {\mu_{\textup{ic}}}{s}$

A constant camera dark count μ_ic,d is added and image counts are distributed following a Gaussian distribution of mean μ_ic and standard deviation σ_ic that represent the readout noise standard deviation σ_d converted to image counts with the analog-to-digital factor s such as:

$\sigma_{\textup{ic}} = \frac {\sigma_{\textup{d}}}{s}$

default: values taken from the literature (reference here):

μ_ic,d = 113 ic
η = 0.95 ec/pc
g = 300
σ_d = 0.067 ec
s = 5.199 ec/ic
CIC = 0.02 ec

Model parameters

The parameters used in camera noise models are summarized in the table below:

parameter	units	description	in model
μ_ic,d	ic	signal offset	none, P, N, NexpN, PGN
η	ec/pc	detection efficiency	P, N, NexpN, PGN
K	ic	overall gain	N, NExpN
sat (read only)	ic	saturation value	N
σ_d	ec	readout noise deviation	N, PGN
σ_q	ic	analog-to-digital conversion noise deviation	N
τ_CIC	ic	exponential tail decay constant	NExpN
A_CIC		exponential decay contribution	NExpN
σ_ic	ic	Gaussian standard deviation	NExpN
g		system gain	PGN
s	ec/ic	analog-to-digital factor	PGN
CIC	ec	CIC offset	PGN

The saturation value is calculated from random distributions using the Bit rate. For more information about the saturation value calculations, please refer to the source code at:

MASH-FRET/source/mod_simulation/Saturation.m

Abbreviations:

ic: image count
pc: photon count
ec: electron count
CIC: clock-induced charges