Estimating the photon count and system sensitivity from the variance and mean?

[stu_the_flat]

Hello

I need a little help understanding a topic. I’m sorry if this makes little sense to anyone, but as I don’t understand the topic it is quite hard to write a coherent paragraph about it!

I have been made me aware of a technique where the photon count can be estimated and a measure of the systems sensitivity can be made.

It involved taking a measurement of the variance and the mean from a sample where the noise follows a passion distribution.

If the mean and the variance are equal to each other the grey scale value in each pixel is an accurate count of the number of photons that have been detected? If I was to scale the variance over the mean that is a measure of the systems sensitivity.

I have never found the variance to equal the mean so I have construct computer simulations to estimate this.

I have searched, but I am unable to find any kind of tutorial to help me understand this concept. If  somebody could point me in the direction of a good source to understand how this method works, I would be very grateful.

Many thanks

Stuart McIntyre

[Bo ZHANG]

Hi,

It seems that the notion of system sensitivity you defined is linked to how well the photon information is survivied in the camera noise. Indeed, any camera detect photons but also generate thermal noise. A pixel in your image P contains thus two components: P = X + Y where X is the photon counting part and Y is the camera noise. Although X is called photon noise, it includes actually all useful information about the underlying fluorescence emission events. Y is indeed the true "noise" in the story because it reflects not any information about the biological process under observation, and it just perturbe the useful part X.

Now, let's say the variance of X = Lambda. Since X is Poisson distributed, Lambda is also the mean of X, i.e., the average photon counts. Y has a normal distribution and let's suppse it to be zero mean with a variance S. Now you define the sensitivity as:
Sensitivity = Mean(P) / Variance(P)  =  Lambda / (Lambda + S) = 1  / (1 +  S / Lambda)

Clearly, the larger S/Lambda is, the larger the sensitivity is. The "ideal" system generates not a single thermal noise, i.e., S = 0, (or put in another way, a system enabling to detect a lot of photons so that Lambda is very large), which has Sensitivity = 1.

For me, when you apply this to real system, I think you must be careful. In fact, from the above hypothesis, we suppose that Y is zero mean. In reality, this is rarely the case. You might have to first estimate the mean of Y of your camera by measuring it on a black scene without any fluorescence emission. Then subtract it from Mean(P) in the computation of sensibility.

Bo ZHANG
Medisys Research Lab
Philips Healthcare
33 rue de Verdun - BP 313
92156 Suresnes Cedex, France
Tel: [phone]
Fax: [phone]

On Fri, Jul 3, 2009 at 2:53 PM, stu_the_flat <[hidden email]> wrote:

Hello

I need a little help understanding a topic. I’m sorry if this makes little
sense to anyone, but as I don’t understand the topic it is quite hard to
write a coherent paragraph about it!

I have been made me aware of a technique where the photon count can be
estimated and a measure of the systems sensitivity can be made.

It involved taking a measurement of the variance and the mean from a sample
where the noise follows a passion distribution.

If the mean and the variance are equal to each other the grey scale value in
each pixel is an accurate count of the number of photons that have been
detected? If I was to scale the variance over the mean that is a measure of
the systems sensitivity.

I have never found the variance to equal the mean so I have construct
computer simulations to estimate this.

I have searched, but I am unable to find any kind of tutorial to help me
understand this concept. If  somebody could point me in the direction of a
good source to understand how this method works, I would be very grateful.

Many thanks

Stuart McIntyre



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[Andreas Bruckbauer]

Hi Stuart,
I have never done this, but as i understand you measure the mean and variance for different exposure and plot mean as a function of variance. This should be linear and the inverse slope is the gain in electrons/count. Multiplying by the quantum efficiency of the chip should give photons/count. I guess for the variance to be accurate you need very homogeneous illumination, otherwise the background variation will influence your measurement. see
http://www.clf.rl.ac.uk/Reports/2006-2007/pdfs/ar06-07_s7rdi_calibrationintensified.pdf

best wishes

Andreas

-----Original Message-----
From: stu_the_flat <[hidden email]>
To: [hidden email]
Sent: Fri, 3 Jul 2009 13:53
Subject: Estimating the photon count and system sensitivity from the variance and mean?

Hello



I need a little help understanding a topic. I’m sorry if this makes little

sense to anyone, but as I don’t understand the topic it is quite hard to

write a coherent paragraph about it!



I have been made me aware of a technique where the photon count can be

estimated and a measure of the systems sensitivity can be made. 



It involved taking a m
easurement of the variance and the mean from a sample

where the noise follows a passion distribution. 



If the mean and the variance are equal to each other the grey scale value in

each pixel is an accurate count of the number of photons that have been

detected? If I was to scale the variance over the mean that is a measure of

the systems sensitivity. 



I have never found the variance to equal the mean so I have construct

computer simulations to estimate this. 



I have searched, but I am unable to find any kind of tutorial to help me

understand this concept. If  somebody could point me in the direction of a

good source to understand how this method works, I would be very grateful. 



Many thanks 



Stuart McIntyre







-- 

View this message in context: http://n2.nabble.com/Estimating-the-photon-count-and-system-sensitivity-from-the-variance-and-mean--tp3201071p3201071.html

Sent from the Confocal Microscopy List mailing list archive at Nabble.com.

---

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