Thanks for the data Stan.  Nice to see someone going to the trouble of getting numbers to add to the discussion.  However the subject line of the thread doesn't seem to be addressed here.   

I've had this problem understanding "accumulation" vs. average for years.  I've heard the argument that accumulation, or adding multiple images amounts to the same thing as averaging (accumulate multiple images, then DIVIDE the resulting pixel intensities by the number of images collected), as the noise does not accumulate to the same extent as the signal.  However the two seem mathematically different, should produce different results and the terms should not be used interchangeably.  What am I missing here?

Thanks,
C


Carl A. Boswell, Ph.D.
Molecular and Cellular Biology
Univ. of Arizona
520-954-7053
FAX 520-621-3709


-----Original Message-----
From: Confocal Microscopy List [mailto:[log in to unmask]] On Behalf Of Stanislav Vitha
Sent: Monday, June 27, 2011 11:49 AM
To: [log in to unmask]
Subject: Re: averaging vs. accumulation for noise reduction - is there a difference?

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Hallo,
thanks everybody for their input regarding this topic. 
I have some results from a simple test.

Long dwell time (200 us) seem to produce essentially the same signal to background ratio  as accumulation of 100 images with 2us dwell times:
signal:  

1 x 200us dwell time:
                         area (pixels)	mean 	STDEV   signal-to-background
specimen             20812	             181.76	34.44     14.63
background          20812	              12.42	8.99

100 x 2 us dwell time, Sum of frames
                          area (pixels)	mean 	STDEV   signal-to-background
specimen              20812	             185.28	33.97     14.73
background           20812	              12.58	8.97


The specimen is a Chroma fluorescent slide occupying half of the field of view, the other half does not have any sample (= background).
The Sum was calculated in ImageJ (Image-Stack-Z Project-Sum of Slices).

FYI,
I also tested for the linearity of the signal versus laser power in the photon counring mode to see when the pile-up error would become noticeable.
Using 10 us dwell time, spectral detector was set to narrow width (2 nm band pass)to restrict the photon flux. The signal seems to scale well with intensity, with just a slight drop off at the highest laser powers (but some of that drop off can be due to photobleahching; after acquisition I zoomed out and the scanned area showed as a darker rectangle):
(results from an area of 16756 pixels)
                            Specimen             background
laser power (%)	mean 	STDEV      mean 	STDEV
0.1		9.36	7.62         0.67	2.13
0.2		11.3	8.42         0.65	2
0.3		13.26	8.89         0.65	2
0.4		15.21	9.69         0.67	2.1
0.5		16.85	10.22        0.68	2.09
1		45.54	16.63        0.68	2.13
2		82.51	22.64        0.67	2.15
4		155.69	31.58        0.66	2.09
8		297.19	43.26        0.73	2.19
16		567.71	60.79        0.79	2.32
32		1049.43	82.74        0.86	2.36


So it seems that I can count about 100 photons per microsecond without having to worry too much about the pile-up. Does anybody know how how the Olympus's "Hybrid photon counting" works? 

Spreadsheed file with more details, graphs are here:
http://microscopy.tamu.edu/instruments/light-microscopy/fv1000-tests

This folder also contains some of the image files.


Sincerely,

Stan Vitha
Microscopy and Imaging Center
Texas A&M University