[ RadSafe ] Convolution, etc.

[Dale Boyce]

See "Radiation Detection and Measurement" Second Edition by Glenn Knoll page 
672

V. Computerized Spectrum Analysis
    A. Deconvolution or Unfolding...

The terms are used interchangeably, and technically are correct, although it 
can be confusing.  For instance when you convolve two Poisson distributions 
you wind up with another Poisson. Each point in one distribution is the 
amplitude of of an admixture of the other distribution centered at that 
point.

Clear as mud, probably.  In gamma spectroscopy the peaks are not convolved 
in the same sense, but the admixture of different gamma lines result in a 
distribution of pulse heights while not a convolution of  intrinsic line 
widths it is a convolution of the system response.

In neutron spectroscopy, especially in sorting out something like Bonner 
sphere data it is somewhat more closely analagous to the convolution of 
intrinsic response.

I'm sure that I haven't gone into enough detail to clear anything up for 
people.  I'd recommend looking at Knoll's book. If anyone is interested, I 
can give some more detailed description of the convolution of functions.  A 
good example is the calculation of the activity of the daughter of a 
radioactive product of an irradiation.  One can either directly solve the 
differential equation, or one can convolve the ingrowth of the daughter with 
the ingrowth of the parent.

This last example is probably a good example of why it is appropriate to use 
the terms deconvolution and unfolding.  If you were to take measurements of 
EOB activity of a daughter of a direct product of an irradiation as a 
function of length of irradiation, you would mathematically solve for the 
amplitudes of the various exponential terms by linear or non-linear least 
squares. The same technique you would use for gamma or neutron spectroscopy.

Dale

Dale E. Boyce
daleboyce at charter.net


----- Original Message ----- 
From: "John Jacobus" <crispy_bird at yahoo.com>
To: <JPreisig at aol.com>; <radsafe at radlab.nl>
Sent: Monday, March 20, 2006 8:19 AM
Subject: Re: [ RadSafe ] A neutron spectrometry note


> Dr. Preisig,
> I have also heard the terms used interchangeably in
> the past with regard to work that was done by the
> Naval Research Laboratory on light emissions from
> TLDs.  The signal is deconvoluted.  The spectrum is
> unfolded.
>
> http://en.wikipedia.org/wiki/Deconvolution
> and http://mathworld.wolfram.com/Deconvolution.html
>
> However, as noted in
> http://rkb.home.cern.ch/rkb/AN16pp/node38.html
> "If f(u) and fy (y) are known it may be possible to
> solve the above equation for fx (x) analytically (
> deconvolution or unfolding)."
>
> --- JPreisig at aol.com wrote:
>
>> Hmmmmmm,
>>
>>      This is from:   jpreisig at aol.com   .
>>
>>       Hey all of you,
>>
>>             Hope all is well where you are.
>>
>>       Lately, I've noticed some researchers/workers
>> in neutron spectrometry
>>       using the terms unfolding and deconvolution
>> interchangably.  This is
>>       not a correct thing to do.
>>
>>             Unfolding (and iterative unfolding) are
>> described in the book
>>       Accelerator Health Physics by Patterson and
>> Thomas.  It has been
>>       commonly used to analyze neutron spectrometry
>> data.  There are
>>       recent improvements in this technique, I
>> think.
>>
>>             Deconvolution (and convolution) are
>> described in the Mathematical
>>       Physics book by Matthews and Walker.
>> Deconvolution is regularly used in
>>       the fields of geophysics and seismology.
>> That's it.
>>
>>              Alpha creep, huh?  Wow.  Creep is also
>> used in seismology to
>>       describe rather slow movements of (earthquake)
>> faults.
>>
>>               Take care.        Regards,   Joseph R.
>> (Joe) Preisig, Ph.D.
>>
>>
>
> +++++++++++++++++++
> "Those who corrupt the public mind are just as evil as those who steal 
> from the public purse."
> Adlai Stevenson
>
> -- John
> John Jacobus, MS
> Certified Health Physicist
> e-mail:  crispy_bird at yahoo.com
>
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