ASTRO: Analytic expression derived for signal to noise ratio for a pixel

This is targeted at the case of imaging a nebula through a narrowband
emission line filter where the nebula has line emission.

The derivation is referenced to the filter and is derived from an equation
published in the 1985 revised edition of the "Infrared Handbook" by Wolfe.

The math may look intimidating but if you even remotely remember integral
calculus of definite integrals, and you take the time to read the words I
added to explain how the integral simplifies and how it is evaluated, then
the material should be within reach.

http://www.narrowbandimaging.com/sig...pixel_page.htm

Richard Crisp wrote:
This is targeted at the case of imaging a nebula through a narrowband
emission line filter where the nebula has line emission.

The derivation is referenced to the filter and is derived from an equation
published in the 1985 revised edition of the "Infrared Handbook" by Wolfe.

The math may look intimidating but if you even remotely remember integral
calculus of definite integrals, and you take the time to read the words I
added to explain how the integral simplifies and how it is evaluated, then
the material should be within reach.

http://www.narrowbandimaging.com/sig...pixel_page.htm




The difference is smaller than I'd have expected. How do the skirts of
the filters compare to the idealized vertical used in the analysis. I'd
doubt both have similar shape. They rarely are close to perfectly
vertical near the top or bottom.

Rick

"Rick Johnson" wrote in message
...


Richard Crisp wrote:
This is targeted at the case of imaging a nebula through a narrowband
emission line filter where the nebula has line emission.

The derivation is referenced to the filter and is derived from an
equation published in the 1985 revised edition of the "Infrared Handbook"
by Wolfe.

The math may look intimidating but if you even remotely remember integral
calculus of definite integrals, and you take the time to read the words I
added to explain how the integral simplifies and how it is evaluated,
then the material should be within reach.

http://www.narrowbandimaging.com/sig...pixel_page.htm




The difference is smaller than I'd have expected. How do the skirts of
the filters compare to the idealized vertical used in the analysis. I'd
doubt both have similar shape. They rarely are close to perfectly
vertical near the top or bottom.

Rick



hehe, grin: one of the things about mathematical modelling is that you can
make
things as complicated as you like: so complicated that you cannot solve in
closed form: have to result ot numerical solutions. My usual approach is to
first identify a simplified case that approaches the situation at hand and
to evaluate it and then do some sanity testing to see if the result makes
sense before I add complexity later.

This one makes intuitive sense in my opinion so I am confident it is
correct; given the simplifying assumptions used.

I can change the shape of the filter side skirts by modeling the filter
response as Sin(x)/x (=Sinc(X)), combining with the Heaviside step
function,
but that would be adding a fair amount of
complexity to the model. A bit less accurate but a bit less complex than the
Sinc(x) case is replacing the vertical filter side skirts with a linear
ramp; perhaps a triangle wave, but it is more complicated and I am not sure
that it will change the results very much.

the thing that would make the results change significantly is adding the
[NII] doublet either side of Halpha: that is noise in an Halpha filter for
su it is a different emission line.

the other thing that would negatively impact the result would be to model
the out of band leakage through the filter when it is supposed to be 100%
blocking.

I don't see doing either any time soon. I am reasonably happy with the
simplified case I analyzed.

Hey, sounds quite eclectic to me. I have saved the file to my harddisk and
will try to understand it later :-)

Stefan

"Richard Crisp" schrieb im Newsbeitrag
news
This is targeted at the case of imaging a nebula through a narrowband
emission line filter where the nebula has line emission.

The derivation is referenced to the filter and is derived from an equation
published in the 1985 revised edition of the "Infrared Handbook" by Wolfe.

The math may look intimidating but if you even remotely remember integral
calculus of definite integrals, and you take the time to read the words I
added to explain how the integral simplifies and how it is evaluated, then
the material should be within reach.

http://www.narrowbandimaging.com/sig...pixel_page.htm

I have a more practical to use version on my website that speaks to how to
assess s/n when you are trying different filters or changing your
collimation etc.

I plan to make a tool that allows you to input an image and it will
transform it to a s/n image where the ADU values directly read out in S/N
(dimensionless ratio).

This should be a nice tool to help answer questions like "what happens if I
collimate my scope" or "what happens if I clean my mirror" or "what happens
if I change filters or sensors or the operating temp of my camera"

I am always interested in the technology side, being a hard core
semiconductor engineer for the past 30 years so this is right up my alley.

here's that other tool but without the image transform utility:

http://www.narrowbandimaging.com/SNR..._data_page.htm

The major difference between this current work and the derivation I created
last week is that in the case of the derivation there are some simplifying
assumptions made to assist in evaluating the integrals. In this current work
the observation is made that nature does the integrations for you when you
go through the process of capturing the image. So from a practical
perspective it is easier to use empirical data than it is to use all the
parameters in the derivation.

IN fact you can use the empirical data coupled with specific knowledge of
the filter transfer characteristics and the QE performance of the camera to
determine some of the parameters needed for the analytical case.

The analytical case is good to use if you are designing something and want
to get a quick back of the envelope assessment of the likely performance,
while the empirical data version is useful if you are comparing hardware
configurations with real hardware.


"Stefan Lilge" wrote in message
...
Hey, sounds quite eclectic to me. I have saved the file to my harddisk and
will try to understand it later :-)

Stefan

"Richard Crisp" schrieb im Newsbeitrag
news
This is targeted at the case of imaging a nebula through a narrowband
emission line filter where the nebula has line emission.

The derivation is referenced to the filter and is derived from an
equation published in the 1985 revised edition of the "Infrared Handbook"
by Wolfe.

The math may look intimidating but if you even remotely remember integral
calculus of definite integrals, and you take the time to read the words I
added to explain how the integral simplifies and how it is evaluated,
then the material should be within reach.

http://www.narrowbandimaging.com/sig...pixel_page.htm

"Richard Crisp" wrote

I have a more practical to use version on my website......

http://www.narrowbandimaging.com/SNR..._data_page.htm
................

Richard, et al:

I missed the beginning of this discussion! Now with the link I see what
this is all about. I'll have to check it out.

One of my observing friends (the owner of the CCD camera I use) is a
research professor of EE and computer science. She specializes in hiding
encrypted data in image files, but she's also done a lot of work for the
USAF on CCD cameras, in particular "fingerprinting" a camera's chip so that
one can always link any image back to a specific chip. I'll pass your page
on to her. She or one of her grad students may fine it useful. If so, you'll
probably find yourself 'cited' in a paper!!

George N

"George Normandin" wrote in message
news
"Richard Crisp" wrote

I have a more practical to use version on my website......

http://www.narrowbandimaging.com/SNR..._data_page.htm
................

Richard, et al:

I missed the beginning of this discussion! Now with the link I see what
this is all about. I'll have to check it out.

One of my observing friends (the owner of the CCD camera I use) is a
research professor of EE and computer science. She specializes in hiding
encrypted data in image files, but she's also done a lot of work for the


a true steganographer huh?


USAF on CCD cameras, in particular "fingerprinting" a camera's chip so
that one can always link any image back to a specific chip. I'll pass your
page on to her. She or one of her grad students may fine it useful. If so,
you'll probably find yourself 'cited' in a paper!!

Well hardly: but it sounds nice.

Turns out that chapter 17 of the "IR Handbook" has a wealth of quality
information about how to use filters to spectrally discriminate targets.
That's essentially what I am doing with emission line filters. It is great
stuff. Even though the book's focus is IR, the equations are equally valid
in the visible light portion of the spectrum.

The earlier analytical work is he

http://www.narrowbandimaging.com/sig...pixel_page.htm





George N

"Richard Crisp" wrote
....
One of my observing friends (the owner of the CCD camera I use) is a
research professor of EE and computer science. She specializes in hiding
encrypted data in image files, but she's also done a lot of work for the


a true steganographer huh?

Ya..... one of the world's experts, from the Czech Republic, and an
amateur astronomer too! She's one of the few female amateurs I know who has
made her own 10-inch Dob. The STL-1301E is really a part of her lab, but she
leaves it at Kopernik!

The earlier analytical work is he

http://www.narrowbandimaging.com/sig...pixel_page.htm


Thanks!!

George N