Gain versus Exposure Time. Image Integration.

[PKay (Peter)]

This is an attempt to sort out thoughts in writing. If you can spot error, please let me know.
Signal to Noise Ratio is another story, and for me is getting no attention (Image Integration processing techniques puts SNR theory into the background).

I am using a ZWO ASI1600MC camera. However the ideas below would apply to any camera.

I have just finished an experiment imaging a star field.
I radically varied the GAIN (from 20, 50, 70, 139(unity) & 200). Keeping the EXPOSURE TIME a constant at 60 sec.
Then I radically varied the exposure time for 2, 30, 60, 120 & 240 sec. Keeping the GAIN a constant.
The results are for me, are quite conclusive .
EXPOSURE TIME is the key element.
GAIN SETTING? In all further work I am setting it at unity (139), and there it will stay.

Proof was further found when taking my morning FLATS. A correctly exposed FLAT will reveal LENS artifacts such as dust particles. GAIN is held constant. Exposure time variation in only tenths of a second can make a huge difference.

In land based photography exposure time (shutter speed) is critical for correct exposure.
Same with astro photography.
And it is dependant on the target and your FIELD OF VIEW.

A bright star such as Sirius is sending out a lot of photons / sec.
You have a small FOV, then an exposure time of 2 sec. might be appropriate.
You have a large FOV, then an exposure time of 30 sec may be the best choice.

For a feint nebula an exposure time of 240 sec. (small FOV) would be a better choice.

What if you have both in the same image?
I think that each element has to be treated separately.
And in this case an understanding of how IMAGE INTEGRATION works is required.
There is more than one way of integrating an image, and the maths involved is horrendous.
A fundamental understanding of how it works is enough.

This is my take on it:
You have 30 images to integrate (30 is the ideal choice by the way, but more on that at some other time).
Draw a line (say 5 pixels long) through the centre of a star in the first image.
Each pixel has a number associated with it (for simplicity the number range is from 1 to 10).
I will just use 5 images (out of the 30).
Image 01: Pixel 01: has the count ( 1, 2, 4, 8, 1)
Image 02: Pixel 01: has the count ( 1, 2 ,4, 8, 1)
Image 03: Pixel 01: has the count ( 1, 2 ,4, 8, 1)
Image 04: Pixel 01: has the count ( 1, 2 ,4, 8, 1)
Image 05: Pixel 01: has the count ( 1, 2 ,4, 8, 1)

After integration the result is the average value (1, 2, 4, 8, 1)

With the above example, it is easy see that if Image 05 was (8, 8, 8, 8, 8 )
The result would be ~ (2, 3, 5, 8, 2).

So what does that mean, and how do we use it?

So in the example of a bright star and a dim nebula (small FOV).
Take 30 images at 2 sec. exposure.
Take 30 images at 240 sec. exposure.
Integrate each data set separately.
Integrate the 2 resulting images.

[JA]

Originally Posted by PKay

This is an attempt to sort out thoughts in writing. If you can spot error, please let me know.
Signal to Noise Ratio is another story, and for me is getting no attention (Image Integration processing techniques puts SNR theory into the background).

I am using a ZWO ASI1600MC camera. However the ideas below would apply to any camera.

I have just finished an experiment imaging a star field.
I radically varied the GAIN (from 20, 50, 70, 139(unity) & 200). Keeping the EXPOSURE TIME a constant at 60 sec.
Then I radically varied the exposure time for 2, 30, 60, 120 & 240 sec. Keeping the GAIN a constant.
The results are for me, are quite conclusive .
EXPOSURE TIME is the key element.
GAIN SETTING? In all further work I am setting it at unity (139), and there it will stay.

Proof was further found when taking my morning FLATS. A correctly exposed FLAT will reveal LENS artifacts such as dust particles. GAIN is held constant. Exposure time variation in only tenths of a second can make a huge difference.

In land based photography exposure time (shutter speed) is critical for correct exposure.
Same with astro photography.
And it is dependant on the target and your FIELD OF VIEW.

A bright star such as Sirius is sending out a lot of photons / sec.
You have a small FOV, then an exposure time of 2 sec. might be appropriate.
You have a large FOV, then an exposure time of 30 sec may be the best choice.

For a feint nebula an exposure time of 240 sec. (small FOV) would be a better choice.

What if you have both in the same image?
I think that each element has to be treated separately.
And in this case an understanding of how IMAGE INTEGRATION works is required.
There is more than one way of integrating an image, and the maths involved is horrendous.
A fundamental understanding of how it works is enough.

This is my take on it:
You have 30 images to integrate (30 is the ideal choice by the way, but more on that at some other time).
Draw a line (say 5 pixels long) through the centre of a star in the first image.
Each pixel has a number associated with it (for simplicity the number range is from 1 to 10).
I will just use 5 images (out of the 30).
Image 01: Pixel 01: has the count ( 1, 2, 4, 8, 1)
Image 02: Pixel 01: has the count ( 1, 2 ,4, 8, 1)
Image 03: Pixel 01: has the count ( 1, 2 ,4, 8, 1)
Image 04: Pixel 01: has the count ( 1, 2 ,4, 8, 1)
Image 05: Pixel 01: has the count ( 1, 2 ,4, 8, 1)

After integration the result is the average value (1, 2, 4, 8, 1)

With the above example, it is easy see that if Image 05 was (8, 8, 8, 8, 8 )
The result would be ~ (2, 3, 5, 8, 2).

So what does that mean, and how do we use it?

So in the example of a bright star and a dim nebula (small FOV).
Take 30 images at 2 sec. exposure.
Take 30 images at 240 sec. exposure.
Integrate each data set separately.
Integrate the 2 resulting images.

Hello Peter,

From a mathematical standpoint on the issue of using the mean (average) to integrate the data...

You've chosen to integrate the pixel level data by taking the average (arithmetic mean) as per your example. In your bright star and a dim nebula example/proposal, integrating the data in this way - the average of two (n=30) sub-group averages, will have the same numerical value as taking the average/mean of all the 60 data that made up those same two subgroups.

It is only when you weight one of those (sub-group) averages, differently to the other, as you might with editing or masking layer levels...., that there would be a difference in the final data value at a point.

Of course there are also other forms of data integration possible, beyond using the mean, such as median*, Sigma, etc ........ , that would affect the final data value that may help in assembling a higher quality/lower noise image.

*As a further example with your supplied data, using the median would have resulted in a final value of (1, 2, 4, 8, 1) compared with the (2, 3, 5, 8, 2) that you calculated for the mean.

Best
JA

[RickS (Rick)]

Hi Peter,

Here are a few comments on your essay:

Don't ignore SNR. It is all that really matters. Image integration is all about SNR and it doesn't make sense to think about it as something different.

Yes, exposure time is the key element. More exposure time collects more photons and more photons means higher SNR (signal increases faster than noise.)

Setting sub time based on FOV makes no sense. Do you mean the scope aperture? That would make more sense but is still an oversimplification. You need to consider focal length and pixel size as well.

Your suggestion of integrating stacks of short and long exposures is close to a useful technique for dealing with very wide dynamic range in an image except that you need to combine the two stacks using HDR techniques, eg. the HDRComposition process in PixInsight. Combining them with image integration won't do anything useful.

If you're interested in developing an understanding of the basics have a look at the articles on Signal to Noise by Craig Stark:

http://www.stark-labs.com/craig/articles/articles.html

Another really good source is the Handbook of Astronomical Image Processing by Berry and Burnell.

Cheers,
Rick.

[PKay (Peter)]

Thank you JA and Rick for your input.
It is exactly what I am after.

I understand your comments, and will re-write the essay incorporating your thoughts.

It is difficult to present these ideas and concepts with out getting too technical, and in a way that most of us can understand.

But I do feel, to exceed in astro photography, you need to know such things.