image sampling, f-ratios, and snr in...

Craig Stark, Stark Labs

Image Sampling, F-ratios, and SNR in Astrophotography

Borg 101 f/4QSI 5403.8”/pixel

Thursday, June 2, 2011

http://www.stark-labs.com

Sample according to your seeing or suffer the consequences

+ =

Long focallength

Small (color)pixels #@#$%&#@!!!!!



Atmosphere, focus, tracking, and optics all blur before the CCD.

http://www.weatheroffice.gc.ca/astro/seeing_e.html



Our CCD samples sections of the sky to make pixels.

Perfect seeingPerfect optics3” separation

High samplingrate

Low samplingrate



What is my sampling rate and what should it be?arcsec/pixel = 206 x PixelSize ÷ FocalLength

4.3 micron pixels

Focal length arcsec/pixel

400 2.2”

1000 0.88”

2000 0.44”

3000 0.3”

For an 8” scope, f/5 and below!



Why not run at high sample rates? What’s wrong with 0.3”/pixel?

For a given camera (a given pixel size), increasing the sampling rate cuts the FOV. You’ll fit less on the chip.

Unless you’re on Mt. Wilson or somewhere else with sub-arcsec seeing, you lost the details before they hit your chip. You’ll never record those details anyway.

High sample rates mean fewer photons per pixel which means worse SNR. You’ll have noisier images.



Sampling beyond the seeing gives no extra detail in the image



Hubble M51Blur by 2 pixels

Hubble M51Blur by 2 pixels

Shrink 75%Rescale back

“Seeing” (2 pixel blur) limited the resolution. This meant I could sample it less (shrink) and not lose anything.



C8 at 0.75”/pix C8 binned 1.5”/pix C8 binned 1.5”/pixresampled 2x

Does the 0.75” have any more spatial detail?Has it even lost something?



Sampling rate affects your SNR100mm scope with 560 mm f/l (f/5.6)

100mm scope with 400 mm f/l (f/4)

Dropping one f-stop boosts SNR by 41%



What is the f-ratio and whyshould I care?

F-ratio = Focal Length ÷ Aperture

Reducing the focal length of your scope drops the f-ratio

Increasing the aperture at the same f/l drops the f-ratio

F-ratio determines the number of photons per area of sky that make it to your CCD well.

Larger scopes at the same f-ratio give more magnification

Foca

l len

gth

Aperture

≈F-ratio



But I heard f-ratio doesn’t matter. It’s a myth, right? Nope...

The “f-ratio myth” page by Stan Moore that started this said, “There is an actual relationship between S/N and f-ratio, but it is not the simple characterization of the ‘f-ratio myth’.”

His page uses a different definition of SNR. Instead of just “how noisy is the image” it measures “how much information is in the image” (including how much spatial detail).

When you look at “pixel SNR” (how noisy is the image), the f-ratio dominates. It’s not just in extreme or marginal cases.



Images courtesy of Mark Keitel

FRC 300 @ f/7.8 FRC 300 @ f/5.9

Does the f/7.8 really not give up any SNR?



8” f/

5.75

4” f/

4

25% as many photons making it into the tube yet less noisy...In the end, almost 3x as many photons per pixel on the 4”.



For extended targets, the photon count per pixel dictates the SNR

Also note effect of read noise for line filter work



Take home messages on F-ratio

Aperture alone doesn’t “rule”. I’d rather image DSOs on an 8” f/5 than a 30” f/15.

F-ratio precisely encapsulates the photons per pixel (from extended objects) per unit time that drives pixel SNR (how noisy the image looks). It (along with exposure time) says if you’re photon poor.

Want higher SNR with the same image time? Drop the f-ratio.

Want more spatial detail with the same time and SNR? Keep the f-ratio and increase the aperture (and hope your skies give it to you).



Sample according to your seeing or suffer the consequences

+ =

Long focallength

Small (color)pixels #@#$%&#@!!!!!

Aaaahh!I’m photon

poor!



Suggestions1. Measure your sky’s seeing

On unstretched data, measure stars’ FWHM

from good nights

2. Figure the highest-resolution sampling

That FWHM divided by 2, 2.5, or 3

2.5” ~1”

3. Figure that focal length (or pixel size) and don’t exceed this

206 x PixSize ÷ FocLen

~1500 mm

4. Feel free to run even significantly less than this.

Don’t sacrifice coverage for wasted resolution



“Undersampled” but smooth stars

~4 arcsec / pixel



Suggestions1. Measure your sky’s seeing

On unstretched data, measure stars’ FWHM

from good nights

2. Figure the highest-resolution sampling

That FWHM divided by 2, 2.5, or 3

2.5” ~1”

3. Figure that focal length (or pixel size) and don’t exceed this

206 x PixSize ÷ FocLen

~1500 mm

4. Feel free to run even significantly less than this.

Don’t sacrifice coverage for wasted resolution


Questions?

Borg 101 f/4 QSI 540 3.8”/pixelThursday, June 2, 2011

image sampling, f-ratios, and snr in...

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