Signal-to-Noise Ratio Explanation
1.
Final images is to reduce these noise sources as much as possible.
2. CCDs are
designed to generate low dark current, and cameras are cooled to remove as
much thermal noise as possible.
4.
Cameras are designed to have low readout noise, dark sites to help eliminate
light pollution and reduce this noise.
Combining Exposures to Reduce Noise
·
The usual method for reducing noise in astronomical images is to stack multiple exposures.
·
In an image,
there is signal and there is noise.
·
While the signal (the light from the object being imaged) stays
the same from image
·
to image, the noise changes.
·
The signal-to-noise ratio (SNR) in an image measures how much
signal there is relative to the noise levels.
·
Decreasing the amount
of noise in an image increases the signal-to-noise ratio and results in a better picture.
For Example
An image with a 300 signal to a 150 noise =2:1
Noise decreases to 100 = 3:1
SNR 200
SNR 300 (noise reduced)
·
Since signal stays constant, does not
change from image to image
Taking two image and averaging two exposures together doubles the
signal. But noise, averaging two exposures increases the noise by only √2, about 1.4 times.
Two
images = 2x2 = 4 signal
Two
images = square root 4 =1.4 noise
All these are part of why it increase or reduce SNR
·
Exposure Time
·
Number of Exposures
·
Object Flux
·
Sky Background Flux
·
Binning
·
Resolution
·
Focal Ratio
·
Dark Current
·
Readout Noise
Exposure
Time
This is probably the most important factor. The most obvious way
to increase ratio (SNR-increasing the ratio increases the quality of the image)
is simply to increase exposure time.
If we increase the exposure time (say from 300 sec to 600 sec)
For most deep-sky images, doubling the exposure time increases the
SNR by √2 = 1.4 times.
Sky glow, from light pollution
sources, prevents us from taking indefinitely long exposures so
SNR must be increased through other means.
Sky glow limitations also imply that there may be an optimal
exposure time for a given imaging system and location, which
we will see is true.
Number of
Exposures
We saw earlier how stacking multiple exposures
increased SNR (better image)
Perhaps stacking multiple exposures taken at the optimal exposure
time would be preferable to a single longer exposure.
We will
see that this is true, and for a variety of reasons.
There are myriad ways to combine image files, and they are
discussed in more detail below. The basic method is to average exposures,
taking the mean value of each common pixel to produce a result with less
noise.
Combining N (36) exposures this way leads to a Sign / Noise Ratio,
increase of √N (36) = 6.
As seen in the examples above, averaging 2 exposures yields a √2 =
1.4 increase in SNR,
and averaging 10 exposures
gives an increase of √10 = 3.16.
averaging 20 = 4.47
From 1.4 to 3.16 (3,16/1,4x100) is 225% increase in SNR
From 1.4 to 4,47 =319% , its only 94% increase, while it goes from
10 to 20 (100% increase). It can also be seen that there is a point of
diminishing returns,
As will be seen below there are other reasons to use a larger
number of subframes; for example, it might be preferable to take ten 5-minute exposures rather
than five 10-minute exposures.
Sky
Background Flux
This is the flux of the sky glow, determined
primarily by light pollution factors.
The sky (whether lit by city lights or the moon or natural
airglow) produces photons that are captured by the CCD and turned into the
background of the image. The image becomes contaminated with noise.
Note that this background in an image is not perfectly black but
has some value.
This value is a function of the sky background flux and the
exposure time. For example, the sky from a dark site might have a flux of 2e-/sec (this is
also a function of focal ratio since it is measured in terms of what the CCD
counts rather than what the sky itself is producing).
In a 5 minute exposure, the
background will reach a value of 300sec x 2e-/sec = 600e-.
10 mins 600 x2e= 1200e-
·
An image taken from a suburban
location and has a background ADU count of 2500.
·
Converting using the equations above gives a value of
3120e-. (Exposure time was again 600 seconds and the flux is 5.2e-/sec),
·
indicating that the sky is much brighter from this location. Compare
to the 600e- of the dark site.
Binning
·
Binning affects the SNR by effectively increasing the sensitivity
of the CCD chip.
The effect is similar to making the focal ratio faster.
·
Binning a CCD 2x2 combines each 2x2 group of pixels into one
"super pixel" which can gather 4 times as much light as a single
smaller pixel during a given exposure.
Thus the system becomes 4 times faster when binned 2x2, equivalent to a 2-stop reduction in focal ratio. However, as described below, resolution determines SNR as well, and since binning decreases resolution, it can also decrease SNR, and if the SNR decreases the noise will increase.
Resolution
Resolution is a major factor in determining fine detail SNR such as that of stars.
·
Increased resolution gives
increased SNR.
·
However, sampling is an important factor as well.
·
(See the section on Nyquist Theorem for more details on sampling.)
·
Undersampled
images (such as those taken with short focal length scopes and/or binned
CCD chips) will have worse SNR
than properly sampled images.
Focal Ratio
Focal ratio is the primary determinant of imaging speed.
·
Deep-sky imagers all know the importance of having a fast scope
for reducing exposure times. If the exposure time is reduced and we
increase the number of subframes, this will reduce noise.
·
Focal ratio also affects resolution, assuming a constant aperture
(in other words, using a focal reducer on a given telescope) and thus affects
SNR in the same way.
More importantly, focal ratio determines exposure time necessary to achieve a given sky background flux.
Determining Optimal Exposure Times
So, in the end, what is the best exposure time to use for subframes?
1.
Shorter exposures allow better combination methods for greater
noise removal.
Shorter exposures are also an advantage in that, if something goes wrong during the exposure (wind, tracking errors, etc.), less data is lost.
2.
The trade off between taking more short exposures versus fewer
long exposures in terms of SNR loss is very slight, as John Smith recommends
the following exposure recommendation:
This
calculator allows you to determine the ideal exposure time for subframes that
will be stacked. It requires that you take a test exposure using your CCD
imaging setup and measure the background sky value. Please refer to the CCD
Imaging Theory page on Optimum Exposures for the details behind these
calculations.
How to Use
the Ideal Exposure Calculator
- 1. Take a test exposure using
your standard CCD setup. Factors that will influence the calculated
ideal exposure time include light pollution, focal ratio, filters, CCD
camera, binning, and object elevation (altitude). It is recommended
that you image an object near zenith, unfiltered, and on a moonless
night. If you change cameras, telescopes, or observing locations,
you will need to adjust accordingly, or take test exposures for each
setup.
- 2. Take an equivalent length
dark frame. Do this even if you have a low-noise camera that may not
normally use darks. This will remove the bias level from the image.
- 3. Calibrate your light frame
by subtracting the dark frame.
- 4. Measure the background ADU
count (background value) using, for example, the Information tool in MaxIm
DL, or similar tool in the program of your choice. Be sure to avoid
measuring the value of any faint nebulosity. Take a few measurements
around the image and take an average to be sure of getting an accurate
value.
- 5. Select your CCD camera from
the pull-down menu below.
- 6. Enter your test exposure
time in minutes.
- 7. Enter the measured sky
background value from the test exposure.
- 8. Select one of the standard
choices for the percent contribution of readout noise. 5% is the
usual figure used but a higher noise tolerance will give a shorter
exposure time.
- 9. Press the Calculate button to determine the ideal exposure time.
