Contents
CCD Basics
Rain Drops in Buckets Analogy
CCD’s Linear Relationship
Why Linearity is Important?
Testing My CCD Linearity
Linearity Test Results
There is nothing simpler than using your camera in your phone.. Just open the app with a click and press a button.. or show your hand. That’s it! You have a picture.. Congratulations!
Beneath this process is such a complex amount of science happening in your hand that it would take many many courses to understand it all. So let’s start your first course.. pay attention now!
Kidding :) First, i have very little idea how that happens, except some very basic knowledge.. second, you will runaway from this blog forever and miss all the good things happening here.
So let’s keep it simple here..
CCD Basics
CCD are made of ‘Picture Elements’ or Pixels. These are very small in size and getting smaller with every new chips being produced. You talk about them all the time.. like ‘my camera is 12 Mega Pixels’ etc.. That’s the total number of pixels in your chip which is in your camera. How big can your print of your picture be or how much you can zoom in before you start seeing pixels, that depends on how many pixels you have in your chip.
Almost all of the imaging devices have CMOS chips in them.. This is a different technology and getting better everyday because of the massive demand in the world. But traditionally CCDs have been used for very light sensitive scientific work. Though it seems CCDs are not the future, most of the astroimagers, for now, still have CCDs in their astroimaging cameras. Specially those who wants to have scientifically reliable data.
Light particles (photons) are coming from the stars, galaxies, nebulae, planets, asteroids, comets, background stars and galaxies (which cannot be distinguished in our images), our atmosphere, ground light being reflected by the atmosphere (what did i miss here.. Alien ships?). These photons are directed to our CCDs by our optical systems (telescopes of all kinds and sizes). Next, these light particles are converted into electron and then collected in pixels from where they can be counted when an image is read.
Rain Drops in Buckets Analogy
The analogy (Figure 1), they give us of pixels capturing photons is of buckets catching rain drops.. this is not a bad one and we do get to visualise how the process really happens.
Every pixel is an empty bucket and can gather photons coming from the optical system in the form of electrons. These electrons will be counted, as best as it can be by the camera and as far as physics allows it.
Figure 1. Rainfall Analogy
So now the question is.. How many electrons will be generated by the imaging chip, for how many photons it receives. This is called the Quantum Efficiency of the chip.. higher the better.. but it can never be 100%.
Next, suppose if the chip is exposed for one second and it receives 100 photon which results in generating 80 electrons.. that’s a QE of 80%… So far so good.
CCD’s Linear Relationship
But what if i expose it to 2 seconds? It should receive 200 photons and it should generate 160 electron. Doubling the exposure is doubling the electrons.. this is a linear trend and is generating a reliable scientific data.
Like everything else, this does not actually happens in the imaging chips and these devices loose linear relationship at some point. That is the reason why astroimagers are always told to expose the imaging chips to somewhere around half the saturation levels. That will be around 30,000 ADUs. So our data needs to peak at this value and not more than that… or does it?
Linearity test can be done with any imaging chip. You can do it with your DSLR as well. Here i tested my camera. The idea is to start an exposure and keep doubling the exposure time with every next image. Then see if the ADU values are doubling or not? and if this value is doubling, to which ADU range this trend continues.
Why Linearity is Important?
Why it is important to have a linear response? Let’s see a simple example.
Photometry is a technique where we measure one star’s magnitude‘s by comparing an other’s whose magnitude is already knows with some accuracy.
Figure 2. shows an illustration where different stars are shown. Bigger the size, brighter the stars hence lower the magnitude numbers. Yes magnitude system seems confusing at first!
Figure 2. An illustration of Stars in an Image
Suppose we want to measure magnitude of Star B, which seems to be a moderately bright star. Long exposing this star field will produce more ADU numbers for all stars and Star A most probably will leave linear ADU count. Which means Star A can have 30,000 ADU in 30 seconds and 45,000 ADU in 60 seconds (it should be 60,000 ADU for a scientifically useful data), while Star B will double its ADU value from let’s say 5,000 to 10,000 with doubling the exposure time.
Take away lesson: We cannot use ADU value of Star A to find ADU value of Star B in this example. Star C can be a right comparison star here.
I hope now you see the critical importance of linear response needed for any reliable data coming from imaging chips. Those who do the ‘pretty pictures’ work, are doing great but adjusting the ‘curve’ in Photoshop destroys any scientific value of an astronomical image.
Testing My CCD Linearity
I slewed my telescope in the sky trying to find a patch of the sky where stars will not clearly saturate my CCD and also will not be very dim. So for me a part i found was centered here at:
Center RA (2000.0): 17h 23m 09.12s
Center Dec (2000.0): +37° 12' 39.0"
I started my exposure with this sequence of exposure times: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 seconds.. doubling the exposure time with every next image and hoping to get double the ADU values.
Image Scale: 0.9470 arcseconds/pixel
Angular/Area Size: 0° 08' 05" x 0° 08' 05"
Position Angle of the CCD camera: 115° 13' from North through East
Figure 3. The chosen star field and the four stars used to measure Linearity of the SBIG CCD
Table 1. shows the exposure values of 11 exposures and the ADU values of four stars marked in Figure 3.
All the images were calibrated with Bias and Dark frames. Dark frames were not taken from the dark frames library but rather taken fresh with matching exposure time of the Raw frames.
Notice with one second exposure, the ADU value is the lowest and increases with increasing exposure time. Now we need to plot this.
Table 1. Exposure time vs ADU values of four stars
Linearity Test Results
Figure 4. shows the graph of this comparison. Look at that.. almost surprising result. The CCD is linear to the very end of pixel saturation level. The ‘grey’ star has a bump in the linear line and i do not know why that happened.. could be a cosmic ray hit that could not be corrected with calibration? or is it something else? I am not sure.
But the other stars show a very very linear response.. this is a happy news. This means i can expose my CCD beyond 60,000 counts and still my data will have scientific value. I can accommodate brighter stars in my images and rely on them for good photometric analysis.
There is a reason why Anti Blooming Gate technology is NOT preferred for scientific CCDs.. and mine is a Non Anti Blooming Gate CCD… happy me :)
Figure 4. Exposure time vs ADU count