Atik 314L+ Linearity test and questions

The Atik 314L uses a Sony ICX285L interline monochrome sensor.  If I look at the linearity curve, it looks like you are very linear from 5sec to 58sec (5000ADU to 52000ADU).  There is a "toe" in the linearity curve below 5000ADU; you should remove these points from your linear fit and see how well things reproduce after that.  Also, you did not run your test long enough to see where top-end nonlinearity sets in; I would continue your exposures until you get close to 65K ADU (maybe up to 100 seconds or so).  You will find the saturation/top-end limit to be the more interesting limit.

There are many reasons why a sensor may not respond nicely to small amounts of light (the "toe" in the curve).  You will rarely be in that regime, as faint objects require long exposures so that the sky background will raise the sensor above these values, and short exposures are usually for bright objects, where the important flux is near the saturation of the sensor.  That said, you should be aware of possible deviations in your photometry if the raw pixel values are ~5000ADU or less.  You can even avoid that issue if your target and comparison star are of the same brightness (same part of the linearity curve).

I don't think changing the temperature will change the inherent linearity.  However, if you are subtracting substantial dark current/bias signal, then errors in these values will affect the toe of the curve (one of the possible problems).  it would not hurt to try the same experiment at colder temperatures and see what you get.

As I mentioned above, non-linearity is one reason why you take care in selecting comparison stars.  The ideal comparison star is spatially close to the target, and has the same brightness and color.  That rarely happens (an example is EW Sct - look at that neat field!).  Then linearity, extinction and transformation become less important.

Nonlinearity is the "norm" for near-IR sensors like InSb and InGaAs because of the way the hybrid sensors are operated.  Our NIR team at USNO-Flagstaff wrote software to "linearize" the detectors (basically, you just invert the linearity curve).  I also applied this to the 1024x1024 sensor I used on the 1.0m telescope for all of my calibration photometry with good success.  I seem to remember that Richard Berry was writing such a linearity  module for AIP4WIN, and other vendors might have one as well.  However, this linearity correction is rarely done unless the nonlinearity is extreme (several percent).  At the one-percent level, it really doesn't contribute much to the photometric error.  Remember, a star profile has pixel values distributed from the peak value to the sky background.

Good luck - and thanks for doing this test!

Arne

Hi Gianluca,

The way this is normally done is to generate a lookup table, 65536 elements in length.  one column is the ADU from your system.  one column is the corrected ADU value.  Then, for every pixel in your image, you use the raw pixel value as an index into the table, retrieve the corresponding true ADU value, and replace the original pixel value in the image with this new value.  It is a very fast operation.  You should do it with the raw pixel values before bias/dark subtraction or flatfielding; in this manner, the raw values only fall in the range 0-65535.  Once you dark subtract, the noise in the dark current can generate negative values (such as an overcorrected hot pixel), and so a simple lookup table is difficult to use without additional logic.  There is an additional assumption that all of the nonlinearity is due to the sensor response and not due to the signal chain digitization.

The harder part is generating the lookup table itself.  What you want is ADU vs ADU, and not ADU vs time.  So you have to make some assumptions:  zero exposure should yield zero counts (or 100 counts, if you are using an SBIG camera; the best linear fit ito your data s used to find the difference between a 1-to-1 relation and your actual device.

The harder part still is how to implement this.  I think MaximDL provides plug-in capability.  Python could be used with PyFITS.  A simple script can be written in "cl" for iraf.  It depends on your programming ability and access.  Perhaps someone can come up with a simple scheme for some common image processing system.

Testing your implementation is easy - you just run your linearization data through it, and see if you now get a straight line response.

Arne