Some years ago I saw somewhere that one should not use a bias and scaled masterdark frame to reduce CMOS camera images but rather use a masterdark with exposure matching the science frame. How do others feel about this?
I have tried both and of course they give different results (just as a result of the noise) but I don’t know how to tell which is ‘better’.
Taking ~64 dark frames at ~10 different exposures at a half-dozen temperatures takes many hours and I just don’t have enough cloudy nights!
Richard
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The answer, I would say in an annoying fashion, is “it depends.” For example, suppose that darks taken over a range of exposure times all yield exactly the same mean value; in that case, you could use the same single master dark frame for all images.
Suppose that the dark value does rise slightly with exposure time, from 5 counts to 10 counts over 60 seconds. Compare that difference to the typical value of your target images. If the sky value is 1000 counts in a typical exposure, with a typical uncertainty of +/- 30 counts in each pixel, then the difference in the dark exposures will disappear in the noise.
I’d recommend spending an hour or two looking at the various sources of noise in your typical images, and looking at a series of dark images with different exposures. Before you spend hours taking a long series of dark frames with different exposure times, make sure that all that work will actually improve the quality of your measurements to a significant degree.
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Hi Richard and Michael,
Arne has implied that the more callibration frames the better. However we have not discussed or seen any evidence for this, particularly if anyone is actually planning to use 64 darks for a master dark. A test of precision and accuracy after using master darks composed of various numbers of original darks would be of interest.
CCD dark current (electrons/per pixel/second) can be estimated based on temperature and substrate voltage. Manufacturers like Teledyne e2v provide a calculation. Once you know the dark current value at your operating temperature, then you can just multiply it by the exposure length, and then use that to scale the dark frame.
e.g. they give you QD/QD0 = 1.14 x 10E6 * T^3 * e^(-9080/T), where QD0 = dark current at 293K (or 20C, about room temperature).
CMOS active pixel devices don’t work like this, as they are active - each photosite (pixel) is surrounded by 4 to 6 transistors, each of which generate heat (and thus thermal noise) when the device is active eg during readout, or when being cleared etc. Some CMOS sensors can be put into a low-power state to reduce this. Bias doesnt work like substrate bias in a CCD either.
Bottom line is that the total read noise is not scalable as a simple function of exposure time.
So you can’t scale darks on CMOS active pixel detectors.
That means you must take darks the same length as the exposure.
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Here is what I have done since 1992.
I have always taken darks both cooled CCDs and DSLRs at the exposure times and approximate ambient temperature of the environment, especially important with uncooled DSLR cameras. With thermo-electric cooled or dewar cooled cameras this is not as much of an issue.
It sure does take time… but what is the rush? Well, T CrB might require a rush some night! 
If we assume the noise process of a sensor is white noise, it isn’t but close enough, then noise goes down by the sqrt(N images). There is a reasonable limit to N from a practical point-of-view. I try to get at least 2x(N science images) and rarely up to 5x(N science images). With a DSLR I use an intervelometer to run the sequence of darks, checking to make sure the DSLR camera is still good, etc.
I always take bias frames, however, I don’t use them. Rarely, I use them instead of darks when taking very fast shutter exposures like trying to capture speckles, very rare. Subtracting your dark frame already contains the “bias” anyway.
Many noise processes are at work when we do photometry. Read noise, thermal dark current, shot noise, etc. are probably the most important.
A lot of work has been done over the decades to characterize and understand CCD/CMOS sensor noise. I would recommend a Google Scholar search and read up. Here is a link to one to get you started… (https://arxiv.org/pdf/1412.4031)
Jim (DEY)
Colin,
My understanding about scaling darks is that it is possible when dark current increases linearly with increasing exposure time. Put another way, that means dark current in e-/pixel/sec will be constant.
I did some tests a while back on my ZWO ASI294MM camera. The results are below. Clearly, at exposures shorter than about 10 sec dark current is not linear, but above about 10 sec it is.
My conclusion is that it is therefore OK to scale darks from this camera as long as the darks are exposed for longer than about 10 seconds.
Perhaps the above is a bit confusing. Clearly, if you want to scale darks, they should be taken at exposures longer than those of the science images.
The mention of 10 sec exposures is only to describe the approximate lower limit of the exposure times at which the dark current is linear.
Hi Roy, I’m glad you added a clarifying reply to your earlier message.
That 10 second constraint you highlight is very camera-specific, and it looks like for long exposures, you could probably get away with it. I’d encourage people to perform their own analysis.
Here’s a few facts we know:
For single star photometry on a CMOS active pixel sensor, the target and reference/check stars need to be in an area of the sensor that is not affected by “Logic Glow” - the thermal effects that often occur along the edges of the sensor where the control logic, digitization logic and power control is located. CCDs have readout amplifiers in the corners. Most CMOS APS devices have logic at the edges. Here are two photomicrographs showing the typical layout:
Processing: sensor_logic.png…
When you get into exposures that are several seconds in length, that glow tends to dominate the edges of the images. So keep your stars of interest away from the edges 
That “logic glow” is not well-characterized by the sensor manufacturers; it is not quantified in their device specification data.
Some sensors can have the logic powered down. This may include both logic at the edges, and row/column/pixel logic. There is usually a transition time between power states. e.g. Power down at or before the start of the sensor (eg 250ms for some sensors), exposure, and then power up the sensor again in order to read it out (again, it could be 250ms). So these transitions are not predictable by the users, as this is usually a “trade secret” and not disclosed by sensor or camera manufacturers. However it helps give lower read noise.
As the sensors have improved, the power management has improved. e.g. a Sony IMX CMOS 4th or 5th generation sensor is much better than a 2nd generation sensor.
With larger sensors, there is a semiconductor “stitching pattern” - which may show up as quadrants or rectangles. The GPixel and bigger Sony sensors exhibit this. The stitching pattern is caused by stepping of the lithography equipment - basically the device can’t be laid down all at once. There is a subtle difference in ADU count or responsiveness at the edges. For sensors like the GSENSE4040, this difference shows up dead centre on the chip - exactly where your target star would go, so you need to offset it. It is difficult to calibrate out this difference.
So that’s why you have to know your camera’s characteristics, and why I recommend darks at the same exposure length and temperature as your lights.
What we have done to address this issue, is create a finite set of dark masters covering the exposure range we commonly use. You then select an exposure for which you have a dark master in your inventory. My impression, correct me if I am wrong, that darks are durable items. You don’t need to reproduce them frequently.
Beyound that I would be curious what people think about the need to have darks at all for the most recent generation of chips. A Sony chip claims < 0.005 e-/p/s at 0C. We are considering simply not using darks with this camera.
For the moment, I think we’re all going to need darks.
There are still hot / dead pixels, and variances between the ADCs and gain channels in the CMOS APS sensor, stitching patterns, and more. Some of the sensors have “cluster defects” where a shorted/dead/hot pixel may cause the neighbours to glow, or give conversion artifacts.
I can confirm what you (BR/MJB) mention about low dark current - We’ve measured several of the current generation Sony sensors, and we see typical dark current < 0.005 e-/p/s at 0C on the IMX455 in our Aluma AC455 cameras, with a read noise typically around 3.6 e- at 1X gain, 1.6 to 1.8 e- at 3X gain.
That’s consistent with the claim.
However, this is achieved with the sensor powered down. Short exposures (eg less than a few seconds) may not power down the chip, so one expects to see higher dark current.
Some of the “hobby cameras” don’t regulate temperature very well at the sensor itself; and with the high megapixel count sensors (24 - 250 megapixels), getting the heat out is an issue. The more rapidly you read the sensor, the hotter it gets, and there will be a differential between what the sensor silicon substrate temperature is, and what the outside of the device package, let alone the TEC (Peltier) and heatsink. So the frequency of reading images can have an impact on the dark current as well.
I liked your comment about darks being “durable”. As the sensors and camera electronics age, it is worth redoing them. Seasonal weather variation - eg typical ambient operating temperatures also affect the equipment. So I typically redo masters every 3 or 6 months, and I archive the old stuff.
Both CCD and CMOS sensors are subject to radiation damage (cosmic ray hits, background radiation from the rock we are standing on), and develop defects or changes in sensitivity. The other thing that has an impact is aging electrolytic capacitors - they dry out over 10+ years, and lose their ability to hold charge. This will cause voltage variations like increased ripple or poorer regulation of the various voltages the sensor needs. This only gets worse over time. Some of it can be calibrated out. But comparing darks over the course of months may show some trends. With CCDs, the substrate bias may change. With the CMOS, noise creeps in to the onboard ADC reference power supplies.
So I think folks should have a plan to update them a few times a year.
Along with blowing the dirt out of the camera fans and heatsinks!
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