By Don Selle
Part 1 of Getting You Exposed, dealt with the concept of Total Exposure time and Exposure Value. It also provided some rules of thumb to help you estimate the Total Exposure time required for various types of targets using your own imaging rig. Having a good idea of the Total Exposure is certainly essential for acquiring high quality data on the low light level targets we image, but it is only one factor we need to consider.
Since most targets will require several hours of Total Exposure time to acquire enough data to assemble a quality image, we will typically acquire that data using multiple sub-exposures (aka sub-frames). The exposure time for each sub-frame when summed will equal the Total Exposure time of the acquired data.
When you think about it, this makes sense. You wouldn’t want to take hours long single exposures as too much can happen. Satellite photo-bombs, mount tracking errors, autoguiding errors, operator error and things that bump your tripod in the night can ruin your sub-frames and result in the waste of a lot of time. Even back in the days of film, to avoid these risks, astro-imagers took multiple exposures, developed them, then scanned and electronically combined them to reduce the noise in the image.
Once the decision is made to make up the Total Exposure time through some number of shorter duration sub-frames, the question arises – how long should each sub-exposure be? Since the risk to individual subframes increases as sub-frame exposure time, shorter may be better, but how to know.
Back in the day when I got started astro-imaging, there was no set answer. The best advice at the time was to set your sub-frame exposure long enough so that the “hump” in the sub-frame histogram started at 25%-33% of the left side of the graph.
I didn’t know it at the time, but this rule of thumb was a statement of the photographic technique commonly referred to as “exposing to the right” or increasing the exposure of your photograph so that details in the shadows are sufficiently exposed but the highlights are not saturated or “blown out”. This way, the darker details can be recovered during processing.
A little explanation is in order here. The photo on the left is a crop from a single sub-frame (it is raw i.e., no processing) with a histogram of the complete frame shown on top of it. The histogram shows the range of pixel brightness levels (0-255-actual values converted to 8-bit color) from left to right across the bottom of the graph with the total number of pixels in the frame which are at each of the brightness levels. While it is not totally apparent, each of the three RGB color channels is displayed on the histogram, as well as statistics for the whole image at the bottom. (There is a lot more information in the histogram, but that’s the subject of a future article!).
This histogram pretty well illustrates the expose to the right rule of thumb. In truth, I estimated the exposure time based on a method which I will describe for you. It relies heavily on the mathematical theory behind signal processing and has been reduced to a couple of simplified calculations and software tools. When the appropriate values representing the performance of your imaging system and the quality of the night sky you are under, will provide a very good estimate of the optimum sub-frame exposure time.
When I updated my imaging system, replacing my older mono CCD camera with a new OSC CMOS camera, I initially continued to use the same routine sub-frame exposure times. I later learned (from my friend and advanced imager John Talbot 1) about how improvements in camera technology which have been incorporated into the newer CMOS cameras can help improve the raw data you capture. I recently have begun to use a new method of estimating my sub-frame exposure times which is based on mathematical signal processing theory as applied to imaging.
I will not go too deeply into the theory. For those who are mathematically inclined and interested should spend an hour and watch Dr. Robin Glover 2, the developer of SharpCap describe the theory and how it is used. Dr. Glover has extended the work done by others and developed some very interesting tools which he has included in SharpCap which will do the calculations for you. In truth, once you have the right information about your camera, optics and the sky brightness where you image, thanks to calculator Glover has made available on the SharpCap website, you can make a very good estimate of optimum sub-exposure time with a simple hand calculation. A precise calculation requires that you take an image of the night sky so that the sky brightness can be measured.
It is worth noting that Glover is neither the first nor the only person to develop the theory and tools necessary to determine optimum sub-frame exposure time using signal theory, and Glover’s approach is very similar to and compatible with what has been done previously which required a direct measurement of sky brightness.
In the current era of very low noise CMOS cameras, Glover has championed the idea of taking very many short exposure sub-frames which in some applications, might eliminate the need for autoguiding, and allow use of mounts with less precise tracking. Dr. Glover has also provided an online tool to assist in estimating the sky’s brightness in order to estimate the optimum sub-frame exposure time.
Signal Processing Theory
Determination of the optimum sub-frame exposure time is based on the application of signal processing theory applied to astro-images. All of the sources of noise that end up in each sub-frame are identified and quantified. These noise sources can be organized into two categories, systematic noise and shot noise.
Systematic Noise - is noise such as dark current or thermal noise and bias pattern noise. This noise can be directly removed from the subframes during calibration with only a small random amount remaining. (See my AP Corner “Let’s Get You Calibrated” https://www.astronomyhouston.org/newsletters/guidestar/ap-corner-let%E2%80%99s-get-you-calibrated#overlay-context=welcome
Shot Noise – Removing systematic noise leaves what is commonly termed Shot Noise, or the noise which is specific to each sub-exposure. Shot noise is comingled in the raw frame and is not removed during image calibration and consists of two major noise sources – Sky Noise and Read Noise. Shot noise is dealt with during image processing, after the calibrated sub-frames are stacked to improve the Signal to Noise Ratio.
Sky Noise This is primarily noise coming from the sky (a.k.a. Sky Background) which is not associated with either the stars or the target in your sub-frames. The biggest component of sky noise is light pollution, but even at the darkest sites there is still a sky background. It is made up of the dim diffuse natural light reaching the Earth from space, as well as the natural sky glow which is due to the light given off by ions created by sunlight striking the atmosphere, when they recombine. Sky noise is mostly removed by subtraction with a small random fraction remaining.
Read Noise Noise is added to each sub-frame by the camera and is commonly called Read Noise. It is generated during the process of collecting the photons, converting them to electrons and then reading them out and converting them from a voltage into a digital number. Read noise (along with any random sky noise) is dealt with by noise reduction algorithms during image processing.
Optimum Sub-frame Exposure - We do need to define what optimum means. The assumption is that as we described above, the risk of outside factors messing up a sub-frame increase with increasing exposure time. This means that finding the shortest exposure which can sufficiently capture the faint detail present in our targets and capturing enough of them in order to significantly improve the signal to noise ratio of these faint details is the optimum sub-exposure time.
Determining Optimum Sub-Frame Exposure Time
The most accurate way to determine your sub-frame exposure is to use a tool which actually makes measurements of your camera and of the sky glow at your imaging site. SharpCap3 has a comprehensive tool to do this for supported cameras called Smart Histogram. When coupled with the Sensor Analysis Tool SharpCap will take images of the night sky, determine the key parameters for your system and measure the sky noise, then do a full calculation for you, of how long your sub-frames should be exposed, and how many to take. I’ve personally not used it but I have gotten good reports from several imagers who have. Frankly, the tools sound very impressive, especially if you use SharpCap and are willing to spend the time measuring the sky background.
If you are like me and already have invested considerable time into learning and setting up an imaging software system and would prefer not to switch horses. You can easily calculate a good estimate of optimum exposure time with the following equation:
R = Camera Read Noise (RN) in electrons
P = Sky Noise rate measured by your camera in electrons per second
C = Preferred % Read noise is of total Shot Noise (where Shot Noise = Read Noise + Sky Noise)
% RN C Factor
1% = 50
2% = 25
5% = 10
10% = 5
20% = 2.3
25% = 1.8
The calculation I made for the example sub-frame exposure was as follows:
R = 2.2 electrons at ISO 3200 for my Canon 6D and a 300mm f/4L lens - value based on review on www.ClarkVision.com
P = 1.92 electrons per sec for Bortle 4.0 location
C = 50
Recommended exposure = 126 seconds – and I used 120 secs, a round number and because I was using a camera tracker and had verified that I was able to get reasonable results with 2-minute exposures without guiding.
Determining the R and C Factor Electrons
From the above formula it is clear that we need to determine two key factors, the read noise in terms of electrons, and the sky background rate in terms of electrons generated in each pixel per second due to the sky flux. Fortunately, there are good resources to determine both values.
Camera Read Noise Electrons
If you own a recent model astro-imaging camera you are in luck, as most manufacturers are now specifying the read noise inherent in their cameras in terms of electrons. Some are even providing data fully characterizing the camera performance at various levels of gain, as shown below for a very popular ZWO monochrome camera. In addition, SharpCap also contains a tool that will allow you to test your own camera.
For DSLRs though, the situation is a little more complicated in that the manufactures such as Sony Canon and Nikon do not publish this information. Fortunately there are several good sources where talented individuals have made the effort to test and publish data on popular DSLRs. For older model DSLRs, especially by Canon, and some Nikons models you can find data on many models on the ClarkVision.com website at:
For a more comprehensive set of data for many DSLR manufacturers and models you can check out the website photonstophotos.net which has a comprehensive set of read noise data.
If your camera is in both sources, my preference would be to follow ClarkVision since its author Roger Clark is focused almost entirely on nightscapes and astrophotography.
Sky Noise Electrons
The calculation to determine sky background is based on the site you are imaging from, the optics you are using, including any filters and characteristics of your camera. Fortunately for us, Dr. Robin Glover has provided a very straightforward website tool that makes this calculation very easy.