What exposure to use for astrophotography using a CMOS DSLR or mirrorless camera

[This is just one of many articles in the author’s Astronomy Digest.]

This is a somewhat tricky subject thatdepends on the camera, the darkness of the imaging site, the dynamic range ofthe object and whether or not a tracking mount is used.

A first point to consider that overridesanything that follows is that one should not over expose parts of the imagethat is being taken.  This is a realproblem when imaging M42, the Orion Nebula. The central region surrounding the ‘Trapezium’ is very bright and onesees many images where this is  blownout.  In fact, when using an ISO of 800,I had to use an exposure of just 12 seconds to prevent over exposing thisregion and thus had to take very many sub frames (subs) to be stacked in orderto be able to bring out the far fainter nebulosity surrounding it.  [It would have been better to use a lower ISOand take fewer longer exposures  as withvery short exposures the readout noise of the camera becomes significant.  The alternative is to combine a number ofdifferent exposure images, effectively making a ‘HDR’ (High Dynamic Range)image.   The sensors in modern Nikon andSony cameras as said to be ISO invariant and there can be an advantage in usinglower ISO values.  An image taken withthese cameras shows little difference if an image is taken at ISO 800 or takenat ISO 100 and then brightened by 3 stops in post processing.  This can even be better, as the ISO 100 imagecan be ‘stretched’ so that fainter parts of the image are brightened more thatthe brighter regions thus increasing the effective dynamic range of theimage  ̶  see article’ What ISO to usefor Astrophotography’.]

Usinga fixed tripod.

Other than the point above, there is onlyone consideration to take account of  ̶  preventing star trailing(unless one is taking a star trails image). The maximum exposure time to prevent star trails firstly depends on theeffective focal length of the lens  ̶ taking intoaccount the crop factor (for a Nikon APSC sensor the crop factor is 1.5, for aCanon APSC sensor 1.6 and for a Micro 4/3rds sensor 2.)  The basic rule is to divide a fixed number bythe effective focal length of the lens. This number is widely quoted as 500 but as the resolution of newer camerasensors has improved over the years   ̶   a better number to use is 300.   With the latest 24 megapixel cameras, someare now using 200 for a full frame camera or 133 for an APSC camera.  [Using these latter numbers the results tendto agree with the calculator linked to below.] One would often downsize the resulting image from 24 megapixels toperhaps 6 megapixels (a reduction to 50%) and then a 270 (APSC) or 400 (FullFrame) rule would, I think, be adequate.]

So, if using the 300 rule, simply divide 300by the effective focal length of the lens. For example:

18 mm lens: 16 seconds

24 mm lens: 12.5 seconds

35 mm lens: 8.6 seconds

50 mm lens:  6 seconds

90 mm lens: 3.3 seconds

However, though not often mentioned,  the declination of the region of sky beingimaged is also a factor as the sky moves faster across the sensor at lowdeclinations (for example the Orion region centred at DEC 0) than at highdeclinations (for example the Plough centred at DEC +65) so somewhat longerexposures can be used when imaging higher declination regions of sky.  If so, oneshould be able to increase the time calculated by the 300 (or other number) ruleby the factors given below using the factor 1/Cos(DEC):

~40 degrees declination  x 1.3

~50 degrees declination  x 1.5

~60 degrees declination  x 2

~70 degrees declination  x 3

An on linecalculator

https://www.sahavre.fr/tutoriels/astrophoto/34-regle-npf-temps-de-pose-pour-eviter-le-file-d-etoiles

This take into account the pixel size ofthe camera (one selects from a very wide range of cameras) and rather thanusing the declination of the object uses the latitude of the observer,direction of imaging and angular height above the horizon.  From these last three it calculates thedeclination of the imaging region and then uses the 1/cos(DEC) formula I haveused above.   The calculator evenspecifies the aperture of the lens that is used so that  it can calculate the size of the Aireydiffraction pattern!  I suspect that thisformula aims to provide absolutely pin-point stars.  [If your camera is not on the list, find afull frame or APSC camera that has a similar number of pixels.]

Removingslight star trailing in Photoshop or GIMP

It is actually quite easy to eliminate alittle star trailing  ̶  which makes stars look like a small sausages.  One should first increase the size of theimage to 200% as this makes the correction easier.  Then the image should be duplicated to givetwo layers and the blending mode should be set to ‘Darken’.  Clicking on the ‘move’ tool (which in Photoshopis is at the top of the toolscolumn) one can then use the up/down/left/right keys to move the upper layer over the lower one a pixel at a time.  It becomes obvious as how to use them.  When the stars have become point like, simplyflatten the two layers and then reduce the image size to 50% to bring it backto nominal size.

Having written all this, the best advice is topurchase a tracking mount.  There is anarticle in the digest (‘Three Tracking Mounts’) which addresses their use.

Using atracking mount

Things now get significantly more complicated!

A quickconclusion when using recent CMOS cameras is this: firstly, do not use the ‘InCamera Long Exposure Noise Reduction’ mode then, when in light pollutedlocations, use 30 second exposures but in  dark locations increase this to 1 to 2 minutes(providing that the tracking is good.)

[This may not agree with much that you mayhave read.  Longer exposures will givebetter results when using CCD cameras as their read noise is considerablyhigher and their read times much longer than with CMOS sensors.  Short sub exposures increase the effect ofread out noise (which are typically  8-10times greater than with CMOS sensors) and reduces the efficiency of the imagingprocess.  For example, my SBIG CCD cameratakes ~10 seconds to read out its 8 megapixel sensor.]

 Let’stry to justify this conclusion and consider an example where one aims to take atotal exposure of  30 minutes.   If the camera and tracking were perfect andthere was no light glow (pollution) or air glow, then theoretically it wouldnot matter whether a single 30 minute exposure is taken (provided that this didnot over expose parts of the image) or 120, 15 second,  subs are taken instead which are laterstacked in ‘Deep Sky Stacker’ or ‘Sequator’.

Neither of these extremes is sensible in thereal world.  It is unlikely that thetracking would be perfect over 30 minutes unless autotracking were used.  It is also highly likely that aircraft willfly across the imaging region and these would need be cloned out from theimage.  It’s also possible that a gust ofwind might upset the image or one could bump the tripod.  (Do not laugh, many of us have done it.)

Conversely, after each 15 second sub perhaps 2seconds is required for the data, usually raw+Jpeg, to be read out to the SDcard, thus the 120 sub exposures will take a further 4 minutes  in total. The good thing about using short exposures  is that if a plane (or the Space Station!) wasvisible in one or two frames, one could simply remove them from the stackwithout any real loss.  This is why it isgood to take both raw and Jpeg files as one can quickly run through all theframes to look for problems without having to process all the raw frames.  An alternative in Deep Sky Stacker is to  usethe ‘kappa-sigma’ clipping mode.  Thisfind the average value for each pixel in the resultant stack of frames andrejects any value in a single frames greater than some deviation from the meanand replaces that value with the mean value   ̶  so removing the intrusion.

There is another advantage if a DSLR ormirrorless camera is to be used with a telescope of medium to long focallength.  In this case, if the atmosphereis somewhat turbulent, some of the captured frames  can be slightly blurred compared to the majority,and a better result with tighter stars will result if these frames are removedfrom the stack provided, of course, that a reasonable number of ‘good’ framesare left.

To try and determine the optimum exposurelength within these two extremes one needs to consider the sources of noise ina real, rather than perfect, camera whilst imaging under skies that may be notbe fully dark.   There are then threesources of noise; sky noise (lightglow and airglow), dark current and readoutnoise.  These add vectorially into thefinal stacked image and, if one dominates, the other two can be essentiallyignored.  This is the case if imagingunder light polluted skies or partial moon light.  Sky Noise will build up a pedestal of noisein the stacked image which will reduce the dynamic range of the image and maskout stars and (particularly) nebulae whose brightness is less than that of thelight pollution.  The only real solutionis to find a really dark sky location  ̶  but then the other sources of noise becomesignificant.

There is one fundamental difference in takinga one single long exposure and stacking a number of sub frames in, for example,Deep Sky Stacker.  The pixel well in the sensor can only hold agiven number of electrons and this can easily be overwhelmed in a long exposureby sky noise or dark current.  If,however, short exposures are used which do not saturate the pixel wells and whichare read out with 14 or 16 bit analogue to digital converters with the data beingstacked later, the stacking program can accumulate these in what, I suspect, are32-bit bit memory locations.   If this istrue, these could accept 16,000 or more sub frames without over filling!  The average value of each pixel is thenoutput with a precision of either 16-bit or 32-bit as Tiff files.

A typical DSLR pixel well can hold 60,000electrons.  So if the sensor has aquantum efficiency of 50% it would saturate after 120,000 photons had fallen onit.  Let us suppose, for example, that30,000 of the photons that would be recorded in a 30 minute exposure were dueto light pollution so the light pollution would not overwhelm the desired image.  This equates to 1,000 photons perminute.  The light pollution, were asingle 30 minute exposure taken, would show a random noise contribution equivalentto the square root of this total number which is ~173.  Now let’s assume that  1 minute subs are used, so ~1,000 photons arecaptured in each frame.  This will have anoise level equivalent to its square root which is ~31 photons.   Now if 30 of these frames are stacked, thenoise would fall by a further factor of the square root of 30 which is 5.4, sothe final stacked light pollution would have a noise level of 31/5.4 which is5.7 photons – vastly less and effectively insignificant.  So, to minimise the random noise in the lightpollution, shorter subs are better.  [Thedark current will still, however, contribute 1/4 of the output image.]

A similar result applies to the sensorsdark current.  In fact with a single 30minute exposure the sensor may well become saturated.  In this case, however, the noise within thesensor is not quite random and may well have a fixed pattern along with somevariability from sub to sub.  This one verygood reason for ‘dithering’ the pointing of the camera during the set of subsso that the dark current is smoothed somewhat.

The dark current increases by a factor of 2for each ~6 degrees Celsius which it is why cameras should be kept as cool aspossible.  [I can mount a small icepackagainst the back wall of my Sony A5000 camera.] However the latest CMOS sensors at room temperature have as low a darkcurrent as older CCD cameras when cooled to -20 Celsius and, if there is anysignificant light pollution present, can probably be ignored.  This is why in the head of the article Isuggested that one should not normally use ‘In CameraLong Exposure Noise Reduction’ which would halve time imaging  the sky.

The final noise contribution is the readoutnoise which adds some noise to the signal as it is read out from thesensor.  For a given total exposure, thegreater the number of sub exposures used, the larger will be its contributionto the final image and, where there is little or no light pollution, this canbecome significant.  So under very darkskies the very lowest noise images would be achieved with longer exposures, soreducing the number of sensor readouts, and exposures of one to two minuteswill be better than, say, the 30 seconds that I suggested under light pollutedskies.   Honestly, there is no point istaking sub exposures longer than this when using modern CMOS sensors.