vlaiv

1 minute ago, AndyThilo said:

Conclusion, thank you @vlaiv, I will be deleting my whole dark library and making new ones :). And I really can't see how flats would improve this?

Good to see that there was only light leak in the darks and that proper darks took care of everything.

You now know that your flats are working properly. Only real issue with that flat panel is that it does not produce much red part of spectrum and your red histogram peak is quite low. It will not cause too much issues - but take more to compensate for this. Also, your color balance will be really thrown off if you don't normalize your flats prior to doing calibration with them.

Just now, AndyThilo said:

Well I’m truly lost 😂

Don't be. Here is quick guide:

1. You've probably taken another set of darks? If not - do it, but take every precaution not to have light leak. Take camera off the scope, use camera cover and aluminum foil - place camera "face down" on desk and do darks.

As far as I can see deltaT is about 35C so you need to do this somewhere where you don't have heating (shed perhaps or basement or ....) as you need ambient temperature to be below 15C.

Compare that with the darks you have already taken - see if you get same gradient / mean ADU level.

2. Try calibrating data that you now have with existing flats (these seem ok) and new darks - just to see if it will work (I sort of doubt it - if there were a light leak, it affected both darks and lights) - if it does work properly - problem solved, if not - it is sign of light leak. This means that you need to examine your setup and change some things.

Light leak will usually come thru extension tubes, or adapters, or filter wheels or OAG. It can be diagnosed by using strong flash light and shooting short darks - which torch shining at different pieces of equipment. Highest mean ADU will tell you where likely leak is. 

9 minutes ago, Physopto said:

I might try a figure closer to that next time out. I am at The Galloway Star Camp next month. So a few more hours spent trying out different levels would not come amiss.

 

Simplest way to test if flats of different histogram peak level are working as they should is to do flat / flat calibration.

You take set at some peak values like 33% (to be reference value), 50%, 75%, 80%, 90% - do couple of each, and do couple of flat darks for each exposure. Create master flats and then divide master flats with each other (33%/50%, 33%/80%, etc) - you should get uniform gray sub (with noise obviously but it should not have any vignetting nor dust shadows evident).

4 minutes ago, Physopto said:

Hi Vlaiv

Yes I can see your argument. I always use around 50% FWD for my CCD (QSI 683), ( what QSI recommended I believe). So I aim for around the 25,000e ish. It is a long time since I did any maths/statistics on shot and thermal noise. So I just aim for what seems to work. I would guess it may be different for the various makes of CCD depending on how they work. Things have changed greatly in the last 25 years or so since I did my first degree.

All I was pointing out is where carastro may have seen or gotten the 33% figure from. I use Maxim DL but have never tried their auto routine so far. I get too little time to waste messing about with experimenting. I beleive in" if it ain't broke, then don't fix it!"

Derek

I figured that you just quoted potential source of 33% statement. On the other hand, I just wanted to point out that not all things should be taken as accurate / set in stone without running logic checks first.

This does not mean that there is no something else that will indeed make 33% recommendation better option for some CCDs out there that I've not taken into account. From what I've seen - figure of 80% works and it works well (I use it) - and logic behind taking flats supports it.

It is certainly worth combining the data in a proper way.

Unfortunately it is a bit complicated topic and DSS does not have option to combine data in such way.

Just combining them as if they were same SNR subs can result in improvement but can also result in worse data. Actual result depends on how different SNR is between the subs, and to make matters worse - there is no single SNR value per sub - each pixel in fact has its own SNR value.

There are couple of things that you can do to address this issue:

1. Stack better subs to one stack and then stack all subs to other stack - inspect stacks to determine which one is better looking - and use that one.

2. If you have license of PixInsight - use that as it has weighted average stacking (not ideal, but better than equal weights stacking)

3. Make two stacks - one of good subs and one of poor subs and then try different weighted combining of those two stacks (simple image arithmetic - 0.8 * good + 0.2 * bad - or other weights, and select combination of weights that gives you best result).

4. Use algorithm specifically designed to handle such cases. Have a look at this thread first:

And if you are up to it - I can make you a small tutorial on how to use ImageJ and plugin that I wrote to stack your data with that algorithm.

In fact, I was wrong in my previous post - I did the math incorrectly.

I used percentages instead of actual numbers (figured it will be easier to understand) - but I should not have done so. SNR involves quadratic relationship (noise is square root of signal) and linearity is not preserved - hence percentages will not match actual numbers. I'll just quickly redo calculation with real numbers to show that this issue is even less than percentages would suggest.

Let's again take 15k FW. 80% of that is 12000e. Noise / one sigma is square root of that - ~109.55 and we have 3000e until saturation (15000-12000 = 3000e). This means that we in fact have 3000/109.55 = 27.38 sigma. Probability that any single pixel will saturate is not 1% but closer to following statement: "Universe is simply not old enough for this event to ever have happened so far given it's probability and all cameras in the world"

In fact, even if you go for 95% histogram peak, you are unlikely to saturate with real sensor - it is still more than 6 sigma event.

13 hours ago, Physopto said:

The target ADU selected should be about 33%  of the saturation level of your camera. This will give the most accurate and noise free raw flats which will result in the best master flat once stacked. Going too high can result in pixels outside the linear range of the CCD and too low can result in poor signal-to-noise in the flat.

Ok, let's discuss this for a moment.

It says that 33% of saturation level will result in most noise free raw flats. Is this statement true?

Most noise free raw flat will be one with best SNR. With flats most dominant type of noise is shot noise. Read noise in comparison is very small (even with old CCD cameras) and due to usual exposure lengths involved, dark current noise is also very small. Therefore we can approximate noise by shot noise associated with light signal.

Let's now compare two SNR values of usual CCD camera that has 15k FW capacity. One flat at 33% and one flat at 50%. Signal value in 33% flat will have on average value of 5000e. Associated shot noise is sqrt(5000) = ~70.71e and overall SNR is therefore 5000 / sqrt(5000) = 5000 / 70.71e = ~70.71e. On the other hand 50% signal level will be 7500e and associated noise will be ~86.60e and therefore SNR will be ~86.60e.

We clearly see that there is example where above statement is not true. In fact, if shot noise is dominant noise source - higher signal value always "wins" in SNR and therefore histogram that has peak higher than 33% will result in better SNR and be more noise free than sub with 33% SNR.

Now let address second part of that statement:

13 hours ago, Physopto said:

Going too high can result in pixels outside the linear range of the CCD

This statement can be interpreted in two ways and we need to address both. In first case it could happen that CCD sensor is not linear in higher range. I can't really argue this case except to say that in recent time that I've been doing astronomy, I have not heard of imaging sensor that is not linear enough over its useful range.

If you do search on linearity for your particular camera model, I'm pretty sure you will find a graph like this:

(atik383L+)

or this:

or this for CMOS camera:

or maybe this:

In second case - it is meant that there could be some sort of saturation and clipping and therefore pixels can register non linear response. This can happen due to shot noise for example. Shot noise can cause signal value to be higher or lower than actual signal level (that is why it is noise). In fact we know what magnitude that noise is, and we can calculate probability that any particular pixel is above saturation point of the sensor.

Let's take value that I recommend often - 80% and see how likely that any one pixel is above saturation point. We know that one standard deviation is square root of that number or 8.95%. This means that 66.7% of pixels will be within 80% +/- 8.95%, and 95.5% all pixel values will be within 80% +/- 17.9%. This is still within 100% saturation point as 80+17.9 = 97.9%. In fact, if we calculate it precisely 1.27% of pixels has chance to saturate in single pixel. In stack of 20-30 flat subs that will produce negligible error. In fact this will hold true only if flat is perfectly flat - and it never is - there is vignetting and only central part of flat need to be taken into account as other parts of flat usually have lower values and are less likely to saturate  (disclaimer: I used gaussian approximation for poisson distribution when large numbers are involved).

Edit: I've made mistake of using percentages where quadratic relationship is involved (things are not linear) - fact is that this percentage is even lower - look at my following post for details

So this statement is certainly true - going too high will saturate, but as we see, even going as high as 80% will make very few pixels saturate (in reality less than 1%) in single subs and resulting error from stacking 20-30 subs will be minimal.

Yes, here is green channel "flat fielded" (sorry, I'm no expert at flat fielding without actual flats and only synthetic thing):

This shows that nothing is inherently wrong with the data, but yes, image is severely vignetted.

Belt of Orion is really shining, so there is not much helping there, they are going to have that severe halo ...

Here is a quick crop and stretch (you need to crop it to remove stacking artifacts as subs were not aligned perfectly):

Yes, part of gradient is due to not taking flats.

Otherwise image looks good, and is not nearly as noisy.

There is a bit of trailing of the stars, but it's not much. I'll try to do synthetic flat to see if that will help and will try processing it a bit to see what I can get.

1 hour ago, AndyThilo said:

That's the thing my darks do remove amp glow. I showed that in the image on my first post. Adding in the flats caused loads of issues. Maybe I'm not understanding it. The best processing method for me to get the cleanest images is manually in PI with no flats as below

Darks polluted with light leak will remove amp glow - that is to be expected. In most cases light leak will act as light pollution. Same way you record your target although light pollution has been added - dark will record amp glow. So will light, once you subtract the two - amp glow will cancel out.

Light leak will not cancel out. That is the issue.

I don't know what your master dark looks like, but one single dark that you posted has gradient. If I do simple removal of dark from that light without doing anything else (no fiddling around with background subtraction, no flat calibration - nothing, just dark subtraction), I get this:

Now you have gradient to the opposite side than on dark. It is clear that dark subtraction caused gradient from dark to be transferred to flat. Amp glow is gone, and that is ok - both have same amp glow, but dark has this gradient that is not present in light.

Few things could be happening here that make a difference between my example and one that you gave from PI.

a)  I'm doing calibration with single dark. Maybe this particular dark is different from other darks for some reason, or maybe each dark is different because of different amount of light leak. You've used average so any differences averaged out, while I used only one that has distinct gradient

b) You used background wipe in PI and PI removed this gradient in same way it would handle LP gradient.

In any case dark is what is causing your flat calibration to fail. I can show you with a bit of math what is going on.

Imagine you have only two pixels rather than whole image (or maybe left and right side of image what ever is easier for you to imagine). One received 70% of light due to vignetting / dust shadow, while other received 90% of light again due to vignetting/shadow/whatever.

Now imagine that both of these pixels are background pixels that recorded just sky background. I say this because this means they ought to be uniform in intensity - there should not be variation (let's for moment leave LP gradients aside - this is just to understand how dark calibration impacts flat calibration).

Let's say that background ADU value is 100ADU. This means that first pixel would record 70e and second pixel would record 90e. We need them to have same value in the end if our calibration is good (because we have even sky background).

These values are just light signal, but light frame also contains bias and dark signal (dark subs contain both as well). Let's say that dark signal is 20e.

So what we recorded in our light frame would be 90e and 110e (70e+20e, 90e+20e). Now let's do calibration to get even background. Our flat will be 0.7 and 0.9 (because 70% and 90% of light reach sensor).

Perfect case:

((90e, 110e) - (20e, 20e)) / (0.7, 0.9) = (70e, 90e) / (0.7, 0.9) = 70e / 0.7, 90e / 0.9 = 100, 100 - we have equal pixels, or uniform sky brightness. Calibration is good because we had proper dark value.

Under correction case - dark has larger value than it should (because of light leak, some additional electrons were accumulated):

((90e, 110e) - (30e, 30e)) / (0.7, 0.9) = (60e, 80e) / (0.7, 0.9) = 60e/ 0.7, 80e / 0.9 = 85.7143, 88.88888

We no longer have uniform sky background, calibration failed, and first pixel still has lower value then second although we used proper flat (0.7, 0.9). Because vignetting / dust shadow is still present - we call that under correction - flat did not manage to fully correct image - but not because flat is wrong - it was because dark was wrong - larger than it should be.

Over correction case - dark has larger value than it should (in reality this rarely happens like that - it happens when lights have light leak and darks have lower value in comparison to lights, but let's do math anyway to show over correction happening):

((90e, 110e) - (10e, 10e)) / (0.7, 0.9) = (80e, 100e) / (0.7, 0.9) = 80e/ 0.7, 100e / 0.9 = 114.2857, 111.1111

Again - no uniform sky background but this time first pixel is brighter than second pixel - "inversion" happened and what was darker in uncalibrated image now is brighter as if flats corrected too much - we call that over correction.

-----------------------------

Above was to show that perfect flats can still fail to do flat calibration if there are issues with either lights or darks.

I believe that both your light and dark subs are polluted with light leak because of:

1) Dark has gradient. It is very unlikely that dark sub can have such gradient, and also such gradient is missing from light sub (but everything that is in dark should also exist in light - amp glow for example - if it's in the dark sub, it will certainly be in light sub as it is feature of dark signal). This shows that gradient is not feature of dark signal and is in fact "external" (only external signal can really be due to some sort of light / radiation)

2) You subs when calibrated show Over correction - that can happen if darks are "less strong" then they should be (see above). Since it is highly unlikely that dark current in darks is less strong than in lights (it can be if we have situation where cooling was not set to same temperature - but from what I can tell - it is not case here) then it must be the case where lights are somehow stronger than they should be. This points to light leak again. Lights have some sort of external signal that did not come thru objective of telescope lens. Otherwise it would be corrected by flats because flats describe how such signal behaves (how much it is attenuated).

Hope this all makes sense.

1 hour ago, AndyThilo said:

One other thing i don't understand. Left is PI manual processing without flats. Right is exactly the same but with flats. The right is also the same as I get using BPP. Both are stretched using STF Autostretch. Nothing else.

You have very red result in your right image because your flat panel is giving off very blue light. It has already been mentioned that red component of flat is very low in value. This can happen due two things. Either camera has very low QE in red part of spectrum (not the case) - or flat source used produces light that has much less of red in it than other two (green and blue). Cool light has this "feature" (with warm light it is opposite - less blue and more red and green).

Since you have low red signal compared to other two - flat fielding with such flat will produce very strong color dis balance.  Nothing that white balancing can't fix, or flat normalization (process where each of color peaks in your flats is normalized to 1 - that removes any color dis balance that flat panel produces).

14 minutes ago, AndyThilo said:

I don’t know how you’re doing that, what software? 

I'm using ImageJ - it is free software for scientific image analysis / manipulation, but that is not really important here - it just helps me calculate some things about light levels. You can't really use the method that I've used to get proper image - it is just estimate and all things that darks otherwise remove won't be removed like this (see amp glow for example - proper dark will remove it).

3 minutes ago, carastro said:

Sorry Vlaiv, I am not a technical person like you, I just do what works, and definitely I find if the flat is too bright it doesn't do it's job.   I was told 1/3 full well when I started imaging and that definitely works for me.  Also I have heard that's what most other people use.  I have never heard of any-one doing 80%.  

Carole 

Fair enough, let's not get bogged down in technical discussion - if 1/3 works for you (and it certainly should) no need to change anything.

24 minutes ago, AndyThilo said:

I’ll have to do them outside to get my -20, but I’ll get it running tonight and stick a bin bag over it as well for good measure. 

It looks like you have light leak of some sorts and it is not only present in darks - it is also there in lights as well. Until you address that, you won't be able to properly calibrate your images. Here is what I've found out:

Here is light / flat:

It shows "inverse" vignetting - and that is fine, that is what you would expect from flat fielding when dark has not been removed. Since dark has gradient on it, I will not be using exact dark frame, but I'll try to guess average value of dark frame and subtract that.

Here is (light-900ADU)/flat - My first guess is that dark needs to be 900ADU:

Maybe a bit better, but still over correction of flats - we need to subtract more. How about another 900ADU - 1800ADU in total:

That is better, and like I said above about 1800ADU is some signal not related to light coming from aperture. If we continue, we will start going into under correction regime instead of over correction.

This is about 2000ADU removed:

And this is 2100 ADU removed:

And 2110ADU:

There last three start to show under correction (edges and corners are darker then the rest of image).

But here is important bit - ADU that needs to be subtracted is around 1800ADU.

Average value of dark that has light leak is ~1174ADU. This means

a) real dark mean value is lower than that, since we know there was light leak - and light leak is going to raise mean value.

b) there is a light leak in lights as well - because we need to subtract way more than 1174 to get flat fielding to work properly.

How do you connect your camera to your scope and is there any light source near by when you record your images?

11 minutes ago, AndyThilo said:

I’ll have to do them outside to get my -20, but I’ll get it running tonight and stick a bin bag over it as well for good measure. 

It is definitely due to darks, here is (light - some_value)/flat:

It shows almost perfect flat calibration. I used 1100ADU as a base and kept increasing it until I got good calibration. I needed to remove dark current and bias for flat fielding to work properly so I needed to guess right amount to be subtracted from lights. In fact I ended up subtracting around 1800ADU.

You can still see amp glow as I in fact did not use dark sub at all.

13 minutes ago, carastro said:

I don't agree with 80% Vlaiv, if the flat is too bright it doesn't work as I have found out to my cost in the early years.

Can you give any explanation why it might not be working?

6 minutes ago, AndyThilo said:

Yep there is definitely problem with flats. It was discussed on another forum...

It is not necessarily a problem that flat source is weak in one component - it just means that flat panel is not producing very white light - it has color cast.

If red is weak - it just means that flat panel has very cool light (probably leds that try to emulate light of very high temperature >7000K or similar).

In fact - your flats seem fine otherwise and only thing that I see wrong with your data are in fact darks - it costs nothing to redo your darks, but this time be careful there is no light leak. Maybe take camera off the scope, cap it off and use aluminum foil and place "face down" on a desk while taking your darks.

10 minutes ago, AndyThilo said:

All files are straight out of APT.

I'm not familiar with APT so I don't know if subs are only recorded as 32bit fits for some reason (it just wastes space) or has something been done to them. I wonder why only lights is recorded in this format?

Ah, sorry, my bad - it looks like I converted file to 32bit without realizing (I always do that with subs and must have done so by impulse when I opened it and then forgot about it).

All is fine with light sub!

12 minutes ago, AndyThilo said:

Darks do have a slight issue with a mark on them. Not sure about light leaks, I did them outside with a black bin bag over everything, and lens cap of course. 

You should first redo your darks - I suspect they are causing issues rather than your flat panel. It will cost you nothing to do that (maybe a bit of time - but it can be done indoors on a cloudy night so not much is wasted).

However, you should maybe change your flat panel - it has very odd distribution of light - one component is 1/10 of value of highest component - third histogram peak is very low at about 4000ADU.

Does your flat panel have distinct color cast to it (maybe bluish light or very warm?)

5 minutes ago, Physopto said:

I don't know if it is somehow my down load but the Flat in Maxim under stretch shows 3 distinct peaks very strange!

Derek

That is quite normal for OSC sensor - R, G and B components of sensor have different sensitivity and one always ends up with 3 distinct peaks when using color camera

5 minutes ago, carastro said:

I am not familiar with either COMS Cameras, or aurora panels.  But I notice your ADU is 30,000.  I know some people do use that, but my understanding is it has to be 1/3 full well depth, and my Atik camera that is 65,000.  1/3 65,000 = 21666.  I always try to keep my flats around 22,000 - 24,000.

Have you used this panel successfully previously with this ADU?

Carole 

Here flats are quite ok as far as saturation is concerned. Not sure where 1/3 rule came from - I've heard it before, but I don't think it is a good rule (unless someone can explain exactly why it is used). Aim at 80% or so histogram is better option. In fact any histogram value is good as long as you don't have low or high clipping. Higher histogram peak value only ensures that you have good SNR for your flats and that you won't be polluting your lights with noise much.

There is also an issue with your darks, or at least it seems so:

left is very stretched dark, while right is light sub without alterations stretched (one that you uploaded).

Dark has gradient over it, while light does not, although light is probably stretched more because it shows amp glow more than dark.

It could be that there was some sort of light leak when you took your darks. Could this be possible?

1 hour ago, AndyThilo said:

I posted it in my original post but DSS is just basic load them in and let it go. PI BPP I used Linear Fit for all, again let it run. For manual, I created Master dark/Bias. Calibrated flats with them then created master flat. Then calibrated lights with all the masters, followed by Cosmetic correction, debayering, star aligning and finally integrated the lights to their final master.

For tests without flats, I just left them out...

Here's a single light - https://1drv.ms/u/s!Ari3AWpbmLZ0gvwzUVAUpJrBlcKLww?e=EF9ptN

Flat - https://1drv.ms/u/s!Ari3AWpbmLZ0gvwyqruJs6BIvrZD6Q?e=2BETne

Dark - https://1drv.ms/u/s!Ari3AWpbmLZ0gvw0Tel6GxLMhRq8sw?e=b7Ct6L

Flat Dark - https://1drv.ms/u/s!Ari3AWpbmLZ0gvw18bGKf7pF8y7PBQ?e=zmnkQ1

Light seems to be already calibrated? It's 32bit format but still 14bit values for some reason???

Could you provide one light sub straight out of camera? Or in case you are 100% sure this is it - what capture software did you use?

What is your calibration procedure and could you post one of these in fits format without any alteration

1. one light

2. one matching dark

3. one flat

4. one matching flat dark

4 hours ago, dannybgoode said:

Actually cropping and enlarging is probably as good a route as any. It’s hard to stop thinking in the same manner as normal photography but if your resolution is correct for the camera / scope combo then that is what matters. 
 

I think I’m right in saying (and I’ll happily be corrected on this) but if you have two camera / scope combos, both with a resolution of 1” per pixel then the target will be the same size for both. 
 

If one of your scopes is of a longer focal length and it reduces the field of view accordingly then all that is doing is ‘cropping’ the image with the scope rather than in software. 

You are certainly correct, but issue is that there are people that don't quite understand what is going on because the way images are displayed by devices.

If you view your image at 1:1 (1 screen pixel for one image pixel, or 100% zoom level), then you are absolutely right - object will have dimensions that correspond to resolution "/px times size of object in arc seconds.

Problem comes when images are displayed how they are usually displayed - to fit screen of display device (be that computer screen or smart phone or tablet or whatever) - then size of object is determined by FOV. This is where cropping starts to change things - it will not change resolution or original object size in the image - it will change FOV (decrease it) and that in turn will make relative size of object larger when viewed on "fit to screen" zoom setting.

1 minute ago, happy-kat said:

Te barlow doesn't that add opportunity for aberrations too.

I totally missed the barlow, and yes - it must be responsible at least a bit for funny star shapes. Tilt and collimation alone should not produce above star shapes, but barlow with tilt might do funky stuff to PSF.

9 hours ago, Pompey Monkey said:

Wow! that's a lot of explanation. Thanks.

The way my, rather limited, interpretation is if you subtract the bias (and dark if necessary on long exposures), then:

• Flats (Vignetting/dust bunnies) are a multiplicative correction factor,
• Gradients are subtractive.

Yes/no?

Ok, now I'm confused

We calibrate our subs so all that remains is light signal. In this process flats are always multiplicative factor and should be applied only to light signal as light is only thing that is affected by blockages and shadowing.

If we look at simplified model, raw sub that comes out of the camera contains bias signal, dark signal, light signal (here we don't discriminate between target and sky and we yet have no idea of vignetting / dust).

We need to remove bias and dark so only thing that is left is light signal. We do this by taking darks. Raw dark contains all but light as scope aperture is covered when taking these subs - all light is blocked. This means that raw dark subs contain both bias signal and dark current signal. If we subtract this from our lights we have done the job (this is my explanation above, no need to fiddle around with bias here for simple calibration).

Once you have only light signal left, the you can correct multiplicative factor of blockage / shadows by dividing by master flat (that also needs to be made out of "pure light" with all other signals removed).

Gradients are quite special - it is guess work rather than calibration. In principle you can't tell if LP gradient is coming from target or not. Both are light and you can't distinguish how many photons belong to sky and how many to the target. You can only guess by using some sort of approximation - like sky is either constant or linear gradient (or maybe simple polynomial of certain degree) and you can't have negative values, but you know that certain parts of the image don't contain target.

So answer to above question would be something like: Vignetting / dust is always multiplicative but for flat division to work properly you need proper removal of all signals but light signal. Gradients are additive/subtractive and in general don't depend on proper calibration - neither proper calibration helps with their removal nor you need proper calibration to attempt to remove them.

Did I get your question right?

4 hours ago, Pompey Monkey said:

Bias should be subtracted from every image read from the camera i.e. lights, flats and darks. Except bias frames, of course

That really depends. I most cases you in fact don't need bias to be subtracted and if you follow "standard" workflow you can actually use any file as bias - even Picasso painting digitized to exact size as your subs

Let me explain and show why is that:

If we observe "regular" calibration procedure being (same thing happens to flats, so we will skip flat calibration for now, and just mention it at the end):

- Master bias is stack of bias subs (for now, we will later substitute in Picasso painting instead)

- Master dark is made by stacking "calibrated" dark subs.

- Calibrated dark sub is dark sub minus master bias

- Calibrated light =  (light - master bias - master dark) / master flat

Let's do a bit of substitution

Calibrated light = (light - master bias - average(dark - master bias) ) / master flat

Now average is regular average sum and division, and if we have "constant" term we can pull it in front of the brackets so let's do that

Calibrated light = (light - master bias - (average(dark) - master bias) ) / master flat.

Let's rearrange that a bit:

Calibrated light = (light - master bias + master bias - average(dark) ) / master flat

Now you will probably notice that we have -master bias and +master bias and fact is that two numbers with same absolute value - one negative and one positive added together will give 0, and we can have any old "number" there it won't change a thing so it is safe to also write this:

Calibrated light = (light - Picasso image + Picasso image - average(dark)) / master flat

and that is equal to

Calibrated light = (light - average(dark)) / master flat

You don't need bias to do proper calibration, and in fact if you use above "standard" calibration flow - you can use any, and I mean literally any sub as master bias - it will make no difference at all.

You only need bias in very special cases - like mentioned above by @Merlin66 - scaling darks - either in form of different exposure length or when trying to optimize dark calibration (darks at different temperature).

20 minutes ago, Phillips6549 said:

It looks to me that the effect is less at the top.

That would mean that tilt is involved. Indeed effect looks like it's getting worse as we move from top to bottom of the image. Whenever you have such linear change of shape - it usually means tilt. It could be focuser tilt or secondary misalignment.

Just now, MartinFransson said:

OK, that sounds like I might be able to try  Just one thing, how do I colour  balance a single (mono) channel? In my world only an RGB image is possible to colour balance...

Thank you for taking your time to explain!

You color balance 3 mono frames - it's like color balancing regular color image but you do it on individual channels.

Simplest way to explain what is going on and explain how to do it would be:

take R_raw, G_raw, B_raw and do RGB compose to get Color_raw then color balance that into Color_balanced and then do RGB split to get R_balanced, G_balanced, B_balanced.

How it actually works is - with pixel math:

R_balanced = c1 * R_raw + c2 * G_raw + c3 * B_raw

G_balanced = c4 * R_raw + c5 * G_raw + c6 * B_raw

B_balanced = c7 * R_raw + c8 * G_raw + c9 * B_raw

where

c1, c2, c3
c4, c5, c6
c7, c8, c9

is color space transform matrix and depends on camera / filters and color space you are aiming to transform to. In general it is not easy thing to find this matrix, but you can do single star calibration, or you can solve for number of stars, or you can inspect QE curves and create transform, or you can take tool to do it for you - PI has star color calibration tool - use that compose RGB image out of mono images, do color calibration, split result again into mono images.