"DisplayCAL" is making me feel ashame.

[Ink stained Fingers]

take one of Your favorite oil-paintings at home and try to make a replica!

- that won't work because you are not able to replicate the surface structure of such painting, and thus the impact on reflective light - but that's not what an inkjet printer is made for. The gamut of such an oil painting is pretty small, that's not where the limitations are. I'm not really clear what you are heading for - is it the differences between a monitor and a printout or the limitations of the proof function to emulate a printout on a monitor ? And what would you get with 'better' and assumed more accurate instruments ?

 

[The Hat]

Contrary to belief, when a true con-artist copies a famous oil painting, then when standing 1 metre back from it, no one can tell the original from the copy, why ?

The real reason why the copy is easier identified is because the forged work is done to a higher quality than the original was, and this flaw can only be seen with the help of a Loupe or X-ray.

He may be the master but he still makes mistakes, but the forger can’t afford that luxury for his work must be able to past closer inspection...

 

[berserk]

OK - take a photo of a test-photo (net is full of them),

Here we go!
Print that test-photo in the same light as you have in your "darkroom" do not twak it.
Now take a new photo of that newly printed test photo. Under a controlled lightsource after drying some time. I have 5300K lamps in my "darkroom" - untick auto white balance and set it manually to your own light temperature in the camera. Now Load the pic with Camera Raw - white balance set as "As Camera". Nothing else changed.

Now let it go through your standard work flow without tweaking it.
Print it!

Compare them.

Did not something happen?
Why?

 

[Ink stained Fingers]

and you take a Fuji or NIkon or Canon camera and get different results , no wonder they are all not profiled to the same color replication standard, auto or fixed white balance would not do that. And is your 5300K lamp of a good flat spektrum type ? Otherwise you'll get even more deviations.

 

[berserk]

Yes - but how many test prints does this pro-photo-artist make only to get it the real exact brightness.
That is very subtle. Then there is all the other things to test-tweak.

I do not think it exist really "PERFECT" profiles.

I'm sure those real experts can make it very very close - not exact. Museums are picky!

Also thinking on all those lights and controlled light settings of the paintwork.

Yep - something for a REAL pro. (CMYK?)

I'm not there at all but like photographing and printing. I spent plenty of money on that - too much.
As said - I'm a retired and started taking pics in the middle of the fiffties. I think I never have made a real technically PERFECT photo, but been close now and then - but many photos of mine I like because of it contents and how it's cut (not to 2:3)

 

[berserk]

@Ink stained Fingers wrote:
"And is your 5300K lamp of a good flat spektrum type ? Otherwise you'll get even more deviations."

They are described "for critical color proofing environments - in artstudios, critical color work, museums and in the industry for exact color matching".

If it's a flat light I do not know - but they costed and seems to work for my purpose. Now You have made me uncertain! I must call Osram and ask if they delivered what I described I wanted. But I did not chose those - in the same column for critical color work, with the suffix "broad spectrum" also 5300K. The Osram engineer insisted on those I have.

Next time I set up an "darkroom" environment - I'll have it done by an expert and pay for it.
I have spent so MUCH time on "reading me into" the subject(s) - time I could have used taking pics or doing other hobbies.

BTW - all those cameras could be calibrated easily in 5300K with X-rite "colorchecker".
However - as I want to say - there is nothing that can be called a "PERFECT PROFILE" - there are to many factors making it impossible. However we can make color profiles that satisfy us.

 

[Ink stained Fingers]

it probably this you are after https://en.wikipedia.org/wiki/Color_rendering_index
or http://lumenistics.com/what-is-color-rendering-index-cri/ and particular Osram lamps are on the good side of it. But this does not solve yet the variances with the unprofiled cameras. You can profile a scanner, it typically does not make much sense for a camera operating in widely varying light conditions, it may work in a studio where you work always with the same lighting equipment and fixed camera settings - WB - exposure

 

[berserk]

The Osram lamp mensioned above has a CRI (color rendering index) of Ra >95.

Cut and paste from the link:
"Numerically, the highest possible CIE Ra value is 100, and would only be given to a source identical to standardized daylight or a black body (incandescent lamps are effectively black bodies), dropping to negative values for some light sources. Low-pressure sodium lighting has negative CRI; fluorescent lights range from about 50 for the basic types, up to about 98 for the best multi-phosphor type. Typical LEDs have about 80+ CRI, while some manufacturers claim that their LEDs have achieved up to 98 CRI.[3]
_______________

That is - I think the engineer at Osram picked the right one for me. On other places they call "CRI- color accuracy"

I just trusted the Osram engineer describing for what use they was intended. He said "I know exactly what You shall have". When I heard him say the word "color proofing" i felt confident.

About that calibrating let's drop it.
My point was academic - just if you do a print and could have a "theoretically exact copy" of that print and then somehow let go through the calibration and printing again - the result would not be good.