Details aside...
If you display the same image on two color-calibrated monitors it should look the same...
And, if you've take a reference image with a color-calibration checkerboard, your software should be able to match that to what you actually photographed...
And, if you've got a proper calibration profile for your printer, then what you print should match pretty well too.
(The usual catch is that printers cannot print exactly the same full range of colors as monitors can display... so some compromises are often required there.)
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I used to be somewhat "into" color calibration - under Windows.
(I assume it's still the same under Windows 11.)
In Windows there are basically two "stages" to the process.
When you "calibrate your monitor" you end up with two separate "pieces".
(The standard software that comes with color calibrators like Gretag Macbeth and Spyder X creates both at the same time when you calibrate your monitor.)
The first "part" is a hardware lookup table (LUT) that gets loaded into the color table in your graphics card.
The calibration software generally includes a little program that runs at bootup and loads this into your graphics card.
THIS part of the correction then applies to everything you run (it basically "hardware color corrects your monitor".)
(I don't know if Apple does this the same way or not...)
The second part is the "monitor profile" itself.
This is stored in some standard location and is only used by programs that "support color management".
(In general you enable color management and then point to the file.)
(This one is a "color PROFILE"... and it includes detailed information about what your display shows AFTER that initial hardware correction.)
(Technically the first one is "a calibration" and the second is "a profile".)
Once you've done all that you can load the profile for your monitor into Photoshop and now you should see "the exact proper colors" on your screen.
You can then calibrate your printer... or get a "premade calibration file" for it.... or, as Boom said, get a profile of THEIR printer from your print service...
Once you do that you can have Photoshop do things like "preview how what you're seeing will look when printed on your printer"...
(Basically you feed the color profile for the printer into the software and tell it to "preview your print".)
The details vary with different software... and it can get rather confusing.
But, if you "check all the right boxes", you should see the right colors on-screen, and they should come out right from the printer...
(Or, at least, you can see onscreen exactly what your print will look like.)
There are also some fun details, like how colors that one or the other device cannot produce, are handled.
For example, if you want to print a rainbow, odds are neither your screen nor your printer can print the full range of colors...
So you have choices about how these "out of range situations" are handled.
For example, if you select "perceptual rendering", the software will "scrunch the colors together a little bit so they all fit into the range your printer can print".
(And then you use the preview feature to "see what the output of your printer will look like" on your screen.)
To be quite honest I USED to calibrate my monitors...
But the last two high-end 4k Dell monitors I bought came with calibration certificates...
And they were about as close to perfect as I would have hoped to get with my calibrator...
So I didn't bother to calibrate them.
(And nothing that I print nowadays is really all that exacting in terms of perfect color matching anyway.)
Gamma refers to the "brightness ramp" of a particular device...
Exactly what a levels of grey show up at what points when you display or print a "black-to-white greyscale ramp".
It's one of the basic parameters you set to match before doing a more detailed correction.
(If the Gamma is wrong you can get an image that is too light or dark or whose "whites" or "blacks" are "crushed" or the opposite.)
When you calibrate the monitor the calibrator actually displays and measures a whole bunch of "color patches" (you get to pick how many).
It then generates an LUT (lookup table) that corrects each color value to display as it should.
It turns out that, with modern RGB monitors, each of the three colors is separate... so, once you correct the "red, green, and blue ramps", everything comes out right.
(In the old days, with CRTs, sometimes one color would interact with another, but that doesn't happen with modern LCD and LED monitors.)
Note that color sp[aces also do NOT fully overlap (so there are colors that exist in RGB that DO NOT EXIST in CMYK, and vice versa...)
Color space has gotten rather more interesting recently too...
While most monitors operate in RGB, and most serious printers use CMYK, most software nowadays can use them somewhat interchangeably... and convert between them at will.
And, in programs like Photoshop, there are various reasons why you might prefer one or the other for various types of edits and corrections.
(And now there are a whole bunch of color spaces BESIDES RGB and CMYK ... like LAB color and the newer HDR variants... )
Yes....Many calibrations. But don't Windows and OS handle color differently?
I know about all the profiles and such. Something to do with the Gamma curve and something else.....
I've seen the number '2.2' bandied about but have no more information....
All I care about is getting my PRINTS to match the Screen.....So when I do a color correction and other
adjustments, I have good confidence I will 'get it right'.
It helps if I can get a Printer Profile for whoever does my printing.....Costco used to be good for that
and I'd attach there profile to anything I really cared about and was never disappointed.
My LG TV also produces decent color. Looking at my recent shots in Zion is very nice.