It's been a long time since I did any amateur astronomy. Other things impinged. (I built my own telescopes in the late 1960's, early 1970's. But also spend thousands of hours of work and testing and refiguring. Two reflectors and one Maksutov with a secondary spot on the meniscus.)
Too bad it seems so difficult today to get hobbyist quantities of various kinds of glass. Used to be dozens of suppliers for hobbyists making telescope mirrors and eyepiece lenses. No more. Most are gone and the few I've called wanted to know "How many tons of that did you want?" Old Willmann-Bell now pretty much offers nothing at all. (I actually bought my Maksutov meniscus from them, way back when.) If you know of anyone offering various types of glasses in hobbyist quantities, I'd love to know about them.
I think Phil's approach is great. It's very simple and you can adjust the curve by changing out resistor values. I could, but I'm not going to do it, prepare a complete set of partial differential equations so that you could optimize it perfectly for some intention. But Phil's recommendation that you just swap values of resistors just makes so much sense. So that's my recommendation.
The one thing I didn't like seeing in Phil's schematic was that there was no provision to manage the case where the potentiometer reaches one end of its sweep. So, I'd add a small resistor there to avoid the risk of directly applying \$3\:\text{V}\$ to your LED. Something like this:
simulate this circuit – Schematic created using CircuitLab
Start out with \$R_S=100\:\Omega\$ and \$R_P=1\:\text{k}\Omega\$. See what that does for your red LED. You can adjust \$R_S\$ to be lower if you need to increase the peak brightness upward. Then adjust \$R_P\$ to get the curve you want. (But you may need to re-adjust \$R_S\$ again, if you make a lot of change to \$R_P\$.)
Start there. There's nothing particularly complicated and it is very easy to set this up on a protoboard and look at it in a dark room (after 10 minutes of adaptation on your part.) It should not take you too long to work it out.
This really isn't something we can calculate using some flawless equation. There is a great deal of variability in LEDs, human responses to light, and limitations in the batteries you use, and more. Also, because you are running a voltage supply that is very near a red LED voltage (near \$2\:\text{V}\$), variations in different red LEDs will have more impact than otherwise. So this really is an experimental thing for you.
It would be possible to arrange things so that there more of a precision circuit that delivers very close to the same red LED current regardless of the vagaries of the red LEDs you use and which would reproduce the same pot-driven behavior curve every time. But it would involve active parts and/or ICs. And unless you were making a commercial product and willing to go through testing with amateur astronomer customers to get their various opinions about the "best feel" for the controls, Phil's circuit with the added \$R_S\$ is probably good enough for many uses.
