I'm not 100% sure, but I believe if you have a .BIN file, then you'll need a .CUE file as well to mount the CD image.

Mounting the image as drive d is not a problem and works great.
When I run the duke3d.exe the game is unable to detect/recognize the mounted CD Drive.

Do you have any idea how to fix this?

If you imgmount as if it was a HDD, the game might get confused if it expected a CD… Manual (README file) specifically lists this as an example for imgmounting CD-ROM:

1imgmount d c:\cdimage1.cue -t cdrom

Duke3d doesn't do any CD checks or need the CD for gameplay. It was only used for systems with really small HDD's.

Does setup have an option to install to the HDD?
If it doesn't you can try copying the Duke3d folder from the virtual CD to your HDD and run it from there

Atomic (in its original not-released-by-interceptor form) does a cd check against a big dummy file on disc IIRC.

Could very well be, I vaguely remember games doing this but not which ones... has been awhile
Back then I may have simply copied the dummy file over as well, or found a way to remove the check

This day and age where 500MB is considered small copying the dummy file over shouldn't be problem, the important think is the game doesn't check for the CD itself.

Whats the name of that dummy file and whre is the file located.
To which directory do I need to put this file?

I just copied the atominst folder to my hatd disk.
I did not found any dos installation executable on theThe Kill A Ton Disk for the Atomic Edition. There was just a folder called atominst which include the game files. Like I said I just copied that folder to my HDD.

So anyone got an Idea how to solve this issue.

Can you give us a contents listing of the CD?

To do this mount the CD in windows, open a command prompt
Change to the CD drive and type:
dir /s >c:\list.txt

This will create list.txt in c:\ that you can post here

Atomic now runs without problems. I started the INST.EXE file located on the Game CD and installed the game and it started.
I think the setup program created the CDROM.INI file inside the file there is a path to "d:\support"
So the problem was caused by that missing file I think.