Hi Faouz
There is a pretty straightforward way to get very close and then with just a bit more work make it exact.
You have to realize that when you delete one of the RGB channels is converts to what is called Spot Channels with CMY spot colors. You effectively have switched to CMYK without the K channel (more on this later)
Here are the simple steps
- Convert your image to a Smart Object
- Open that Smart Object
- Within the Smart Ojbect delete the blue channel and File Save (or Cmd/Cntl + S)
- Go back to your main file (that is in RGB) and Photoshop will display in RGB the desired image
The above are the simple steps that get you close. To get virtually exact, you need to have a CMYK profile that does not use K by creating a custom profile where you remove the black channel generation.
- Go to Edit > Color Settings
- In Working Spaces use the CMYK dropdown and choose Custom at the very top
- Type in a unique name (I used CMY)
- In the separation type use GCR and set the dropdown to None (this makes sure that Blacks are not created with the K channel)
- Leave the other settings at default and click OK
- Now to actually save this profile again go to the CMYK working spaces dropdown and chose the Save CMYK option. This will save this setting for future PS sessions.
- Now in both the main file (which has the single Layer Smart Object) and also in the opened Smart Ojbect file, use the Edit > Color Settings and set the CMYK workspace to your new unique CMY profile.
When I used the above it helps convert back from CMY to RGB more accurately.
So there is a way yet other posts show ways of getting very similar results without the above pushups.
Hope this is helpful.
