I think that the best way to understand the sub-images in the “split details” tools is with an example, which you can easily reproduce yourself.
Here, I opened a sample image and added a “split details” layer with 5 levels, such that the base level is visibly blurred:
Then I added a “clone layer”, targeting the “split details” layer and with the sub-image initially to “0”. This gives you the the same image as shown by the “split details” layer itself, which is the base level:
If you now change the sub-image to another value (here I set it to “1”), you can access the various details levels (I have called the clone layer “detail level 1”):
They details levels are built as “fluctuations” around 50%, because they represent the difference between one blur level and the next one, and therefore they need to “encode” positive as well as negative variations. The details can be added back to the blurred image using the “grain merge” blend mode:
In fact, if you put each detail level on top of each other, and above the blurred base level (corresponding to sub-image=0), and blend them in “grain merge” mode, you will get back the original image…
Finally, if you put a clone of the background layer between the “split details” and “detail level 1” layers, with the “detail level 1” layer blend in “grain merge” mode, you effectively increase the sharpness/local contrast of the image, because you add some high-frequency details to the original image data:
Just try and play with the different combinations, and feel free to ask me further questions.
For example, try to see the effect of changing the sub-image (and therefore the frequency range of the detail level) in the last step, and see how details at different scales are enhanced…