In a lot of cases, you'll be getting a designer or design agency to design showcases for you, and they can set up the document in Photoshop or InDesign to exactly match Showcase's slide dimensions in pixels.
However, you might be trying to export your own images from Powerpoint, and finding that the backgrounds do not fit in the Showcase frame - they end up with space around them in some way or another.
It is possible to export slides from Powerpoint in Showcase-specific dimensions - it takes a few steps, but we'll go through it together.
First, figure out the pixel dimensions of the Showcase you are building. You can see this by selecting "Slide background" for the showcase you are working on - the dimensions are specified down the bottom of the panel, next to the 'information' symbol.
If you're creating a showcase from scratch and you're fine with the default ratio of 4:3, the pixel dimensions you'll want are 2048 x 1536. This resolution looks great on a wide range of devices. The instructions below use 4:3 resolution as an example.
Your next step depends on whether you are using Mac or Windows.
Let's start with the Windows steps. On recent versions of Powerpoint, you should find the option "Slide size" under the "Design" tab. On earlier versions of Powerpoint, similar controls may be found under "Page Layout".
You want the "Custom Slide Size" option as highlighted. On the window that appears, choose your dimensions in centimeters. This can get tricky to work out, as the Showcase dimensions are specified in pixels, but for 2048 x 1536 pixels, try 54.4 cm x 40.8 cm.
Now it's time to save the images. Go to File > Save as. You want to choose the file format as PNG. Once done, click 'Tools' next to the Save button, and then "Compress pictures" down the bottom.
Set the compression to 220ppi.
Once saved, you can check the resultant dimensions from Windows Explorer, by selecting the image and choosing "Properties". You can see this one is pretty close to the 2048 x 1536 we need - if it's slightly bigger, that's fine, as it will still scale down when in the showcase.
You can now add this image to your slide background.
If using Powerpoint for Mac, the process is slightly simpler. You can still determine "Slide Size" from the Toolbar, but this time it is under the "Themes" tab:
And for Mac, you specify your custom slide size as 26 cm x 19.5 cm.
Once done, you also use Save As > and select PNG as the file type. Then, choose "Options" from the bottom left of the Save dialog.
In the following dialog, you will be able to specify exact pixel dimensions from the area down the bottom. So here is where you can choose 2048 x 1536, if that's what you ended up going for. Sometimes these numbers will default to one pixel out due to rounding - that's ok!
You can now add these images as well to your slide backgrounds in showcase, and they should fit nicely, filling up the screen.