I'm looking for a relatively cheap camera to shoot photos of an 0.18 percent grey card and I'm expecting close to real life luminance (not 100% accurate but close). Don't have the budget for DSLR at the moment.
You need a camera with spot metering. Try checking out camera specs over at Dpreview. Choose a camera, go to "spec" tab, scroll down to "Metering modes"
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I did a quick look and found this one, $109, with spot metering.
http://www.dpreview.com/products/canon/compacts/canon_elph170is/specifications