If you have a couple of ball bearings (new or very clean) you can make yourself a ball end mic out of your digital calliper.
Take one and tape it to the measuring side of the jaw, as far out as you can on the flat portion.
And tape the other on the other jaw directly opposite.
You can tape over the measuring side of the ball, but best not to for accuracy.
Close the jaws and zero the caliper for measuring the distance between the two. For those with dials and verniers... you'll have to subtract this measurement from what you measure.
Now you'll be able to measure the thinner parts of the disk. Of course you need a point mic to measure the depths of the grooves.