I was introduced to this method by someone's website or blog in Japanese, I don't recall who/where.
I finally got around to trying it.
These are my coins/pics.
It is much better than taking pictures at different angles, which is what I did the last time I counted reeds.
You can buy this set of stainless steel measuring spoons in Japan for 100 yen (about one US dollar).
The diameter of the largest one is 5 cm, perfect for crown size coins/silver dollars.
The packaging is in Portuguese and Japanese, so if anyone is in Rio you might be able to buy them there.
Of course anything reflective and of the same size/shape should work.

Put the coin in the spoon, you should see the edge reflected.
To take a usable photograph, you may need a good quality camera, and lots of light.
You need to focus on the edge of the coin, not the center.
Don't worry about how the coin looks in the photo. It will probably be very bright.
Once you get a clear picture of the reeds, count them with your paint program:
This coin has 198 reeds. (year 1882 one yen)

This is the boring part...you can see I made a mistake below, between 40 and 50. 193 reeds is correct. (year 1889 one yen)

* NB this coin is heavily damaged on the other side, which is why the bottom edge looks weird