This is long, sorry. I’m a novice at photography. Other than my iPhone I have never owned a camera until two months ago. The attached unedited photos are taken with a Canon DSLR Rebel Xsi, a 31mm extension tube, EF-S 18-55MM F/3.5-5.6 IS STM, and a Nikon macro lens. I made huge strides because others shared what they knew. So I will pass this on.
The best low cost solution is bright sunlight. Shadows are the enemy, so it’s best to use two lights of equal strength. Meaning the same lumens, kelvins, watts, etc. place them either opposite each other with the gem in the middle, or you can put a weaker light under a piece of clear acrylic and one light straight down over the lower one.
Looks like your okay on the background So, get a white sheet of paper or any other white stiff object (I use the pressed styrofoam stuff that covered my iPad during shipping). Now cut a hole in it large enough, so when you look through your camera’s viewfinder you can see your gem. Now focus and take your picture.
The idea is for the two opposing lights to eliminate the shadows under the stones and the paper you’re holding in front of your camera pushes the light back towards the gem. With open fronts light escapes, or if your camera is black it will absorb the light.
Your angle looks okay, but it’s best to shoot the gem at a 45 degree angle to the gem’s table. Since the degree can change for every gem, you may need to focus squarely on the center then move up/down to find the best shot.
It’s worked for me every time. If you need photos of my setup let me know.