Hammel tweeted that she wept when she saw the rings, yelling and making "my kids, my mom, even my cats look."
Webb is the world's biggest, most powerful telescope, operating 1 million miles (1.6 million kilometers) from Earth. It rocketed into space last December.
The observatory is in good health, according to NASA, except for one item.
NASA reported this week that a mechanism on one of Webb's instruments showed signs of increased friction late last month in one of four observing modes. Observations are on hold in this one particular observing track, as a review board decides on a path forward.