An Ascendometer is a self-contained, portable unit used to analyze neural activity in the brain. The device was nicknamed as such by Cameron Mitchell, though Samantha Carter wished she had thought of it first.
By scanning the target, the device shows synaptic activity, including the areas of the brain that are responsible for advanced mental abilities, such as telekinesis.
The device was found on P3X-584, a planet which was the site of a secret laboratory on Anubis. It was there that Anubis created Khalek, an advanced human which he planned to let ascend. When SG-1 found the planet they also found a DNA resequencer and the device, which was later named by Cameron Mitchell and used to find out how advanced Khalek was. After Khalek's death the device remained in the possession of Earth. (SG1: "Prototype")
One year later the Atlantis expedition encountered another DNA resequencer-like device in Atlantis, which evolved Dr. Rodney McKay to a certain point. To find out how advanced he was the team decided to bring in the ascend-o-meter from Earth. (SGA: "Tao of Rodney")