100 times more powerful than a standard telescope? Really?

We’ve been asked this question so many times that we thought you could be interested in maths leading to this bold statement.

This story started when we first demoed the EVSCOPE's proof-of-concept at star parties. There, amateur astronomers with their own telescopes told us that, with an EVSCOPE system, you were observing deep-sky objects as well as or sometimes better than with a 1m telescope. Compared to our 114mm telescope, this meant the EVSCOPE was at least as powerful as a telescope collecting 100 more times light.

We then did our own maths to turn this feeling into a fact. The limit in magnitude with the EVSCOPE is 18.2 in visible from San Francisco. We measured this directly from downtown through our observations with the EVSCOPE's proof-of-concept (pre-prototype). It’s, therefore, a conservative estimate.

In San Francisco, we can see the zenith stars with a magnitude of less than 2 (visual magnitude limit). We then used Scopecity's calculator, which is based on a Bradley Schaefer program that calculates the limiting stellar magnitude an observer can expect to see with various types and sizes of telescopes, and under various conditions. It is fully discussed in Sky & Telescope magazine, November 1989, page 522, and is now an online tool vetted by an amateur astronomer (Of course there is a long debate about magnitude limit calculation with telescope https://www.cloudynights.com/topic/402886-magnitude-visible-by-telescope/ ).

We calculated what would be the magnitude limit for the same size telescope (4.5” reflector) with a resolution power of 150 and with the following parameters (age 35, extinction coefficient 0.4, seeing of 3 arcsec (which is what we have in cities)).

This turned into a theoretical limiting magnitude of 10.94 for a standard telescope, leading to a 4.86 gain in magnitude with the EVSCOPE . Note that it’s again a conservative estimate, we are comparing here a measured magnitude (for the EVSCOPE ) and a theoretical one (the Scopecity tool), the theory is usually more optimistic than measures.

We translated this magnitude difference into flux ratio, with the flux ratio an accurate description of the intensity of your observation experience. We then got a result of 87.9. As this whole calculation relies on conservative estimates and on a proof-of-concept less efficient than the final product, we serenely decided to claim that the EVSCOPE to be shipped will be 100 times more powerful than a normal telescope.

Science is in essence debatable, and obviously, our estimate is, but, when we say the EVSCOPE is 100 times more powerful than a standard telescope, we mean it.