Could we build a world-class telescope out of smartphone cameras?

TL;DR: no, but it might be possible with many amateur telescopes.

I was chatting with a friend the other day, and a question arose:

Could we create a distributed smartphone telescope that competes with professional land-based scientific telescopes?

Since a telescope primarily works by collecting and focusing light in an area (called an “aperture”), you should be able to do the same thing with any camera system, ignoring field-of-view (zoom) limitations.

At first, based on the ubiquity of decent smartphone cameras, my intuition was to think that you could do this with maybe 100,000 app installs.

I was very wrong.

How do astronomers look at stars?

Modern ground-based telescopes are measured on one primary metric: light gathering area. This represents how much light they’re able to capture when forming their image. Since more light means more photons, and more photons means better resolution, this effectively measures how powerful a telescope can be.

The European Extremely Large Telescope, currently under construction, will have a light gathering area of 978 square meters, and it will be the largest ground based telescope in existence when it is complete. This is the very minimum baseline measurement we’ll have to meet, before other considerations (like atmospheric distortion and corrections for noise, color, pixel grids, etc).

How many iPhones would it take to do the same thing?

Let’s take the iPhone 6 camera for argument’s sake. The camera has the following specs:

Aperture: f/2.2
Focal Length: 4.15mm

The f-number is defined by the following formula:

N = f / D

Where N is the f-number, f is the focal length, and D is the aperture diameter. From these we can determine that:

D = .00415 / 2.2 = .00189 meters

Since the aperture is approximately a circle, we can thus calculate that an iPhone camera’s light gathering area is:

A = pi r^2 = pi (.00189/2)^2 = 2.79 * 10^-6 square meters

Finally, we simply divide our desired light gathering area (978 m^2) by the calculated area for the iPhone camera to get the number of iPhones needed to capture the same amount of light:

978 / (2.79 * 10^-6) = 350 million iPhones

This assumes that you could get every one of the iPhones pointed at exactly the same place at the same time, that you have bandwidth and algorithms that can perfectly reconstruct a composite image from imperfectly sampled smartphone images, that there is no atmospheric distortion, and that you only wish to watch the sky for, say, 1/30th of a second.

Short answer? Too many iPhones.

In reality, ground-based telescopes watch a specific point for many minutes at a time. They move and rotate with the earth’s star field as they watch the sky, and dynamically correct for atmospheric distortion using many techniques (including an artificial laser “star”, articulated mirrors, and high altitude).

If we truly wanted to reach the quality of a real telescope, we’d probably need to increase our number of iPhones by at least a factor of 10 (to 3.5M iPhones).

Ultimately, this is probably a field that is best served by specialized hardware designed for its purpose.

P.S. What about Amateur Telescopes?

This is much more realistic. First, amateur telescopes can be computerized to follow a star field, so they can observe for longer periods. Secondly, they have much more advantageous numbers. Let’s use a typical beginner computerized telescope as an example:

D = .65 / 5 = .13 meters

A = pi (.065^2) = .0132 m^2

Number of telescopes needed:

978 / .0132 = 73,682 telescopes

As a bonus, since these telescopes are computerized, you could release an app that automatically positions them correctly and syncs the image capture with other telescopes, thus improving the accuracy of the overall picture.

Since each telescope costs only $400, this is theoretically achievable with only $30M (or many, many amateur astronomers) plus computing resources. Not too bad.

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