I am a camera

Actually, I am not a camera. That was a quote from "Into the Lens", a song by Yes. You should find it on the Internet and listen to it while you read this blog.. or not.

Astrophotography is a fun hobby. To get great photos, you need to put out some substantial funds, but to get nice shots, like my shots of Venus...

You just need a phone camera, a way to connect it to a tripod, and an inexpensive telephoto lens.

You also have to have an intimate knowledge of your scope and your camera.

For any photographic work, you need to know your camera's field of view and resolution, and if you don't have this in your phone's specs, you can easily determine them like I did for my phone camera. Here's my setup.

I carried my portable podium onto the patio with a half meter ruler held up by optical bench stands (those are from an inexpensive set I bought from Home Science Tools. Great company. You could probably make your own.) Under the podium, I stretched out 20 feet of a tape measure.

On the bottom photograph above, there's a plumb bob I threw together using a random piece of plastic I had lying around. I hung it from my phone tripod clamp with a 1/4 20 wing nut and cord. I clamped that to my phone so I could tell how far away I was from the ruler using the tape measure.

To figure out the angular field of view, I stood back until the ruler filled the camera view from one side of the frame to the other. 

That was right at 2 feet (27 inches).

Next, to determine the camera's resolution, the distance at which two close objects at a specified separation can just be seen as two separate objects, I moved back until the millimeter markings on the ruler just blurred into indistinguishable marks.

That was at 28 inches.

So, why would I want an angular field of view? Many terrestrial scopes, including binoculars, give their field of view in terms of width in feet at 20 feet. That's okay when you're working at distances that can be expressed in feet, or even miles, but astronomers work in distances from astronomical units (1 AU is the average distance from Earth to the sun) to light years (a light year is about 6 billion miles) to billions of light years.

If you draw a great circle around the Earth, at any distance, it is composed of 360 degrees. The moon, as seen from Earth, has a diameter of about half a degree (we say it "subtends" an arc of 0.5 degree.) So does the sun, although the sun is much bigger. That's why the moon can block out the sun in a total eclipse. Astronomers work with arcminutes (an arcminutes is one sixtieth of a degree) and arcseconds (60 arcseconds make up an arcminute, 3600 arcseconds make up a degree). Binary stars, as seen from Earth have a separation of from 20 to less than one arcseconds.

Next...the math.

I have set up a right triangle here. The angle from one end of the ruler to the camera, back to the center of the ruler is half the angular field of view. I know the distance from the ruler to the camera (d), and I know that the half ruler is 250 millimeters long (it's a half meter ruler). I can use trigonometry to figure out the angle.

I need everything to be in millimeters, so 27 inches is 685.8 mm. The tangent of my angle is 250 mm/685.8 mm, so the half angular field of view works out to be 20° and the full field of view is 40°.

Mount Evans, pictured here, is 40 miles away. The tangent of half my view angle is the half width of my view field divided by the distance. That means the half width is equal to the tangent of half the angular field of view times the distance, or 14.6 miles. My full field of view at 40 miles is about 29.8 miles.

I figure that my measured distance to the ruler could have been off by 2 inches in either direction, so I can calculate my error by recalculating my field of view at 29 inches and 25 inches and that error turns out to be about ±3°.

I can calculate the resolution of my camera using the same method but, instead of using half the ruler, I use half a millimeter. The distance from the ruler where I can just make out millimeter markings is 31 inches or 787.4 millimeters. That gives me a resolution of 0.07° ± 0.005° . That's a far cry from being able to see binary stars as two stars, but, at least, I can see the sun and moon as a disk instead of just a point source of light.

My camera's electronic zoom does not increase resolution at all but my telephoto lens does. If I wanted to check the resolution of my camera with an optical system like a telephoto lens, binoculars, or a telescope, I wouldn't use trigonometry, I would just see if I could see a pair of stars with a known separation.

Angular field of view is a more flexible measure than width of view at a given distance, but now you know how to find your camera's angular field of view.