How do you calculate a telescope’s image circle and field of view at infinity focus?

Question

I’m trying to understand the geometry behind image circle / sensor coverage for prime-focus astrophotography, rather than just using an online calculator.

My setup is a Celestron NexStar 130 SLT (130 mm aperture, 650 mm focal length) with a Nikon D80 attached via T-ring/T-adapter. I’ve also used a 2× Barlow to reach focus. How can I calculate, at near-infinity focus, the projected image size or field of view on the sensor from the telescope’s focal length and sensor dimensions?

I’d like the underlying formula so I can compare how different telescopes would perform on the same camera sensor.

user5052 · Answer

I am not sure about the answer to Would the image circle size decrease if I was able to ditch the Barlow lens?

But if you look at the JavaScript of that page you will see

var sensorw = "Sensor Width"
var sensorh = "Sensor Height"
var maxres  = "Max Res"
var focleng = "Focal Length"

var thisF = sensorw * 3438/focleng;
var thisF2 = sensorh * 3438/focleng;
var thisF3 = sensorw * 3438/focleng * 60/maxres;
var thisF4 = focleng/Math.sqrt(sensorw * sensorw + sensorh * sensorh);

Values:

thisF = Arc Min of Sky- Width:
thisF2 = Arc Min of Sky- Height:
thisF3 = Arc Seconds/Pixel:
thisF4 = Magnification (X):

This is how that page calculates it

How do you calculate a telescope’s image circle and field of view at infinity focus?

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