Understanding Image Scale and Field of View

When it comes to telescopes for visual observation, bigger is better: a larger aperture will gather more light and the observer will see more at the eyepiece. For CCD imaging, on the other hand, aperture is less important. What really matters is focal ratio. The focal ratio determines how much light is picked up by the CCD chip in a given amount of time. If you want shorter exposures you need a faster (smaller) focal ratio. An 8" telescope with a focal ratio of f/10 gathers the same amount of light as an 8" telescope at f/5. But the focal length of the f/10 telescope is twice as long (2000mm vs 1000mm) so the light from a given area of sky is spread out over 4 times as much area at the focal plane of the f/10 scope, making it 4 times slower than the f/5 telescope. You could compensate for this factor by using a camera with pixels that were twice as large (4 times the area), but in general most cameras have similar sized pixels. So for a given camera, a smaller focal ratio telescope is always faster.

Why do many CCD imagers have large-aperture instruments, even if they rarely observe visually with them? The answer is image scale. An 8" diameter telescope operating at f/3.3 has the same focal ratio as the Palomar 200" telescope. But the focal length of the 8" telescope is 670mm while that of the 200" is 16,800mm! First, note that this means with a given pixel size, even though the 200" gathers 625x more light than the 8", it also spreads it out over 625x the area, so both are the same "speed" because the focal ratio is the same. This is why most professional telescopes use cameras with much larger pixels than amateur cameras. Second, the image scale of the 200" telescope is much greater even though the speed is the same. For example, a 9-micron camera pixel would cover 2.8 arcseconds on the 8" and just 0.1 arcsecond. If an object is, say, 60 arcseconds in size, it will appear just 21 pixels wide on the 8" and 600 pixels wide on the 200".

It gets trickier when you factor in field of view. With a given CCD camera, field of view is dependent only on focal length. This means a telescope which gives a greater image scale also gives a smaller field of view. Often this is not a problem since a large image scale is typically used to image smaller objects such as galaxies. However, the field of view can be made greater on a given telescope by using a larger CCD chip, so it is possible to have both a wide field and a large image scale by using the right combination of telescope and camera.

One more variable, then some examples which will make sense of all this mess. The number of pixels in the CCD chip will determine how large the final image appears on a computer monitor (it also affects print size should you choose to output your images to paper). More pixels means a bigger display size, regardless of the physical size of the pixels. Therefore, a sensor with 12 million tiny 3.1-micron pixels in a 4242x2830 pixel array will give a larger image on-screen than a 1024x1024 array with big 24-micron pixels, although the second chip is physically larger.

Examples

Sample images shown to scale at 1/8 actual display size

A) B)

Using the same CCD chip on two scopes with different focal lengths affects the field of view and image scale, but not the display size.

• CCD: 9-micron pixels, 765x510 array
• Telescope A: 500mm focal length
• Telescope B: 1000mm focal length

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A) B)

Using the same telescope with different CCDs affects the field of view and display size, but not the image scale.

• Telescope: 500mm focal length
• CCD A: 9-micron pixels, 765x510 array
• CCD B: 9-micron pixels, 1530x1020 array

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A) B)

Using different CCDs and different telescopes can lead to any number of results, but it is possible to end up with equivalent fields of view. In this case, a large CCD with a long-focal-length scope gives the same field as a small CCD on a short-focal-length scope, but the image scale is greater on the larger instrument. The display size is also considerably larger in the second image due to the larger camera's greater number of pixels.

• Telescope A: 400mm focal length
• CCD A: 7.4-micron pixels, 640x480 array
• Telescope B: 1250mm focal length
• CCD B: 6.8-micron pixels, 2174x1482 array