What is a field stop?

 

The three limits of behavior can also be described using the concept of a field-stop. In the low magnification limit the field-stop of the system is the objective lens whereas in the high magnification limit the field-stop is the pupil of the eye. If the eye is allowed to move, the field stop is the edge of the eyepiece. I have taken two series of photographs that illustrate the different behaviors. To do that, I needed to make two very different telescopes. The first is a low magnification telescope shown here.

The telescope is constructed very simply from a cardboard mailing tube, lined with flock paper. The objective has a focal length of 500 mm and the eyepiece is a negative lens with a focal length of -170 mm. The magnification is therefore approximately 3. Both lenses have diameters of 50 mm. This is probably larger than was available in good quality in 1609, but I wanted to make sure that the exit pupil was large. In fact, the exit pupil is 17 mm in diameter, much larger than either a daytime adapted eye, about 3 mm, or a night-adapted eye, about 6 mm.

I took a series of photographs through this telescope, in daylight, simply by putting a camera on a separate tripod behind it. The camera had a 50 mm lens mounted on it, with the aperture set to f16. The diameter of its iris opening is then 50 mm / 16, or approximately 3 mm. This is much less than the size of the exit pupil. The top photograph is taken through this set-up. I included in the view an object that may be familiar to you. It is a yellow, white and blue planisphere. The planisphere is 16 inches across and it was 160 feet from the telescope, so it has an angular size of 0.5 degrees, which is about the same as the angular size as the Moon. This gives a scale to the photograph. I claim that the objective lens is the field stop in this limit. This means that if I change the size of the objective the field of view scales in proportion. In the center photograph, I have put a mask in front of the objective, reducing its diameter by a factor of two, and the field of view has gone down in proportion. If you put a mask over the objective of a modern telescope, the field of view is pretty much unchanged. Just for fun, in the third photograph, I put a star shaped mask in front of the objective and the view is masked the same way. Try this with your TeleVue refractor!

My second telescope is a much more conventional Galilean replica.

The objective has a focal length of 1000mm. Its diameter is 25.4 mm, but by the time it was mounted this was masked to about 23 mm. I used two eyepieces, with focal lengths of -50 mm and -30 mm, giving magnifications of 20 and 33 respectively. The eyepiece diameters were also 25.4 mm. The exit pupils with the two eyepieces were 1.15 mm and 0.7 mm, which are both much smaller than a dark adapted eye.

I took a second series of photographs using this telescope. The planisphere still subtends an angle of 0.5 degrees. I used the 20x magnification eyepiece so that the exit pupil of the telescope is 1.15 mm in diameter. This time, the iris of the camera lens is the field stop, and I took the photographs using different apertures for the 50 mm lens on the camera. The telescope was not adjusted at all during the series.

For the first photograph the aperture is f16 so that the iris opening is about 3 mm, similar to a daytime human eye. The field of view is very narrow.
In the second photograph the aperture is f8. The iris opening is about 6 mm, similar to a night adjusted human eye. The field of view is doubled.
The aperture is has been increased to f4, corresponding to a diameter of about 12 mm. Notice that the outer edge of the field of view corresponds to the iris diaphragm of the lens.
Finally the lens is wide open at f1.4. The diameter of the iris is about 36 mm. If you could find an alien with eyes this big she would have a fine view!

A more serious comment is that the last photograph gives you some idea of what you can see by moving your eye around behind the eyepiece. Clearly the image of the whole planisphere, and hence of the whole Moon at night, is getting out of the telescope. A related point is that the telescope can also be used to project an image of the Sun, and the image of the entire disk of the Sun is projected.

In this series of photographs I didn't reach the final limit, that the eyepiece of the telescope acts as the field stop. If the camera lens could have been opened much more, or if I had moved the camera slightly to one side, I would have seen the slightly rough edge of the mounting of the eyepiece limiting the view.