At infinity focus (focus at the rear focal point of the lens), the effective aperture is always the
same as the aperture setting. The exit pupil may be only half the distance from the focal point
with a P=1/2 lens, but the size is also halved and the angle it makes with the detector is
unchanged (see above diagram). At any focus closer than infinity, the front aperture setting and
the effective aperture will start to diverge as you would expect with the effective aperture. The
difference is that the resulting effective aperture will vary depending upon the pupillary
magnification. Again, this is best seen with a diagram.
same as the aperture setting. The exit pupil may be only half the distance from the focal point
with a P=1/2 lens, but the size is also halved and the angle it makes with the detector is
unchanged (see above diagram). At any focus closer than infinity, the front aperture setting and
the effective aperture will start to diverge as you would expect with the effective aperture. The
difference is that the resulting effective aperture will vary depending upon the pupillary
magnification. Again, this is best seen with a diagram.
We have previously discussed the concept of effective aperture and have found that it is related
to the size of the aperture and the distance the aperture is from the detector. A small aperture
that is close to the detector is equivalent to a larger aperture farther away - i.e. as long as they
make the same angle with the detector they will have the same effective aperture.
We have been talking about the "aperture" previously for this discussion, but the real work of the
effective aperture is done at the exit pupil. As previously defined, the exit pupil the apparent size
and position of the aperture as seen through the lens. This all means that the pupillary
magnification have an effect on the effective aperture, although predominantly with close-up and
high magnification.
To set the stage for this discussion, you need to know how the pupil moves in relation to the rear
principal plane as the pupillary magnification is changed. With a symmetric lens (P=1), the
entrance and the exit pupils are equal in size. So, a 100mm f/4 lens will have a 25mm entrance
pupil and a 25mm exit pupil. In this case the entrance and the exit pupils will be positioned at the
principal planes. The effective aperture at infinite focus will be focal length divided by the exit
pupil - 100/25 or f/4.
For non-symmetric lenses (P<>1) with the same f/number, the exit pupil will travel along this
same cone forward or backward depending upon the pupillary magnification, its size and position
proportional to the pupillary magnification. This concept is easier to see in a diagram. A point that
took me a while to figure out is that the diameter of the cone as it crosses the rear principal plane
will always be the same same size as the entrance pupil, no matter what the pupillary
magnification is.
to the size of the aperture and the distance the aperture is from the detector. A small aperture
that is close to the detector is equivalent to a larger aperture farther away - i.e. as long as they
make the same angle with the detector they will have the same effective aperture.
We have been talking about the "aperture" previously for this discussion, but the real work of the
effective aperture is done at the exit pupil. As previously defined, the exit pupil the apparent size
and position of the aperture as seen through the lens. This all means that the pupillary
magnification have an effect on the effective aperture, although predominantly with close-up and
high magnification.
To set the stage for this discussion, you need to know how the pupil moves in relation to the rear
principal plane as the pupillary magnification is changed. With a symmetric lens (P=1), the
entrance and the exit pupils are equal in size. So, a 100mm f/4 lens will have a 25mm entrance
pupil and a 25mm exit pupil. In this case the entrance and the exit pupils will be positioned at the
principal planes. The effective aperture at infinite focus will be focal length divided by the exit
pupil - 100/25 or f/4.
For non-symmetric lenses (P<>1) with the same f/number, the exit pupil will travel along this
same cone forward or backward depending upon the pupillary magnification, its size and position
proportional to the pupillary magnification. This concept is easier to see in a diagram. A point that
took me a while to figure out is that the diameter of the cone as it crosses the rear principal plane
will always be the same same size as the entrance pupil, no matter what the pupillary
magnification is.
| Effective Aperture and the Exit Pupil |
Above: The size and position of the exit pupil in relation to the
rear principal plane is proportional to the pupillary
magnification.
rear principal plane is proportional to the pupillary
magnification.
Above: The same apertures as above for a 100mm f/4 lens.
Effective apertures at 1:1 magnification in blue.
Effective apertures at 1:1 magnification in blue.
The formula that defines this relationship of the effective aperture to the pupillary magnification is:
N' = N*((m/P) + 1) (where N' = effective aperture, N = lens aperture setting, m =
magnification, and P = pupillary magnification)
The long and the short of it is that with a P>1 you will lose less aperture as the magnification is
increased and the opposite for a P<1. A larger effective aperture (smaller number) means more
potential image resolution. Sounds like all high magnification lenses should have a P>1 - well
maybe not as we will discuss the plusses and minuses of this situation in the next installment.
N' = N*((m/P) + 1) (where N' = effective aperture, N = lens aperture setting, m =
magnification, and P = pupillary magnification)
The long and the short of it is that with a P>1 you will lose less aperture as the magnification is
increased and the opposite for a P<1. A larger effective aperture (smaller number) means more
potential image resolution. Sounds like all high magnification lenses should have a P>1 - well
maybe not as we will discuss the plusses and minuses of this situation in the next installment.