The smaller-looking zenith
moon is due to the resting focus according to the proponents of
oculomotor micropsia. When viewing the full moon directly overhead, in
a clear sky, there are no other distance cues, and the eye adjusts to
its resting focus a distance of 1 or 2 meters. Further support offered for this
hypothesis is the effect of dark surroundings, which bias the eyes to adjust to
the dark focus distance of about one meter.
To test this hypothesis,
measure the moon or sun at a close distance from your eye using
a ruler or similar instrument, or pinch the moon or sun with your thumb
and index finger at a close position. The moon or sun looks small and
has a small measured size.
If you move the ruler or the pinching thumb and index finger
aside and focus on the moon or sun, now the moon or sun looks much
bigger. Measure the moon or sun at arm's length, which is about one
meter away from your eye,
with the ruler or pinch the moon or sun with your thumb and
index finger at arm's length. Then move the ruler or the pinching thumb
and index finger aside.
The moon or sun looks about the same size as the measurement on
the ruler and the space between the thumb and index finger. This
experiment proves that we do focus on a distance of approximately one
meter while viewing the zenith moon or sun.
However, I do not think that this focusing distance of one meter is the resting focus as hypothesized.
It is suggested that we adjust
our eyes to a resting focus when no distance cues are available.
But there are no distance cues available at sea and we still
perceive the horizon moon as larger over the ocean. Additionally,
viewing the moons through a tube effectively removes all the distance
cues.
Yet we do not adjust our eyes to the resting focus; rather we
focus on the opening of the tube. When the tube is shorter, we focus on
a shorter distance; when the tube is longer, we focus on a longer
distance.
The situation of no distance cues created by the tube viewing
does not make our eyes to focus on a specific spot, i.e., one meter
from our eye. Finally, the resting focus should be achieved when we are
not actively focusing on any object;
so our eyes are at rest, not doing any thing such as
converging, accommodating, viewing, and perceiving. Instead, we are
trying very hard and actively to focus on the zenith moon when the
resting focus occurs.
The resting focus, in fact, is the converging point.
The reason why it is approximately one meter from our eye is
that it is the focusing distance allowed by the minimum converging
angle when we look at an object as faraway as the moon or sun and have
such a perceived size.
As discussed in the previous article, the converging point cannot be moved forwards anymore
when the minimum converging angle has been reached. At this point, an
object that moves further away will be out of focus and appear smaller.
All in all, the one meter converging point is the furthest
position we can focus on when we view the zenith moon, which is
regulated by the minimum converging angle.
I would expect that any object casting the same perceived size
as the zenith moon will have the same converging point no matter where
it is located. Therefore, the so-called resting focus is not caused by lacking of distance cues, but by the perceived size and minimum converging angle.
Likewise, the dark focus is the converging point set for viewing an infinitely far distance.
Nonetheless,
how far we can place the converging
point depends on the size of the objects we are focusing on.
For a small object such as an ant the minimum converging angle
can be reached at a very close distance; thus we can hardly focus on an
ant at one meter.
On the other hand, for a large object such as the horizon, which
is probably the largest object on Earth, the minimum converging angle
will be reached at a very long
distance.
This is the main point of my proposal: the horizon moon looks
larger because we can bring the converging point closer to the largest
object on Earth, the horizon, in comparison to the zenith moon which is
viewed through a much closer converging point to the viewing eye and
farther away from the viewed object.
This effect can be likened to the telescope. When you focus
your telescope on an object, all those other objects in the view field
will be enlarged as well.
We can also use the paper tube to simulate this effect. If you
view both the horizon moon and the zenith moon through one paper tube,
they look the same size. Now view the zenith moon through two paper
tubes and view the horizon moon through one tube.
As a result, the zenith moon looks larger than the horizon moon
because the converging point is closer to the viewed object while
viewing it through two paper tubes.
Similarly, both moons look the same on the photograph taken
with the same focal length; but the zenith or horizon moon would look
larger if taken with a longer focal length lens.
Converging our eyes on the horizon is like viewing objects
through a longer tube or longer focal length lens. Consequently, the
larger-looking horizon moon is due to the fact that we can physically
converge our eyes closer to the moon thanks to the horizon nearby which
is the largest object in this world; as a result, the horizon moon also
looks nearer like being viewed through a telescope.
There is no need for subjective interpretation, taking into
account, computing, compensating, calculating, inference (conscious or
unconscious), guessing, expecting, processing, cuing, reasoning, and
whatsoever.
There is one aspect of the Moon illusion that has been neglected by all the researchers.
It is that people perceive the horizon moon as larger and at
the same time perceive the sky as smaller. So there are two aspects
regarding the Moon illusion: one is the recognized larger-looking
horizon moon and another is the overlooked smaller-looking sky.
For instance, when people claim they perceive the horizon moon
as 10 times larger, at the same time they also claim the horizon moon
seems to occupy almost half of the sky.
I think that the negligence is due to the fact that they did
not have a proper concept to account for this second aspect of the Moon
illusion.
The researchers have had enough troubles already to deal with
the larger-looking horizon moon; the second phenomenon would confound
the explaining efforts even more. Fortunately, the concepts of the
converging point and the visual field volume can help explain this
phenomenon.
Take a look at the diagram below, which we have seen many times
before. If we move the converging point from the Focus1 to the Focus2
position, the sub-visual field is getting narrower around the far
object.
This illustrates why the sky appears to be smaller when we
focus on the horizon. The two aspects of the Moon illusion are
essentially represented in this single diagram.