Most of the conspiracists' case against Apollo is based on alleged
anomalies in Apollo lunar surface photos. The most commonly alleged
anomaly is that the shadows supposedly cast by the parallel rays from
the sun appear to point in different directions in photos taken on the
lunar surface. Now there are a lot of reasons why that happens, but
we concern ourselves here with the concept of perspective.
Simply put, perspective is why things look smaller the farther
they are away from the viewer. It is why railroad tracks converge at
the horizon. It is why the dotted line on the highway blurs into the
illusion of a solid line in the distance.
All this happens because our field of view -- what we see in a given
direction -- is a cone with its apex at our eye and extending away
from us. The human field of vision is not a precise cone because
facial features like the nose and brows intrude upon it. A camera
also has a field of view, but it is pyramidal because the product is a
square or rectangular photograph.
Fig. 1 - The field of view of the Apollo lunar surface
camera equipped with the Zeiss Biogon lens, as seen from
The Apollo astronauts used modified Hasselblad 500/EL cameras fitted
with the Zeiss Biogon lens and shooting 70 millimeter film. This
particular arrangement produces a field of
view with an angular width of 53.5°.
Fig. 1 shows what that field of view would look like if made
visible and seen from above. At the very bottom of the figure is the
camera lens. The dashed vertical line is the optical axis, a line of
sight parallel to the axis of the lens. But the field of view
contains many other lines of sight -- an infinite number of them, in
fact -- and they are not parallel. There is a difference of
approximately 27° (half the field of view) between the line of
sight at the optical axis and the line of sight at the edge of the
field of view. The optical axis corresponds to the point at the exact
center of the photograph. In Apollo photographs this corresponds to
the central fiducial. A point on the
boundary of the field of view would be at the edge of the photo.
The dotted lines in Fig. 1 between the boundaries and the optical
axis represent other possible lines of sight that would also
correspond to certain points on the photograph. They are included to
emphasize that lines of sight radiate outward from the focal point,
and the resulting photograph will contain all those lines of sight.
Fact: The direction of line of sight varies across any
photograph, both horizontally and vertically.
SUNLIGHT AND THE FIELD
Light radiates in all directions from any source of light. The
sun is no exception. The sun is so far away from the earth and moon
that by the time the light reaches us, it's essentially parallel. If
you were standing on the surface of the earth or moon, everything you
could see lit by the sun would be illuminated from the same direction.
Fig. 2 -
The Apollo camera field of view compared to parallel lines
representing the parallel light rays from the sun. Left: The
optical axis is aligned with the direction of light rays --
up-sun or down-sun. Middle: The optical axis is
perpendicular to the light rays. Right: The left boundary of
the field of view is parallel to the light rays.
But not all objects will be seen from the same direction. In the
previous section we established that the line of sight varies across
the field of view. In Fig. 2 the Apollo lunar surface camera field of
view is superimposed on a set of parallel lines representing the
parallel light rays from the sun, as seen from above. Pay special
attention to how those lines of sight intersect with light rays at
various points. Note how in each scenario, different lines of sight
intersect with the parallel rays at different angles.
The angle formed by the line of sight and the direction of
illumination is called the "phase angle", and "phase" here obviously
relates to the familiar concept of the phase of the moon. The phase
angle determines many things about what a particular object looks
like: whether there's a glare from it, how bright it appears, how much of
it is lit, etc. Each line of sight in Fig. 2 corresponds to a certain
phase angle, since that line of sight will form the same angle with
any ray in a set of parallel light rays.
Fig. 2 (right) presents an interesting special case. The left
boundary is parallel to the light, producing a phase angle of 0°.
But at the right boundary there is a phase angle of 53.5°. This
is a significant difference.
Fact: The phase angle is different at each point in any
photograph; it varies horizontally and vertically.
Prior to the 15th century, artists had difficulty accurately
representing the appearance of objects and their relationship to their
They knew that the lines which receded from the viewer needed to be
depicted at an angle, but they were not sure what that angle should
be. Most of the time they just guessed, and most of the time they got
Fig. 3 -An illustration from an early manuscript
showing a typical difficulty in accurately reproducing the apparent
shape of foreshortened objects. (Detail from the Kaufmann
Haggadah, ca. 14th C., in Sharon Keller, The Jews: A Treasury of
Art and Literature, NY: Levin Associates, 1992.)
In Fig. 3 the side wall of the illustrated tower recedes from the
viewer. The base is drawn at one angle while the balcony and rail of
the tower are drawn an an incompatible angle. The eye rejects this as
an accurate rendition of the tower.
Medieval artists (Brunelleschi is generally credited) eventually
discovered the solution. If they extended the parallel lines that
receded directly away from the viewer, they discovered they would meet
at the horizon at a single point in the horizontal center of the field
of view where the distinction between them would vanish. Hence the
term "vanishing point" where parallel lines in a field of view will
appear to meet. Thereafter they could "construct" a scene by drawing
a temporary horizon and a vanishing point and lay out features
following those lines.
Raphael's "School of Athens" in the Vatican is an excellent
example of the simplest version of this so-called linear perspective.
Raphael (who, incidentally painted himself as the kneeling scholar in
the central foreground) correctly renders the apparent angle of the
features of the walls receding directly from the viewer.
Fig. 4 - Raphael's "School of Athens". The yellow
line is the theoretical horizon. The red lines are the
extensions of the directly receding lines which meet at the
(Annotations by Clavius.)
These principles apply to photography too. Fig. 5 shows a photograph
intentionally taken to employ linear (single-point) perspective.
Fig. 5 - Architect Raymond Krappe's Pregerson House
photographed by Julius Shulman in linear (single-point)
perspective. (L.A. Obscura, annotations by Clavius.)
The artistic approach is not just a trick. A geometrical and
mathematical transformation relates the conceptual drawings in Fig. 2
with the photograph in Fig. 5. The lines receding from the viewer in
Fig. 5 (red annotations) are similar to the parallel lines in Fig. 2
(left). The transverse lines in Fig. 5 -- the front edge of the
porch, steps, and roofline -- are analogous to the parallel lines in
Fig. 2 (center). Lines exactly perpendicular to the optical axis will
not appear to have a vanishing point.
But what about Fig. 2 (right)? What if the lines in question
aren't aligned with the optical axis or transverse? This was the next
step in realistic rendering -- two-point perspective. This is the
most common method used by artists today. If you don't look at an
object head-on but instead at an angle, each set of parallel lines
will have a separate vanishing point.
Fig. 6 - Coulter's department store in Los Angeles.
Each set of parallel lines has a different vanishing point.
(Julius Shulman, L.A. Obscura. Annotations by Clavius.)
Fig. 7 -The vanishing point for the staircase is not
on the horizon. Many other sets of parallel lines are apparent,
each with its own vanishing point.
(© Cornerstone Architectural Photography. Used by permission.)
That's what we see in Fig. 6. The photographer is looking at the
corner of the building and both the front wall of the building (red
lines) and the side wall (pink lines) recede toward the horizon.
Neither vanishing point is at the center of the field of view. And in
this case neither vanishing point is within the field of view. This
is perfectly allowable and does not violate the theoretical
conceptualization. Except for perfectly transverse lines, all sets of
parallel lines will have a vanishing point.
Examples of perspective can be arbitrarily complex (Fig. 7)
because some scenes will have many sets of parallel lines going off in
different directions, not always meeting at a vanishing point on the
horizon. Those that meet at the horizon, in one- and two-point
perspective, are not only parallel to each other, but also to the
ground. This includes horizontal rows of windows (Fig. 6), structural
beams, and floor panels and tiles (Figs. 4 and 5).
Fact: Any group of parallel lines which is not exactly
perpendicular to the optical axis of a photograph will appear
to converge to some vanishing point. In many cases that
vanishing point will not lie on the horizon.
SHADOWS AS PARALLEL
The oft-quoted premise of the conspiracists is:
Parallel light rays must
cast parallel shadows.
If the ground is perfectly flat and level, that's absolutely true.
On earth we have parking lots and other reasonably flat and level
surfaces on which we can observe shadows. However, the moon has no
such natural features. The ground is rarely flat and level. But
that's the topic of another discussion. We want to test the
conspiracists' claim under the assumption of a flat and level surface
in order to isolate and characterize the effects of perspective.