Forward motion of JFK's head between Z-frames 312 and 313 has been
widely accepted. Though frame 312 if very clear, 313 is quite blurred.
I believe that there is very little, if any, actual head motion and that
perceived motion is actually the result of a failure to account for the
effects of the blurring in 313.
Motion blurring is produced by a combination of camera movement and
movement of the objects being photographed. I think it is easier to
follow what is happening in blurs if the camera is assumed to be still
and the image is thought to move across the film. All stationary
objects move at the same rate across the film while moving objects move
on the film at different rates. All the objects being measure here are
in the car, which is moving at a constant rate. The motions of the car
and camera combine to produce an apparent movement of the car across the
film and only this apparent motion need be considered. The value at a
particular spot on the film is actually a combination of all parts of
the image that move across it during the exposure.
A few months ago, I posted a model to explain some of the strange
things observed in frames 402-418. The lamppost is partly invisible
though it has sharp boundaries, a man seems to disappear behind an
invisible post, and a strange green triangle of grass extends into the
street in frame 405. The model assumes that when a bright area is
blurred across a dimmer one (or vice-versa, it really doesn't matter
which comes first), very little gradient is produced at the boundary.
Instead, the bright area obliterates (I used the term dominates in the
original post) the dimmer one and a sharp boundary is produced. What
seems to happen is that a spot on the film which is exposed partly to
the bright region and partly to the dimmer one comes out looking like
the bright region even if the fraction of exposure to the bright region
is very small. I propose no underlying basis for this phenomenon but it
does seem to fit the observations very well. This same phenomenon
occurs in 313. By comparing the widths of the buttons, or lights (or
whatever they are) on the roll bar in 313 to 312, one can see that they
are much wider in 313 due to motion blurring. However, the boundary
between the back of JFK's head and the top of the curb is quite sharp in
313. Likewise, the edge at the top of the back seat is fairly sharp.
How does one account for sharp edges in such a blurred frame? In the
case of the head against the curb, I would explain it this way. The
curb is very bright compared to the head, so all parts of the film hit
by both the curb and the head come out as curb. Similarly, the seat
back is more directly illuminated and thus brighter than the seat top,
so when back is blurred across top, the entire blur appears as top.
The blurring in 313 appears to be nearly horizontal, but which way
is it blurred, right to left or left to right? Since the car is farther
to the left in 313 than 312, I conclude that the blurring is right to
left, i.e., the image of the car is moving to the left across the film.
This means that, if an object producing a blur is brighter than the
background, the right edge of a blur is where the image was when the
shutter opened and the left edge of the blur is where the left edge was
when the shutter closed. Consider the lights on the roll bar. They are
brighter than the grass behind them, so they obliterate the grass when
they are blurred across it. This means that the entire blur comes out
as roll bar light. So the right edge of the blur is where the right
side of the light was when the shutter opened and the left edge of the
blur is where the left side of the light was when the shutter closed.
Now consider the head against the curb. Unlike the lights, the head
could be moving relative to the car. If the head moves to the right
(forward) faster than the car is moving to the left, then the image of
the head would be moving to the right across the film. Otherwise, it is
moving to the left. This means there are two possible interpretations.
If the head is moving left to right on the film, then the boundary
between curb and head represents its position when the shutter closed.
Otherwise, it represents its position when the shutter opened.
Now to actually measure head movement. The key is to measure the
head against a reference point on the car such that both measurements
either represent positions when the shutter opened or when it closed.
Otherwise, the measurement will include camera motion during the
exposure interval as well as head movement! The problem is, we don't
know which end of the exposure interval the position of the head
represents. So we must try it both ways and see if one makes more sense
than the other. I believe that the results obtained from assuming the
head represents a "shutter open" position makes more sense.
In the following table, all results are in a coordinate system in
which the frames are 6 units horizontal and 4 units vertical. The
values represent the differences in lengths between 312 and 313. All
values represent movement to the right.
Seat to JFKhead 0.11 Seat - boundary
of top edge of back seat and curb
RBR to JFKhead 0.02 JFKhead - boundary of
back of JFK's head and curb
RBL to JFKhead 0.11 RBR - right edge
of farthest roll bar light
JBChead 0.10 RBL - left
edge of farthest roll bar light
RBR to seat 0.11 JChead - width of
bright part of Connally's forehead at hairline
RBL to seat 0.00
First, note the measurements between the roll bars light and the seat.
The boundary between the back and top of the seat is moving left across
the top so the bright back should obliterate the top and the resulting
edge represents a shutter close position. The distance to the left edge
of the light , another shutter close position, remains constant. The
"movement" between the right edge of the light and the seat is actually
the camera movement during the exposure interval. Note also that this
is almost the same distance that Connally's forehead expands, which
should be another measure of camera movement. Now observe that
measuring the head against the right edge of the roll bar light, which
is a shutter open position, shows very little movement. Measuring
against the left edge of the light, a shutter close position, shows much
more and that the distance corresponds exactly to the camera motion
measured above. Converting these values to actual distances requires
the field of view of the frames and the distance to the car. If the
distance is assumed to be 60 ft. (a guess) and the FOV is taken to be 10
degrees (I have measured this but not terribly well. I do think it is
ballpark) then 0.11 represents a movement of about 2.3 inches. Not
quite the 3.8 inches that has been claimed, but in the neighborhood.
0.02 represents about 0.4 inches. The FOV and distance together produce
a linear scale factor. If the values are scaled so that the larger one
is 3.8, then the smaller one would be 0.7 inches.
The bottom line is that these measurements are consistent with two
different scenarios. If the head position is taken to be a shutter open
position, then the head moved forward about 0.4 (or 0.7) inches, hardly
a significant amount. In this case, the right light edge to head
difference is just the camera motion and is consistent with the other
measures of camera motion. If head position is taken to be a shutter
close position, the head suddenly moves forward about 2.5 (or 3.8)
inches. In this case, the right light edge to head difference is
actually the head motion and coincidentally is exactly the same as the
camera motion. (This would mean that the forward head motion exactly
matches the movement of the camera so that the head remains on the same
spot on the film. I think the first scenario, being simpler and
requiring no coincidence is the more reasonable assumption unless there
is other evidence to support a forward head motion.