What follows below is the text only of a manuscript that I started to
prepare in the mid 1970s and which includes figures and illustrations
and is laid out more clearly than what you see here but this is
provided to give you a glimpse into what may someday come about as a
complete publication. So, I hope you live with the shortcomings of
this material and appreciate it for what it is ... or was, in 1978! I
found the typewritten text as prepared by my secretary and recently
(in 2003) OCRd it and that is how this version came to be today. It is
given here with erros included so you will have to use a bit of
ingenuity to figure out what some formulas mean. However, helpful
suggestions are always welcome! Send to me at andpph@rit.edu
- Andrew Davidhazy
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Streak, Strip and Scanning Photographic Systems - an overview of
historical and current technologies
Andrew Davidhazy Imaging and Photographic Technology School of
Photographic Arts and Sciences Rochester Institute of Technology
Although this manuscript concerns itself primarily with streak, slit,
or smear or scanning recording, it is appropriate that the fundamental
characteristics of a focal plane shutter be quickly reviewed in order
to better understand a system that is basically patterned after focal
plane shutter design and operation.
FOCAL PLANE SHUTTERS
Exposure
As is generally known, a focal plane shutter consists of a variable
aperture slit passing in front of a stationary film. The assumption
that photographs taken with this kind of a shutter are ÒinstantaneousÓ
is only accurate to the extent that in the time frame of most common
events, the real and measurable transit time of the slit from one side
of the film gate to the other is insignificant. However, as events
become short lived or if they assume a different shape in a short time
or if the image of the event moves from one point on the film plane to
another during the transit of the slit across the film gate then the
focal plane shutter delivers a distorted reflection of reality.
This happens because it does not uncover or cover the whole film at
the same time, or instantaneously, but it does so rather in a
sequential manner.
(Figure 1)
Referring to Figure 1, the bold rectangle represents the film gate and
C1 and C2 the leading and trailing curtains that make up the edges of
the slit which travels across the film in a specific time primarily
determined by such variables as spring tension, curtain inertia, etc.
At T=2 the first curtain C1 has already exposed a short section of the
film while curtain C2 is waiting for the specific length of time set
on the shutter speed dial before it is released. At T=3 curtain C2
just starts to cover up those areas on the film which were first
uncovered by the first curtain. At T=4 both curtains are moving across
the middle portions of the frame while at T=5 the first curtain has
reached the right edge of the gate and it remains for curtain C2 to
complete the exposure by covering up the rest of the frame.
For a constant curtain velocity the exposure time is basically
determined by the slit width. It is the length of time it takes the
slit to move a distance equal to its width, or the time interval
between the uncovering and covering of a given point on the film.
Efficiency
However, the effective exposure time of two shutters that have the
same total exposure time may differ considerably. This difference is
caused by variations in shutter efficiency. The efficiency of focal
plane shutters depends on the numerical aperture of the lens in use,
the width of the slit and the distance from the slit to the film
plane.
As shown in Figure 2, these factors are related as follows:
A E = ------------- (d) A + ----- N
Where E = efficiency A = slit width D = slit distance from film N = f
number of lens in use
When the slit width is just the same as the diameter of the cone of
light from the lens reaching a point on the film, then the efficiency
of the shutter is 5O%. Decreasing the size of the aperture or
increasing the size of the shutter slit achieves higher efficiencies.
The slit width can be made larger for a given exposure time by
increasing the speed of the curtains. Thus, fast curtain speeds
contribute to increased efficiency of focal plane shutters, as long as
the distance between the film and the moving slit remains the same.
The nearer the curtains are to the surface of the film the greater the
efficiency.
Finally, while for a pupil, diaphragm or leaf shutter total time is
constant and effective time changes with aperture, just the opposite
is the case for the focal plane shutter.
Distortion
Consider, as shown in Figure 3A, a focal plane shutter in which the
slit (assumed here to very narrow) is moving from left to right at an
even speed so that it is located at equidistant positions T1, T2, T3,
and that the elapsed time between each position is the same. Then, the
image of a horizontal bar moving upwards, also at a constant speed,
will be recorded by the moving slit at positions L1, L2 and L3. Since
the curtain is continuously moving across the film plane it
successively records the image of the horizontal bar so that the final
image appears as shown in Figure 3B.
If the bar had been moving at a constant speed but the slit of the
focal plane shutter had accelerated, then the image would appear as in
Figure 3C and if it had decelerated then the image of the bar which
was straight as it moved up on the film plane would appear curved as
shown in Figure 3D.
Conversely, if the shutter maintained an even velocity across the film
plane but the bar accelerated as it went up the frame, the resulting
photograph would appear as in Figure 3D and if it had slowed down as
it went up it would look like Figure 3C.
(Figure 3) From knowledge of the vertical speed of the image across
the film plane an estimate of the cameraÕs shutter speed is possible.
This is similar to using a television receiver as a shutter tester.
Conversely, the speed of the barÕs image across the film plane can be
determined if one knows the shutter curtain speed. Multiplying this
speed by the cameraÕs reduction factor gives the speed of the real bar
in front of the camera. Without knowledge of the shutter slit speed
this determination is impossible and even a guess as to the true shape
of the bar as it crossed the field of view of the camera would be hard
to make.
Further, consider the situation of a square object imaged at the film
plane of a camera equipped with a focal plane shutter. When the square
is at rest, the moving slit records the square with a height to length
ratio of 1:1. Then, if as in Figure 4A the speed of the slit and the
image are the same then either one long stretched out image with the
correct height results on the film if the square was imaged on the
slit as it moved across the frame or no exposure at all results if a
portion of the square happened not to coincide with the position of
the open slit at any one time. When as in Figure 4B the image of the
square moves in the same direction as the slit but at one-half its
speed, then by the time the slit reaches the point where the right
edge of the square was at the time the slit first uncovered the left
edge, the right edge will have moved a distance equal to one-half its
length to the right. As the square continues to move to the right so
does the slit and it finally catches up to the right edge of the
square after it has moved over a distance equal to its original
length, and therefore the image recorded on the film does not present
the original 1:1 height to length ratio but a 1:2 ratio.
It is interesting to note that when the direction of travel of the
image of an object with a height to length ratio of 1:2, as in Figure
4C is moving in a direction opposite but equal to the speed of the
focal plane shutter then the object is compressed exactly by a factor
of 1/2 so that now it appears to be as high as it is long. The
alteration of the proper height to length ratio of an image by virtue
of the motion of the image with respect to the moving slit can be
determined from the following relationship:
slit velocity ML =
------------------------------------------------------ absolute speed
difference between image and slit
where ML is the amount the proper length of an image is magnified.
In this case it is assumed that the size of the slit is of negligible
dimension.
Using the example of Figure 4D, the velocity of the slit is 1, the
velocity of the image in the opposite direction is .5. Then, ML is
1/1.5, which makes ML equal to 2/3. This means that the proper image
length is multiplied by 2/3 to arrive at the length of the distorted
image (in this case the result is a compressed image).
Another situation is illustrated in Figure 3f where the motion of the
image is at right angles to that of the moving slit. This results in
the leading and trailing edges of the moving subject to appear slanted
instead of being reproduced their proper relationship to the subjectÕs
other two sides.
Going further, if the subject is stationary but spins in place it will
sequentially show a different aspect or edge view to the moving slit
and may reproduce as a Òbow tieÓ as shown in Figure 3g.
The examples mentioned above assume that the curtains in a focal plane
shutter travel at constant speeds as indicated by the equidistant
positions of the slit in these diagrams. Unfortunately, this is not so
and further distortion of a more complex nature is introduced into the
final results by the acceleration of the slit as it moves across the
film gate.
In summary, keeping in mind that moving objects are distorted due to
the fact that focal plane shutters expose the film sequentially, it
would be most questionable and almost impossible to make accurate real
shape determinations of moving objects using cameras equipped with
this type of a shutter.
The only reason that they are widely used in cameras is that they have
many advantages that outweigh the possibility that images made with
them might exhibit distortion. The reason that this distortion
associated with focal plane shutters is generally not a problem is
that the curtains in modern shutters move across the focal plane at a
rate at least an order of magnitude greater than the rate at which
most images move.
To see pictorial examples of what can happen when focal plane shutters
move too slowly see the section on slit-scan photography discussed
later in this book.
STREAK and STRIP PHOTOGRAPHY
Introduction
Streak, slit, smear or scanning recording cameras have two general
features in common with focal plane shutter cameras. One is a slit
shutter, the width of which can be varied to set a desired effective
exposure time and the other is that recording takes place sequentially
over a finite amount of time. The difference is that with streak/strip
photography the slit shutter remains stationary and open all the time
and sequential exposure is achieved by moving the film behind it at
some desired speed.
Streak and strip recording cameras can generally be divided into two
groups. The first of these, streak cameras, includes making of records
of subjects that, without moving, change some characteristic that one
wishes to track, and those that move in a direction parallel to the
slit built into the camera. The second group, strip cameras, deals
with the photography of subjects that move in a direction
perpendicular to the slit and parallel to the direction that the film
moves.
Streak Cameras
These include those cameras that have made streak recording a most
useful tool in ballistics and explosives research. These are the high
speed film streak cameras and the rotating drum and rotating mirror
streak cameras. They are intended primarily to provide a record of
subject image displacement along the slit vs. time. The film records
provided by these cameras are valuable when subject velocity or change
in velocity needs to be determined.
These cameras can also be used to study the duration of one or more
events such as the total time a leaf shutter is open compared to the
fully open time or to determine the frequency of repetitive phenomena,
such as the rate at which a fan turns or the stitching rate of a
sewing machine. They are also useful for determining whether events
are simultaneous or not or the temporal discrepancy of events presumed
to be simultaneous.
Scanning Strip Cameras
The second group of cameras, generally probably best referred to as
ÒstripÓ cameras because invariably the images they produce are on
short strips of film, deliver real looking photographs of subjects by
scanning their images over time. They record subjects that travel in a
direction perpendicular to the cameraÕs slit shutter and parallel to
the film motion direction and in the opposite direction as the film is
moving behind the slit. Because of the optical system in the camera
subject motion is reversed and the image of the subject thus moves in
the same direction as the film. These are by far the most numerous and
ÒcommonÓ of the lit equipped, moving film, cameras available. They
take the form of high speed synchroballistic cameras, aerial
photomapping cameras, racetrack photo-finish cameras, wide angle,
panoramic, scanning cameras, peripheral cameras, and others.
Strip cameras attempt to present a stationary image with respect to
the moving film, as would be the case if a focal plane shutter were to
photograph a motionless subject. This is accomplished by moving the
object in front of the camera in such a direction and speed that when
its motion is reversed and reduced by the reduction factor of the lens
in use, the image travels across the slit at approximately the same
speed and direction as the film is moving behind it.
Velocity Recording and Time Resolving Streak Cameras
Moving Film Streak Cameras
High speed streak film cameras sometimes are modified high speed
rotating prism motion picture cameras. They are very simple and
consist of a film supply spool, a lens, a slit, a film take up spool
and some method of rapidly moving the film from one spool to the
other. See Figure 5. As mentioned earlier, these cameras are usually
intended for the study of events that move in a direction parallel to
(and their image on top of) the slit in the camera. If the motion of
the film is horizontal then the slit generally aligned at right angles
to it and thus is vertical. Therefore, its aperture usually restricts
the horizontal angle of view of the camera to a couple of degrees or
less and the camera responds only to subject position changes that
occur along and upon the open slit. Anything else is not recorded and
thus it can be said that streak cameras are one-dimensional cameras
rather than two-dimensional ones as are normal instantaneous
snapshots. That is, the latter have height and length. Streak
photographs only have height or dimension along the slit aperture.
Most importantly, however, photographs made with streak incorporate
time as the second dimension.
In order to further explain the method whereby a streak camera makes a
direct record of subject velocity consider the following: As shown in
Figure 6 three vertical lines, A, B and C on a film are moving from
right to left behind the slit, 5, or a streak camera. At the same time
a horizontal barÕs image, I, is moving up along the slit. The width of
the slit restricts the films s view of the bar to a small horizontal
section. As each portion or line on the film moves into position
behind the slit, the upward moving image appears at a different
height. Since the event is continuous, and, if the object and the film
had a constant velocity then the resulting photograph of the event
would show a straight line crossing the film from the lower edge to
the upper.
The vertical displacement per horizontal distance unit on the film is
directly related to image speed along the slit and film speed past the
slit. In most high speed streak cameras an attempt is made to keep the
speed of the film constant over a known period of time. Then
variations in velocity of the image will appear to either bend the
line up if the subject accelerates or curve it in a direction parallel
to the direction of film travel if it slows down. The magnification or
reduction of the camera lens has to be taken into account to make
accurate velocity and acceleration measurements.
In Figure 7, for example, on illustration of a streak record of a
projectile in flight, its image moved from bottom to top of a strip of
film. It is known that the camera had a reduction factor of 100:1.
Then, a distance, which is one foot in reality, will appear to be
1/100Õ on the film or .12Ó along the slit. This can be marked-off
directly along the vertical axis. If the film moves within the camera
so that 1/10Ó of film passes by the slit in 1/100 of a second, then
the horizontal axis can be marked off in 1/10 inch increments, each
corresponding to 1/100 sec. It is now possible to calculate the
velocity of an object that moves along the slit at an unknown rate by
direct measurements made from the film or from enlargements made at
known magnifications.
Of course, if the film is marked up before enlargement then the system
from there onwards becomes magnification independent.
From the data in Figure 7 the projectile appears to have moved at a
constant speed along the slit since the line recorded by the camera
has a constant slope. Its speed can be determined from the following
formula:
change in D
V = ----------------
change in T
Where V is velocity, D is real distance covered by the projectile and
T is the time required to move the above distance. In this example the
projectileÕs image moves from one edge of the film to the other or a
total of 84 inches. Allowing for a camera reduction factor of 100:1
the real distance recorded is 7 feet.
Further, The projectileÕs image travels from one edge of the film to
the other in 7/100 second. Therefore, since V = change in distance /
change in time = 7 / 7/100 which is 100 feet per second. Any straight
line that has a steeper slope than this one will indicate that the
subject is traveling faster and lesser slopes indicate the object is
traveling slower than this figure. This is, of course, assuming that
the rate of movement of the film behind the slit remains constant.
Obviously, quantitative results or measurements require that one know
or be able to determine accurately the rate at which the film is
moving past the slit or the rate at which the image of the slit is
wiped onto stationary film in rotating mirror cameras discussed later.
There are various methods of determining the rate of movement of the
film but one of the most common is the inclusion within the camera of
a neon or LED timing light driven either by the frequency of the AC
line or by a separate timing light pulse generator. Since the interval
between flashes of the timing lights is accurately known, then, if the
distance between marks is constant as the film moves past the open
slit the film it must also be moving at a constant speed. The actual
speed is easily determined from knowledge of the frequency of the
pulses and the distance between them. There are many other schemes for
feeding and placing timing information on the film. These range from
simple mechanical means to sophisticated electronic ones.
For all types of streak cameras the rate at which the film can be
moved behind the slit, or the image of the slit can be wiped onto
stationary film, is usually specified as the cameraÕs minimum and
maximum Òwriting speedÓ given in feet/second or meters/second. The
ability of a given camera to depict small changes in time is also a
function of how narrow the slit can be made. The narrower, the higher
the time resolution capability of the camera. Diffraction imposes a
limit on the degree to which a slit can be narroWed. However,
generally, the faster the film or image of the slit can be made to
move the better the time resolution that can be expected from the
camera or the higher the speed of any given event can be and still be
able to accurately determine its rate of change.
In case that a cameraÕs writing speed is not sufficiently fast for a
particular application, it may still be possible to use the camera if
the distance between the camera and the subject can be increased
without altering the behavior of the subject. For example, the speed
of a projectile can be measured over a distance of one foot or over a
distance of 10 feet, but to achieve the same horizontal displacement,
the camera photographing the projectile at one foot needs a 10-fold
increase in film speed over the camera that does the photography at 10
feet. NEW: In other words, for a given subject velocity, decreases in
camera magnification cause the slope of the moving image across the
film to become less.
A NEW FIGURE GOES HERE
Moving film type streak cameras have to accelerate in order to reach a
certain film speed past the slit and generally, speed or time between
equidistant points on the film changes with time. Although such
changes in film velocity will be indicated by changes in the spacing
of timing markers on the film, this is mentioned here simply so that
it is not forgotten that this possibility must be taken into account
when measurements are made from the developed film.
Rotating Drum Cameras
When higher rates of film movement past the slit are required than can
be achieved by simply pulling the film from one spool to another in
order to achieve greater Òtime resolutionÓ to measure events which
move at greater rates of speed, then cameras with different
configurations are used.
Some of the most common of these are the rotating drum streak cameras.
These are illustrated in Figure 8 and Figure 9. The drum type camera
typically holds a length of film wrapped around the inside or the
outside of a drum that can be rotated at high speeds. Since the
diameter of the drum and its rate of rotation can be accurately set
and measured it is a fairly simple matter to determine the rate at
which the film is moving past the slit of this particular type of
streak camera.
From here on the method of determining subject velocity is the same as
that described earlier for moving film type cameras. The major
limitation of drum type streak cameras is that the camera can only
record events that generally last less time than it takes for the drum
to go around once. That is, of course, unless it is possible to allow
double exposure or ÒrewriteÓ. For example, photography of projectiles
in flight can usually take place over more than one revolution due to
the fact that probably the image takes up only a small portion of film
along the length of the slit. Or, possibly because the moving edge of
the objectÕs image can usually still be interpreted properly in spite
of double exposure. However, drum cameras usually are equipped with a
secondary, ÒcappingÓ shutter, to prevent rewrite. However, inclusion
of such a capping shutter causes these cameras to lose a major
advantage in relationship to synchronization.
This advantage is that when they are employed to photograph
self-luminous events they are inherently Òalways alertÓ and ready to
record the event at any random time as long as light can be excluded
from the scene. This capability to respond instantly and without
complex synchronization schemes or devices is unlike moving film type
cameras or rotating mirror streak cameras that are discussed later.
With these either the event has to be made dependent on camera
operation or the camera made dependent on event occurrence.
A second advantage of drum type streak cameras is the very high lens
aperture systems available. A major limitation is their relatively
slow writing speed capability compared to rotating mirror types. This
is primarily due to mechanical stresses built up in the drums and
bearings.
Rotating Mirror Cameras
These are the highest speed film type streak cameras and their
configuration is illustrated in Figure 9. In these cameras the film is
held stationary in an arc at the center of which is located a mirror
sometimes made of high strength steel or even beryllium. This mirror
can be rotated at speeds in excess of 50,000 RPM. The mirror reflects
an image of the slit aperture located in front of a relay lens onto
the stationary film. The camera, because of the constraint of having
to operate with a relay lens system has a very low effective aperture.
Under most circumstances this type of camera is used with
self-luminous phenomena. A capping shutter is invariably built into
the camera and synchronized to the rotating mirror in such a manner
that usually only one image sweep is allowed to reach the film plane.
This allows photography of opaque, reflective subjects moving across a
highly illuminated field such as by transmitted light as in a
Schlieren system.
In order to increase the time resolving power or writing speed of
these cameras, it might seem logical to extend the optical arm of the
camera. However, this soon becomes an exercise in compromises. As the
optical arm of a mirror type streak camera is increased the image gets
dimmer. One reason for this is that for a given diameter objective
lens the longer the distance between the lens and the film the smaller
the effective aperture. Since, as the aperture is becoming smaller the
image is moving faster, the combination of factors calls for dramatic
increases in the illumination level of the subject and this eventually
limits the design parameters to a set of compromise specifications.
Another approach is to make the slit width narrower but this too
results in loss of light, which is generally in short supply already.
While drum type cameras are always alert, rotating mirror cameras have
to be synchronized with the event to be photographed and elaborate
electronic devices are built into the camera to sense the rotational
speed as well as the instantaneous position of the mirror so that the
time delay between event initiation and beginning of event image sweep
over the 900 or so available for recording to occur at the appropriate
instant.
WHAT IS THE END OF THE ABOVE PARAGRAPH ABOUT????
A number of refinements to the basic rotating mirror camera have been
developed. These improvements include longer recording times made
possible by imaging onto stationary film held around the inside
circumference of a drum. The principle of operation and analysis,
however, is the same as that used for linearly moving film or drum
type streak cameras.
Timing Applications of Streak Cameras
When high speed streak cameras are not employed to photograph the
linear velocity of objects then one of their most common applications
is the determination of the temporal duration of an event that does
not suffer from being reduced to a single dimension. Of course, this
type of information is automatically recorded along with velocity
information and it is only mentioned here to clearly specify that
these cameras are used for event duration as well as event velocity
investigations.
A common application of streak cameras in these combined roles is in
the photography of spark gaps or exploding wires, Figure 10A, or
something as familiar as the operation of leaf shutters, Figure 10B,
or focal plane shutters, Figure 10C.
Streak cameras can also be used to photograph rotating objects to
determine rotation rates, Figure 10D, or other cyclic events such as
the up and down motion of sewing machine parts to determine the
frequency, the speed and the direction of motion of the various
components.
Streak cameras are not suitable for the photography of events that are
erratic in their position or direction of motion. This might be an
event such as the measurement of the speed of collapse of a bursting
balloon.
Summary
The inherent advantage of a drum type streak camera is the fact that
large aperture optical systems are readily available and that for
self-luminous events the camera is always alert and ready to record
the event. The advantage of spinning mirror streak cameras is that
high writing speeds are easily attainable. Both cameras suffer from
the short length of time during which recording can take place and
thus the advantage of a moving film type camera is the relatively long
time over which the camera is accessible to new information and the
fact that capping shutters are not needed since the film only goes
past the slit once.
STRIP CAMERAS
The second major group of streak cameras is by far the more numerous
and we will deal with each application separately. They can, however,
be grouped into five distinct categories: cameras which determine the
speed of a moving object e.g. synchroballistic cameras; cameras which
measure the arrival time of objects at a particular point and cameras
which are stationary while recording a moving subject e.g. photofinish
cameras and microfilm copying cameras; cameras which take photographs
of motionless subjects but which introduce subject motion by moving
the cameras, e.g. aerial mapping cameras; cameras which take wide
angle or panoramic photographs and, finally, cameras intended for
peripheral photography. Enlargers that are used to print streak
photographs are designed after a combination of features found in most
of the above five camera groups.
As explained in earlier detailed descriptions of the operation of a
streak camera, the direction perpendicular to the orientation of the
slit is the time axis and the axis parallel to the slit is the
distance axis. Velocity recording streak cameras are used to make
measurements of subject image velocity along the slit based on
measurements of displacements along both these axis.
Synchroballistic Cameras
There is a way to measure subject velocity and to gain an
understanding of its behavior as well by a method used primarily in
ballistics research known as synchroballistic photography.
In this application the objectÕs image crosses the slit shutter
perpendicular to it and in such a way that its direction and speed
approximate the speed of the film past the slit. The situation is
analogous to a focal plane shutter making an exposure of a stationary
object or one which is moving in the same (or opposite) direction as
the moving slit.
Consider a situation as in Figure 11 in which the image of an object
with a height to length ratio of 1:1, a square, moves at a constant
speed across the slit of a streak camera. Further, assume that the
speed of the film past the slit is also constant and exactly matches
the speed of the image. Then, a specific point of the image will
remain fixed on a particular point on the film as the two pass by the
slit. As far as the film was concerned, the image was stationary
during exposure and this condition renders a photograph that shows the
subject having a known height to length ratio with exactly the same
ratio on the film. Therefore if a photograph is made of an object the
height and length of which are known but the speed of which is in
question and a streak photograph taken under the above conditions
shows the image to have the originalÕs height to length ratio, then
the conclusion is that the image of the subject and the film were
traveling at the same speed Then, by simply accounting for the
reduction factor of the lens system in use the true speed of the
object as its image crossed across the slit can be made as follows.
Image Speed x Camera Reduction Factor = Subject Speed
For example, if the film is known to travel at 100 feet/second and
that the lens has a reduction factor of 40 and a square subject
appears square on the film, by simply multiplying 10 feet/second times
40, the speed of the object is determined to be 400 feet/second. With
this method, the measurement of subject speed can be reliably
determined and at the same time a ÒrealÓ looking image of the subject
is recorded. Obviously, when making a record in this manner the
assumption is made that the shape of the object has not changed while
it is in front of the camera compared to its shape at rest.
Determinations of rotation of the subject while under way can be made
by marking it with something as simple as a horizontal line and
carefully noting its shape on the streak photograph. A curved record
of a straight original line indicates that the subject was rotating in
flight. Rotation rate can be estimated by noting the number of degrees
displacement per unit of time.
The method even works fairly well if the subject has some motion
component other than one strictly perpendicular to the slit, but then
the horizontal shape of the subject will appear to be distorted.
Even when the resulting photograph does not match exactly the
height-to-length ratio of the original object, a good determination of
its speed can still be made by correcting the known film speed by a
factor arrived at as follows:
SL Ô~ x Film Speed = Image Speed (correct this so it is right)
The subject length, 5LÕ is divided by its height, 5HÕ and the
resulting number is multiplied by the number resulting from dividing
the height of the image, ÔHÕ on the film by its length, ÔL~. This is
the correct factor to use for multiplying the known film speed past
the slit to determine the unknown image speed. When this is then
further mu1tiplied by the reduction factor of the lens system, the
true speed of the object in front of the camera can be calculated.
In the example in Figure 11B, the image is moving at an unknown speed,
but analysis of the photographic record shows that the recorded image
of the subject has a height to length ratio of 1:2 while the
originalÕs ratio was 1:1. The known speed of the film past the slit is
10 feet/second while the optical reduction factor of the system is 40.
Subject length divided by height is 1, and image height divided by
image length is _. Then, the correct factor to use is _ and the speed
of the original subject is the film speed multiplied by the correction
factor and further multiplied by the optical reduction factor: 10
feet/second x _ = speed of image x 40 = speed of object which is equal
to 200 feet/ second. When the image of an object is traveling across
the slit at a speed slower than the rate at which the film moves
behind the slit, the originalÕs height to length ratio will appear to
be extended while if the image travels faster than the film, the
height to length ratio of the original object will appear to be
compressed. The magnification of the length of any subject
photographed by these cameras is directly related to the ratio of the
speed between the film and the image, as follows:
Length Magnification = Film speed / Image speed
Determinations of speed are irrelevant of the direction of the
subjectÕs motion if the slit is very narrow since horizontal dimension
then is only dependent on slit transit time. The only differences
between an object which moves in the opposite direction rather than
the same direction is, one, that it will be less sharp since image
points traveling in a direction opposite to that of film travel are
exposed on different film points over the time it takes them to go
from one side of the slit to the other and two, that the image will
appear reversed from left to right compared to the original subjects
orientation. The first effect can be minimized, but not eliminated, by
making the slit as narrow as possible thus making the total exposure
time for a point on the film as short as possible, but the reversal in
subject orientation is inherent to the system.
This is caused by a reversal in the order in which subject image
points are recorded compared to the order in which they are recorded
when image and film are moving in the same direction. As shown in
Figure 11C when the film and image move together the arrowhead is
imaged and recorded first and thus the film record shows the arrow as
it was on the original subject. When, as in Figure 11D, the film and
image move in opposite directions the arrowhead is still recorded
first and its record has been moved by the film past the slit edge by
the time the tail is recorded. This yields a film record in which the
arrow orientation is reversed as compared to its orientation on the
original subject.
Generally, exposure time for streak cameras is the reciprocal of the
slit width in mm. divided into the speed of the film past the slit
also in mm. or, in other words, the time it takes the film to move
from one edge of the slit to the other. Efficiency depends, just as
with focal plane shutters, on the numerical aperture of the lens used,
the slit width and the distance between the slit and the film or image
plane. It is not unusual to find that with very narrow slit widths
some streak cameras operate at efficiencies close to 50%.
When the absolute speed difference between film and image is zero the
subject appears as sharp as possible. When the image moves faster or
more slowly than the film but in the same direction, the motion
stopping ability of the slit shutter can be increased by reducing the
slit width to produce a shorter total exposure time. When the image
moves in the opposite direction to that of the film a much greater
reduction in slit aperture is needed to achieve the same degree of
sharpness. For example, when film and image travel in the same
direction at 9 cm/sec. and 11 cm/sec respectively their absolute speed
difference is 2 cm/sec. and an exposure time of, letÕs say, 1/100
second produces a blur of 2/10 mm. in the image. When the image moves
in the opposite direction, however, the speed difference between the
two is 20 cm/sec., thus a 1/100 sec. exposure would yield a 2 mm. blur
in the image. The slit size has to be reduced to yield an exposure
time of 1/1000 second in order to reduce blur to the same degree as
when the film and image move in the same direction.
When streak cameras do not achieve fast enough writing speeds,
electronic imaging devices that scan an area in a manner similar to
streak cameras but at a much faster rate are used. These electronic
cameras can exceed writing speeds of 100 inches/microsecond and have
become invaluable tools, particularly in explosives research.
Elapsed Time Cameras
With synchroballistic cameras the objective is usually to determine
the speed and attitude of an object traversing a particular area in
space.
Low speed applications of this same system generally are intended to
determine differences in the time of arrival at a particular spot of a
number of objects. A particularly good example of this type of camera
is the photofinish cameras in-stalled at most racetracks.
Although their basic operation is the same as that of synchroballistic
cameras described earlier, photofinish cameras have been misunderstood
by most laymen and even many photographers so we will review their
operation here.
A photofinish camera, shown in Figure 12, consists of a film supply
chamber, a take up chamber, a vertical slit (the leading edge of which
is lined up with the edge of the finish line on the racetrack) and
some means of transporting the film at an even speed behind the slit.
In addition to these requirements most of these cameras have rotating
segmented shutters included near the edges of the film that record the
position of the finish wire as a series of vertical lines. The
distance between these lines corresponds to a known time interval for
a particular rate of rotation of the shutter in the camera. Some
cameras have independent timing lights incorporated to establish
elapsed time between edge markings.
Referring to Figure 12, as the horses approach the finish the camera
operator sets the film in the camera into motion. When the first horse
crosses under the wire, its nose is the first part to be recorded by
the camera. As the image of the horseÕs nose moves across the slit it
does not move with respect to the area on the film that first recorded
the nose since the speed of the film is made to closely match the
average speed of the image of the horse across the slit. After the
nose, sequentially, the rest of the horse is recorded onto the moving
film. By the time the second horseÕs nose arrives at the finish wire,
the image of the winning horseÕs nose or length is already recorded on
the film and its recorded image has moved away from the slit.
Again, referring to Figure 12E, horse number eight has not arrived at
the finish wire by the time number fiveÕs nose is starting to be
imaged on the moving film and should it eventually not cross under the
wire, the photofinish camera will not show that horse number eight was
ever a participant in the race.
The horizontal axis in a photofinish record is interpreted directly as
elapsed time between the orders of arrival of the horses. If the speed
at which the film is moved within the camera is not exactly constant
the photofinish camera still accurately indicates the order of finish
although the horses might look distorted at various points along the
film. Measurements of elapsed time between the order of finish of the
various horses can also be obtained independent of the rate of
movement of the film with reasonable accuracy as long as the time base
generator, whether segmented shutter or timing light, is delivering
accurate timing marks on the film edges.
Photofinish photographs cannot be interpreted as ÒrealÓ since the
horizontal dimension does not correspond to ÒwidthÓ as in a snapshot
but rather to Òtime.Ó
When viewing a photofinish picture it should be remembered that the
Òfinish lineÓ seen in published prints is added after the fact for
measurement purposes only and most of the time simply for esthetic
reasons since the fans expect to see a finish line.
It is interesting to note that pictures for first, second or third
place all show the horses in the same position except that the Òfinish
lineÓ has been moved to just touch the nose of the first, second or
third horse. See Figure 13A,B, C.
This further emphasizes the fact that in a photofinish print the
finish line is not any particular line, but that any vertical line
from one end of the print to the other is the finish line. Another way
of saying this would be to refer to the whole print as a record of the
finish line.
In order to preclude the possibility of one horse covering up the
order of arrival of another situated further away from the camera, a
mirror is placed on the opposite side of the track from the camera. In
this manner the camera records the horses, as they cross the finish
line, from both sides. The mirror image can usually be seen on the top
quarter of the photograph.
Another useful variation of this technique is in the
microfilm-duplicating field. The duplicating streak or more generally
known as strip camera is aimed at a moving stage upon which are placed
the documents to be recorded. The speed of the stage is adjusted to
equal the film speed in the camera multiplied by the
camera reduction factor. For example, if the film moves in the camera
a 10 ips and the subject is being reduced by a factor of 10 then the
stage is adjusted to provide a speed of 100 inches per second. The
reason for a constantly moving duplicating system is the speed with
which copying can be performed since nothing has to come to a halt and
as long as images pass in front of the cameraÕs lens the moving film
will record them. The system is particularly suitable for applications
where a very large number of originals need to be microfilmed in a
short period of time.
Aerial Mapping Cameras
In a photofinish camera the camera and, therefore, the position of the
slit in space are stationary. When the camera is set in linear motion
then the area that the slit in the camera is responsive to continually
changes. Cameras that employ this variation of strip recording are
primarily aerial photomapping cameras. The optical geometry of this
type of a camera is not unlike that of duplicating cameras and is
described in Figure 14. The camera is aimed at the ground so that the
orientation of the slit is perpendicular to the direction of motion of
the airplane. Aerial cameras are usually focused at infinity since the
distance between them and the ground is so great. Once proper altitude
is achieved by the plane the film in the camera is set in motion in
the same direction that of the airplane and at a speed which is
determined by the ground speed of the airplane. The proper speed of
the film is determined by:
a=A
Where A is the subject speed past slit or the ground speed of the
plane
R is the reduction factor of the optical system a is the film speed
past slit
In aerial photography the appropriate film speed in inches per second
for a particular mapping mission would be determined as follows:
Film speed =
ground speed(mph) x 5200(ft/mile) x 12(inches/ft) = 3600 sec/hr x
camera reduction
Therefore, if the optical system of an aerial camera has a reduction
factor of 10,000 and the plane is flying at 600 mph, the film has to
be adjusted to run at:
a = 600 x 5280 x 12 = 1.056 inches per second 3600 x 10,000
In practice most aerial cameras of this type have an electronic
interlock between the planesÕ ground speed measuring system and the
rate at which the film moves in the camera so that changes in the
velocity of the plane over the ground will immediately alter the speed
of the film within the camera and sometimes also change the lens
aperture to maintain the same effective exposure throughout the film
run. Changes in altitude are generally ignored because at large
overall distances from the ground the change in the reduction factor
of the lens hardly affects the rate at which the film speed has to be
changed in order to maintain the proper imaging characteristics of the
camera.
One of the most famous strip photographs of this kind was a photograph
made in 1957 by the Air Force in which a continuous record of the U.S.
was made in less than three hours of a strip of land 20 miles wide by
3,200 miles long extending from New York City to Los Angeles.
A novel application of this linear motion streak technique is its use
in recording subjects at a closer range. A case in point would be the
photography on one piece of film of all the homes along a street or a
row of cars parked in a lot.
Consider, as in Figure 16A, the situation where a single camera is
first used to record instantaneously the appearance of a number of
cars lined up in a parking lot, and then the appearance of the same
subject made with a moving streak camera.
In the instantaneous record the sides of cars off the optical axis are
clearly visible. The marker lines between cars become obscured by the
cars off to the side. The cars located behind the first row appear
smaller. Parallel lines converge towards one point. These are direct
consequences of the photograph obeying the rules of perspective.
When a linearly moving streak camera records the same subject it
instantaneously records only that part of the total subject that lies
on the axis established by the slit and lens. Since the slit limits
the horizontal view of the subject only a small vertical segment is
recorded at any particular time. As the camera is, however, moving
these individual segments are continuously recorded and the final
record appears as in Figure 16B. In this photograph there are no sides
of cars visible. The marker lines between cars are all clearly
visible. These parallel lines moving away from the camera do not
converge, however. The cars located behind the first row appear as
tall as in the previous instantaneous record but they are just as wide
as the cars in the front row. This is caused by the camera responding
to changes in subject distance from the camera as changes in
magnification. However, subject length is recorded only as a function
of film speed past slit and image speed over the slit. That is, a 10
foot long subject will appear the same length on the film regardless
of distance from the camera.
The camera thus can only properly render the height to length ratio of
an object at one specific distance from the camera At other distances
the original ratio will be expanded if the subject is further away
than the distance the film speed is set for and at closer distances
objects will have their ratio compressed.
Thus, linearly moving streak cameras eliminate perspective clues in a
direction parallel to that of film travel. If a strip camera with a
vertical slit moves horizontally, then the photographs will lack
horizontal perspective.
In order to determine the speed at which the streak camera must move
in front of a stationary subject to photograph the subject so that the
image on the film will retain the originalÕs height to length ratio,
the following tables and equations are
used. They are given to help in quickly relating to each other the
parameters of camera to subject distance, optical reduction, rate of
film movement in the camera and speed of the camera past a stationary
subject or of the subject past a stationary camera. These tables are
particularly useful applied to ÒhomeÓ built or modified equipment
described later.
Table 1 - Approximate speed in mph the camera must move past subject
or subject past camera when camera reduction factor and camera film
speed are known.
REDUCTION Factor of lens 100:1 200:1 300:1 400:1 500:1 1,000:1
10,000:1 Film speed in camera in inches/sec
.125 .7 1.5 2.2 2.8 3.6 7 70 Speed of camera
.25 1.5 2.8 4.5 6 7 15 150 Past subject or
.5 2.8 6 9 12 15 30 300 Subject past
1.0 6 12 18 25 30 60 600 camera in MPH
For reduction factors and in camera film speeds not given above the
required camera speed past the subject is given by the following
formula.
A = .057 Ra
Where A = Camera speed in miles per hour past subject or subject
speed in miles per hour past subject
R = reduction of lens a = speed of film in camera in inches/second
.057 = constant relating inches per second to miles per hour
This equation is a simplified form of the one given earlier for
determining the ground speed of a plane doing aerial mapping.
As is evident from Table 1, the greater the reduction factor of the
lens being used to photograph and the greater the speed at which the
film is pulled past the slit in the camera, the greater the speed of
the camera past the stationary subject in the case of aerial or
similar photography or the greater the speed of the -subject past the
camera must be in applications such as microfilm copying or
photofinish cameras.
Since most calculations used with strip cameras include the reduction
factor of the camera lens being used the following table is given to
quickly indicate the reduction factors achieved with various common
lenses at specific distances from a subject.
Table 2 - Distance in feet from camera to subject with various lenses
for specific reduction ratios.
REDUCTION 100:1 200:1 300:1 400:1 500:1 1,000:1 10,000:1
Lens Fl
7.5 mm 2.5 5 7.5 10 12 25 250 Distance
20mm 6.5 13 20 26 33 66 660 in feet
35mm 11 22 33 44 55 110 1100 between
50mm 17 33 50 66 83 170 1700 subject
200mm 65 130 195 260 325 655 6500 and camera
For lenses and magnifications not given above approximate camera to
subject distance for desired reduction factor with a known focal
length lens is given by the formula:
R (D - fl) x 305 ilL
Where R = reduction desired D distance from lens to subject in feet
focal length of lens in use in mm.
305 = constant to convert distance from mm to feet Sometimes it is
impossible to measure the distance from camera to subject but a good
approximation of subject height can be made. For this case the
reduction factor of the lens being used can also be estimated as shown
in the following table and equation.
Table 3 - Height of subject that will be 24mm high (the image height
using 35mm film) at certain subject reductions regardless of lens
focal length used.
100:1 200:1 300:1 400:1 500:1 1000:1 10000:1 Subject height in
feet 8 16 24 32 40 80 800
Camera reduction
factor 100:1 200:1 300:1 400:1 500:1 1,000:1 10,000:1 Subject
height in feet 8 16 24 32 40 80 800
For reduction factors not included in this guide, the approximate
subject height that will just fill a 24 mm high frame is given by the
following equation.
H= .08R
Where
H = subject height in feet
R = reduction
.08 A constant relating frame height in nun to subject height in
feet
In most technical applications it is desirable to keep the direction
and speed of film and image coincident and the slit perpendicular to
the edge of the moving film. However, when the slit is not
perpendicular to the film motion and the film and image move parallel
to each other but their speeds are different then the shape of the
resultant image will appear slanted to the right or left depending on
the slit slope and the difference in speed between the film and the
image.
Assume that, as shown in Figure 17, the slit in the streak camera is
inclined at an angle of 45 degrees to the direction of travel of the
film, the film moves at an even speed past the slit and the vertical
subjectÕs image moves at _ the film speed. The moving image arrives at
the slit and starts to be recorded at the bottom edge of the film
first. As the image of the bar pro-gresses from left to right the
portion of it which the film records progressively moves towards the
top edge of the film. At the completion of its transit from point T1
to point T2 the recording of the bar is complete. Since in the same
length of time the area on the film which first recorded the arrival
of the image has moved twice as far to the right as the barÕs image,
the resultant record appears as a diagonal line with a slope exactly
opposite that of the slit in the camera.
The resultant slope of the image for a given slit slope is determined
by the following equation:
1= S 5
S ~ (~)
Where I~ ÑS ÑS
Iv resultant image slope slit slope film speed past slit image speed
past slit
This indicates that when film and image speed are the same, verticals
in the subject will appear vertical regardless of the slope or shape
of the slit. However, when speeds are unequal, then the faster the
image speed in relation to the film speed the more closely the image
slope will tend to match the slit slope.
Another case occurs when subjects which are vertical and which are
photographed by a camera moving in a linear fashion but in such a
manner that the slit is not parallel to the vertical subject, then
these originally vertical subjects will appear inclined in the
photograph recorded by the camera. A good example of this would be a
streak camera mounted in a car with film parallel to the motion of the
car attempting to photograph build-ings built along a street going up
or downhill.
Conversely, if the slit and the camera are made to be vertical in the
above example, thus matching the building orientation then horizontal
features on the ground, such as rooftops, will appear inclined. The
horizon line in each case would, however, remain horizontal and
parallel to the film edge. See Figure 18A, 18B.
Changes in the shape of the slit present another avenue for creative
experimentation and technical control. S shaped slits, offset slits,
double slits and other shapes and combinations can be constructed to
achieve a variety of effects. Along with changes in slit shape,
changes in slit width provide yet another dimension for the creation
of unusual images.
As long as the distance from one edge of the slit to the other in a
direction parallel to film motion remains the same, exposure time from
one edge of -the film to the other will also be the same and
consistent. Exposure time then is determined by the transit time for a
given point on the film across the slit. However, when slit width is
specified as the perpendicular distance between the edges, then
exposure time is dependent on this distance and the angle of the slit
at any point with respect to the direction of film motion.
Exposure time for inclined slits is determined by the follow-ing
relationship:
DE=VE 1 sin a Where: DE = exposure time with inclined slit
V ~e Exposure time when same size slit is perpendicular to film
travel a = angle at any point between slit edge and direction of
film travel
From this equation it can be determined that a curved slit where the
perpendicular distance between edges remains constant will produce
uneven exposure from one edge of the film to the other.
The second way of specifying slit width, and the easiest to make, does
not yield changes in exposure in a direction perpendicular to film
motion. This kind of slit is made by drawing the desired shape on the
opaque slit material and cutting the two
pieces apart along the drawn line. Then the two are separated exactly
the amount one desires the slit width to be. Since this automatically
causes the perpendicular distance between the two edges to change
according to the angle of the slit and thus maintains the horizontal
distance, or the one parallel to film travel, the same, exposure
remains the same from one edge of the film to the other.
Panoramic Cameras
Streak photography is particularly useful in applications requiring
wide-angle pictures due to the sequential exposure nature of the
system. The camera placed on a turntable or other rotating support is
turned in a direction perpendicular to the slit orientation and
opposite to that of film travel. In general the axis of rotation of
the-camera, should be around the rear nodal point of the lens. In more
practical terms, it can be between the lens and the slit or even
behind the slit. It should not be wound a point in front of the lens.
These cameras resemble the moving lens and moving slit with stationary
film panoramic cameras such as the Widelux and the old Kodak ÒCirkutÓ
panoramic cameras made specifically for photography of large groups of
people. See Figure 19.
The wide angle scanning strip camera is shown diagrammatically in
Figure 20. The lens on the camera determines the vertical angle of
view of the camera, or the angle parallel to the orientation of the
slit. The lens in use in turn determines the length of film which
must pass by the slit for every complete
revolution, or every 360 degrees perpendicular to the slit, (or
portion thereof if smaller than full panoramas are desired) recorded
by the camera.
Assuming that the film frame is the normal 35mm film gate aperture,
then the vertical angle of coverage of the lens is first determined
from manufacturer-supplied data, from available tables or
mathematically determined. The vertical angles of coverage for six
common lenses on a 35 mm camera are given below:
7.5mm Fisheye 180 degrees
20 mm 65 degrees
35 mm 37 degrees
50 mm 26 degrees
100 mm 13 degrees
200 mm 7 degrees
The vertical angle of coverage of any lens for the short dimension of
the 35mm format can be approximately determined by dividing the focal
length of the lens into 1300.
The exact vertical angle of coverage for non-distorting lenses is
given by the following formula.
Optical L = 2 tan1 (24)
From knowledge of the time it takes the camera to turn a full
revolution, the amount film that must be advanced in the streak camera
in the same time can be determined as follows:
(H x 24 Film required for 360 degree coverage (V
The vertical to horizontal angle of coverage ratio must first be
determined and then multiplied by the height of the frame. For
example, assuming that a 35mm panoramic streak camera will be using a
35mm lens, then the vertical angle of coverage, 37 degrees, divided
into 360 degrees (which will be the horizontal angle), is 9.7. Then,
since the 35mm camera has a frame height of 24mm and it is for this
frame height that the angles of cover-age are given, 24mm is
multiplied by the previously found factor to arrive at a required
length of 233x~im. Therefore, if the camera turns at the rate of one
revolution every ten seconds, then the camera must advance 233mm also
in 10 seconds, or 23.3mm per second, in order for the photograph to
appear as a correct panoramic representation of the subject
surrounding the camera. In actuality this would be the length required
regardless of the film size used as long as the lens remained the
same.
It is appropriate to mention here that while the above discussion seems
make sense it is not the most appropriate method for determining the
amount of film required for a 360 degree panorama. For most practical
purposes the amount of film required is equal to the circumference of
a circle whose radius is equal to the focal length (or image distance
if the lens is focused on a nearby subject). So, the required length
is simply:
2 x f x pi or about 6.28 times the focal length of the lens
For coverages less than the full 360 degree panorama a fractional amount
is required that reduces the above amount by the number of time the
angle of coverage fits into 360 degrees. A discussion related to the
difference between the two methods will be included here.
Generally, when taking panoramic photographs it is important to keep
the axis of rotation of the camera vertical. If the camera does not
rotate around a vertical axis the horizon line will appear to be
higher at one point of the panorama than at the opposite point along
the 360-degree circle. Tilting the camera down or up will just raise
or lower the horizon line.
If the camera is tilted from left to right, then the only effect will
be that vertical subjects will appear to be tilted in a direction
opposite to that of the camera tilt.
The primary disadvantage and difficulty with wide-angle photographs
made with streak panoramic cameras is the large length to height ratio
that is usually inherent to them.
For example, if one wishes to see a print of a complete 360-degree
view in which the vertical angle is 37 degrees (taken by using a 35mm
lens on a 35mm panoramic camera) the height to length ratio of the
print must be 1:9.7. This means that if we wish to make the vertical
dimension of the print 10 inches, the print would measure over 8 feet
in length. When a 200mm lens is mounted on the camera the ratio is
1:52 and a 36-exposure roll would cover slightly more than a full
360-degree panorama.
The advantage of using a long focal length lens for wide-angle
pictures is that objects at a distance can be recorded over a wide
horizon angle, such as in photographs of boats or mountains, without
including a large amount of foreground or sky. Photographs taken this
way may be more economical since the camera essentially becomes a
large format camera but only uses that part of the film that is really
useful. Panoramic distortion is evident when a wide-angle photograph
taken with these cameras is viewed as a flat print. All horizontal
lines in the original subject appear curved towards the horizon line
of the final flat photograph.
A practical way of looking at these photographs and eliminating
panoramic distortion is to place the viewer at the center of the
photograph, essentially assuming the position of the camera at the
time the exposure was made. Thus, the photographs become
self-correcting in terms of ÒpanoramicÓ distortion. See Figure 22.
When viewing sections of a 360-degree view, as long as the curvature
remains the same as that which the complete view would have had and
the viewer is looking at the print from the center of curvature, the
print will have proper perspective and appear
essentially distortion-less. Photographs made with a regular camera of
this print from the center of curvature appear exactly the same as if
the picture had been taken of the original subject regardless of the
focal length of the lens used on either the panoramic camera or the
copy camera.
It is interesting to note that if a panoramic camera is used for
architectural photography tilting the camera up in order to take a
whole building will not result in the building appearing to Òfall
backwardsÓ as when a regular camera is tilted for this purpose.
Instead, the camera will automatically correct for this kind of
distortion at the expense of some loss of sharpness in some portions
of the pictures. Making the slit size narrower can minimize this. The
reason for this is that as explained earlier the camera records equal
angular displacements as equal distances along the film. Since the
slit is vertical with respect to the direction of movement of the film
every vertical line in the subject will appear vertical on the film.
The camera only records one vertical portion of the subject at a time.
Since the edges of a vertical building are vertical the streak camera
will record each edge as such when the slit arrives at each edge of
the building. Therefore, since both sides are recorded as vertical
lines the building appears not to be tilted backwards. See Figure 23.
However, since the top of the building is farther away than the bottom
it will be Òstretched outÓ by the streak camera. The stretching out
and blurring are caused by the fact that there is a real speed
difference between the rate at which the bottom part of the building
goes by the slit and the rate at
which points near the top go by the slit. Because the streak ~camera
can only accommodate one particular image speed properly, and that is
the one which matches the rate of film travel past the slit, any image
point moving at a different rate will suffer from blurring due to
relative motion between image and film while in transit over the slit
aperture.
The fact that the top of the building appears curved is caused by
panoramic distortion, which as discussed earlier, causes parallel
horizontal lines in the subject (perpendicular to slit orientation) to
appear to curve towards the horizon when the panoramic photograph is
viewed as a flat print.
In order to photograph ÒeverythingÓ surrounding the panoramic camera,
a fisheye lens could be attached to it. Since this lens has a 180
degree coverage along the diameter of the circular image lined up
along the slit, and the rotating streak camera takes care of the 360
degree horizontal coverage, the resulting photograph covers 180 degree
vertically and 360 degree horizon-tally and that should include
everything surrounding the camera. See Figure 24.
This image, however, suffers from pronounced distortion along the top
and bottom. It is essentially the same kind of distortion that is
evident in Mercator projections of the globe. This causes equal
horizontal angular displacements along the poles (top or bottom) and
the equator (middle of photograph) to record as equal distances along
the horizontal axis of the photo-graph. Since this is not the case in
reality, the circumference of the sphere being shorter at the poles of
a globe than at the equator, in this kind of wide-angle photograph
there is consider-able blurring along the top and bottom of the image.
The blurring and distortion are caused by the large angle of view of
the fisheye objective. It is not experienced when narrower angle of
view, rectilinear, lenses are used and as long as the camera is kept
level.
A special situation occurs if a camera equipped generally with a very
wide-angle lens is tilted so that the angle of view of the lens
extends beyond the axis of rotation of the camera. Then the lens
delivers onto the slit an image that includes subjects both in front
of and behind the axis of rotation of the camera and the camera will
make a graphic record or interpreta-tion of INFINITY. See Figure 25A &
B. That is, if infinity can be defined as the distance at which the
poles of a sphere are projected when its surface is tangent to the
inside of a cylinder and the sphereÕs polar axis is coincident with
the axis of the cylinder.
Photographs taken under the above conditions show extreme blurring
along the Òinfinity lineÓ. The records of objects located behind the
axis of rotation appear upside down and 180 degrees out of phase with
their own records when located in front of the axis of rotation. Left
to right image reversal is also evident.
Peripheral Scanning Cameras
Panoramic cameras take 360-degree photographs while looking out at a
subject. They can be turned inwards to take peripheral or 360 degree
photographs of the surface of a subject. Usually these peripheral
cameras find application in archeological studies (generally known as
cyclographs), piston and cylinder wear records and in forensic
photography for rifling comparisons of bullets.
The main reason for anyone wishing to make a peripheral photograph is
the desire to be able to see all sides of a subject at once on a flat
piece of paper. It is far easier to mail a photographic record of all
sides of an object than to mail the original three-dimensional object,
especially when it is large or valuable.
Basically there are two ways of making peripheral photographs. The
first is analogous to taking pictures of a moving subject with a focal
plane shutter. This method is particularly useful with a restricted
range of subjects that are mostly cylindrical in shape.
Although the method is widely used it is somewhat more difficult to
execute properly with improvised equipment than the second method
discussed in detail later.
The camera, usually of a 1arge format, 4x5 or 5x7, has a focal plane
shutter consisting of an adjustable width slit which can be made to
move across the film plane in synchronization with the image of a
rotating subject placed in front of the camera. This can be
accomplished by a set of pulleys and belts. Figure 26. As was
explained earlier, if a subjectÕs image moves at the same speed and
direction as the slit in a focal plane shutter camera the image will
be spread out over the whole frame. The one variation by which the
peripheral camera prevents this from happening is that while the
subject moves across the field of view of the lens it 4so rotates.
Therefore it presents a different subject area to the film while the
moving shutter sequentially uncovers the film. The camera is set up so
that a little over one revolution of the subject in front of the
camera will be recorded over the width of the film plane.
There are at least two factors that must be taken into account when
round objects are photographed by this camera. First, one must make
sure that one revolution of the object can be properly accommodated
onto the available film surface. For this, the subjectÕs height to
circumference ratio is first deter-mined and the camera is set at such
a distance from the surface of the object that the height to length
ratio of the subject matches the height to available frame width of
the camera.
Second, the subject cannot exceed certain circumference and height
specifications because of the mechanical interlocking between the
moving rotating subject stage and the camera. The one advantage of
this system is that the image is recorded onto one piece of sheet
film.
Unusual photographs can be taken with a camera of this kind when
applied to subjects not moving at the same speed or direction as the
moving slit. When the shutter scans vertically, a vertical rotating
subject will appear as a corkscrew The top of the photograph may show
one side of the subject and so may the bottom, but points in between
will be intermediate views including the back view at the middle of
the photograph. Placing the slit in front of the camera and opening
the shutter of the camera can simulate a slow moving slit at the focal
plane. Thus the film will only be exposed as the slit traverses
through the angle of view of the lens. Figures 27A and 27B.
The second method of taking peripheral photographs is by far the most
practical and it lends itself to the greatest variety of applications.
The only requirement beyond a variable speed scanning strip camera is
a turntable, also variable in speed if possible.
The essentials of the system call for the slit, lens and turntable to
be lined up along the same axis so that the axis of rotation of the
turntable falls directly onto the slit in camera.
Obviously, for most applications a vertical slit will be used. Thus,
the surface of the turntable will be horizontal. The turntable should
turn at an even speed and its size should be appropriate for the
subject it will be holding.
There is a direct relationship between turntable speed and speed of
film past the slit. They are essentially related by the magnification
of the optical system. Thus, knowing the surface speed of the object
on the turntable and the reduction factor of the lens on the camera
the speed at which the film must move past the slit can be determined
from the following formula:
.4
Fv= Sv
4
Where Fv = film speed past slit in camera R = vertical reduction
factor
Sv subject surface speed (circumference x RPS of turntable) Subject
surface speed in inches per second is given by multiplying the subject
circumference in inches by its speed in revolutions per second. Then,
dividing this speed by the optical reduction factor of the lens, the
speed at which the film needs to be moved past the slit is determined.
From here on it is simple matter of dividing the slit width in inches
by the Li speed in inches per second to arrive at the exposure time
LionÕ that particular transit rate of the film. A standard light meter
reading is taken of the rotating subject and the f-stop is ad-justed
to give proper exposure for that exposure time.
As the camera and subject are independent of each other, many
different subject diameters can be accommodated with ease. When very
small objects are photographed one must align the rotating subject
with care, especially when as in ballistic comparison photographs, two
different subjects will be compared to each other.
It is interesting to note that if one is willing to tolerate some
distortion, the subject does not have to be a perfect cylinder but it
can have depressions or protrusions. Parts that protrude from the
average circumference of the subject will appear com-pressed and those
that are depressed will appear spread out. By this technique, full
360-degree portraits can be taken. See Figure ??
The subject is placed on a rotating turntable with the slit aimed at
the center of rotation of the head. When these photographs are later
displayed on rotating cylinders a close approximation to reality is
achieved since the viewer tends to ignore the straight vertical sides
of the cylinder and concen-trates mainly on the changing features of
the portrait.
Interesting distortions can be made by having the subject off center
or changing expressions as the camera is recording the back of the
head or having the subject move laterally at the same
time, or turning while being imaged on the streak cameraÕs slit.
Photographs bearing a strong resemblance to cubist vision have been
made this way.
Peripheral cameras have also been used to photograph the interior
walls of cylinders by placing a mirror at 45 degrees inside the
cylinder and then imaging the moving reflection onto the slit of a
streak camera.
In this context, the peripheral camera is more of a panoramic camera
in that the camera looks out by way of a mirror to cover a 360-degree
view of the wall of the cylinder. However, instead of rotating the
camera as in a panoramic photograph, the subject is made to rotate and
the camera is kept stationary. In any event, the result is the same as
if a panoramic photograph had been taken.
Enlarging Streak Photographs
As mentioned in the section dealing with panoramic cameras, wide angle
and peripheral photographs tend to be very difficult to handle and use
because~ their height to length ratio is usually unwieldy. In order to
make prints with an acceptable vertical dimension, the horizontal
dimension often would necessitate an enlarger capable of holding at
least ten inches of film and an easel capable of accepting paper up to
10 feet long.
The answer to this constraint is to use an enlarger that operates
basically as a streak camera in reverse. The enlarger is identical to
a microfilm-copying camera with a moving stage except for the fact
that a lamp-house is fitted above the moving film.
As shown in Figure 30, the film and paper move in opposite directions
and at such a speed that there is no relative motion between the image
projected by the lens and the moving paper below. The proper speed
relationship between the film and the paper are simply determined from
knowledge of the magnification that the particular lens on the
enlarger is set to. The speed of the film past the slit is multiplied
by the magnification factor of the lens and that is the speed at which
the paper must be moved on the easel.
The advantage of this system is that the length of the image becomes
relatively unimportant as long as it is not so long that when the
height of the streak record is enlarged to fit the width of the paper,
the paper length required does not exceed the length of the paper roll
available.
The main disadvantage is that there is an obvious difference between
the time that one edge of the enlargement is exposed and the time the
exposure is completed at the other end.
Consider that if a certain light source is used to enlarge a strip of
35mm film 5Ó long in a 4x5 enlarger and the Proper exposure for a
print 40Ó x 17 feet is ten minutes, then after the ten-minute exposure
time the print can be developed.
However, assuming that the 5Ó long strip is printed by a streak
enlarger the total time from beginning of exposure to end increases
considerably.
When a 4x5 enlarger is used each image point on the paper receives an
exposure for ten minutes; therefore, the same must be true in the
streak enlarger. If the slit size is assumed to be 1/10 inch, it will
be enlarged to be 4Ó in size when the slit is
enlarged to fill a 40Ó roll of paper from edge to edge. This is an
enlargement of 40X linear. The paper must be pulled, then, at the rate
of 4Ó every ten minutes so that every point along the paper is exposed
for ten minutes. Then, it will take ten minutes times 17 feet divided
by 4Ó to complete the exposure of the en-largement. In this case it
would be 10 x 50 = 500 minutes or over eight hours!
Obviously, one solution is to use a wider slit width in the enlarger,
but this requires that film and paper movement speeds increase in
accuracy. Another is to use a brighter light source, but there are
practical limits to this as well. In any case, it is still the most
practical way of making large enlargements and it is possible to feed
the roll of paper directly from the en-larger into a chemistry train
so that shortly after the print is completely exposed it is also fully
processed.
bla
9/78
DOUBLE SLIT VELOCIMETRY
CIRCULAR/CONICAL PANORAMIC AND PERIPHERAL PHOTOGRAPHY
3D PANORAMIC PHOTOGRAPHY
DIGITAL CAMERAS AND LINEAR ARRAYS THAT MIMIC THE FILM CAMERAS Ð
SPECIAL CASES RELATED TO STATIONARY NATURE OF CCD PHOTOSITES AS
OPPOSED TO MOVING FILM BEING THE MEMORY OF IMAGE EVENTS TAKING PLACE
ON A SLIT SHUTTER.
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