LONG EXPOSURE IMAGES OF VERY DISTANT LIGHTS:
THE EFFECTS OF ATMOSPHERIC SCINTILLATION
by
Bruce Maccabee
When the exposure time is a large fraction of a second the image of a distant light
such as that of a star or planet can be changed from what it should look like, a bright
white point of light, to a "squiggly" line (or smear or streak) which has varying
intensity (varying image brightness)and varying color along the squiggly line. The
reason for these changes in the image is a combination of (a) camera motion and (b)
atmospheric scintillation. Let us consider, first, the
effect of camera motion.
CAMERA MOTION ELONGATES OR "STRETCHES" THE IMAGE
Camera motion during the exposure time causes the image to become elongated into a straight or curved line. Typically the
camera motion is quite random, as when the camera is held by hand (not on a tripod and not rigidly clamped to a structure),
so the elongated image looks "squiggly," i.e., there are seemingly random straight and curved segments of the elongated
image which could range from being a (nearly) straight line to being a closed loop (or several closed loops). Experiments
have shown that the amount of random motion or "squiggliness" increases with the magnification or "zoom" factor. When a person
holds the camera there can be small random variations in the camera pointing direction that are a result of breathing by
the camera operator. Experiments have shown that when a single location on the camera body is pressed against a rigid surface,
such as a car or a post, the slight body motion caused by breathing or by one's pulse is enough to rotate the camera pointing
direction by a fraction of a degree. This small rotation is magnified by the "zoom" factor. A typical video records 30 frames
(pictures) per second. The slight camera motion causes the image to move around in a random manner. However, at 30 frames
per second there is not much motion during a single frame. Hence the image in a given frame of a typical video is smeared only
slightly by ordinary, uncontrollable hand motion. However, when the frame rate is slowed, as in the "night mode" operation
of a JVC type camera, the exposure time per frame is lengthened and hence the image elongation is greater (the length of the
image increases with exposure time). In particular, when the JVC-type camera is operated at night and a distant light or a
star or planet is the object being recorded, the frame rate drops to 2/second or 1/2 second per frame. The combination of this
slow frame rate and the zoom magnification is sufficient to create very elongated images such as shown above and below.
ELONGATION AS "TIME TO SPACE" CONVERSION
Consider, now, videotaping a light which changes rapidly in intensity or color (or both). Such changes would be detectable
as variations in the image from frame to frame under normal operation (30 frames/second) when the camera pointing direction is
perfectly steady (e.g., a tripod-mounted camera), as long as the time between changes was considerably longer than 1/30 sec,
or, equivalently, the pulsation or oscillation rate were considerably less than 30 Hz. (If the changes are at a steady rate,
i.e., if they form a steady oscillation, that is faster than 30 Hz the changes could still be detected as an "aliased"
signal, i.e., the apparent oscillation frequency as recorded by the camera would not be the actual oscillation frequency of the
light.) If, on the other hand, the frame rate is very low, it is still possible to detect variations in the light by using
the "time to space conversion" effect (the operating principle upon which the "streak camera" is based).
In this case the camera is rotated to scan across the direction to the light so that
at the beginning of a frame exposure the light image is at one point on the image plane (CCD in a video camera or film in a
film camera) and at the end of the exposure time the image is at another point on the image plane. When this angle scanning
is done at a constant rate there is a one-to-one correspondence between distance between two points at different locations on
the image and the time difference between those points. The angle scan begins at one end of the elongated image and ends at
the other end, so the total length of the image (e.g., as measured in microns or millimeters on the image plane) corresponds
to the total exposure time. If the image is of a steady light then the image has a uniform intensity along its length as long
as the scan rate (e.g., in degrees per second) is constant. If the scan rate is not constant, as happens with a hand-held
camera, there are variations in brightness and width along the length of the image of a distant, steady light. If the scan
rate is constant and the light pulsates at a steady rate, this pulsation will show up as image brightness variations at regular
intervals along the image. If the scan rate is not constant the spacings between the pulses will change, with the spacings
being roughly proportional to the scan rates (e.g., faster scan rate, greater distance between pulsations).
The pictures below provide illustrations of the "time to space conversion" effect as applied to the images of both steady and
pulsating lights at a power station that was about 2 miles away. The typical mercury vapor or sodium vapor streetlights do not
emit constant light. Instead they pulsate with the alternating electric current which powers them. These intensity
pulsations are fast and are not noticed by a person simply looking at the lights or even videotaping the lights with
a camera mounted on a tripod (or other rigid mount). However, if the camera pointing direction is turned, as described above,
the "time to space conversion" makes the pulsations visible. (A person can see the pulsations with the naked eye by turning
his eyes rapidly while looking generally in the direction of one of these pulsating lights.) An incandescent light, on the
other hand, does not have brightness pulsations (or the pulsations are so small as to be only detectable with special
equipment) because the thermal mass of the filament averages over the power pulsations in the alternating current. In the
pictures below one sees the time to space conversion images of both pulsating and steady lights. I obtained these images by
intentionally turning the camera slightly while videotaping in the night mode so these are 1/2 second exposures. The upper
red images were made by two red, incandescent lights on the sides of the smokestack. The very bright (overexposed) white lights
incandescent spotlights. Both mercury vapor and sodium vapor lights created the lines which are made up of series of pulsations
or "dot images." The atmospheric scintillation effect described below may also have affected the images.
TIME-TO-SPACE CONVERSION EFFECTS ON IMAGES OF VERY DISTANT LIGHTS
When light travels long distances (tens to hundreds of miles) through the atmosphere it is modified by the atmosphere. The
modification with which most people are familar are the brightness pulsations or "twinkling" of stars. Stars which people can
see are basically constant light sources. Yet, when viewed through the atmosphere they appear to change randomly in brightness
and, especially when viewed through a telescope or zoom lens, to move laterally by small amounts.
Something else happens: color dispersion. Color dispersion is the basic property of a prism that "splits" light into its
component colors. The atmosphere can do this because air can act as a very weak prism. When light travels long distances
through the atmosphere the prism effect can cause light of varying colors to enter the camera aperture (lens opening) at
varying times. This effect of the atmosphere can be approximately duplicated by putting a triangular prism in front of a
camera and shining a small light (or sunlight) through the prism so as to make the color spectrum appear at the lens of the
camera. Then rotate the prism slightly back and forth to make the different colors pass through the lens into the camera.
The images below show what the JVC camera recorded when pointed at the planet Mars, which is a reasonably bright
exoatmospheric light source (basically a reflector of sunlight). The light from Mars traveled many tens of miles through the
earth's atmosphere before reaching the small aperture of the camera. The atmosphere caused the various colors of the light to
arrive at the camera aperture at various random times, and these varying "bursts of a single color" were recorded during the
1/2 second exposure time as variously colored "image blobs" lying along the squiggly "time to space conversion" line. Examples
of this effect are shown in the first illustration (video frame) above and in the illustrations below. (Note: the color and
brightness variations of the original images from the camera have been limited to 256 levels and by the .jpg compression that
has been used to reduce the byte size of this article.)
I obtained these images of planet Mars with a JVC GR D850 mini-DV camera at 40 - 70X zoom with one part of the camera pressed
against the body of a car. I attempted to hold the camera perfectly steady. There was no noticeable hand vibration caused by
imperfect control of my muscles. Still, the image moved. I then realized that the breathing and the pulse in my hand were enough
to cause slight motions of my hands and these motions were enough to rotate the camera very slightly. I could not
prevent the camera from rotating just by pressing one part of the camera against the car. Had I pressed a flat surface of
the camera against a flat surface of the car I might have stopped the vibration. However, I had no convenient flat surface
that would allow me to press the camera against it and still be able to point toward the planet so I was limited to
"single point stabilization," which does reduce but does not eliminate the hand vibration, as would would happen
if the camera were mounted on a tripod.
CONCLUSION
The image of a distant light (tens of miles or more) seen through the earth's atmosphere as recorded on a hand-held camera, even
one which is pressed against a solid support (at a single contact point on the camera), can be an elongated "squiggle" (a randomly
curved or straight line) consisting of bursts or "dots" of varying image brightness and color. Sometimes a line image in a single
frame (e.g., 1/2 sec exposure time) or motion of an image over several frames (e.g., at 30 frames/sec) is interpreted as evidence
that the object or light being filmed was moving linearly or randomly. This interpretation could be correct if it were known that the
camera was on a tripod or that several parts of the surface of the camera were pressed against a rigid support
such that the camera could not rotate in any direction. However, unless the rigidity of the camera pointing direction can be
assured, one must allow for the possibility or probability that the apparent image motion is a result of uncontrollable hand
vibration.