The experiments that we ran were designed to re-create optically the various types of images that can be produced by gravitational lenses in space. We produced and recorded many different images that mimicked ones that have been found in space. The real images that we have compared our experimental results to are from the Hubble Space Telescope.
Our experiments created various types of images, including rings, points, arcs, crosses, and other multiple images. The images produced seemed to degenerate from circles to arcs to points as the pinhole was moved farther away from the center of the imaging field. Our control setup involved the apparatus set up without the lens in position. The image produced in the control consists of a single bright, white point in the center of the image field.
Rings were formed by our lenses when the pinhole was aligned with the central bright spot in the light from the lens. At this point, light passing through the lens passed through the pinhole located at the center of a circular region on the lens. A double ring was formed often, indicating that light was being bent from the edge of the lens as well as from the center of the lens. The image of a ring was often accompanied by a fuzzy circular spot in the center of the image. This showed that some light traveled through the center of the lens. This usually appeared very dim because the light arriving at this point traveled through the thickest part of the lens and the center part of the lens was not polished smooth where it had been cut. (See Figure 8.)
The arcs that were formed by the lens were actually partial images of the ring structure. They were formed when the pinhole was placed so that it was inside the first bright ring but outside of the central bright spot. The farther the pinhole was placed from the center of the image, the dimmer the arcs became. The arcs were always formed in pairs that were symmetrically aligned over the center of the image. The arcs also shortened as the pinhole was moved away from the center. (See Figure 9.)
The
broken arcs and rings were derived from the complete arcs and rings. They
formed for several different reasons.
When
a double ring structure formed, the outer ring, which was created from light
lensed from the edges of the lens, was always broken into three parts. After
careful analysis, it was determined that the lens holder had three clips which
effectively blocked off the light coming from the edges of the lens. This
created the three shadows that are separated by 90o on the image of
the outer circle.
Another source of the broken rings and arcs came from the aperture. If the
beam of light passing through the aperture was made smaller, it only hit part
of the lens. The ring structure requires that the light passing through the
lens should be symmetrical across the center. If some quadrant of the lens
were not hit by the light, then the set up that normally gave a ring or an arc
was incomplete and produced a broken image.
Broken arcs were created when the lens was positioned at an angle to the
incoming light. When the lens was placed at this angle, light was lensed at
angles that vary much more than if the lens was perpendicular to the light
source. As the pinhole was pulled away from the center of the imaging field,
we noticed the same image degeneration from arcs to points as we saw in the
images from the first part of the experiment. However, the increased
variations in the light rays created more interference. The interference
caused the degeneration to occur unevenly, so the arc would break into several
pieces, giving us our broken arcs. This created the broken arc structure that
looked very similar to the broken ring structure. (See Figure 10.)
The
linear points that were produced came from several different arrangements of
the experimental apparatus. They were formed when the pinhole was placed in
the outer part of the imaging field. Linear points usually formed in pairs.
They therefore produced an even number of reflected images aligned on both
sides of a central image. This did not occur if the pinhole was aligned too
far to the edge of the imaging field. In that instance, the angle of the light
coming out of the lens could not be bent far enough to pass through the
pinhole. As with the arcs, the central image was often fuzzy or too dim to be
seen on the large screen. The point that was closest to the central maximum
was always the brighter image of the pair. This occurred because the lens
could focus more light through the pinhole onto this point since it was closer
to the center and required less bending of the light by the lens in order for
it to be imaged through the pinhole. (See Figure 11.)
Non-linear
points did not usually occur in lenses where the light passed through the lens
at right angles to its axis of rotation (if it were a galaxy). They occurred
only if part of the image had been focused from the outside edge of the lens.
In this case, the extreme bending of the light rays through the lens offset the
image form the normal patterns. Non-linear images also formed if the aperture
was set so that only part of the lens was focusing the light. In this case,
fainter reflections and other refractions could cause very faint images to be
seen. These were visible only because the much brighter images had been
blocked. (See Figure 12.)
When light struck the lens at a 45o angle, the great majority of the images appeared to be non-linear. Many different combinations of images were formed as well, with point images often being mixed with arc images. The same variations in brightness among the images occurred. Twins were found in these images as well, but more often, an arc was paired up with a point image. Another peculiarity was found when we saw groups with three points where the images formed a trigonal planer arrangement around the dim central one.
The
Einstein cross is one of the most famous examples of a gravitational lensing
image. In our experiment, the cross was formed by using the light source at
45o to the plane of the lens. When the pinhole was placed in the
center of the imaging field, a four part image was formed. The pinhole could
be positioned in the imaging field so that the four points were at right angles
to each other. The four points of the cross were particularly bright. Other
fainter images could be seen on the imaging screen as well, including the dim
central image in the middle of the cross and a second set of points for a
larger, dimmer cross. The top point to this second set was missing, however,
and it was determined that the shadow from the lens holder was blocking it.
The outer cross, though not perfectly perpendicular, was therefore formed from
light rays that had been bent from the outside edges of the lens. (See Figure
13.)
Interference patterns in the light were formed by light being bent at slightly different angles. When passed through the pinhole, a slight diffraction effect could have occurred where the light rays created some destructive interference. This interference appeared in the images as broken, blurred, or distorted images. Another source of distortion was the thickness of the lens itself. The amount of light coming out of the lens was considerably lower than the amount going into it.
The three lenses that were used had the same basic shape. The major difference was the length of the stem protruding from the center of the lens. The three different lengths (short (S), medium (M), and long (L)) were used to mimic three types of gravitational field sources. The longer the stem of the lens, the more concentrated the gravitational field that it represents. Therefore, lens L was the closest approximation to a gravitational point source, while lens S most closely mimicked a large galaxy. By using the three types of lensing and running the experiment with two different angles for the light, we were able to create a wide sampling of images for our qualitative observations.
There
were several general characteristics that could be observed in all of the three
lenses when light struck them at right angles to the plane of the lens. The
images formed on the screen depended solely on the position of the point within
the imaging field.
When the point was placed at the exact center of the imaging field, a ring
image was produced. The outer ring was also produced by the lenses, except for
the situation where the aperture prevented the light from reaching the outside
of the lens. In those cases, the broken ring image was produced.
All of the other images formed by these lenses were linear arrangements.
Depending on the position of the pinhole in the imaging field, different
combinations of images were produced. The imaging field contained a slightly
brighter circular portion in the center that had a radius of approximately
one-third to one-half the radius of the entire field. When the pinhole was
placed in this central region, distinct five part images were produced. These
images consisted of the dim, fuzzy central point; a twin pair of very bright
points; and a pair of arcs on the outside. The central point was the small
portion of light that came straight through the lens. The twin points were the
main part of the image and were formed from light that was refracted from all
parts of the lens. The outer arcs were degenerate forms of the outer ring.
The central location of the twin points meant that light had to be refracted
less in order to form the image. Between these two points, the one closest to
the center of the field was the brighter one for the same reasons as stated
above.
When the pinhole was placed in the outer part of the imaging field, linear
patterns were still produced but the arcs were no longer formed. These images
had three parts, consisting solely of points. As in the previous images, the
point closest to the center of the imaging field appeared the brightest. Most
of the points formed were very dim, and the main point was almost too faint to
appear on the large screen. If the pinhole was placed too close to the edge of
the imaging field, several distortions occurred. Because of the extreme
refraction of light required to create these images, they were sometimes
created in a slightly non-linear position. Another effect was that some of the
images were too dim to be seen on the large screen because not enough light was
refracted through the pinhole. Other distortions included one point splitting
into two fuzzy images that appeared right next to each other.
The orientation of the linear image was dependent on the positioning of the
pin hole as well. When the pinhole was placed above or below the center of the
field, the linear images were aligned vertically. Similarly, a pinhole to the
left or right of the center created linear images that were aligned
horizontally. The general rule for the orientation of the images was that they
were aligned parallel to a line connecting the center of the field to the
pinhole.
All
three of the lenses produced very similar images when they were rotated
45o with respect to the light rays. With this set up, no rings and
almost no linear images were produced. The great majority of the images were
combinations of arcs and points, broken rings, Einstein crosses, and other
non-linear arrangements.
One of the most interesting features observed was the combination of a bright
point and a bright arc. The arc was unique in that its outside edge was
pointed towards the center of the field. These two images were usually
accompanied by much fainter images of points arranged in relatively symmetrical
patterns around the two central ones. The arc would sometimes be imaged as a
broken arc. This occurred when the pinhole was placed towards the outside of
the imaging field. It is therefore most likely that these broken arcs are
actually the degenerate form of the complete arc.
Images consisting of only points were not as common as in the other part of the
experiment. Rather, the points usually formed along with an arc-type image.
When the image did consist of only points, they were never in a linear
arrangement. The points actually seemed to lie on a curve that pointed towards
the center of the field with the brightest image of the group.
Another combination of points that was seen several times was the three part
image that was arranged in the shape of an equilateral triangle. This image
contained the hazy central point, which once again represented an image formed
from light that came through the lens without refracting. These images were
also accompanied by some form of a degenerate arc, whether it be two points or
an arc that was about to split into two points.
The Einstein cross was the only symmetrical pattern to be imaged when the lens
was aligned in this fashion. The image was formed when the pinhole was placed
slightly off of center in the imaging field. By making very slight adjustments
in the alignment of the apparatus, an image with an exact perpendicular
arrangement could be seen. The pinhole could be shifted slightly in any
direction and still produce an Einstein cross. However, the image did not form
in the same uniform, perpendicular arrangement. The image was dominated by
four main points which were the brightest part of the image. This could be
seen on the large screen as well. The image also contained the central fuzzy
spot, indicating that light had been able to pass straight through the lens.
The cross was also accompanied by a second cross that could be seen outside of
the brighter one. This image was very dim, slightly non-linear, and the top
point was missing. This second image was probably formed from light being
lensed from the outside edge of the lens.
The three different lenses produced slight alterations between their images. This was much more noticeable when the lenses were tested with the light coming at a 45o angle to them. In this part of the experiment, several consistent observations were made. The lens with the longest stem was also the thickest. The greater the thickness of the lens, the greater the angle of refracted light produced. As the length of the stem on the lens became larger, the imaging field contracted in the plane of the angular deviation. The lens with the long stem also created images that were more tightly contracted in the horizontal plane for the same reason. The thickest lens also created the most variations in the types of images produced.
The
images produced by light striking perpendicular to the plane of the lens
created several variations when compared with those images that were produced
when the light rays passed through the lens at the 45o angle. When
the lens was arranged facing the light, all of the images formed were
symmetrical to the center of the imaging field. The basic images were the
rings, the symmetrical arrangements of the arcs and points, and the degenerate
forms of these images. The only exceptions were the distortions when the
images were produced from the edge of the imaging field.
In contrast, most of the images created by the second part of the experiment
were not symmetric to the origin. The great majority of the images were
nonlinear images of points and combinations of points and arcs. There were
also many more degenerate images produced. The only symmetrical images that
were produced were the Einstein crosses, and these were only formed at one
specific alignment of the pinhole with the imaging field. The arcs in these
images were inverted so as to point in the opposite direction than the arcs in
the first part of the experiment. The systematic alignment of the images in
relation to the angular position that was seen with the other data set did not
appear for these images.
In conclusion, we can say that the linear images were only formed when the lens
and the pinhole were carefully aligned to produce the image. If there was any
significant deviation from these conditions, the images were no longer
symmetrical or as predictable.
The three lenses that were used represented three different types of gravitational lenses. The thickest lens represented the most concentrated warping of space-time, as in the case of a black hole. The thinnest lens is representative of a more diffuse gravitational field, such as a distant galaxy or galaxy cluster. The first part of our experiment involved lenses that were aligned so that plane of the lens was perpendicular to the direction of the light beam. In space, there is usually not such a perfect alignment of point source, lens, and viewing position. Some angular deviation of the gravitational object in space so that the lens is not aligned with the light rays is more common. This was tested for in the second part of the experiment. There are, however, many more variations in space that can produce diverse images that were not tested for in our experiment.
|
|
The image on the left was found by using the long lens at 90o relative to the light source. The pin hole was positioned at the center of the refracted image on the cardboard. The picture on the right was taken by the Hubble Space Telescope. Both exhibit characteristics of the Einstein ring formation. (See section IV.B.2.)
|
|
The image on the left was found by using the medium lens at 90o relative to the light source. The pin hole was positioned 1/5 of the radius out from the center of the refracted image on the cardboard. The picture on the right was taken by the Hubble Space Telescope. Both exhibit characteristics of the twin arc formation. (See section IV.B.3. for futher information on arcs.)
|
|
The image on the left was found by using the short lens at 45o relative to the light source. The pin hole was positioned at 1/2 the vertical radius away from the center of the refracted image on the cardboard. The picture on the right was taken by the Hubble Space Telescope. Both exhibit characteristics of the giant arc formation. (See Section IV.B.4.)
|
The image on the left was found by using the short lens at 45o
relative to the light source. The pin hole was positioned 3/4 of the radius
out from the center of the refracted image on the cardboard. The picture on
the right was taken by the Hubble Space Telescope. Both exhibit
characteristics of the non-linear point formation. (See section IV.B.6.)
|
|
The image on the left was found by using the short lens at 45o relative to the light source. The pin hole was positioned at the center of the refracted image on the cardboard. The picture on the right was taken by the Hubble Space Telescope. Both exhibit characteristics of the Einstein cross formation. (See section IV.B.7.)
