Now you're probably wondering ... at a time when, the bigger the optic - the
better the observing (otherwise known as aperture fever) where is this guy
coming from. Well ... some years ago (ca. 1990-91) I wanted to know what the
limits of observing with
the minimum of optics might be. I wondered if sunspots could
be visible through a pinhole camera. It turned into a physics project that
I eventually published in TPO Magazine titled: "PINHOLE SUNSPOTS - Or,
Could the Ancient Egyptians Have Observed Sunspots?". Anyway, this is about that project as well
as some links to other pinhole sites, including one that uses a CCD camera
and pinholes to observe stars. - BDM.
or, Could the Ancient Egyptians Have Observed Sunspots?
Could the early Egyptians have viewed sunspots? Or, for that matter, is it even possible
that any early peoples could have observed these solar blemishes before the discovery of
the telescope and its application to astronomy by Galileo? Non-telescopic observations
are not limited to just ‘naked-eye’ observing on a hazy day as one might surmise. There
is one optical device for which the technology has been available for thousands of years
if some curious individuals were only around to serendipitously stumble upon it. This
technology is that of the pinhole camera, an optical instrument consisting of only a
small circular hole and a screen upon which to project an image. Pinhole observation of
sunspots? Hum-bug, you say? Well, maybe not.
First, let me relate a little historical trivia concerning early solar observations,
and pinhole imagery, although not necessarily related to one another.
- Early Chinese astronomical records reveal that large sunspots had been
visually observed a thousand or more years prior to the renaissance discoveries.
- Solar, as well as stellar, alignments of corridors in the Great Pyramid
at Gisa have lead some archaeologists to interpret them as having been used for
astronomical observations while under construction.
This short treatise is by no means a proof of some archaeological certainty. Especially
in the light of the circumstantial evidence just presented. It is, rather, a unique
attempt to illustrate some of the criteria required to ascertain the degree of
resolution of sunspots that might be observed using pinhole optics and to discuss a
simple experiment in which the derived theoretical results are proved.
- In the late 1700s a pinhole projected image was recorded to have been
accidentally observed by a Bedouin in his tent when he noticed an inverted view
of the people outside appearing on his tent wall, this image being projected
through a small hole in the wall opposite.
- Solar eclipse observers have noticed for hundreds of years, possibly much
longer, the crescent images of the Sun produced when the light from the partial
eclipse phases passed through small gaps between the leaves of trees.
Pinhole Optics and Resolution
Most optical devices rely on refraction or reflection to provide an image on a screen
or film plane. A pinhole camera is a device which uses neither lenses nor mirrors to
produce its image, but rather only a small circular aperture, or ‘pinhole’. This
apparent lack of what one might consider an imaging optic does not mean that such an
arrangement of hole and screen cannot produce an image. It does and with the greatest
depth of field. What it looses when comparing it to other optical instruments is its
light gathering capabilities due to the relatively small aperture to screen distance
ratio, i.e. the inverse square law. However, even with this shortcoming it still is a
candidate for observing the sky’s brightest object, the Sun.
Now the questions begging to be answered are:
The resolution of any optical instrument is the limit established by the diffraction
pattern, a property resulting from the wave nature of light, as it passes through any
finite aperture (Figs. 1a and 1b).
- Can such a device actually resolve details such as sunspots on the Sun’s
- Is there an optimum resolution for such an instrument?
Consider two point sources. Each point will be
imaged through an aperture as a central maximum of intensity, or Airy Disk (after
physicist George Airy 1801-1892), surrounded by alternating dark and light diffraction
rings. If the points are close, the diffraction patterns will overlap (Fig. 2).
Two points are resolved by an optical instrument when the image separation reaches
0.61X/Sin(u), where X = the wavelength of light and u = the angle formed by the
aperture radius and the screen distance (Fig. 3).
This method for determining the
resolution is known as the Raleigh Criterion and is a mathematical description of when
the maximum of the diffraction pattern from one point source coincides with the first
dark ring by the second point source, and where there is a clear separation of the
intensity maxima in the combination pattern, i.e. You can still discern two points,
not two so close they appear as one.
The equation defining the radius Z from the center of the Airy Disk to the first dark
ring of a diffracted point image may then be defined as:
If a screen is placed some small distance behind a small aperture where a bright
object (the Sun?) is on the other side of the aperture, an image of the object will
be produced by the light rays passing from the object straight through the ‘pinhole’
and onto the screen. However, if the screen is too close to the hole, no image will
result since some distance is required for an image to be formed. If the screen is
placed too far from the hole then diffraction effects (interference phenomena of the
light photons due to there inherent wave nature) will come into play degrading the
image. Therefore, there must be some optimum distance from the pinhole to the screen
at which the image produced will be clearest, i.e. maximum resolution.
Z = 0.61X/Sin(u) = 0.61Xl/r
Z = radius of the first dark ring of the Airy Disk|
X = wavelength of the light
l = aperture to screen distance
r = aperture radius
The maximum resolution for an aperture having no lens or mirror should occur when the
radius of the pinhole equals the radius of the central maximum of the Airy Disk,
i.e. Z = r. Then the equation becomes:
Assuming visible light to have an average wavelength of approximately 5.5x10-7 mm
(550 nanometers) and multiplying each side of the equation by a factor of two to
obtain the pinhole diameter, the relationship of the optimum pinhole diameter to
screen distance becomes:
r2 = 0.61xl, and r = sqrt (0.61Xl)
Choosing several pinhole diameters and entering them into the latter expression results
in a list of optimum screen distances for each pinhole. By taking these computed
distances and knowing the angular diameter of the Sun (32 minutes of arc), the resultant
solar image diameters produced at the screen may be calculated thereby giving an
indication as to which screen distance to pinhole diameter relationship might be optimum.
If the resulting solar image diameter is divided by the pinhole diameter a relative
resolution criteria indicator (relative to each other) is obtained since the pinhole
diameter is a measure of the limit of the resolution in our situation (when
we substituted Z = r).
d = sqrt(0.610.00055l) = 0.0366sqrt(l), or|
l = 745d2||where:||
d = pinhole aperture diameter (in mm), and |
l = aperture to screen distance (in mm)
Plotting the Relative Resolution vs. Pinhole Diameter (Fig. 4) results in a distinct
proportional relationship which forces us to the, seeming odd sounding, conclusion
that the larger the pinhole, the better the relative resolution of the solar image.
The limit then is the distance at which the solar image becomes too dim to see due to
increased hole-to-screen distance.
Testing the Optimum Resolution and Screen Distance
To test the aperture diameter to screen distance theory, I first simulated the Sun by
taking a 375 watt flood lamp, placing a mask in front of it having a circular opening
of 3.0 cm diameter and positioning it 3.2 meters from a sheet of aluminum foil into
which had been poked three holes of 1, 2 and 3 mm diameter (Fig. 5).
diameter to distance ratio simulated the same angular diameter as the Sun (about 0.5
degrees). I then placed a screen behind the pinholed foil and searched for the optimum
distance at which each projected image appeared clearest. The distances obtained
were 0.7-0.8 m, 2.8-3.1 m and 6.5-7.0 m, respectively. These results correspond
well with the calculated results in Table I.
Diameter in mm
Distance in M
Diameter in cm
| 1 || 0.745 || 0.69 || 6.9 |
| 2 || 2.98 || 2.8 || 14.0 |
| 3 || 6.2 || 6.2 || 20.6 |
| 4 || 11.9 || 11.1 || 27.8 |
| 8 || 47.7 || 44.4 || 55.5 |
| 16 ||190. || 177. || 111. |
| 32 ||760. || 707. || 221. |
I then placed a strip of paper 1.5 mm in thickness across the simulated Sun to see
if the projected images would resolve this 1/20 solar diameter object. It did, and
very clearly, in all cases which lead me to believe that at least large sunspots would
be visible in a pinhole projection.
The Sunspot Projection Experiment
Rather than build a huge stone observatory pyramid or other clumsy pinhole observing
device, since long pinhole to screen distances were required, and my research budget
was minimal, I decided to ‘cheat’. I decided to use a reflection pinhole. I acquired
a first-surface mirror to reflect the Sun’s light which would allow me to direct the
Sun’s light with very little effort over the long distance needed to attain a
sufficiently large projected solar image.
The small mirror was mounted with masking tape on the head of a camera tripod for
stability and maneuverability. I then chose a sufficiently large hole by taking another
strip of masking tape, punching a hole in it with a commercial paper hole-punch, and
affixing the tape to the mirror surface. This produced a mini-mirror pinhole
aperture (d) of 5.9 mm diameter. Calculating the optimum screen distance (l) for
the clearest image resolution (25.9 m), I placed the tripod behind Sperry Observatory
(at Union County College, Cranford, NJ) so that I could reflect the Sun’s image through
the rear door onto a white oak-tag screen set up in the darkened building (Fig. 6).
The resulting solar image was 24.1 centimeters in diameter. Noting several sunspots
visible, I proceeded to trace their images onto the screen (This is much more difficult
than it sounds since the Sun is a fast moving target, particularly at this projection
size and no tracking involved. Several attempts were made at marking the sunspot positions
and shapes to assure reasonable accuracy.) Five sunspot were easily identified
(Fig. 7a), two very large and three moderately sized ones. After acquiring this
data I made projection drawings using a 4-1/2 inch reflector for comparison onto a
standard size solar observing sheet.
To make the two sets of data comparable in size, I Xerox reduced the pinhole projected
data using the proper reduction ratio to make the two drawings of equal size. Also,
instead of copying onto paper, the reduction was made onto clear sheet Mylar which
allowed me to flip the image over since the pinhole projected image had been left-right
reversed with respect to the standard drawing.
Comparison of the drawings reveals very similar images. The only differences are:
the three very small sunspots in the 4-1/2 drawing that do not appear in the data
from the pinhole projection; and the degradation of detail around the pinhole projected
spots is of much lesser quality.
Notes and Conclusions
The only optical imaging problem I encountered was thermal air turbulence due to the
solar image being projected parallel to the ground from the cold outdoors into the
warm observatory. This, however, did not appear to degrade the image in any great detail.
The intensity of the 24 cm solar image was easily bright enough for viewing and a
larger pinhole could have been chosen, at least one producing twice the projected
solar diameter. However, increasing it much beyond this would decrease the image
intensity to the point that much of the gained detail (due to the greater relative
resolution) would probably be lost to a dim image since the intensity of the image
decreases geometrically as a function of d/l2.
Comparing the results in Fig. 7 clearly indicates that the large sunspots, as well
as those of moderate size, could easily have been viewed using pinhole projection by
some ancient observers had they been so inclined.
Astronomy Pinhole Web Sites
Comet Pinhole Photography
- This page documents
the making of a movie of Comet Hyakutake using a pinhole camera and a CCD.
Stars and constellations are also captured in the images. - Peter McCullough,
University of Illinois
- During the June 10, 1994 annular
solar eclipse, the Indiana University Astronomy Department had pinhole
cameras set up around the observatory for the public to view the partial phases.|
Maintained by BDM