INTRODUCTION. Photometry in astronomy means the
measurement
of stellar brightness. Instruments include the human eye,
phototubes
and solid-state detectors, and the new CCD cameras. The
brightness
of any given star seen from earth depends on two factors: the intrinsic
brightness, or size, of the star, and the distance of the star from
earth.
The intensity of starlight as a function of distance follows a
well-known
mathematical relationship. This relationship will be investigated
with an artificial star in the lab (a Light Emmiting Diode - LED) and a
CCD camera. Because other astronomical measurements, such as
color,
can determine a star's intrinsic brightness, the brightness seen from
earth
can be used to determine the distance of the star from earth.
Camera. The CCD camera is fitted with a normal
photographic
lens rather than a telescope. For astrophotography the telescope
serves as the camera "lens", with a much longer focal length. We
will make electronic digital photographs of the LED "star" from several
different positions. We will also take a "Dark" image for
each distance of the LED. The dark image will be obtained by
keeping all parameters identical and turning off the diode power.
The room is not completely dark, but that is OK. We will later
subtract the "dark" image. Each image is saved with a filename
that indicates the distance and the time exposure. The camera is
the color DSI and is controlled by the software "envisage", and the
lens is a 50 mm FL attached through a T-Thread to C-Thread
adapter. The lens aperture is set to f/11. The exposure
times for the 1.0 meter distance is 0.04 sec.
Analysis. Immediately
after recording each image and the dark frame, both the image and
several dark frames are loaded into the analysis software:
MaximDL.
Since these are digital images, we can perform simple arithmetic on the
images. We will subtract the average dark frame from the original
image
to obtain the net image which is the image due to the diode
alone. We will measure the brightness of the star for each
distance using a "Photometry" tool in MaximDL. Set-up the radius
of the aperture to 9 pixel radius, gap to 8 pixel, and sky annulus to
10 pixel thickness.
Enter your data in your notebook in a table similar to that shown
below.
Do NOT use this paper for your data; use your data book!
Any hand-out with data on it will be torn-up by the instructor!
We will record data with the distance ranging from 1.5 m to 6.0 m.
| Distance - LED to Camera (m) | Exposure Time (sec) |
Star Brightness (ADU) |
Star Intensity (ADU/sec) |
Normalized Intensity |
Inverse Square |
| 6.0 |
If you missed the lab and need the data, get the data from classmate.
Data Plot. Plot the distances on the horizontal axis and the intensity on the vertical axis. Be sure to plot each data value as a distinct symbol such as an "o" or an "x". Connect the plotted points with a smooth curved line. Compare the plotted graph with what you expected earlier.
Normalized plot. This section requires a calculator and it requires extending the data table. In order to observe the mathematical form of the intensity vs. distance we will first normalize the intensity. This means divide each intensity by the largest intensity. The largest normalized intensity will have the value of 1.0. Make a new plot showing the normalized intensity vs distance. It should look very similar to the first plot but the numbers will be different.
Inverse square plot. It is hypothesized that intensity of a point source should diminish as the inverse square of the distance from the source. To test this relationship we will plot an inverse square of the distance (normalized) vs distance as well as the normalized intensity. For each of the data distances d, calculate the following quantity: (d0/d)2 where d0 is the smallest distance in the data set. Make another column in the data table: (d0/d)2 . Plot this quantity on the same graph as the normalized intensity vs d. Be sure to use different symbols for the inverse square plot. If there is good agreement between the inverse square plot and the normalized intensity plot, then the intensity follows the inverse square law. Be sure to write your conclusions in your notebook and summary. In a later activity we will set up a computer spreadsheet to calculate these items and to plot using computers.
Note: Your summary should include the expanded data
table
and it should include 2 graphs: 1) the original data plot
of
intensity vs. distance. 2) the normalized plot and the inverse
square
plot overlaid on the same axes. The graphs should be plotted by
hand
on graph paper. The summary should describe the layout of the
experiment
and show a conclusion.