\setcounter{figure}{0}
\setcounter{table}{0}
\hspace*{3.0in}Name:{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}


\begin{Large}
\section{\bf Reflectance Spectroscopy}
\end{Large}
 
\subsection{Introduction}

With this lab, we will look at the wavelength dependence of the visible reflectance of various objects, and learn what this can tell us about the composition of those objects.  This is one technique by which we determine the composition of various solar system objects ({\it e.g.} Martian rocks, asteroids, clouds on Jupiter).  We will specifically apply this method of investigation, using a hand-held reflectance spectrometer, to the reflectance characteristics of several different colored sheets of construction paper.  We will then use these known spectra for different colors to identify some ``mystery'' objects for which we know only their reflectance as a function of wavelength.\\
\\
We will use an ALTA reflectance spectrometer for this lab.  This is an instrument that can quantitatively measure the reflectance in nine wavelength channels covering visible and near infrared wavelengths.  The ALTA reflectance spectrometer provides measurements in units of millivolts. As the intensity of the measured (reflected) light changes, the displayed number (voltage) will change in the same proportion.  That is, if the intensity of measured reflected light decreases by a factor of two, the displayed value will also decrease by a factor of two.  What we will ultimately be interested in for each wavelength and for each object is the percentage of incident light that is reflected.  That is, if all the light of a particular wavelength is reflected, that object has a 100\% reflectance at that wavelength.  If none of the incident light is reflected (it is all absorbed), the object has a zero-percent reflectance at that wavelength.\\
\\
When we apply reflectance spectroscopy to solar system objects, the Sun is the source of the light that is reflected.  Thus, if we know the spectral characteristics (intensity as a function of wavelength) of the Sun, we can measure the intensity of reflectance at our chosen wavelengths accurately.  With the ALTA reflectance spectrometer, we do not use sunlight as our `source'.  Rather, the spectrometer itself has nine bulbs (arranged in a circular pattern) that emit light of specified wavelengths (indicated on the buttons on the front of the instrument) and one detector which measures reflected radiation.  The emitted light reflects off the object of interest and is measured by the detector located at the center of the circular pattern of bulbs. By proceeding through the nine wavelengths, we obtain the intensity of reflected light at each wavelength, and from this we can determine the reflectance spectrum of our objects of interest.

\subsection{Exercises}

Start by pressing one of the wavelength buttons on the front of the spectrometer and while depressing this button, turn the spectrometer over.  You should see one of the bulbs arranged in a circular pattern illuminated (unless you are pressing one of the two near-infrared wavelength buttons).  Release the button you are holding and press a different button; you should now see a different bulb illuminated.  Remember, the `bulb' at the center is actually the detector, which measures the reflected light.

\begin{enumerate}
\item  Our first order of business is to determine what the instrument signal is when no light is available.  This is called the {\it dark voltage} value and must be subtracted from all subsequent measurements with the spectrometer.  Turn the spectrometer on and set it down on the table; the value currently in the display area is the dark voltage.  Write this number down, as it will be subtracted from all subsequent measured values. Also write the unit number or letter of the spectrometer. ({\bf 2 points})\\
\\
{\bf DARK VOLTAGE READING = \hrulefill}\\
{\bf SPECTROMETER \# or Letter = \hrulefill}\\
(located in the upper right corner on the front of the spectrometer)

\item  Now, since our spectrometer is not calibrated (we do not know what millivolt values to expect for 100 percent reflection, and there is no reason why this value must be the same for each wavelength), we will use a piece of white poster board to determine the `standard' against which our reflectance spectra of several colored papers will be compared.  In order to do this, we will measure the value (in millivolts) of reflected light from the white poster board for each of the nine wavelength channels of the spectrometer.  Do this by:\\
\begin{itemize}
\item{Placing the spectrometer onto the white poster board}
\item{Sequentially pressing the nine wavelength buttons on the spectrometer}
\item{While pressing each button, note the millivolt value that appears in the display and write this value down in Measured Value column of Table~\ref{voltage-tab} for the appropriate wavelength}
\end{itemize} 

Remember, we are measuring the intensity of the light that has been: a) emitted by the spectrometer bulb, then b) reflected off the poster board, and then finally, c) measured by the spectrometer.\\
\\
Since it is a white surface that we are measuring the reflectance from, we will expect that the reflectance (percent of light reflected) will not vary too much among the nine wavelengths (since `white' is the combination of all wavelengths).  We will assume that each wavelength is 100 percent reflected from the white surface.  After determining the measured `calibration' values for each wavelength, subtract the `Dark Voltage' value from these calibration values to obtain the `standard' value for each wavelength, and write these values in the right-hand column of Table~\ref{voltage-tab}.  ({\bf 9 points})
\vspace{1in}
\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c|c|c|}\hline
{\bf Wavelength} & {\bf Measured Value} & {\bf Standard}\\ 
(nanometers) & (millivolts) & (Measured - Dark Voltage)\\ \hline \hline
470 &  & \\ \hline
555 &  & \\ \hline
585 &  & \\ \hline
605 &  & \\ \hline
635 &  & \\ \hline
660 &  & \\ \hline
695 &  & \\ \hline
880 &  & \\ \hline
940 &  & \\ \hline
\end{tabular}
\caption{White poster board calibration determination.  (Recall that 1 nanometer = 10$^{-9}$ m = 1 billionth of a meter.)}
\label{voltage-tab}
\end{center}
\end{table}

\item  Rather than comparing the reflectance spectra of rocks on Mars, as the Mars Pathfinder camera did, or clouds on Jupiter (as the Voyager and Galileo spacecraft have done), you will obtain and compare the reflectance spectra of several different colors of construction paper.  When you have measured the spectra of the three pieces of colored paper, you will plot their spectra.\\
\\
For each piece of colored paper,
\begin{itemize}
\item  Measure the reflectance of that piece of paper at each wavelength in the same manner as you determined the spectrometer's `Measured Value' above, writing the corresponding millivolt value for each wavelength in the Meas. column in Table~\ref{specdata-tab}.
\item  For each wavelength for each piece of paper, calculate the Measured minus Dark Voltage value.  To do this, subtract your instrument's Dark Voltage value from the Meas. column value at each wavelength for each colored piece of paper.
\item  Determine the Reflectance value of each colored sheet of paper at each wavelength using the formula below, in which `STANDARD Value' is the value in the right-most column of Table~\ref{voltage-tab} at the appropriate wavelength. The REFLECTANCE values you arrive at should have values between 0 and 1. Write your calculated reflectance values in the ``Reflect." columns of Table~\ref{specdata-tab} for the appropriate colored piece of paper. ({\bf 20 points})
\end{itemize}

{\bf Reflectance} = $\frac{{\bf Measured Value - Dark Value}}{{\bf STANDARD Value}}$


\begin{table}[htbp]
\begin{center}
\begin{small}
\begin{tabular}{|c||c|c|c||c|c|c||c|c|c|}\hline
{\bf $\lambda$} & \multicolumn{3}{c||}{\bf Red Paper} & \multicolumn{3}{c||}{\bf Green Paper} & \multicolumn{3}{c|}{\bf Blue Paper}\\ \hline 
(nm) & Meas. & Meas.-Dark & Reflect. & Meas. & Meas.-Dark & Reflect. & Meas. & Meas.-Dark & Reflect. \\ \hline \hline
470 & & & & & & & & & \\ \hline
555 & & & & & & & & & \\ \hline
585 & & & & & & & & & \\ \hline
605 & & & & & & & & & \\ \hline
635 & & & & & & & & & \\ \hline
660 & & & & & & & & & \\ \hline
695 & & & & & & & & & \\ \hline
880 & & & & & & & & & \\ \hline
940 & & & & & & & & & \\ \hline
\end{tabular}
\caption{ALTA Reflectance Spectrometer Values (millivolts)}
\label{specdata-tab}
\end{small}
\end{center}
\end{table}

\item  On the sheets of graph paper at the end of this lab, plot the Reflectance values [column 3 Reflect. values in Table~\ref{specdata-tab}] you have calculated for each of the 3 colored pieces of paper. For each piece of colored paper and the calculated Reflectance values, draw a dot at the appropriate Reflectance value (y-axis) and appropriate wavelength point (x-axis). After you have drawn all 9 dots for a single sheet of colored paper, connect the dots. This curve you have drawn is a {\bf Reflectance Spectrum.}  Repeat this procedure for your Reflectance results for the other two sheets of colored paper. Clearly label your three resulting curves. ({\bf 15 points})

\item  Compare your three curves (reflectance spectra of the colored sheets of paper) with the spectra of the two mystery objects (A and B).  The two mystery curves are the spectra for two separate objects.  These objects are included among those listed below.  Using your knowledge of the color of the objects in the list below, a) determine which object each of the mystery spectra corresponds to, and b) describe below how you have made this determination.  You may find it useful to refer to Figure 6.6 on page 157 of your text to relate wavelength to color.  ({\bf 7 points each})
\begin{center}

\begin{tabular}{|c|c|c|}\hline
Tomato & blade of grass & White Paper\\ \hline
Black Paper & Eggplant & Navel Orange\\ \hline
Pink Flamingo & Neptune (page 215 of text) & Lemon\\ \hline
\end{tabular}
\end{center}

{\bf Object \# ~~~~~~~~:}\\
\vspace{1.5 in}


{\bf Object \# ~~~~~~~~:}\\
\vspace{1.5 in}

{\bf Mystery Planet:}\\
The last graph in this lab shows a reflectance spectrum for a newly discovered planet that was just visited by a NASA spacecraft.  Does this planet have vegetation on its surface?  Justify your answer.  ({\bf 5 points})\\
\vspace{2in}

\begin{figure}[htbp]
\centerline{{\includegraphics[width=21cm]{reflect_red.jpg}}}
\end{figure}

\begin{figure}[htbp]
\centerline{{\includegraphics[width=21cm]{reflect_green.jpg}}}
\end{figure}

\begin{figure}[htbp]
\centerline{{\includegraphics[width=21cm]{reflect_blue.jpg}}}
\end{figure}

\begin{figure}[htbp]
\centerline{{\includegraphics[width=21cm]{reflect_planet.jpg}}}
\end{figure}
\mbox{ }

\end{enumerate}
\newpage
~ ~ ~\\
\newpage
\hspace*{3.0in}Name:{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}\\

\subsection{Take Home Exercise (35 points total)}

On a separate sheet of paper, answer the following questions:

\begin{enumerate}

\item  Why does the planet Jupiter appear brighter in the night sky than Mars, even though Mars is much closer to Earth than Jupiter?  [Hint: the third column in Table 8.1 on page 200 of your textbook might be helpful.] ({\bf 10 points})\\

\item  Imagine that the colored lightbulbs in the Alta reflectance spectrometers emitted twice as much light as they actually do. In this brighter bulb situation, would you determine ``Reflect.'' values that are the same as those you have written in Table~\ref{specdata-tab}, or would you determine different (larger, smaller) Reflect. values with these brighter bulbs? Why? ({\bf 10 points})\\

\item  Clearly describe a concept you have learned in this lab, or last week in class, during our discussions about radiation.  Describe something that you have not already addressed by answering other questions in this lab. ({\bf 15 points})\\
\end{enumerate}

\subsection{Possible Quiz Questions}

\begin{enumerate}

\item What is meant by the term ``wavelength of light''?

\item What are the physical units of wavelength?

\item What is the definition of the word ``spectroscopy''?

\item If a blade of grass is ``green'', why does it look green?

\end{enumerate}

\subsection{Extra Credit (ask your TA for permission before attempting, 5 points)}

Look up the spectrum of chlorophyll. Note that a spectrum can either
be a ``reflection'' spectrum or an ``absorption'' spectrum. One is simply the
inverse of the other. So, depending on the author's preference, they will
plot one or the other type of spectrum for chlorophyll. Chlorophyll
is why most plants look green. Describe how chlorophyll interacts with
light. What does chlorophyll do for plants? Why do you think it works
this way? Rocks, ices, and gases all have complicated spectra, absorbing
some wavelengths of light, and reflecting (or transmitting) others.
The uniqueness of the spectra of these items allows astronomers to
determine the composition of an object by using spectroscopy.\\
\clearpage
~ ~ ~\\
\newpage
