Using a Laser Pointer to Measure the Data Track Spacing on CDs and DVDs
Objective
The objective of this project is to learn how to use a
diffraction pattern to measure the pitch
(spacing) of the data tracks on
CDs and DVDs.
Introduction
CDs and DVDs are everywhere these days. In fact, you probably
receive one free in the mail every month or two as an advertisement for an
Internet service provider.CDs and DVDs store huge amounts of binary data
(patterns of 0's and 1's) which your player can "read" with a laser, lenses,
light detector, and some sophisticated
electronics.
CDs and DVDs are both multi-layered disks, made mostly of
plastic. The layer that contains the data (DVDs can have more than one
data layer) consists of a series of tiny
pits, arranged in a spiral, tracking from the
center of the disk to the edge. The data layer is coated with a thin
layer of aluminum or silver, making it highly reflective.
How small are the pits?
Well, their diameter is 500 nanometers (nm). How small is that? A millimeter
(mm), which you can see with your unaided eye, is one-thousandth of a meter.
Imagine how much you have to shrink a meter to get down to the size of a
millimeter. Now imagine shrinking a millimeter by the same amount. That takes
you down to a micrometer (μm), or one-thousandth of a millimeter. You have to
shrink a micrometer one thousand times more to get down to the size of a
nanometer. A typical human hair is about
100 μm wide. The pits on a CD are 0.5 μm
wide. So you could fit 200 pits across the width of a typical human hair! The
diameter of the pits is also similar to the wavelengths of visible light (400 to
700 nm).
On the CD, the pits have some blank space ("land") on either
side of them. This means that the adjacent data tracks of the spiral are
regularly spaced (something like 3 times the pit diameter). This regularspacing
of the spiral tracks, slightly larger than the wavelengths of visible light,
produces the shimmering colors you see when you tilta CD back and forth under a
light. The colors result from diffraction of the white light source by
the CD.
What is diffraction? That is a bit harder to describe, so
we'll start with a related concept that is easier to understand: interference.
Interference is what happens when waves collide with each other. If the peak of
the first wave meets the peak of the second wave, the peaks add together to form
a higher peak. If the trough of the first wave meets the trough of the second
wave, the troughs add together to form a lower trough. If the peak of the first
wave meets the trough of the second wave, the peak is made smaller. And if the
peak of the first wave is the same size as the trough of the second wave, they
can actually cancel each other out, adding to zero at the point of interference.
You can see a demonstration of interference with the Ripple Tank Applet link in
the Bibliography.
The first screen shot shows the results of a single wave source (choose
"Setup: Single Source" from the first drop-down list and "Color Scheme 2" from
the fourth drop-down list). To avoid the complications of ripples reflected from
the walls of the tank, click on the "Clear Walls" button (simulates an
infinitely large tank, so reflections are eliminated):
The second screen shot shows the results of two wave sources (choose
"Setup: Two Sources" from the first drop-down list):
The diagonal black lines are regions of destructive interference (where peaks
of one wave met troughs of the other). If you run the applet yourself, you'll
see that, though the waves keep moving, these regions are a steady feature. This
is a simple example of patterns that can form when waves interfere in
well-defined ways.
There are many more simulations you can try with the Ripple Tank Applet to
give you a better understanding of interference and diffraction. Take some time
to explore with it.
When there are a large number of wave sources, or an array of
obstacles that a wave interacts with, the result is usually described as
"diffraction" rather than "interference", but it is basically the same
fundamental process at work.
So, how can you use diffraction to measure the data track
spacing on a CD or DVD? The diffraction pattern from a bright, monochromatic
source (e.g., a laser pointer)
interacting with a regular structure can be described by a fairly simple
equation:
|
d(sin θm - sin θi ) = mλ
(Equation 1) |
-
In this equation, d is the spacing of the
structure (in this case, the data tracks).
-
θm is the angle of the mth
diffracted ray, and θi is the angle of the incident
(incoming) light. Both angles (θm and θi)
are measured from the normal, a line perpendicular to the diffracting
surface at the point of incidence (where the light strikes the CD).
-
m is the order of the diffracted ray. The
reflected ray (when θm = θi) has order 0
(zero). Rays farther from the normal than the reflected beam have order 1,
+2, +3, etc. Rays closer to the normal have order −1, −2, −3, etc. In
certain cases, for example very small d, some or all of the negative
m orders may actually be diffracted through such a large angle that
they are on the same side of the normal as the incident light. When the
diffracted beam is on the same side of the normal as the incident light, the
angle for the diffracted beam is negative.
-
λ is the wavelength of the light.
The Experimental Procedure section will show you how to
produce and measure a diffraction pattern with a CD and laser pointer. It will
also show you how to use the equation to calculate the track spacing.
Terms, Concepts and Questions to
Start Background Research
To do this project, you should do research that enables
