Laser Tracking on the CD Scaled Views of a Compact Disc

<strong>Laser</strong> <strong>Tracking</strong> on the CD
The laser beam in the compact disc player must precisely track a row of pits which encode the
binary data on the disc. In the "three-beam" system, a grating is used to produce the first order
diffraction maximum to each side of the main beam. Those diffracted beams overlap the track, and
the reflected light from the two side beams should be equal, on the average, if the main beam is
centered on the track. If they are unequal, then their difference can be used to generate an error
voltage to correct the tracking. The illustration of the side beam positions is not to scale; they
deviate about 20 micrometers from the main beam.
Scaled Views of a Compact Disc
Data on a compact disc is stored in the form of pits in the plastic substrate.
A reflective layer of aluminium is applied to reflect the laser beam. A protective coating is then
applied to the top. The laser system reads the data from below.

Detection of CD Pits
The tracking laser beam sees the pits as raised areas which are about a quarter-wavelength high for
the laser light.
The reflected light from the pit is then 180° out of phase with the reflection from the flat area, so the
reflected light intensity drops as the beam moves over a pit. The threshold of the photodiode
detector can be adjusted to switch on this light level change.
CD Response to Defects
The signal from a compact disc is relatively insensitive to the presence of small defects such as dust
or fine scratches on the bottom surface of the CD because the laser beam is fairly large at that point,
about 0.8 mm. As illustrated below, typical dust particles are much smaller than that. As the laser is
further focused down to about 1.7 micrometers at the depth of the pits, any shadow from the small
defects is blurred and indistinct and does not cause a read error. Larger defects are handled by errorcorrecting
codes in the handling of the digital data.
Error-Correction of CD Signals
The data on a compact disc is encoded in such a way that some well- developed error-correction
schemes can be used. A sophisticated error- correction code known as CIRC (cross interleave Reed-
Solomon code) is used to deal with both burst errors from dirt and scratches and random errors from
inaccurate cutting of the disc. The data on the disc are formatted in frames which contain 408 bits of
audio data and another 180 bits of data which include parity and sync bits and a subcode. A given
frame can contain information from other frames and the correlation between frames can be used to
minimize errors. Errors on the disc could lead to some output frequencies above 22kHz (half the
sampling frequency of 44.1 kHz) which could cause serious problems by "aliasing" down to audible
frequencies. A technique called oversampling is used to reduce such noise. Using a digital filter to
sample four times and average provides a 6-decibel improvement in signal-to-noise ratio. For more
details, see the references.

Data Encoding on Compact Discs
When the laser in a compact disc player sweeps over the track of pits which represents the data, a
transition from a flat area to a pit area or vice versa is interpreted as a binary 1, and the absence of a
transition in a time interval called a clock cycle is interpreted as a binary 0. This kind of detection is
called an NRZI code. The particular NRZI code used with compact discs is EFM (eight-to-fourteen
modulation) in which eight bits of data are represented by fourteen channel bits. In addition to the
actual digital sound data, parity and sync bits and a subcode are also recorded on the disc in
"frames" . In a given frame, 408 bits of audio data are recorded with another 180 bits of data which
permit a sophisticated error-correction code to be used. A given frame can contain information from
other frames and the correlation between frames can be used to minimize errors. In addition to
detection, a significant amount of computation must be done to decode the signal and prepare it for
conversion back to analog form with a DAC.
Detection of Compact Disc Data
The pits which encode the digital data on a compact disc are tracked by a laser. The reflected light
from the pits is out of phase with that from the surrounding area, so the reflected light intensity
drops when the laser moves over a pit area. The nature of a photodiode is such that it can be used as
the sensing element in a light-activated switch. It conducts an electric current which is proportional
to the light falling on it. The photodiode and switch can be adjusted so that a transition to a pit area
will switch it off, and a transition from a pit area will switch it on. Either transition is interpreted as
a binary 1, while the absence of a transition in a given clock cycle is interpreted as a binary zero.
The data on the disc is encoded in a sophisticated way, so that decoding is necessary before sending
the digital signal representing the sound to a digital-to-analog converter (DAC) for reconversion to
analog form.
Cylindrical Lens for Positioning
A clever use of a cylindrical lens generates a correction signal to position the main focusing lens for
the detector in a compact disc player. The combination of a symmetric lens and a cylindrical lens
produces a circular beam at only one distance past the cylindrical lens. A segmented photodiode
arrangement can detect whether the beam is circular and generate an error voltage to reposition the
main lens so that it is. The error voltage drives a coil which can rapidly reposition the lens in
response to changes in distance to the CD as it rotates.

CD Storage Capacity
A compact disc can store more than 6 billion bits of binary data. This is equivalent to 782
megabytes, and at 2000 characters per page this is equivalent to about 275,000 pages of text
(Rossing). Because the analog-to-digital conversion for making CD's samples sound waveforms at
44.1 kHz, the amount of data involved in the recording of high-fidelity sound is very large. The 12
cm diameter compact disc can hold 74 minutes of digital audio which has a frequencies over the full
audible range of 20-20,000 Hz. The signal-to-noise ratio and the dynamic range can exceed 90
decibels.
Calcite
Two images through
calcite crystal
Polarizer transmits the
ordinary ray.
Polarizer rotated about 90°
transmits the extraordinary ray.
Because of its birefringence, calcite forms two images of the arrow. Rotating a polarizer over them
shows that the light which forms the two images is polarized at right angles.
Calcite
These three clear calcite crystals are just the beginning of the vast variety of forms in which calcite
appears. Since it is soluble in acidic water, it can be dissolved and recrystallized with a large
number of different inclusions. All of the samples pictured here are on display at the Smithsonian
Museum of Natural History. The indices of refraction for the o- and e-rays are 1.6584 and 1.4864

espectively. This gives total internal reflection critical angles of 37.08° for the o- and 42.28° for the
e-rays when in contact with air. This means that for any angle between these two values, the o-ray
will be totally reflected but the e-ray will be partially transmitted. This gives linear polarization
since only the e-ray emerges.
Calcite is used in polarizing prisms such as the Nicol prism, the Glan-Foucault prism, and the
Wollaston prism.
Calcite, CaCO 3 , is the most abundant of the carbonate minerals.
Clear calcite has many optical applications because of its large birefringence.
Calcite manganoan. From Idarado Mine, Ouray, Colorado. Sample size 15-18 cm.
Calcite with duftite inclusions from Tsumeb, Namibia. Sample size about 12 cm.
From Tsumeb, Namibia. Sample size about 12cm

Both calcite samples above are about 12-15 cm in width. The right image above is from Santa
Eulala, Mexico
Calcite
The varieties of calcite, CaCO 3 , are so numerous and so varied that an entire display case at the
Smithsonian Museum of Natural History is devoted to just calcite. Calcite is the most abundant of
the carbonate minerals. The sample shown above and in the closeup view below is called cobaltian
calcite. The sample is about 9x12 cm. The 3.9 carat gem at right is from Spain. All these samples
are part of the gem and mineral exhibit at the Smithsonian Museum of Natural History.

The calcite gem above is 52.3 carats and is from Balmat, New York. At right above is a 110.7 carat
calcite gem from Africa. The 122.3 carat gem below right is from Chihuahua, Mexico. The large
gem below is 1865 carats and is from Balmat, New York.

The red calcite gem above is 150.6 carats and the gem at right is 70.2 carats. They are from Baja
California, Mexico
The faceted calcite ball above left is about 3.5x3.5 cm. The oval-cut gem above right is about 8x6
cm.

This huge single crystal of calcite is about 30x45 cm and is from Iceberg claim, Dixon, New
Mexico. It shows the characteristic calcite geometry and shows the large birefringence of calcite in
the double image of the text placed behind it.
Calcite
The mineral calcite, also known as Iceland spar, is a widely used material in optics because of its
birefringence. Its birefringence is so large that a calcite crystal placed over a dot on a page will
reveal two distinct images of the dot. One image will remain fixed as the crystal is rotated, and that
ray through the crystal is called the "ordinary ray" since it behaves just as a ray through glass.
However, the other image will rotate with the crystal, tracing out a small circle around the ordinary
image. This ray is called the "extraordinary ray".
The indices of refraction for the o- and e-rays are 1.6584 and 1.4864 respectively. This gives total
internal reflection critical angles of 37.08° for the o- and 42.28° for the e-rays when in contact with
air. This means that for any angle between these two values, the o-ray will be totally reflected but
the e-ray will be partially transmitted. This gives linear polarization since only the e-ray emerges.
Calcite is used in polarizing prisms such as the Nicol prism, the Glan-Foucault prism, and the
Wollaston prism.
A simple demonstration of the large birefringence of calcite is to put a dot on a piece of paper and
put the calcite crystal over it. You see two distinct dots. By putting a piece of polaroid over the
crystal and rotating it, you can show that the two images of the dot are made up of light polarized at
90° with respect to each other. Rotating the polaroid will show one dot, then both in transition, and
then just the second dot as you reach 90°.
The video segment below shows the successive disappearance of the two dots as a sheet of polaroid
is rotated over them

Fresnel's Equations
Fresnel's equations describe the reflection and transmission of electromagnetic waves at an
interface. That is, they give the reflection and transmission coefficients for waves parallel and
perpendicular to the plane of incidence. For a dielectric medium where Snell's Law can be used to
relate the incident and transmitted angles, Fresnel's Equations can be stated in terms of the angles of
incidence and transmission.
For light from a medium of index n 1 =
incident upon a medium of index n 2 =
at an angle θ i = °
the angle of transmission is θ t = °
Fresnel's equations give the reflection coefficients:
= and =
The transmission coefficients are
= and
=
Note that these coefficients are fractional amplitudes, and must be squared to get fractional
intensities for reflection and transmission. The signs of the coefficients depend on the original
choices of field directions.
You can choose values of parameters which will give transmission coefficients greater than 1, and
that would appear to violate conservation of energy. (For example, try light incident from a medium

of n 1 =1.5 upon a medium of n 2 =1.0 with an angle of incidence of 30°.) But the square of the
transmission coefficient gives the transmitted energy flux per unit area (intensity), and the area of
the transmitted beam is smaller in the refracted beam than in the incident beam if the index of
refraction is less than that of the incident medium. When you take the intensity times the area for
both the reflected and refracted beams, the total energy flux must equal that in the incident beam.
For further details, see Jenkins and White.
Checking out conservation of energy in this situation leads to the relationship
which applies to both the parallel and perpendicular cases.
Parallel case: Reflected % and transmitted %.
Perpendicular case: Reflected % and transmitted %.
Reflection and Transmission
Typical reflection and transmission curves for external reflection. These curves are the graphical
representation of the Fresnel equations. Note that the reflected amplitude for the light polarized
parallel to the incident plane is zero for a specific angle called the Brewster angle. The reflected
light is then linearly polarized in a plane perpendicular to the incident plane. This polarization by
reflection is exploited in numerous optical devices
Internal Reflection Curves
The illustration shows typical reflection curves for internal reflection. Internal reflection implies
that the reflection is from an interface to a medium of lesser index of refraction, as from water to
air. These curves are the graphical representation of the Fresnel equations. Note that the reflected

amplitude for the light polarized parallel to the incident plane is zero for a specific angle called the
Brewster angle. The reflected light is then linearly polarized in a plane perpendicular to the incident
plane. This polarization by reflection is exploited in numerous optical devices. Another
characteristic of internal reflection is that there is always an angle of incidence c above which all
light is reflected back into the medium. This phenomenon of total internal reflection has many
practical applications in optics.
Reflection and Transmission
External Reflection
Fresnel's equations describe the reflection and transmission of electromagnetic waves at an
interface. That is, they give the reflection and transmission coefficients for waves parallel and
perpendicular to the plane of incidence. For a dielectric medium where Snell's Law can be used to
relate the incident and transmitted angles, Fresnel's Equations can be stated in terms of the angles of
incidence and transmission.

For light from a medium of index =
incident upon a medium of index =
at an angle = °
the angle of transmission is = °
Fresnel's equations give the reflection coefficients:
= and =
The transmission coefficients are
= and
=
Note that these coefficients are fractional amplitudes, and must be squared to get fractional
intensities for reflection and transmission.
You can choose values of parameters which will give transmission coefficients greater than 1, and
that would appear to violate conservation of energy. (For example, try light incident from a medium
of n 1 =1.5 upon a medium of n 2 =1.0 with an angle of incidence of 30°.) But the square of the
transmission coefficient gives the transmitted energy flux per unit area (intensity), and the area of
the transmitted beam is smaller in the refracted beam than in the incident beam if the index of
refraction is less than that of the incident medium. When you take the intensity times the area for
both the reflected and refracted beams, the total energy flux must equal that in the incident beam.
For further details, see Jenkins and White.
Checking out conservation of energy in this situation leads to the relationship

which applies to both the parallel and perpendicular cases.
Parallel case: Reflected % and transmitted %.
Perpendicular case: Reflected % and transmitted %.
Reflection and Transmission
Internal Reflection
Fresnel's equations describe the reflection and transmission of electromagnetic waves at an
interface. That is, they give the reflection and transmission coefficients for waves parallel and
perpendicular to the plane of incidence. For a dielectric medium where Snell's Law can be used to
relate the incident and transmitted angles, Fresnel's Equations can be stated in terms of the angles of
incidence and transmission.
For light from a medium of index =
incident upon a medium of index =
at an angle = °
the angle of transmission is = °
Fresnel's equations give the reflection coefficients:

= and =
The transmission coefficients are
= and
=
Note that these coefficients are fractional amplitudes, and must be squared to get fractional
intensities for reflection and transmission.
You can choose values of parameters which will give transmission coefficients greater than 1, and
that would appear to violate conservation of energy. (For example, try light incident from a medium
of n 1 =1.5 upon a medium of n 2 =1.0 with an angle of incidence of 30°.) But the square of the
transmission coefficient gives the transmitted energy flux per unit area (intensity), and the area of
the transmitted beam is smaller in the refracted beam than in the incident beam if the index of
refraction is less than that of the incident medium. When you take the intensity times the area for
both the reflected and refracted beams, the total energy flux must equal that in the incident beam.
For further details, see Jenkins and White.
Checking out conservation of energy in this situation leads to the relationship
which applies to both the parallel and perpendicular cases.
Parallel case: Reflected % and transmitted %.
Perpendicular case: Reflected % and transmitted %.
Blue Sky
The blue color of the sky is caused by the scattering of sunlight off the molecules of the
atmosphere. This scattering, called Rayleigh scattering, is more effective at short wavelengths (the
blue end of the visible spectrum). Therefore the light scattered down to the earth at a large angle
with respect to the direction of the sun's light is predominantly in the blue end of the spectrum.

Note that the blue of the sky is more saturated when you look further from
the sun. The almost white scattering near the sun can be attributed to Mie
scattering, which is not very wavelength dependent.
Clouds in contrast to
the blue sky appear
white to achromatic
gray.
The water droplets that make up the cloud are much larger than the molecules of the air and the
scattering from them is almost independent of wavelength in the visible range.
Rayleigh Scattering
Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be
extended to scattering from particles up to about a tenth of the wavelength of the light. It is
Rayleigh scattering off the molecules of the air which gives us the blue sky. Lord Rayleigh
calculated the scattered intensity from dipole scatterers much smaller than the wavelength to be:

Rayleigh scattering can be considered to be elastic scattering since the photon energies of the
scattered photons is not changed. Scattering in which the scattered photons have either a higher or
lower photon energy is called Raman scattering. Usually this kind of scattering involves exciting
some vibrational mode of the molecules, giving a lower scattered photon energy, or scattering off
an excited vibrational state of a molecule which adds its vibrational energy to the incident photon.
Mie Scattering
The scattering from molecules and very tiny particles (< 1 /10 wavelength) is predominantly
Rayleigh scattering. For particle sizes larger than a wavelength, Mie scattering predominates. This
scattering produces a pattern like an antenna lobe, with a sharper and more intense forward lobe for
larger particles.
Mie scattering is not strongly wavelength dependent and produces the almost white glare around the
sun when a lot of particulate material is present in the air. It also gives us the the white light from
mist and fog.
Greenler in his "Rainbows, Haloes and Glories" has some excellent color plates demonstrating Mie
scattering and its dramatic absence in the particle-free air of the polar regions.
Rayleigh and Mie Scattering

Sky Saturation and Brightness
As a qualitative examination of sky brightness and the saturation of the blue sky color,
measurements of the color of the sky photograph were made from a computer monitor using Adobe
Illustrator's color tools. None of the data should be taken as quantitatively reliable since the original
photo had been transformed several times, and the measurements were taken from a non-calibrated
computer monitor. Nevertheless, it might be useful as an example of the progressions of sky color.
A series of points on the sky image were chosen starting from the left, indicated by the white dots
superimposed on the image above. It is clear to the eye that the progression leads to a brighter sky
and to a blue color which is less saturated, or more pastel. Measurements of the color and brightness
were made at each point based on amounts of red, green and blue present. In the graph at upper left,
the blue brightness was normalized to 1 and the red and green expressed as a fraction of the blue.
One result was that the green was significantly brighter than the red. This is consistent with
Rayleigh scattering which emphasizes the shorter wavelengths. Another result was that the red and
green increased as a fraction of the blue, indicating that the color was becoming less saturated. This
can be interpreted as blue mixed with an increasing fraction of white light, which is consistent with
the light being a combination of Rayleigh and Mie scattering. As you approach the sun's direction,
the Mie scattering accounts for a larger fraction of the total light, and the Mie scattered light is
essentially white. The graph of overall brightness above is just the sum of all three colors, with a
maximum of 1 being white on the monitor. The increasing brightness along the path of the data is
again consistent with a combination of Rayleigh and Mie scattering. The Mie scattering has a strong
forward lobe and increases as you approach the sun's direction.
Hue
Hue, along with saturation and brightness make up the three distinct attributes of color. The terms
"red" and "blue" are primarily describing hue - hue is related to wavelength for spectral colors. It is
convenient to arrange the saturated hues around a Newton Color Circle. Starting from red and
proceeding clockwise around the circle below to blue proceeds from long to shorter wavelengths.
However it shows that not all hues can be represented by spectral colors since there is no single
wavelength of light which has the magenta hue - it may be produced by an equal mixture of red and
blue.

There are many different mixtures of wavelengths which can produce the
same perceived hue. The achromatic line from black to gray to white
through the center of the circle represents light which has no hue.
The distribution of hue around a circle is used in commercially available paint and pigment mixing
guides like the Color Wheel
Saturation
Saturation, along with hue and brightness make up the three distinct attributes of color. Pink may be
thought of as having the same hue as red but being less saturated. A fully saturated color is one with
no mixture of white. A spectral color consisting of only one wavelength is fully saturated, but one
can have a fully saturated magenta which is not a spectral color. Quantifying the perception of
saturation must take into account the fact that some spectral colors are perceived to be more
saturated than others. For example, monochromatic reds and violets are perceived to be more
saturated than monochromatic yellows. There are also more perceptably different levels of
saturation for some hues - a fact accounted for in the Munsell color system
There are many different mixtures of wavelengths which can
produce the same perceived hue. The achromatic line from
black to gray to white through the center of the circle
represents light which has no hue.

Note that the blue of the sky is more saturated when you look further from the sun. The almost
white scattering near the sun can be attributed to Mie scattering, which is not very wavelength
dependent. The mixture of white light with the blue gives a less saturated blue.
One of the features of the commercially available Color Wheel is to help visualize the effect of
adding white paint or pigment. It makes the color less saturated as shown in the image below.
Brightness
Brightness, along with saturation and hue make up the three distinct attributes of color. The
brightness of a colored surface depends upon the illuminance and upon its reflectivity. Since the
perceived brightness is not linearly proportional to the reflectivity, a scale from 0 to 10 is used to
represent perceived brightness in color measurement systems like the Munsell system. It is found
that equal surfaces with differing spectral characteristics but which emit the same number of lumens
will be perceived to be equally bright.
If one surface emits more lumens, it will be perceived to be brighter in a logarithmic relationship
which yields a constant increase in brightness of about 1.5 units with each doubling of brightness.

The images above from the commercially available Color Wheel depict 10 levels of brightness for
gray or achromatic light.