Nanotechnology Corporation
Advanced Industry Research Park
Ann Arbor, MI 48109
Atomic Force Microscopy for New Business Area Development
Vincent Giang, Devin Hopper, Adam Sentz, James Vance
ME495, Laboratory 3
Department of Mechanical Engineering
University of Michigan
Ann Arbor, MI 48109-2125
Section 009 Team 1
December 11, 2013
The Honor Pledge: “I have neither given nor received unauthorized aid on this assignment nor have I
concealed any violation of the Honor Code.”
__________________________________________
__________________________________________
__________________________________________
__________________________________________
ABSTRACT
We were requested by the directors at Nanotechnology Corporation to calibrate and conduct testing
utilizing an Atomic Force Microscope. This testing was focused in several various areas, since
Nanotechnology Corporation is looking at expanding their business into new markets. Our first task
involved scanning a CD sample and determining the maximum amount of storable data on this medium.
We were also requested to find the maximum spot size of a laser that could read and track this data with
high fidelity. Another objective involved scanning a sample for microtubules. We were requested to use
our test data to find the diameter and persistence length of the microtubules and from this, calculate their
stiffness. These calculations would be used to determine the effects of various drugs on the microtubules.
Lastly, we were asked to characterize the stiffness of a cantilever beam by measuring the power spectral
density of the displacement of its tip. We determined that maximum storable amount of data on a CD,
DVD, and Blu-ray disk to be 0.91 ± 0.31 GB, 4.76 ± 1.57 GB, and 22.4 ± 11.5 GB, respectively. We
calculated the maximum spot size of the laser for the CD to be 0.83 ± 0.06 µm. The DVD’s max spot size
was 0.368 ± 0.033 µm and Blu-ray was 0.128 ± 0.019 µm. We found the diameter, persistence length, and
stiffness of the microtubules to be 25.4 ± 8.7 nm, 1527.2 ± 1186.5 microns, and 5.4x10-24 ± 3.3x10-23
Nm2, respectively. Lastly, we determined the stiffness of the cantilever beam to be 0.0121 ± 0.0023 N/m.
We have completed these tasks and the following report serves to present our results, conclusions, and
recommendations.
INTRODUCTION
We conducted testing using an Atomic Force Microscope (AFM) in order to help Nanotechnology
Corporation expand into new markets. This included the electronics industry, specifically regarding
recordable media technology. We also scanned microtubules to observe their changes when exposed to
new drugs, such as taxol. This could allow Nanotechnology Corp. to expand potentially into
pharmaceutical markets. Lastly, we found the power spectral density of a cantilever beam’s tip
displacement, so that we could ultimately determine its stiffness. We found several scientific articles,
referenced throughout this report, that illustrate the need for this testing and similar conclusions that have
been drawn from the results. These scholarly reports also help to authenticate our testing methods and
results. The work we have performed in these experiments is very important both to the increase in
revenue for Nanotechnology Corporation and to scientific advancements of the industries we have
become involved in. Specifically, we accomplished four main objectives. These included: determining the
maximum amount of storable data on a writable media, finding the maximum spot size of a laser that
could read and track this data in high fidelity, evaluating the effects of certain drugs on the stiffness of
microtubules, and lastly, characterizing the stiffness of a cantilever beam by calculating its power spectral
density.
NOMENCLATURE
Table 1: Defining all variables used, along with units
Variable
Value/Units
a
microns
dt
microns
db
microns
E
N/m2
I
m4
k
N
kb
1.38x10-23 m2kg*s-2K-1
L
microns
Lp
microns
2
Definition
Amplitude of First Mode
Track Length
Bit length
Young’s Modulus
Second Moment of Area
Stiffness
Boltzmann Constant
Microtubule Length
Persistence Length
N
NA
Δs1
Δs1
T
t
ν
microns
microns
Kelvin
seconds
seconds-1
Number of Observations
Numerical Aperture
Segment Length of First Mode
Segment Length of First Mode
Temperature
Time
Frequency
METHODS
We were asked to use the Atomic Force Microscope (AFM) to scan several different types of samples.
The AFM uses a piezoelectric tickler to vibrate a small cantilever beam up and down over a sample. As a
voltage is applied over the tickler, it forces the beam up and down as the sample moves beneath it. This
creates a digital picture of the sample. There were several preliminary steps we needed to take to set up
the microscope. We took a probe containing a small cantilever beam and placed it into a probe holder
using tweezers. We then inserted this probe holder into the microscope. We started the software and
utilized the camera on the microscope to ensure that the probe was properly located over the sample. We
utilized adjustment knobs in order to make small changes. We needed to center the laser spot over the tip
of the cantilever beam, so that we could take accurate measurements. We did this using two knobs on the
AFM that controlled the laser’s position in the x and y planes. We needed to set the position of the laser
on the program’s interface to have a value between 0.2 and 0.4 in the top-bottom direction and 0 in the
left-right direction. After these steps were accomplished, we began lowering the tip of the probe towards
the sample. After manually using the motor control to decrease the sizable distance between the probe and
the sample, we utilized “Tip Approach” to slowly minimize this distance. The AFM did this
automatically, decreasing the distance a few microns at a time until the two were in contact. Once the
probe and sample were in constant feedback, we began our scan.
Calibration
We first needed to calibrate the AFM using a silicon sample chip containing gratings of known pitches
and depths. We compared our empirical measurements to the known dimensions of the gratings in order
to determine the calibration factors of the device. We then calculated a scaling factor by dividing the
known length by the measured length. We then multiplied this by the existing scaling factor of the AFM.
CD Sample
We scanned the CD sample and used the Gwyddion software to measure the pitches and lengths of each
pit. We could use this data to determine the maximum spot size of a laser and the storage capacity of the
entire disk. We repeated this scan several times to ensure our sample was an accurate portrayal of the
entire CD. This procedure was repeated with the DVD and Blu-ray sample provided by Nanotechnology
Corporation.
Max Spot Size
Spot Size Assumptions: We were asked by Nanotechnology Corporation to comment on the maximum
spot size of a laser than can be used to read and track data with high fidelity. In order to find the largest
allowable spot size of a focused laser that can be used to track and read data with high fidelity, a few
assumptions must initially be made. The first is that the laser spot size diameter is modeled using a
Gaussian distribution defined by (truncated by) the 1/e2 irradiance level and corresponding beam width
diameter. This assumes that there is a finite diameter for which enough power per unit area, called
irradiance, can define the spot size entirely for detection purposes. The second assumption is that the lens
to disc clearance remains near constant (Tilt limited by a servo mechanism) [1] so it doesn’t drastically
alter the spot size by moving out of the laser focal length. We assume that the disc is a single layer type
only.
3
Fig. 1 - Left: Transition from pit to land creates destructive interference encoding “1” by the photo
detector. [12]
Fig. 2 - Right: Gaussian distribution showing the laser spot size diameter at the 1/e2 (13.5%)
intensity level. [10]
Reading and Encoding: The way optical pickups relay information from CDs, DVDs and Blu-ray discs
is by sending and receiving laser light, which passes over high and low indentations circumferentially
along the media called pits and lands respectfully. The pit depths are strategically written into the media
so that when the laser spot transitions from a pit-to-land or land-to-pit interface half of the laser intensity
is 180 degrees out of phase. This causes destructive interference which ends up reflecting little or
theoretically no light back to the optical pickup. This signal is then read as a “1” while and when there is
no transition a “0” is read instead as illustrated in Fig. 1 [12]. When the laser is completely over a pit or
land the signal relayed is a “0”.
Max Spot Size Limitations: There are several limiting parameter considerations when selecting the
maximum allowable spot size for the CD, DVD and Blu-ray media devices. First, the spot size diameter
cannot exceed the minimum pit length or minimum land length (3T) because the spot diameter would not
be able to distinguish two pit-to-land or land-to-pit “transitions” at once according to Lesurf [13]. Other
limitations governing the maximum spot size is that it cannot overlap adjacent tracks so the pitch and
ultimately the capacity restrict spot size. A third limitation on the spot size is that the pit width must be
greater than the wavelength of the laser used. This is done for increased fidelity read by the optical pickup
diode so not to confuse a transition “1” with a “0”.
Microtubule Scanning
Another objective we were requested to fulfill involved the measurement of microtubules to test the
AFM’s capabilities in scanning organic samples, so that Nanotechnology Corporation can service a
broader range of customers. The sample was prepared by mixing a solution containing microtubules with
a drug that caused them to break apart into smaller lengths. This mixture was pipetted onto the surface of
a glass substrate as a 4 mm diameter drop, and was allowed to sit for approximately 15 minutes. The
sample was then rinsed with deionized water and allowed to air dry.
We used two samples of microtubules. The calibration coefficients that were previously determined were
applied. We ran scans at 20x20 microns and 10x10 microns over the center of the sample. From these
scans, we were able to obtain one image of microtubules, but the distortion of the scan was such that it
was unreliable to obtain data from. We used other scans from a similar AFM machine from the same
sample group as the ones we used, but were of better resolution and less distortion. To analyze the
4
images, we used Gwyddion AFM software. The data could then be used to find the persistence length of
the microtubules and, using the Equipartition Theorem, the stiffness of them.
Power Spectral Density Calculation
Finally, we were requested to characterize the stiffness of a compliant cantilever beam by finding the
power spectral density of the displacement of the tip. To do this, we tested the cantilever beam by
vibrating it at 50 kHz for 5 seconds several times. We focused the laser of the AFM on the very tip of the
cantilever beam to measure its displacement. We then took the data that was output and used Matlab to
solve for the root mean square. We repeated this experiment with the laser refocused on the base of the
cantilever beam. With this data, we could find the noise and subtract it from our tip data to develop a
more precise measurement. We used the Equipartition Theorem (Eq. 1) to find the stiffness of the
cantilever beam using the root mean square.
1
𝑘 𝑇
2 𝐵
1
2
= 𝑘⟨𝑥 2 ⟩
[Eq. 1]
RESULTS
This section will state the findings and calculated results. This includes how we determined the storage
sizes for our CD, DVD, and Blu-ray sample, the diameter, persistence length, and flexural rigidity of our
scanned microtubules, and the stiffness of a cantilever beam used in the AFM.
CD, DVD, and Blu-Ray
The standard area of a CD, DVD, and Blu-ray disc that allows for recording was assumed to be between
the radii of 22.2 mm and 59.0 mm, based upon reference from European Computer Manufacturers
Association (ECMA). [8] Data written on these media storage disks are recorded on a spiral track that
spans within the allowed area. We assumed this entire track was a summation of multiple circumferences
within the recording area. With a known track length, we were able to determine the amount of channel
bits on a device by finding the average channel bit length. To do so, we first found all the different pit
lengths and pitches on the samples using Gwyddion software to take measurements. CD samples were
scanned by our team while the DVD and Blu-ray images were scanned on a similar AFM machine and
provided by Nanotechnology Corporation. The scanned images of the CD, DVD, and Blu-ray samples
are shown in Figure 3.
CD
DVD
Blu-ray
Pit Length
Pitch
Figure 3: Scanned CD, DVD, and Blu-ray images; DVD image shows how pits and pitches were
measured
We then created a histogram that graphs the occurrence of different measured pit lengths into organized
equal-sized bins ranging from the smallest to largest measured pit length. The smallest and largest pit
length on disc were defined as 3T and 11T, respectively. Discrete pit lengths were incremented by 1T
within this range. In the ideal situation, if these media storage disc were manufactured to complete
5
accuracy, we would see only 9 lengths with occurrences in the histogram. Due to manufacturing
inaccuracies and uncertainty in our Gwyddion measurements, our histograms showed clusters instead of a
distinct distribution, which we were able to use to estimate and determine the mean of each of the
definitive 9 pit lengths. This is a common procedure as shown in the study done by Choi et al., in which a
histogram was used to find the 9 discrete pit lengths of their sample. [5] The channel bit length was then
found by taking the difference between neighboring definitive pit lengths (i.e. 4T - 3T) and averaging the
differences.
To calculate the number of channel bits on each disc, we divided the entire track length by the average
channel bit length. We then considered the encoding of data on all discs to be an eight to fourteen
modulation by converting the channel bits to data bits. Channel bits are the bits of data that have been
encoded with eight to fourteen modulation and written to the disk. Data bits are the binary code that the
machine reads, without the encoding. The data bits were then converted to bytes to give us the storage
capacity. The equation of conversion is shown below in equations 2 and 3.
#𝑜𝑓 𝐶ℎ𝑎𝑛𝑛𝑒𝑙 𝐵𝑖𝑡𝑠 =
𝐵𝑦𝑡𝑒𝑠 = # 𝑜𝑓 𝐶ℎ𝑎𝑛𝑛𝑒𝑙 𝐵𝑖𝑡𝑠 ∗
𝑑𝑡
[Eq. 2]
𝐴𝑣𝑔 𝑑𝑏
1.4112 𝑏𝑖𝑡 𝑠 −1
4.3218 𝑏𝑖𝑡 𝑠 −1
∗
1 𝑏𝑦𝑡𝑒
[Eq. 3]
8 𝑑𝑎𝑡𝑎 𝑏𝑖𝑡𝑠
A histogram was created for all the samples. The histogram for the CD is shown in Fig. 4. Similar
histograms for the DVD and Blu-ray can be found in Appendix A2 and A3, respectively.
3T
4T
5T
6T
7T
8T
9T
10T
11T
- Okay
- Good
- N/A
Figure 4: Histogram shows the pit length distribution in CD sample.
From each histogram, we obtained an average bit length. We developed a Matlab code that took these
measurements and outputted a storage size for each device. The code to find CD, DVD, and Blu-ray
storage size is displayed in Appendix C1, C2, and C3, respectively. Table 2 below lists the values of
average bit lengths, pitches, and storage sizes.
Table 2: Calculated storage sizes based on average bit length and pitch
Sample
Bit Length (μm)
Pitch (μm)
CD
0.290 ± 0.040
1.40 ± 0.04
DVD
0.096 ± 0.012
0.80 ± 0.05
Blu-ray
0.048 ± 0.021
0.34 ± 0.04
Storage Size (GB)
0.91 ± 0.31
4.76 ± 1.57
22.4 ± 11.5
Error: Our calculations of the storage size for each medium has several potential sources of error. Firstly,
the AFM has an inherent resolution error. Also, we did not scan the entire medium, only a small portion
6
of it and then extrapolated our findings to the entire disk. Lastly, error could be introduced when using
Gwyddion, since the length of each line to measure the pit width was determined simply by naked eye.
Determining the Max Spot Size
The maximum allowable spot size for the three media types discussed, CD, DVD, and Blu-ray, were
evaluated separately because each were limited by parameters discussed earlier [13]. There are many
different ways to determine spot sizes as illustrated below and listed in Table 1. The max (truncated) spot
size our team chose is slightly wider than the pit width but shorter than the smallest pit length in
accordance with Pohlman [13, 14].
Minimum pit length method based on published data: The maximum theoretical spot size for the CD
was 1.7 ± 1µm, for the DVD it was 0.39 ± 0.1µm and for the Blu-ray it was 0.149 ± 1µm based on the
fact that the spot diameter cannot exceed the minimum pit length according to Lesurf [13].
Approximation method based on published data: The approximated spot size used in industry for a
CD is 1.73 µm, for a DVD its 1.0 µm and for a Blu-ray it is 0.476 µm by using the following formula
where numerical aperture (NA) is defined as the sin of the marginal ray angle illumination optics
according to the Blu-ray Disc Association [3, 15].
λ
Ideal Spot Size = NA
[Eq. 4]
Measured Max Spot Size: The maximum spot size using our measured data for the CD was 0.83µm, for
the DVD it was 0.368µm and for the Blu-ray it was 0.128µm based on the fact that the spot diameter
should not exceed the minimum pit length [13].
Table 3: Measured sample parameters versus industrial standards
CHARACTERISTICS CD
DVD Blu-ray
Measured
All values [µm]
CD
Laser Wavelength [3]
0.780 0.65
0.405
0.780
Track Pitch [3, 15]
1.60
0.74
0.320
1.40 ± 0.04
Min. Pit Length [3]
0.83
0.40
0.149
0.830 ± 0.060
Pit Width [15]
0.50
0.32
0.13
0.45 ± 0.073
Pit Depth (1/4 λ) [7]
0.125 0.16
0.073
Airy Spot Dia. [15,3]
1.7
1.0
0.476
*FWHM [4]
0.58
0.66
0.28
Measured
DVD
0.65
0.8 ± 0.05
0.368 ± 0.033
0.32 ± 0.08
Measured
Blu-Ray
0.405
0.34 ± 0.04
0.128 ± 0.019
0.17 ± 0.05
*Characteristics that were not measured directly, calculations were assumed to share the same values as
those published by their listed reference.*FWHM is the full width half maximum spot size. Refractive index is
assumed to be 1.55 for all three media and numerical apertures are 0.45, 0.6 and 0.85 for CD, DVD and Bluray respectively.
Microtubule Sample
We obtained an image of microtubules using our samples and AFM, Figure 5, p.8, but it had too much
noise to use to obtain data. We used images of microtubules obtained from another similar AFM using
samples from the same sample set as ours, Figure 5, p.8, to get data.
Diameter: Using Gwyddion, we obtained the diameter of the microtubules to be 25.4 ± 8.7nm by
measuring the diameters of 9 different microtubules and finding the average diameter, accounting for a
factor of error due to the inability of the cantilever tip to clearly determine the edge of an object. We used
the height measurement feature, as it clearly showed the location of the microtubule but with a greater
7
precision than the distance measure feature. The precision of measure was 1 nm versus 1 micron,
respectively.
Figure 5: Left image of microtubules was taken in lab, however it was too noisy to measure, while
they are visible in the right image. The microtubules were identified as the distinct white strands.
Persistence Length: We calculated the persistence length of the microtubules, Lp, to be 1527.2 ± 1186.5
microns by comparing the 9 microtubule samples against each other in CAD software and retaining the
scale of each microtubule sample from the image it was taken from. The ends of the microtubules were
overlaid and the other ends were brought to where they could all intersect. The distance from the end
where the microtubules were connected to the microtubules’ intersection was used to determine the length
L and the peak to peak amplitude of the microtubules at L/2 was used as Δs1, the amplitude of the
microtubules at the first mode. From this we obtained an approximation for the cosine decomposition of
the first mode. Using the variance calculated from this using equation 5, we found the persistence length
Lp with equation 6.
2
var(a1 ) = (√L (Δs1 /6))2
L2
Lp = n2 π2 var(a
1)
[Eq. 5]
[Eq. 6]
Flexural Rigidity: We calculated the flexural rigidity EI of the microtubule to be 5.4x10-24 ± 3.3x10-23
Nm2, which was estimated using the persistence length Lp and the Principle of Equipartition, equation 7.
The temperature T that was used was 296 K.
EI
bT
Lp = k
[Eq. 7]
Error: Errors in the measurement of microtubules came from the probe’s imperfections when scanning
the surface. This would lead features to seem larger or smaller than reality. Errors were also present in
measuring the microtubules in Gwyddion, as those measurements had to be done in the software.
Power Spectral Density of Cantilever Beam
In order to find the power spectral density of the cantilever beam’s tip displacement, we vibrated the
cantilever beam at 50 kHz and recorded data for 5 seconds. With the outputted time and voltage data, we
used a Matlab program (located in Appendix B1) to plot our data and to solve for the root mean square
value for both the cantilever’s tip and for the base of the cantilever. This Matlab was partially provided to
us by the directors at Nanotechnology Corporation, but we made additions to the program, including
8
PSD (𝑚2 /Hz)
experimenting with our mass and damping coefficient to ensure our model accurately fit our data
distribution. This model created a curve that we could determine the area under, since the integration of
the Fast Fourier Transform gives the power spectral density. We used a cumulative trapezoidal method to
determine the area under the model curve. Figure 6 shows the distribution of our data with the noise from
the base of the cantilever beam subtracted. The curve fit represents our Matlab model and closely
approximates our empirical data. With the root mean square, we were able to calculate the expected
stiffness of the cantilever using the Equipartition Theorem (Eq. 1, p. 5).
Frequency (Hz)
Figure 6: A predicted model of the Power Spectral Density fit against the data collected in testing.
We then calculated the actual stiffness of the beam based on the Young’s modulus of the material (silicon
nitride) and the dimensions of the beam. We used Eq. 8 to do so and verify our Matlab model. Through
our Matlab program, we found the stiffness of the cantilever beam to be 0.0121 ± 0.0023 N/m and
through Eq. 8, we determined a value of 0.0136 N/m.
𝑘=
3𝐸𝐼
𝐿3
[Eq. 8]
Error: Our main sources of error arose from the extraneous signals in the room since the AFM is
extremely sensitive. For example, the WiFi signal from a cell phone could cause a random peak in our
data that could skew the calculated area under the curve.
DISCUSSION
CD/DVD/Blu-ray
The standard CD, DVD, and Blu-ray storage size is approximately 0.7, 4.7, and 25 GB, respectively as
stated by the Blu-ray Disc Company. [2] Our calculated storage size of a CD was 0.91 ± 0.31 GB. The
DVD sample had a size of 4.76 ± 1.57 GB and the Blu-ray sample was calculated to be 22.4 ± 11.5 GB.
According to our sample, measurements and storage values, we cannot conclusively comment on the
manufacturing quality of the discs, due to our large error values. The main error we see from our
differences in storage sizes, especially with the CD and Blu-ray sample, was how we identified the mean
value we calculated for each definitive pit length. The estimation of the locations of definitive pit length
clusters were visually distributed because the distinct occurrence of clusters were not consistent.
9
Multimedia Recommendations
In order to develop a new universal multimedia player using the three media types requested CD, DVD
and Blu-ray we researched technologies currently available in the market as well as patents and related
technical journals. Of the current technologies available, every method alters the laser spot size applied in
order to read the media since one spot size cannot accomplish detection of all three media as discussed
earlier. Achieving multiple spot sizes is done a couple of ways including multiple laser diodes such as in
many computer readable and writable systems as well as in Microsoft’s X-box gaming system [3, p.11].
Another way to accomplish multiple spot sizes is by using multiple objective lenses such as LGE’s
Harmonic Optical Element currently used in Sony’s PlayStation 3. The Harmonic Optical Element works
by passing a single 405 nm blue-violet laser through an objective lens altering the phase function to
obtain wavelengths of 780 nm and 650 nm as described by Fedor [9, 4].
The device uses a birefringent material to polarize light depending on the light’s direction using the single
blue-violet laser which alters the focal length and laser spot size for each of the different substrate
thicknesses [4]. According to the Blu-ray disc founders, “This material (birefringent) is sandwiched
between two substrates and has the same refractive index as the bonding material for a certain
polarization direction, but has a different refractive index for a perpendicular polarizing direction
compared to the first polarizing direction.” [4] Figures 7 and 8 illustrates this below.
Fig. 7 Compatible Objective Lenses are a
hybrid of a diffractive and refractive lens [4]
Fig. 8 Harmonic Optical Element [9]
Microtubules
The microtubules that we observed had a diameter of approximately 25.4 ± 8.7nm. This indicates that the
microtubules are assembling, as 30 nm is roughly the size of fully assembled microtubules [11]. The
height measurement feature was used to obtain this because the height measurement can be found from
the tip of the cantilever, whereas the width would be found from where the microtubule interacted with
the sides of the cantilever, which it was not designed for. The persistence length and flexural stiffness of
the microtubules are 1527.2 ± 1186.5 microns and 5.4*10-24 ± 3.3x10-23 Nm2, respectively. This is close
to the value calculated by other sources, 5200 microns [11] for the persistence length and 2.2x10-23 Nm2
for the flexural rigidity [11]. This means that on the cellular level these microtubules would be fairly stiff.
Power Spectral Density of Cantilever Beam
As stated earlier, we derived a stiffness through our Matlab model of 0.0121 ± 0.0023 N/m and through
Eq. 8, p.9, of 0.0136 N/m. These values are within error bounds of each other, leading us to believe that
we have performed this calculation correctly using Matlab. According to Cleveland et al., who performed
a similar experiment, they arrived at a spring constant result of 0.028-0.18 N/m, depending on the
10
cantilever beam. Given the slight differences in experimentation and relatively small differences in our
calculated k values, we believe this study further confirms our testing accuracy. [6]
CONCLUSION
CD/DVD/Blu-ray
Assuming the same area of recording, the spiral tracks to be the summation of circumferences, and eight
to fourteen modulation across all devices, the CD, DVD, and Blu-ray discs we sampled from were
calculated to have storage sizes of 0.91 ± 0.31, 4.76 ± 1.57, and 22.4 ± 11.5 GB. Relating to standard
storage values, we cannot comment conclusively on the manufacturing standards of the discs, due to our
large error bounds. We identified the main source of error to be the inconsistent distribution of pit lengths
we measured from our samples.
Max Spot Size of Laser
Assuming that your target demographics are commercial businesses and residential consumer markets, we
believe that if Nanotechnology Corporation wants to enter the universal multimedia player market
immediately you should follow a researched technology such as LGE’s harmonic optical element
solution. Either way we suggest you use a single wavelength laser and utilize a multiple objective lens to
limit the size. This seems to be the consensus from companies such as Sony and Phillips. Even though
cutting edge technologies are on the horizon, such as the use of holographic optics or ultra-violet
wavelength laser diodes, consumers and businesses will still have use for devices that read and write
using older media. It will take time to usher in radically newer technologies as history has shown with
updates such as tapes to CD to DVD to Blu-ray discs.
Microtubules
Although we weren’t able to obtain clear images with our AFM, we have proved that AFMs are generally
capable of studying organic samples. We were able to determine that the average diameter of the
microtubules was 25.4 ± 8.7 microns, the persistence length was 1527.2 ± 1186.5 microns, and the
flexural rigidity was 5.4x10-24 ± 3.3x10-23 Nm2. The greatest source of error was the measurement of the
microtubules in Gwyddion, as this had to be done manually, and even the microtubules that were
measured could have been several microtubules stuck together or bent at an artificially created angle by
the preparation process.
Cantilever Stiffness
After vibrating the cantilever beam at 50 kHz for 5 seconds, we were able to determine that the stiffness
of the beam is 0.01212 ± 0.0023 N/m. Our main source of error came from extraneous signals in the room
that affected the AFM.
RECOMMENDATIONS
Max Spot Size of Laser
Nanotechnology Corporation should follow previously researched technology, such as the harmonic
optical element solution. We also recommend the use of a single wavelength laser and a multiple
objective lens to limit the spot size.
Microtubules
With this level of understanding of the microtubule behavior, we can superficially determine the
properties of microtubules that have been treated with drugs, but to have greater certainty, we must refine
our data acquisition techniques or obtain more samples to get more accurate data. We believe that the
results of our machine could be improved by using a cantilever with a sharper tip and systematically
imaging the surface of the substrate to obtain as many images of microtubules as possible. Because the
11
methods of calculation involved analyzing groups of microtubules for averaged data, increasing the
number of microtubules that we can analyze will improve the accuracy of our measurements.
FUTURE WORK
CD/DVD/Blu-ray
Retrieving more samples from a device to calculate the storage size would more accurately determine if
the CD, DVD, or Blu-ray disc was manufactured to exact specifications. The channel encoding
modulation should also be investigated for the DVD and Blu-ray and should be considered in the
conversion process from channel to data bits.
Microtubules
We would need to take more samples to improve the accuracy of measurements. This would also involve
the use of better examination techniques to more accurately measure the data.
Power Spectral Density of Cantilever Beam
We would need to run additional tests at varying frequencies and time durations to further refine our
model.
ACKNOWLEDGMENTS
We would like to acknowledge Professors Meyhofer, Reddy, and Nagourney for their assistance in these
experiments. We would also like to give appreciation for the assistance of Chuming Zhao in carrying out
our testing.
12
APPENDICES
A1: Histogram of measured DVD pit lengths categorized into 9 sections to determine the
definitive pit lengths from 3T to 11T.
4T
6T
5T
8T
7T
9T
10T
11T
- Okay
- Good
- N/A
Number of Observations
3T
DVD Pit Length (µm)
A2: Histogram of measured Blu-ray pit lengths categorized into 9 sections to determine the
definitive pit lengths from 3T to 11T.
4T
5T
6T
7T
8T
Number of Observations
3T
Blu-ray Pit Length (µm)
13
9T
10T
11T
- Okay
- Good
- N/A
B1: Matlab code used to calculate the root mean square value to find cantilever beam stiffness.
%Adam Sentz, James Vance, Vincent Giang, Devin Hopper
%December 11, 2013
%ME 495 Lab 3
%Power Spectral Density Code
%This code shows you how to compute the power spectral density
%of a simulated signal that is 5 seconds long
[time1, V1] = textread('50000hz_sample1b.txt', '%n %n','headerlines', 7);
[time2, V2] = textread('50000hz_sample2b.txt', '%n %n','headerlines', 7);
[time3, V3] = textread('50000hz_sample3b.txt', '%n %n','headerlines', 7);
[time4, V4] = textread('50000hz_sample4b.txt', '%n %n','headerlines', 7);
[time5, V5] = textread('50000hz_sample5b.txt', '%n %n','headerlines', 7);
[time6, V6] = textread('50000hz_sample6b.txt', '%n %n','headerlines', 7);
[time7, V7] = textread('50000hz_sample7b.txt', '%n %n','headerlines', 7);
[time8, V8] = textread('50000hz_sample8b.txt', '%n %n','headerlines', 7);
[time9, V9] = textread('50000hz_sample9b.txt', '%n %n','headerlines', 7);
[time10, V10] = textread('50000hz_sample10b.txt', '%n %n','headerlines', 7);
N = 2^18; % number of points, HAS TO BE A POWER OF 2
T = 5; % You will have to define T, the total time based on your sampling speed and the number of points
t = [0:N-1]/N;
t = t*T; % define time in seconds
f1 = V1*(1000/10^9)*(.22/.57); %define function, random signal superimposed on a sinusoidal wave
f2 = V2*(1000/10^9)*(.22/.57);
f3 = V3*(1000/10^9)*(.22/.57);
f4 = V4*(1000/10^9)*(.22/.57);
f5 = V5*(1000/10^9)*(.22/.57);
f6 = V6*(1000/10^9)*(.22/.57);
f7 = V7*(1000/10^9)*(.22/.57);
f8 = V8*(1000/10^9)*(.22/.57);
f9 = V9*(1000/10^9)*(.22/.57);
f10 = V10*(1000/10^9)*(.22/.57);
p1 = abs(fft(f1))/(N/2); % absolute value of the d: this is evaluating cn=(an^2+bn^2)^0.5. See previous
slides
p2 = abs(fft(f2))/(N/2);
p3 = abs(fft(f3))/(N/2);
p4 = abs(fft(f4))/(N/2);
p5 = abs(fft(f5))/(N/2);
p6 = abs(fft(f6))/(N/2);
14
p7 = abs(fft(f7))/(N/2);
p8 = abs(fft(f8))/(N/2);
p9 = abs(fft(f9))/(N/2);
p10 = abs(fft(f10))/(N/2);
p1 = p1(1:N/2).^2; % Squaring to obtain cn^2
p2 = p2(1:N/2).^2;
p3 = p3(1:N/2).^2;
p4 = p4(1:N/2).^2;
p5 = p5(1:N/2).^2;
p6 = p6(1:N/2).^2;
p7 = p7(1:N/2).^2;
p8 = p8(1:N/2).^2;
p9 = p9(1:N/2).^2;
p10 = p10(1:N/2).^2;
PSD1=p1.*T/2; %PSD is the power spectral density. Obtained from Cn^2 by multiplying with T/2
PSD2=p2.*T/2;
PSD3=p3.*T/2;
PSD4=p4.*T/2;
PSD5=p5.*T/2;
PSD6=p6.*T/2;
PSD7=p7.*T/2;
PSD8=p8.*T/2;
PSD9=p9.*T/2;
PSD10=p10.*T/2;
PSDbase = (PSD1+PSD2+PSD3+PSD4+PSD5+PSD6+PSD7+PSD8+PSD9+PSD10)./10;
std(PSDbase)
freq = [0:(N/2)-1]/T; % find the corresponding frequency in Hz
kb = 1.381*10^-23;
temp = 296;
c = 10^-9.25;
%m = 1.77e-9;
m = 10^-12.75;
vo = 10^4.22;
k = m*(vo*2*pi)^2;
f1 = logspace(-1,5,131072);
model = (1/(2*pi)^4)*(4*kb*temp*c)./(m^2*((vo^2-f1.^2).^2+((c.*f1)/(2*pi*m)).^2));
Integrated = cumtrapz(freq,model);
RMS1=[(Integrated(end))] % RMS value obtained from the frequency domain integral. In is a function
for integrating that you will have to write
%RMS2=fmean %RMS value obtained from time domain integral
15
%If the entire frequency range is included the time domain and frequency
%domain integrals should agree
%This code shows you how to compute the power spectral density
%of a simulated signal that is 5 seconds long
[time1, V1] = textread('50000hz_sample1.txt', '%n %n','headerlines', 7);
[time2, V2] = textread('50000hz_sample2.txt', '%n %n','headerlines', 7);
[time3, V3] = textread('50000hz_sample3.txt', '%n %n','headerlines', 7);
[time4, V4] = textread('50000hz_sample4.txt', '%n %n','headerlines', 7);
[time5, V5] = textread('50000hz_sample5.txt', '%n %n','headerlines', 7);
[time6, V6] = textread('50000hz_sample6.txt', '%n %n','headerlines', 7);
[time7, V7] = textread('50000hz_sample7.txt', '%n %n','headerlines', 7);
[time8, V8] = textread('50000hz_sample8.txt', '%n %n','headerlines', 7);
[time9, V9] = textread('50000hz_sample9.txt', '%n %n','headerlines', 7);
[time10, V10] = textread('50000hz_sample10.txt', '%n %n','headerlines', 7);
N = 2^18; % number of points, HAS TO BE A POWER OF 2
T = 5; % You will have to define T, the total time based on your sampling speed and the number of points
t = [0:N-1]/N;
t = t*T; % define -me in seconds
%V = (V1+V2+V3+V4+V5+V6+V7+V8+V9+V10)./10;
f1 = V1*(1000/10^9)*(.22/.57); %define function, random signal superimposed on a sinusoidal wave
f2 = V2*(1000/10^9)*(.22/.57);
f3 = V3*(1000/10^9)*(.22/.57);
f4 = V4*(1000/10^9)*(.22/.57);
f5 = V5*(1000/10^9)*(.22/.57);
f6 = V6*(1000/10^9)*(.22/.57);
f7 = V7*(1000/10^9)*(.22/.57);
f8 = V8*(1000/10^9)*(.22/.57);
f9 = V9*(1000/10^9)*(.22/.57);
f10 = V10*(1000/10^9)*(.22/.57);
avef = (f1+f2+f3+f4+f5+f6+f7+f8+f9+f10)./10;
fsquared = avef.^0.5;
fmean = mean(fsquared,1);
p1 = abs(fft(f1))/(N/2); % absolute value of the d: this is evaluating cn=(an^2+bn^2)^0.5. See previous
slides
p2 = abs(fft(f2))/(N/2);
p3 = abs(fft(f3))/(N/2);
p4 = abs(fft(f4))/(N/2);
p5 = abs(fft(f5))/(N/2);
p6 = abs(fft(f6))/(N/2);
p7 = abs(fft(f7))/(N/2);
p8 = abs(fft(f8))/(N/2);
16
p9 = abs(fft(f9))/(N/2);
p10 = abs(fft(f10))/(N/2);
p1 = p1(1:N/2).^2; % Squaring to obtain cn^2
p2 = p2(1:N/2).^2;
p3 = p3(1:N/2).^2;
p4 = p4(1:N/2).^2;
p5 = p5(1:N/2).^2;
p6 = p6(1:N/2).^2;
p7 = p7(1:N/2).^2;
p8 = p8(1:N/2).^2;
p9 = p9(1:N/2).^2;
p10 = p10(1:N/2).^2;
PSD1=p1.*T/2; %PSD is the power spectral density. Obtained from Cn^2 by multiplying with T/2
PSD2=p2.*T/2;
PSD3=p3.*T/2;
PSD4=p4.*T/2;
PSD5=p5.*T/2;
PSD6=p6.*T/2;
PSD7=p7.*T/2;
PSD8=p8.*T/2;
PSD9=p9.*T/2;
PSD10=p10.*T/2;
PSD = (PSD1+PSD2+PSD3+PSD4+PSD5+PSD6+PSD7+PSD8+PSD9+PSD10)./10;
std(PSD)
PSDfinal = abs(PSD - PSDbase);
freq = [0:(N/2)-1]/T; % find the corresponding frequency in Hz
kb = 1.381*10^-23;
temp = 296;
c = 10^-9;
%m = 1.77e-9;
m = 10^-12.75;
vo = 10^4.22;
%k = m*(vo*2*pi)^2;
f1 = logspace(-1,5,131072);
model = (1/(2*pi)^4)*(4*kb*temp*c)./(m^2*((vo^2-f1.^2).^2+((c.*f1)/(2*pi*m)).^2));
loglog(freq,PSDfinal,f1,model,'r'); % plot of the power spectral density
Integrated = cumtrapz(freq,model);
17
timef=t(1:131072);
RMS1=[(Integrated(end))] % RMS value obtained from the frequency domain integral. In is a function
for integrating that you will have to write
avefc = avef(1:131072);
RMS2=[(trapz(timef,avefc.^2))/T]^0.5 %RMS value obtained from time domain integral
%If the entire frequency range is included the time domain and frequency
%domain integrals should agree
%k = .01212
C1: Matlab code to calculate CD storage size
%Calculating cd sample size
%Vincent Giang
Lb = .29*10^-6; %average bit length [m] calculated from sample
Lp = 1.4*10^-6; %average pitch [m]
Ri = 22.2*10^-3;
Ro = 59*10^-3;
TL=0;
for i = Ri:Lp:Ro,
Circ = 2*pi()*i;
TL = TL+Circ;
end
TL
NumCBits = (TL/Lb);
Convert = NumCBits*(1.4112/4.3218);
TotalBytes = (Convert/8); %Convert bits to bytes
InMB = TotalBytes/(1048576) %Convert bytes to megabytes
%CD Storage = 900MB
C2: Matlab code to calculate DVD storage size
%Calculating DVD sample size
%Vincent Giang
18
Lb = .096*10^-6; %average bit length [m] calculated from sample
Lp = .80*10^-6; %average pitch [m]
Ri = 22.2*10^-3;
Ro = 59*10^-3;
TL=0; %Total Length
for i = Ri:Lp:Ro,
Circ = 2*pi()*i;
TL = TL+Circ;
end
TL
NumCBits = (TL/Lb);
Convert = NumCBits*(1.4112/4.3218);
TotalBytes = (Convert/8); %Convert bits to bytes
InMB = TotalBytes/(1048576) %Convert bytes to megabytes
% DVD Storage = 4.76 GB
C3: Matlab code to calculate Blu-ray storage size
%Calculating DVD sample size
%Vincent Giang
Lb = .048*10^-6; %average bit length [m] calculated from sample
Lp = .34*10^-6; %average pitch [m]
Ri = 22.2*10^-3;
Ro = 59*10^-3;
TL=0; %Total Length
for i = Ri:Lp:Ro,
Circ = 2*pi()*i;
TL = TL+Circ;
end
TL
NumCBits = (TL/Lb);
19
Convert = NumCBits*(1.4112/4.3218);
TotalBytes = (Convert/8); %Convert bits to bytes
InMB = TotalBytes/(1048576) %Convert bytes to megabytes
% Blu-ray Storage = 22.39 GB
REFERENCES
[1] Ackerson, B., Bertholf, D., Choike, J. Stanley, E., Wolfe, J., 1998, “Red & Blue Laser CDs: How
much data can they hold?”, The Consortium for Mathematics and Its Applications (COMAP), pp. 8.
[2] Blu-ray Disc Association, 2012, “BD vs. DVD,” Company website, http://www.bluraydisc.com/en/aboutblu-ray/whatisblu-raydisc/bdvs.dvd.aspx
[3] Blu-ray Disc Association, 2012, “White Paper Blu-ray Disc Format”, 3rd Edition, pp. 1-46.
[4] Blu-ray Disc Founders, 2004, “White Paper Blu-ray disc format, Key Technologies”, pp.1-8,
http://www.blu-raydisc.com/Assets/Downloadablefile/4_keytechnologies-15264.pdf
[5] Choi T., Felix D., Kasanavesi S.K., and Milster T.D., 2004, “Data Recovery from a Compact Disc
Fragment,” Proceedings of SPIE, (5380), pp. 116-127.
[6] Cleveland J.P., Manne S., Bocek D., and Hansma P.K., 1992, “A nondestructive method for
determining the spring constant of cantilevers for scanning force microscopy,” Review of Scientific
Instruments, (64) No. 2, pp. 403-405.
[7] Cope, John A., 1993, “The Physics of the Compact Disc.”, Physics Education, 28, (15), pp. 15-21.
http://cartan.emoka.net/content/download/807/5072/file/The%2520physics%2520of%2520the%2520com
pact%2520disk.pdf.
[8] ECMA, 2010, “Recordable Compact Disc Systems CD-R Multi-Speed,” Standard ECMA-394,
Edition 1, pp. 2-4,2-5
[9] Fedor, A., 2009, “Diffractive Optics: Harmonic optical element simplifies Blu-ray optics”, Laser
Focus World, http://www.laserfocusworld.com/articles/print/volume-45/issue-2/features/diffractiveoptics-harmonic-optical-element-simplifies-blu-ray-optics.html
[10] Fischer, R., 2008, Optical System Design, Second Edition, McGraw Hill Professional, pp. 199-212,
Chap. 11.
[11] Gittes F., Howard J., Mickey B., and Nettleton J.,1993, “Flexural Rigidity of Microtubules and Actin
Filaments Measured from Thermal Fluctuations in Shape,” The Journal of Cell Biology, Vol. 120, No. 4,
pp. 1-3, 7
[12] Kait, G., 2013, Spectrum Purifier and Codename Turquoise II CD and CD Tray Colorizers, Machina
Dynamica, http://www.machinadynamica.com/machina23.htm
20
[13] Lesurf, J.C.G., 2001, Information and Measurement, Second Edition, CRC Press, pp. 83-91
[14] Pohlman, K., C., 1989, “The compact Disc: A Handbook of Theory and Use”, A-R Editions, Inc.,(5)
pp. 47-62, Chap. 3
[15] Webb, Colin E., Jones J.D.C., 2004, “Handbook of Laser Technology and Applications”, (1-3), pp.
2402.
21