ESC471H1
Engineering Science Capstone Design
Optical Tweezers Preliminary Design Report
Date
October 22nd, 2010
Group Members
Maryam Badakhshi
Shannon O’Keefe
Laura Poloni
Hasmita Singh
Instructors
Professor Foster
Professor Nogami
Table of Contents
Date ............................................................................................................................................................... 0
Group Members ............................................................................................................................................ 0
Instructors ..................................................................................................................................................... 0
1. EXECUTIVE SUMMARY .............................................................................................................................. 3
2. LASER SAFETY DESIGN............................................................................................................................... 4
2.1 – Requirements and Constraints......................................................................................................... 4
2.2 – Detailed Design ................................................................................................................................ 5
2.2.1 – Optical Fiber Enclosure ............................................................................................................. 7
2.2.2 – Open-Beam Enclosure ............................................................................................................... 8
2.2.3 – Interlocks ................................................................................................................................... 9
2.3 – Assessment of Laser Safety Design ................................................................................................ 13
3. EXPERIMENTAL DESIGN .......................................................................................................................... 14
3.1 – Requirements, Constraints and Criteria......................................................................................... 14
3.1.1 – Technical Constraints: Laser Safety......................................................................................... 14
3.1.2 – Experimental Constraints and Criteria .................................................................................... 14
3.2 – Assessment and Revision of Experiment ....................................................................................... 17
3.2.1 Experiment Assessment ............................................................................................................. 17
3.2.2 Student Assessment ................................................................................................................... 18
3.2.4 Instructor/TA Training ................................................................................................................ 19
3.3 – Deliverables .................................................................................................................................... 20
3.3.1 Student Materials – Protocols ................................................................................................... 20
3.3.2 Instructor/Teaching Assistant Materials .................................................................................... 20
3.3.3 Safety Sheet ............................................................................................................................... 20
3.3.4 Safety Sign .................................................................................................................................. 20
3.3.5 Lecture Presentation .................................................................................................................. 20
3.3.6 Laser Safety Quiz ........................................................................................................................ 21
4. BUDGET ................................................................................................................................................... 22
5. SCHEDULE ............................................................................................................................................... 23
5.1 –Weekly Milestones .......................................................................................................................... 23
5.2 – Critical Tasks ................................................................................................................................... 24
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ESC471 – Optical Tweezers Preliminary Design Report
6. CONCLUSION ........................................................................................................................................... 25
7. REFERENCES ............................................................................................................................................ 26
APPENDIX A – Assessment of Alternative Solutions ................................................................................... 27
APPENDIX B – Discussions with Client ........................................................................................................ 27
APPENDIX C – Existing Optical Trap Experiments ....................................................................................... 31
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ESC471 – Optical Tweezers Preliminary Design Report
1. EXECUTIVE SUMMARY
This report outlines the laser safety design for the newly acquired Optical Tweezers system which is
necessary to ensure that the apparatus is safe for undergraduate student use. As well, experimental
revisions will be incorporated into the existing experiment with a focus on user-experience, which will
allow the introduction of the Optical Tweezers experiment into the Advanced Physics Laboratory at the
University of Toronto. This research-level apparatus which has been acquired by the University of
Toronto Physics Department will provide students with the opportunity to combine the theoretics of
physics, nanoengineering, and biomedical engineering in a modern research environment. However,
before this apparatus is employed by students, provisions must be made to ensure that the laser beam
used in the experiment is secure and will not cause harm to the user.
We will address the hazards associated with the laser source of the Optical Tweezer system by
implementing engineering and administrative laser safety controls. Our solution involves the enclosure
of the open-beam region of the laser as well as the inclusion of an interlock designed to instantly turn
off the laser when the open-beam region is exposed. We will also implement a protective encasing to
enclose the delicate fibre optic. Such measures will ensure that the optical trapping apparatus is safe for
students who have not completed the full day laser safety training course prior to executing the
experiment. As well as fulfilling the technical laser safety constraints, our experimental design also
ensures that students will still be able to manipulate the apparatus and apply the optical tweezers setup
to determine trap stiffness. A complete experimental protocol, teaching assistant lab manual, and other
appropriate safety provisions will be developed and provided to instructors to enable the smooth
functioning of the laboratory and assure that proper safety protocols are obeyed.
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ESC471 – Optical Tweezers Preliminary Design Report
2. LASER SAFETY DESIGN
The existing optical tweezers system necessitates the inclusion of enclosures during full
power operation and associated interlocks.
2.1 – Requirements and Constraints
Table 1 lists the technical constraints for the optical tweezers apparatus, developed in
consultation with Professor Bailey, Professor Ryu, and Dr. Sandu Sonoc (Certified Laser Safety Officer,
Radiation Protection Service):
Table 1 Technical Constraints
Item
ID
T1
T2
T3
T4
T5
T6
T7
Description of Constraint
The Optical Tweezers experiment must be made safe for undergraduate students who have not
taken the full day laser safety course and should be classified as a Class 1 laser.
The optical tweezers system employs a 980nm laser with a maximum power output of 330mW.
If the laser is exposed, it is considered a Class 3B laser. Appropriate measures must be taken to
enclose the optical path of the beam at the region where the laser is exposed. If the enclosure
is opened for beam alignment, the laser power output must be reduced to 5mW (Class 1) or
the laser must be completely shut off.
The light path where the beam is exposed to air should be enclosed.
The fibre optic should be enclosed for protective purposes. It would be helpful to be able to
observe the fibre optic under the enclosure.
The reflected beam should not leak out from the sample stage, and the user must be able to
move the sample stage using the knobs (Refer to #7 in Figure 1).
There are x, y, and z knobs for sample stage movement. These must be accessible when the
beam is on.
Budgetary constraints: Additional components added onto the existing apparatus should not
exceed CDN $1000.
The design must prevent students from inserting an object into the path of the laser which
could cause the beam to diverge.
Interlocks should not automatically reset. If an interlock is opened and the beam is turned off,
the beam should not turn back on automatically when the interlock is closed again; the laser
should need to be turned back on.
**T7  when the interlock is closed, the beam turns on.
The optical tweezers apparatus and a detailed schematic are shown in Figure 1 below:
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ESC471 – Optical Tweezers Preliminary Design Report
Figure 1 Optical Tweezers apparatus and detailed schematic
a)
b)
Existing Apparatus
Detailed schematic [H5]
2.2 – Detailed Design
The design consists of three components:
1. Enclosure for the Optical Fiber (“Optical Fiber Enclosure”)
2. Enclosure for the open-beam segment of the apparatus (“Open-Beam Enclosure”)
3. Interlock to ensure the Open-Beam Enclosure is in place when the laser diode is ON (“Interlock”)
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ESC471 – Optical Tweezers Preliminary Design Report
The existing apparatus is shown in Figure 2a and the preliminary design is shown in Figure 2b.
Figure 2 Existing Apparatus and Preliminary Design
(a) Existing Apparatus
(b) Preliminary Design showing Optical Fiber Enclosure, Open-Beam Enclosure, and positions of Microswitches for the
Interlock
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ESC471 – Optical Tweezers Preliminary Design Report
(c) Detailed Preliminary Design showing dimensions of Enclosures
2.2.1 – Optical Fiber Enclosure
The trapping source (1 in Figure 1) in the OTKB Optical Trapping Kit is a temperature stabilized 330 mW
(max) SM fiber-pigtailed laser diode with a central wavelength of 980 nm. The output of the laser is
collimated using a FiberPort (2 in Figure 1), which allows the aspheric collimation lens to be precisely
positioned along 5 axes (X, Y, Z, Pitch, and Yaw)Error! Reference source not found.. The optical fiber
connecting parts 1 and 2 is usually made of very thin layers of glass like material (usually Silica), but
other materials such as fluorozirconate, fluoroaluminate, and chalcogenide glasses can also be used
Error! Reference source not found.. This wire must be handled with extra caution due to its sensitive
material. There are numerous ways to harm this wire, including: pulling on the fibers, exceeding the
maximum loading rate and bend radius, or twisting the cable and dropping an object on the fibre Error!
Reference source not found.. Due to the potential occurrence of these situations, it is an essential part
of our design to enclose this section of the laser with a protective box. This protective box will be
mounted on top of parts 1 and 2, including the fiber optic wire. This enclosure can be seen in Figure 2b
and 2c, as well as Figure 3b.
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ESC471 – Optical Tweezers Preliminary Design Report
Since the optical fiber does not present any potential laser safety hazards, any transparent material
would be sufficient for the coverage and at the same time would allow the fiber optic to be visible to
users. Thus, the enclosure be constructed from Plexiglass. L-brackets will be attached to the Optical
Fiber Enclosure to facilitate securing the enclosure with screws to the optical breadboard that the
apparatus rests upon (hardware and overall schematic shown in Figure 3).
Figure 3 Hardware Required for Optical Fiber Enclosure
(a) L-brackets
(b) Optical breadboard contains threaded holes for securing optical
components with screws [L1].
(c) Overall schematic depicting Optical Fiber Enclosure secured to Optical Breadboard with L-Brackets and screws
2.2.2 – Open-Beam Enclosure
As previously noted, this laser is currently classified as a Class 3B laser when the laser beam is not
covered by a physical barrier 0. This occurs in the Optical Tweezers system between sections 2 and 4 as
depicted in Error! Reference source not found.. Persons operating an open-beam Class 3B laser are
required to participate in the full day laser training session [Proposal 13], which is not feasible for
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ESC471 – Optical Tweezers Preliminary Design Report
students in the Advanced Physics Laboratory course. If the open-beam sections of the apparatus are
covered by an optically dense material, this laser can be re-classified as a Class 1 laser and it can be
handled by students wearing appropriate laser safety goggles, and the laser safety training would not be
necessary.
However, for polarization applications, the keyway on the FiberPort can be rotated about the optical
axis so that the orientation of a linearly polarized collimated beam can be set. A 2X beam expander (3 in
Figure 1) is used to fill the aperture of the focusing objective (6 in Figure 1) Error! Reference source not
found.. The laser diverges at this section and thus increases the probability of occurrence of a harmful
situation during alignment. In addition, since the light in this wavelength (980 nm) is not visible to the
human eye, there is a high probability for harmful effects to occur without the knowledge of the
student.
Therefore, it is necessary to enclose the open-beam region of the apparatus while the laser is being
operated at full power. However, it is also necessary that students are able to remove this enclosure to
align the laser, at which point the laser should be shut off.
The design of the Open-Beam enclosure is shown in Figure 2b and 2c. In order to ensure that the
student is safe at all times, this enclosure will be constructed from a material with the appropriate
optical density required for the laser diode being used. This will ensure the safety of the student when
turning on the laser in the case that the laser was left misaligned from the previous user. The laser used
in this apparatus is a 980 nm IR laser diode [H5]. For this wavelength, an optical density greater than 6
(OD 6+) is required, and a suitable material for this is the LV-F-2009 plastic laser filter from Lasermet Ltd.
[L3], which can be ordered in a variety of sizes.
The enclosure will be secured to the optical breadboard (shown in Fig. 3a) using L-brackets (shown in
Fig. 3b) attached to the sides of the enclosure and the appropriate screws that fit into the breadboard.
2.2.3 – Interlocks
An interlock will be utilized in combination with the open-beam enclosure. This enclosure will be in
place when the laser is being operated at full power, and the associated interlocks will be designed to
ensure the laser automatically shuts off when the open-beam enclosure is not secured in its proper
position.
The interlock will take advantage of the built-in interlock feature of the laser diode, and will consist of
several microswitches that will act as a sensor that the open-beam enclosure is in place. The LM14S2
Butterfly Laser Diode (Figure 4) is equipped with a Remote Interlock Connector [M1] that enables the
external control of the laser state (on/off). In order for the laser diode to turn on, a short circuit must be
applied across the terminals of the connector [M1]. The laser diode is currently configured with a
shorting device installed in the Interlock Connector, allowing the laser to operate normally. This shorting
device can be removed by unscrewing it from the input, and the interlock feature can be used by
installing a 2.5mm mono phono jack into the input [M1].
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ESC471 – Optical Tweezers Preliminary Design Report
Figure 4: Picture of the LM14S2 mount
Interlock Connector
The design of the interlock system connects the output of the mono phono jack to an external switch
that is only ON when the Open-Beam Enclosure is in place. This external switch consists of four microswitches in series that create a short circuit across the mono phono jack when the open-beam enclosure
is properly secured. These micro-switches are positioned on the inside of the enclosure to prevent
students from tampering with them. Three of the micro-switches will be located along the bottom of the
enclosure, so that they are closed when the enclosure is placed on a flat surface. An additional
microswitch will be placed along the top of the enclosure, so that it will contact a component of the
apparatus underneath when the enclosure is in place. The positions of the micro-switches are shown in
Figure 5b.
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ESC471 – Optical Tweezers Preliminary Design Report
Figure 5 Schematic showing Interlock
(a) Connection between Interlock and Open-Beam Enclosure
(b) Positions of Microswitches (shown in red, in series and connected to Interlock Connector)
The following diagram shows the schematic of the proposed circuit and its connection to the interlock.
Please note that the Interlock will be connected to this circuit through the 2.5mm mono phono jack.
Figure 5: Schematic of the circuit
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ESC471 – Optical Tweezers Preliminary Design Report
Current of 10mA
InterLock
Wire from second connection/ Input to the interlock
1K Ohms
5V DC
Wire from first connection
Ground
This circuit is powered by an unregulated AC to DC power supply through a 5V DC voltage regulator. The
current through the interlock must be of 10mA and the open circuit voltage is 5V DC [M1]. These criteria
are met by choosing the resistor value to be of 1k Ohms.
Below is a diagram (top view) of the Enclosure and the circuit components of the laser safety kit. The
resistor is mounted on a circuit board, as well as the power supply kit and connection. The resistor will
be also enclosed such that it will not be accessible to the students to remove or damage.
Figure 6: Diagram of the enclosure with the circuit components
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ESC471 – Optical Tweezers Preliminary Design Report
2.3 – Assessment of Laser Safety Design
The laser safety design outlined above transforms the existing system from a Class 3B laser into a Class 1
laser, with the inclusion of the Open-Beam Enclosure and the Interlocks which will ensure full-power
operation only proceeds when the enclosure is in place and turned off otherwise. The critical region
where the laser beam is exposed is addressed through the design, and a full enclosure surrounding the
region prevents students from inserting objects into the path of the laser leading to undesirable effects.
This elegant design utilizes the built-in interlock feature, multiple microswitches which are
inaccessible/cannot be easily manipulated manually by students , and the design does not involve the
addition of any active components to the circuit. Additionally, this design was preferred by the client
over the alternative proposed solutions (Refer to Appendix A).
A reasonable laser safety design will be categorized as one that has a limit of two by-passes:
-need to expand on this. Also show that Prof. Bailey has approved this.
The design will undergo a thorough testing phase during which we will attempt to surpass the
safeguards in order to determine its weaknesses. If a vulnerability is discovered, appropriate measures
will be taken to improve the design and address the issues.
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ESC471 – Optical Tweezers Preliminary Design Report
3. EXPERIMENTAL DESIGN
The optical tweezers experiment is designed for use by students in the Undergraduate Advanced Physics
Laboratories (APL). The existing Optical Trap experiment, created in Professor Ryu’s lab by Jimmy Shen
will be revised based on the requirements, criteria and constraints that have been developed. The
experiment consists of several sub-experiments that aim to empirically determine the stiffness of the
optical trap. The focus will be placed on performing one method of obtaining the optical trap.
3.1 – Requirements, Constraints and Criteria
3.1.1 – Technical Constraints: Laser Safety
The Laser Safety program at the University of Toronto was developed to assist the University community
in the control of laser hazards, and must meet the following regulatory requirements [From Proposal 4]:




U of T Health and Safety Policy
Occupational Health and Safety Act of Ontario
ANSI standard Z136.1
ANSI standard Z136.1 for educational institutions
The laser diode that serves as the source for the Optical Tweezer system has an output power of
330mW 0. Therefore, this laser source is classified as a Class 3B laser and can pose many risks to users of
the system since a portion of the Optical Tweezer system has an open beam. In order to remain
compliant with laser safety regulations, users must participate in the University’s Laser Safety Program
training prior to operating or working with the system and as well as participate in the University’s
medical surveillance program. Since this lab will be part of the third and fourth year Advanced Physics
labs, in which the experiment would be carried out by a maximum of three students, each for a threeweek period, it is not feasible for the students to receive this training which is offered monthly.
Therefore, the system must be reconfigured such that the laser beam cannot be exposed at full power.
The inclusion of safety features will redefine the system as a Class 1 laser, for which there is a low
probability of injury and does not require users to attend the full-day laser safety course. The design for
the reconfiguration of the system to ensure laser safety is outlined in Section 2 (Laser Safety Design) of
this document.
3.1.2 – Experimental Constraints and Criteria
The current Optical Trap experiment consists of a general description of each experiment, questions to
be answered by the student as well as an appendix containing additional details about the various
components of the apparatus including some procedural details. However, there are numerous
limitations to this experiment. The main limitations are summarized below:



Insufficient procedural instructions to carry out the experiments
Lack of a Teaching Assistant (TA) manual providing further details
Inclusion of safety precautions and laser safety details in the lab manual
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ESC471 – Optical Tweezers Preliminary Design Report
In order to design the experiment from the perspective of the end-user experience and with a holistic
approach, such limitations must be addressed.
The inclusion of a detailed procedure and appropriate safety precautions allows the laboratory to be
executed safely and with ease, while at the same time maintaining the challenge of figuring out a
complex apparatus and how it functions. Providing additional information and training for the TA will
enable him/her to be well-acquainted with the experiment and provide better assistance. As such, these
limitations will be addressed through the development of a revised experiment, and have been included
in the experimental criteria.
As well, the goals for the APL include presenting the student with the “opportunity to work on
interesting and challenging experiments, deepen their understanding of the underlying Physics, and to
further develop laboratory, analysis and communication skills.” [H1]. Additionally, the “experiments in
this course are designed to form a bridge to current experimental research. A wide range of experiments
are available using contemporary techniques and equipment. Many of the experiments can be carried
out with a focus on instrumentation.” [H2]. As such, the following development of constraints that
constitute a “good laboratory experiment,” ranging from experimental constraints, to the experimental
protocol and method of evaluation, will reflect the objectives of the APL as well as approaches
considered in educational journals.
3.1.2.1 Experimental Constraints
Table 2 lists the Experimental Constraints for the proposed solution.
Table 2 Experimental Constraints
Item Description of Constraint
ID
E1
The experimental procedure should be executed within 18 hours over the course of 3 weeks.
Advanced Physics Laboratory structure.
E2
The room door must be closed and locked with a temporary “Laser Work in Progress” sign placed
outside the room door.
This sign can be provided by Sandu Sonoc, the Senior Radiation Safety Officer.
E3
Appropriate laser safety glasses must be worn at all times when using the equipment.
E4
The beam will not be pre-aligned prior to the student commencing the lab.
E5
The beam should be turned off when changing samples.
Changing the sample involves moving somewhat reflective material in and out of the beam path.
The beam must be turned off when this occurs. Normally, no light should reflect out when
changing the sample, but there is a chance that if someone sticks something in (eg. A pen to
indicate the beam position), then inserting an object may cause the beam to reflect wildly.
E6
The laser power supply key should be kept by the technologist.
E7
The experiment should be carried out individually, in accordance with APL structure.
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ESC471 – Optical Tweezers Preliminary Design Report
3.1.2.2 Student Assessment Criteria
Table 3 lists the Student Assessment Criteria for the experiments to be carried out on the Optical
Tweezers System.
Table 3 Student Assessment Criteria
Item Description of Criteria
ID
SA1 The mark composition for the laboratory should not be completely data-driven, and should
include a combination of data analysis within the student’s lab notebook as well as more general
questions pertaining to the lab that assess the student’s understanding. It should also include a
discussion with the TA/Professor regarding the results obtained.
This is in accordance with APL structure, and the consultation with the TA/Professor would
enhance oral and written communicability of technical material [H3].
SA2 Adequate time must be provided to the student for completion of the lab write-up.
SA3 The write-up should include a brief discussion of a research paper that utilizes Optical Tweezers
to bridge the experiment to current experimental research [H2].
3.1.2.3 Experimental Protocol Criteria
Table 4 outlines the criteria for the Experimental Protocol that will accompany any experiment to be
carried out on the Optical Tweezers System.
Table 4 Experimental Protocol Criteria
Item Description of Criteria
ID
EP1 Clear and succinct safety instructions must be given to the students through the experimental
write-up, from the instructor, and displayed on the wall near the equipment.
EP2 The experiment should provide more detailed procedural steps to facilitate the execution of the
experiment. This will ensure that a proper procedure is followed and leaves less room for
erroneous conduct around a high-powered laser.
EP3 The entire experiment should be divided into sections or a series of experiments that investigate
different concepts such that they can be carried out over the course of the 3-week lab.
The experiment should not be repetitive or tedious.
EP4 A more detailed experimental protocol should be provided to the TA/Professor to enable them to
assist the students when necessary. This should detail the potential pitfalls that may be
encountered [H4].
EP5 The protocol should include the background and theory pertaining to the lab, as well as clearly
detailed schematics of the apparatus [H4].
EP6 A list of relevant websites and papers that will aid the student in understanding the laboratory
concepts or equipment should be included.
EP7 The experiment should incorporate a variety of skills and techniques [H4].
3.1.2.4 Training Criteria
Table 5 lists the criteria pertaining to the training that a user of the Optical Tweezers System will require.
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ESC471 – Optical Tweezers Preliminary Design Report
Table 5 Training Criteria
Item
ID
Tr1
Tr2
Tr3
Tr4
Tr5
Description of Criteria
The TA/Professor present during the laboratory session should be well acquainted with the
experimental procedure and apparatus and should be available for assistance.
The student must require minimal initial training in order to execute the lab.
An introduction to the lab should be given by the TA/Professor to acquaint the student with
the lab concepts, the equipment, expectations and clearly stated safety instructions.
An instructor/TA manual should be provided, which includes additional details such as
information on the safety features and disassembling enclosures.
The TA supervising the experiment must attend the full day Laser Safety Training course.
3.2 – Assessment and Revision of Experiment
The revised experiment will encompass the requirements, constraints and criteria that have been
outlined, in order to create an improved laboratory experiment that will be usable by a modern student
for the APL. The purpose of this optical trapping experiment is to capture and observe particles within
the photon generated electric field. The stiffness of the optical trap maintaining particle position can
then be determined. This stiffness, analogous to the spring constant, k, of Hooke’s Law, establishes the
rate at which a trapped particle responds to an applied force and moves through the optical system [S1].
The focus will be placed on using Stokes’ law of drag force to determine the stiffness of the optical trap.
3.2.1 Experiment Assessment
The optical tweezers laboratory experiment will consist of two parts:
i.
Laser Safety and Applications
The optical trapping experiment would not be possible without the use of a high intensity laser to
provide sufficient photon force to trap small particles and beads. However, the current laboratory
experiment neglects to mention safety precautions for the laser and its alignment lenses. Our updated
experimental design will address this through the inclusion of a detailed description of laser safety
precautions. In the revised experiment, a presentation will be delivered which includes details regarding
laser safety. This will include “best practices” as well as components of the apparatus that must be dealt
with extra precaution. Students will then be required to demonstrate their understanding of such
procedures prior to commencing the lab (Refer to 3.3.6), which will ensure that students fully
comprehend the apparatus they will be working with.
ii.
Optical Trapping
In order to ensure that students are fully able to make use of and understand the optical trapping
apparatus, our experiment to determine optical trap stiffness will make direct use of modern physics
and fluid mechanics principals taught to second year engineering science students in PHY294 and
AER210, respectively. Students will employ Stokes’ Drag to measure deflections of trapped particles. By
drawing upon previously acquired academic theory and applying this knowledge in a practical setting,
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ESC471 – Optical Tweezers Preliminary Design Report
students will be able to make connections between theoretical knowledge and realistic applications, and
thus evaluate their learning progress. This concept of directing how the optical trapping experiment is
“perceived, learned, and used” by students is a fundamental concept of user experience design, a subset
of experience design that aims to affect “all aspects of the user’s interaction with a product” [S2]. The
purpose of drawing upon previous academic knowledge to make use of cutting-edge research
technology is to encourage students that the rigorous academic theory completed in their first two
years is indeed directly applicable to real-world applications. To aid the students in understanding the
applications of Optical Tweezers, links to relevant websites and research papers will be provided.
The existing experiment is partitioned into several sub-experiments, which aim to empirically determine
the optical trap stiffness through various methods. Although the focus will be placed on one of these
methods, the sub-experiment structure will be maintained to preserve the variability in the methods
and the feasibility of the lab over the course of three laboratory sessions. Furthermore, the experiment
encompasses a variety of skills and techniques, as the student must first gain familiarity with the
complex apparatus and procedures, employ a specific method in order to trap beads, perform data
analysis and apply relevant theory in order to calculate the trap stiffness as well as present and
communicate this information to the instructor and/or the TA. As such, this experiment serves to
deepen the student's understanding of the underlying Physics and enhance their laboratory skills
pertaining to the use of the optical tweezers instrumentation, thereby addressing the guidelines of the
APL.
3.2.2 Student Assessment
To demonstrate complete understanding of the safety regulations surrounding the optical tweezer
apparatus, students will be expected to complete a short quiz prior to commencing (refer to 3.3.6).
Doing so will help to ensure that the experimental constraints are met and the experimental protocol is
followed. Sample laser safety questions students are expected to answer are below:



What safety precautions must be taken before turning on the laser?
o The room door must be closed and locked with a temporary “Laser Work in
Progress” sign placed outside the room door
o Laser safety glasses must be worn by all students at all times
Under what circumstances is it acceptable to open the laser beam enclosure?
o The laser is turned off and attempts to turn the laser back on will not begin until the
laser is fully enclosed once again
During which portions of the experiment must the laser be turned off and why?
o When changing samples, the laser beam must be turned off to avoid reflection
Students will also be required to demonstrate their understanding of the theory and applications
regarding Stokes’ Drag and Optical Trapping by answering several theoretical questions. Sample
questions are described below:

Derive the expression for the drag coefficient in detail.
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ESC471 – Optical Tweezers Preliminary Design Report


Show that the forces acting on the bead are in the low Reynold’s number regime.
Demonstrate that the assumptions of Stokes’ drag are appropriate.
Once laboratory safety constraints are met, students will be free to explore the process of optical
trapping on their own, in accordance with individual learning styles. According to David A. Kolb’s
Experimental Learning Theory, the processes by which individuals conceptualize ideas and form
conclusions vary and can be classified into 4 main learning styles: the converger, accommodator,
assimilator, and diverger [S3]. Therefore, to accommodate the unique learning styles of students, our
laboratory protocol and assessment will provide students with the opportunity to demonstrate the
knowledge they have gained in their own preferred method of expression. Though students will be
required to answer several theory based questions regarding the experiment, some of which can be
found above, the methods in which the questions are solved can be adapted to suit individual learning
styles. Furthermore, students will be required to draw their own conclusions about the Stokes’ Law and
optical trap stiffness. These conclusions can be formed in accordance with the students’ preference. For
example, a student with a convergent learning style may wish to use deductive reasoning to focus on
specific problems that arise in the lab, while an accommodator may prefer to learn through actively
completing and comparing several different experimental methods. By working safely to measure
particle deflection and drag forces affecting the beam in an individualized approach, students will gain a
unique and detailed understanding of the components and uses of the optical tweezers apparatus.
The mark composition for the lab will consist of assessment of the data analysis, answers to the more
general theoretical questions (given above) as well as a discussion with the instructor and/or the TA.
Also, the write-up must include a brief description of a research paper utilizing the Optical Tweezers to
make the student aware of recent experimental research, which is in accordance with the objectives of
the APL. The informal laboratory report, which is to be completed directly in the lab notebook, must be
submitted one week following the completion of the lab to provide adequate time for the student to
carry-out the necessary research and clearly grasp the concepts addressed through the labs.
3.2.4 Instructor/TA Training
Instructors and teaching assistants will be provided with a more detailed laboratory manual so that they
are well-acquainted with the apparatus and can provide assistance to the students. The instructor
and/or the TA supervising the lab must attend the full day Laser Safety Training course. This will ensure
that the supervisor is familiar with the safety procedures pertaining to the lab and can clearly and
succinctly convey these to the students.
In addition to laser safety, the instructor manual will also contain a detailed marking scheme, to aid in
the assessment of the laboratory write-up submitted by the student. Having these marking details will
ensure consistent and fair grading between various TAs and semesters. A final section, providing
instructors with helpful hints and common solutions to experimental problems (if/when they arise), will
help teaching assistants provide aid to students in a quick and effective manner. This section will be
constructed from the problems that arise while the experiment is developed and carried out.
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ESC471 – Optical Tweezers Preliminary Design Report
3.3 – Deliverables
3.3.1 Student Materials – Protocols
One of the main improvements that will be made to the experiment is the inclusion of a more detailed
procedure for executing the necessary steps. This will eliminate time spent on figuring out the apparatus
and leaves less room for dangerous practice through the inclusion of specific instructions. As the optical
tweezers operate with the use of a high-powered laser beam, such provision is necessary to ensure that
appropriate procedures are followed. The lab manual will also include laser safety procedures/details to
ensure that students are aware of proper practices.
3.3.2 Instructor/Teaching Assistant Materials
An instructor (TA) manual will be created, which will include additional details surrounding the
experiment. For instance, a description of the safety features that will be designed will be outlined in the
instructor/TA manual. These details will not be included in the student manual as students should not
have the necessary information to prompt tampering with the enclosures and interlocks. However, the
in the case that the instructor or TA requires access to the enclosed components (such as to perform
beam alignment), sufficient details will enable them to do so. Details on performing laser beam
alignment may also be included.
3.3.3 Safety Sheet
A safety sheet will be mounted on the wall adjacent to the optical tweezers apparatus, and will detail
safety procedures that must be obeyed while performing the lab. It will also have a short description of
different types of beams and explanation on why these safety procedures are necessary for this specific
apparatus.
3.3.4 Safety Sign
While the optical tweezers are in operation, a temporary "Laser Work in Progress" sign must be
mounted on the outside of the door (MP248) which will be provided by Dr. Sandu Sonoc.
3.3.5 Lecture Presentation
A brief presentation, approximately 10 - 15 minutes in length, will be prepared and delivered for peer
and instructor review. The details of this presentation will be included in the laboratory instructor
manual and can be repeated by TAs to introduce students to the lab. This presentation will ensure that
will acquaint students with laboratory concepts, the equipment, expectations, and clearly specific safety
instructions.
This presentation will begin with a brief overview of the theory behind and applications of optical
trapping. Once students are aware of the purpose and uses of this apparatus, focus will be on ensuring
safe operation of the equipment. Details on laser safety and specific rules that must be followed will be
reviewed. Finally, a brief description of each of the major components of the apparatus will be
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ESC471 – Optical Tweezers Preliminary Design Report
delivered. This portion of the presentation will focus on laser safety, and how proper operation of each
component is required to ensure a safe and secure experiment.
3.3.6 Laser Safety Quiz
The lecture presentation will be followed by a short laser safety quiz. This quiz will be based on the main
safety concepts discussed in the presentation, which will reflect the main concepts from the full day
Laser Safety Training course. The purpose of this quiz is to ensure that the student comprehends the
safety instructions and can safely proceed with the experiment. This is modeled after the IBBME
teaching laboratory style, which begins with a safety quiz proceeding a brief presentation on safety
procedures.
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ESC471 – Optical Tweezers Preliminary Design Report
4. BUDGET
Table 6 outlines the estimated costs for the implementation of the laser safety design as well as the
materials necessary for conducting the experiment described in section 3.2.1. As seen from this table,
the total expenditure for the preliminary design will be_____. This is within the constraint of CDN $1000
defined by Prof. Bailey.
Table 6 Preliminary Design Budget
Component
Optical Fibre
Enclosure
Open-Beam Enclosure
Safety Interlock
Item
Plexiglass (1/4” thickness)
Amount Required
2 ft2
Estimated Cost
$50 [plexiglass]
Screws
L -brackets
Optical Density Filter
Screws
L-Brackets
2.5. mono phono jack
Microswitches
Wire
Solder and Soldering Iron
10
10
$7.20/pkg of 10 [skrews]
2
2
1
4
2m
N/A (already have
this)
5ML in aqueous
solution
$7.20/pkg of 10 [skrews]
Experimental Methods Polystyrene Micro
particles
$6
$2
$5
N/A
$250 [polystyrene]
Total Estimated Cost:
[plexiglass] http://www.professionalplastics.com/PLEXIGLASS-ACRYLICSHEET-EXTRUDED
[screws] http://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=1437
[polystyrene]
http://www.sigmaaldrich.com/catalog/ProductDetail.do?lang=en&N4=89904|SIGMA&N5=SEARCH_CO
NCAT_PNO|BRAND_KEY&F=SPEC
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ESC471 – Optical Tweezers Preliminary Design Report
5. SCHEDULE
5.1 –Weekly Milestones
The laser safety design and development of an improved experiment will be executed in parallel.
An outline of the major tasks to be completed each week is provided in Table 7.
Table 7 Schedule for
Week
October 18th, 2010
October 25th, 2010



Laser Safety Tasks
Design interlock circuit
Develop detailed schematics of
Optical Fibre Enclosure and OpenBeam Enclosure
Purchase circuit components and
enclosure materials (filter,
plexiglas, screws, L pieces)




November 1st, 2010


November 8th, 2010

November 1st, 2010

November 15th, 2010

November 22nd, 2010

November 29th, 2010

December 6th, 2010
Build Circuit Component of the
Laser Enclosure
Test the Interlock with the
external switches
Construct fiber optic and openbeam enclosure components
Integrate the enclosure and
circuit components together
Test the completed circuit and
enclosure kit
Test the completed circuit and
enclosure kit

Experiment Tasks
Attend Laser Safety Training
course
Review existing experiment and
develop a general procedure
from papers
Gain familiarity with the various
components of the apparatus
Speak with Bryan Keith to
obtain sample bead and
additional materials
Gain familiarity with the various
components of the apparatus

Execute lab and record
procedural details
 Execute lab and develop a
detailed procedure
 Execute lab and develop a
detailed procedure
 Execute lab
 Refine procedural details
 Develop TA manual
Develop written description of
 Execute lab
enclosure and Interlock system
 Refine TA manual
for TA manual
 Create safety sheet
Experiment Walk-through
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ESC471 – Optical Tweezers Preliminary Design Report
Note: Enclosures will be constructed in the Physics Department Machine shop. As suggested by
Professor Bailey, team members will either receive machine shop training or provide the dimensions
and have the design fabricated by the machine shop manager.
5.2 – Critical Tasks
Table 8 outlines the critical tasks that must be completed in order to implement the laser safety design.
Table 8 Critical Tasks for Implementation of Preliminary Design
Task
Description
Path Forward
Attend Laser Safety
Training
Two out of the four group members will have
received laser safety training, which is
sufficient to proceed with the project as
determined by Prof. Bailey
Laura has already completed
Laser Safety Training. Hasmita
will have completed Laser Safety
Training by 4 PM on Oct. 22,
2010.
Order the optical
density filter plastic
for construction of
the Open-Beam
Enclosure
This material is necessary for constructing
the open-beam enclosure, which must be in
place before group members without the
laser safety training are able to operate the
apparatus.
Purchase the 2.5mm These components are necessary for
mono phono jack
preliminary prototyping as well as for the
and microswitches
final design implementation.
2.5mm mono phono jack can be
purchased at most electronics
stores (i.e. Radio Shack).
Microswitches can be purchased
at Creatron.
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ESC471 – Optical Tweezers Preliminary Design Report
6. CONCLUSION
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ESC471 – Optical Tweezers Preliminary Design Report
7. REFERENCES
[L1] “Performance Series, 60 mm (2.4") Thick, High Stiffness, Standard Damping Breadboards.”
Thorlabs. http://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=1857
[L2] Laser safety manual? Should find reference for this....
[L3] “Plastic Laser Filter Windows.” Lasermet. http://www.lasermet.com/filter-windows-plastic.php
[H1] University of Toronto Physics Department. “Advanced Physics Laboratory Course Homepage.”
12 September 2010. http://www2.physics.utoronto.ca/~phy326/
[H2] “Engineering Academic Calendar 2010 – 2011.” University of Toronto.
http://www.undergrad.engineering.utoronto.ca/Assets/UndergradEng+Digital+Assets/calendar1
011/Chapter+8.pdf
[H3] Panel on Undergraduate Engineering Education, Committee on the Education and Utilization of
the Engineer, Commission on Education and Technical Systems, National Research Council.
Engineering Undergraduate Education. Washington, DC: National Academy Press, 1986, pp.82.
[Online]. Available: http://www.nap.edu/openbook.php?record_id=589&page=82. Accessed Sept
26, 2010.
[H4] E. Bell, “Laboratory Exercises”, Biochemistry and Molecular Biology Education, vol. 29, no. 3,
2001. [Online]. Available: http://onlinelibrary.wiley.com/doi/10.1111/j.15393429.2001.tb00086.x/pdf. Accessed Sept 26, 2010.
[H5] “Optical Trapping Kit Schematic ”. Thorlabs.
http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3959
[M1] LM14S2 Butterfly Laser Diode Mount Operating Manual
http://www.thorlabs.com/Thorcat/10600/10614-D02.pdf
[M2] Thorlabs.com [Online], Available :
http://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=3328
[M3] Operation Manual ,Thorlabs Instrumentation,Laser Diode Combi Controller, Thorlabs Inc., 435
Route 206, Newton, NJ 07860
[S1] Neuman KC, Block SM (2004). "Optical trapping". Review of Scientific Instruments 75 (9): 2787–
2809.
[S2] Donald Norman: Invisible Computer: Why Good Products Can Fail, the Personal Computer Is So
Complex and Information Appliances Are the Solution. MIT Press. 1999.
[S3] Kolb, David (1984). Experiential learning: Experience as the source of learning and development.
Englewood Cliffs, NJ: Prentice-Hall.
[From Proposal 4] D. C. Appleyard, K. Y. Vandermeulen, H. Lee, M. J. Lang, Optical trapping for
undergraduates, Department of Biological Engineering, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, 22 September 2006.
[From Proposal 5] “PL980P330J - 975 nm, 330 mW, Butterfly Laser Diode, SM Fiber, FC/APC .”
Thorlabs. http://www.thorlabs.com/thorProduct.cfm?partNumber=PL980P330J
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ESC471 – Optical Tweezers Preliminary Design Report
APPENDIX A –Alternative Laser Safety Solutions
**all references below are from the proposal
Each of the alternative laser safety solutions consists of two components: making the laser safe for
students to use and also assuring that the laser itself is protected while in use.
In order to protect the laser, it is necessary to enclose the Optical Fiber that connects the output of the
laser diode to the FiberPort component of the apparatus that collimates the laser beam. Each of the
alternative solutions includes an enclosure for the Optical Fiber as outlined in Section 2.2.1.
Alternative Solutions for User Safety
As previously noted, this laser is currently classified as a Class 3B laser when the laser beam is not
covered by a physical barrier 0. This occurs in the Optical Tweezers system between sections 2 and 4 as
depicted in Error! Reference source not found.. Persons operating an open-beam Class 3B laser are
required to participate in the full day laser training session [13], which is not feasible for students in the
Advanced Physics Laboratory course. If the open-beam sections of the apparatus are covered by an
optically dense material, this laser can be re-classified as a Class 1 laser and it can be handled by
students wearing appropriate laser safety goggles, and the laser safety training would not be necessary.
However, for polarization applications, the keyway on the FiberPort can be rotated about the optical
axis so that the orientation of a linearly polarized collimated beam can be set. A 2X beam expander (3 in
Figure 1) is used to fill the aperture of the focusing objective (6 in Figure 1) Error! Reference source not
found.. The laser diverges at this section and thus increases the probability of occurrence of a harmful
situation while re-aligning is being performed. In addition, since the light in this wavelength (980 nm) is
not visible to the human eye, there is a high probability for harmful effects to occur without the
knowledge of the student.
Therefore, it is necessary to enclose the open-beam region of the apparatus while the laser is being
operated at full power. However, it is also necessary that students are able to remove this enclosure to
align the laser, at which point the power output of the laser would have to be reduced to 5mW (Class 3R
laser) so that laser hazards are eliminated.
Alternative Solution #1
Electromechanical: Control of laser depending on enclosure state (open/closed)
It is one of our goals to make the laser safe for students by limiting the amount of power going through
the laser after it has gone through Fiber Controlled Laser Source (part 1 in Error! Reference source not
found.) and the fiber optic wire. This can be done by inserting an optical density filter between the Fiber
Port Collimator (part 2 in Error! Reference source not found.) and the Beam Expander (part 3 in Error!
Reference source not found.). The optical density filter would reduce the power of the laser beam to
the desired 5mW. This filter can be purchased from Thorlabs and mounted on the laser 0 using the
Magnetic Mount already available to us.
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ESC471 – Optical Tweezers Preliminary Design Report
It is required by our clients that the students should not be able to open the enclosure around parts 1
and 2 when the laser is on and the power through the laser is more than 5mW. In order to address this,
we would attach a touch sensor plan on top of the magnetic mount of the filter that will be turned on
when the box is closed. The output of this touch sensor is input to an external control button. This
control button will allow students to open the enclosure when the laser is on. For example, if the box is
closed, the laser is on, and the magnetic mount is not inserted, the touch sensor will open the control
button’s circuit and the latch that is controlled by the button will not work.
Figure A1shows a rough schematic that demonstrates the connections:
Figure A1 Block diagram of the laser enclosure, the magnetic mount, and connection to the touch sensor and control button
Figure A2 demonstrates how the latch is controlled by the touch sensor:
Figure A2 Control of Latch using Touch Sensor
The addition of the enclosure to the pre-existing apparatus is estimated to be about CDN $100, including
the material and the latch. Since the magnetic mount has already been purchased, it will not be an
additional cost. The sensor is priced at about CDN $50 on the Thorlabs website, and other parts that
may need to be purchased (including circuit components, the control button, etc.) will cost about CDN
$200. We estimate the total cost to be about CDN $500, which meets the budgetary constraints of CDN
$1000.
Alternative Solution #2
Microcontroller: Control of laser depending on enclosure state (open/closed)
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ESC471 – Optical Tweezers Preliminary Design Report
Another method of controlling the laser power output would be through a microcontroller design. The
controller (ITC510) would be interfaced with the IEEE488 that is based on the IEEE488.2 standard. This
includes the IEEE488.1 standard for the hardware settings 0. This interface can be used to control
whether the laser is on or off by taking advantage of built in hard codes that can control the operation
status of the laser 0.
The microcontroller device would be controlled based on an electrical connection made when a
magnetically-mounted optical density filter (described in Potential Solution #1) is inserted in the laser
pathway. When the optical density filter is inserted in front of the laser, the microcontroller receives the
positive signal that the laser is safe. This would allow the laser to operate at its maximum power. If the
mount is removed while the laser is in “on” mode at full power, a negative signal will be sent through
the connection to the microcontroller which will result in a reduction of power or shut off the laser
completely. Through this direct control of the state of the laser through the microcontroller, the
experiment would be considered laser safe as the laser would be turned off in appropriate
circumstances.
As in Proposed Solution #1, the addition of the enclosure to the pre-existing apparatus is estimated to
be about CDN $100, including materials and fabrication. The cost of the microcontroller is estimated to
be CDN $100, with additional electrical components costing another CDN $50. This brings the total cost
of this proposed solution to CDN $250, which is within our budgetary constraints.
Alternative Solution #3
Mechanical: Control of laser depending on enclosure state (open/closed)
A third possible solution for ensuring the safety of the users from the laser depending on the enclosure
state is to use an enclosure that consists of two components: 1) A left half of box which would be fully
enclosed with plexiglass, and 2) A right half which consists of an optical filter and is not enclosed at the
top (A3). These two components would be connected and placed on a track, which would allow
movement of the box along the track. When the experiment is in operation once the beam has been
aligned, component 1 would be in front of the beam as it is a fully enclosed box. It would protect laser
beam from being exposed to the human eye and causing harmful effects, as it will be operating at full
power (330mW). When the laser beam alignment takes place, the box must be slid along the track so as
to place component 2 in front of the beam. This component would filter the high power beam and
enable the student to safely perform beam alignment. The exposed top would allow appropriate access
to the apparatus once the filter reduces the power of the beam to the acceptable value of 5mW. Thus,
while the experiment is being carried out, the enclosed box would prevent exposure to the beam, and
while beam alignment is taking place, the optical filter will reduce the laser beam power. This would
enable the re-classification of the system to a Class 1 Laser. In addition, to prevent foul play, the entire
enclosure will slide along a T-Track which will include barriers at either end. This physically prevents the
box from being removed from the track and disables students from fiddling with the proposed interlock
system, ensuring their safety at all times (Figure A3A3).
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ESC471 – Optical Tweezers Preliminary Design Report
The addition of the multi-component enclosure to the pre-existing apparatus is estimated to be about
CDN $250, including materials for the plexiglass and tracks, as well as fabrication of the unique design.
The cost of the optical density filter is estimated to be CDN $50. This brings the total cost of this
proposed solution to CDN $300, which is within our budgetary constraints.
Figure A3 Design of Proposed Solution #3; Mechanical Solution with 1) Fully enclosed plexiglass component, and 2) Optical
filter component
APPENDIX B – Discussions with Client
Table B1 lists the discussions held with our client regarding our preliminary design.
Table B1 Discussions with Client
Date
October 6, 2010
October 14, 2010
Summary of discussion
Further clarification on the proposed design was given to Professor Bailey in order
to outline where the “sliding box” would be placed.
The initially proposed solution was ruled out due to its feasibility and vulnerability.
Upon speaking with Thorlabs Tech Support (the manufacturer), the interlock
solution was discussed and clarification was received on whether the laser had to be
reduced to 5mW when the enclosure was open or if we could simply shut off the
laser. Professor Bailey agreed that using the built-in interlock and shutting off the
laser was an acceptable solution. The enclosure should be closed with screws
and/or a lock so as to make it inaccessible to students. CAD drawings of the
enclosures are to be developed to provide further details.
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ESC471 – Optical Tweezers Preliminary Design Report
APPENDIX C – Existing Optical Trap Experiments
The following information has been obtained from the “Optical Trap” laboratory manual, published
August 9, 2010, by the lab of Professor William Ryu, of the Department of Physics at the University of
Toronto.
Experiments
Optical traps operate best when the trapping laser wavelength and the diameter of the trapped bead
are comparable [4]. In this regime, neither of the two approximations are valid and theories regarding
trapping in this regime are very complex. Hence the stiffness of traps working in this regime cannot be
accurately predicted. Given the fact that different beads and laser powers will often be required during
experiments, empirical methods of determining the stiffness of an optical trap is crucial. The calibration
experiments outlined in this lab will take you through a variety of methods to determine the trap
stiffness. The first method will employ the equipartition theorem for a trapped bead undergoing thermal
fluctuations; the second method will seek to measure the detection of the trapped bead under external
forces produced by Stokes' drag; the third method will take advantage of the high data acquisition rates
offered by the quadrant detector to produce the power spectrum of a trapped bead and infer the
stiffness from theoretically predicted features.
Figure 3. Linear relationship of the displacement and velocity Appleyard 2007.
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ESC471 – Optical Tweezers Preliminary Design Report
1) Equipartition
For each degree of freedom in the motion of particle, there will be 1/2kBT of thermal energy, where kB
is the Boltzmann constant and T is the temperature in Kelvin. When the bead is not trapped, the thermal
energy is converted into kinetic energy and the bead will undergo random walk in the medium. If the
bead is in a harmonic trap, the thermal energies become potential energies manifested in a small
displacement. Over large sample sizes the fluctuations will give the result:
(1)
where {x2} is the variance of the x displacements (Instructions on recording .avi videos from CCD camera
are given in Appendix A and instructions on converting the videos to positional data are in Appendix D).
2) Stokes' Drag
A more direct way of measuring the stiffness is simply to apply an external force and measure the
deflection. At low Reynolds numbers, external force may be applied to the trapped bead by oscillating
the sample stage. The liquid inside the will move in unison with the sample stage and for liquid velocity v
the drag force applied to the bead will be:
(2)
Since the strength of the optical trap decreases as you move further into the medium, the optimal
working distance for the optical trap is a few microns above the coverslip. Because of the proximity of
the trapped bead to the boundary, Stokes' drag will not be suffcient in calculating the drag coefficient B.
For a better approximation of the drag coefficient you will have to correct for wall effects with the
formula:
(3)
where r is the radius of the bead and h is the height of the center of the bead with respect to the
coverslip surface. (Directions on finding the height, h, are given in Appendix C).
Once the bead is trapped, you can begin recording the positional data from the CCD camera while
oscillating the sample stage (Refer to Appendix A). If the bead is assumed to be in equilibrium, then the
drag force, Fd, will be balanced by the trapping force, Ft = kx, from which the stiffness, k, may be
calculated.
The maximal deflections of the bead will correspond to the maximal external force from the surrounding
liquid. Thus you will need to measure the maximal deflections at several different frequencies and find
the displacement to force relationship to calculate the stiffness. The maximal deflection, xmax, should be
half the width of the data in the x-direction and the maximal force, Fmax, should correspond to the
maximal velocity Fmax= Bvmax.
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ESC471 – Optical Tweezers Preliminary Design Report
3) Power Spectrum
In the low Reynolds number regime, the equation of motion for the bead will be that of a massless
damped oscillator:
(4)
Where x is the displacement of the bead and B is the drag coefficient.
The external Brownian force F(t) is random, and is essentially white noise with an amplitude of
(5)
The Fourier transform of equation (4) is:
(6)
Thus, the power spectrum of the position is given by:
(7)
Equation (7) is a Lorentzian with a cornering frequency of fc = k/ which will give the stiffness, k.
Since taking the power spectrum require high frequency components, the 30 fps acquisition rate of the
CCD camera will not be sufficient, thus a quadrant detector with a high data acquisition rate must be
employed (instruction for using and calibrating the quadrant detector are found in Appendix A). The
spectrums of many data sets (taken at a the same power and bead height) may be averaged to reduce
the noise level at high frequencies.
Figure 4. Ideal power spectrum with label of corner frequency
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ESC471 – Optical Tweezers Preliminary Design Report
Extra Experiments
Blur Correction for the CCD Camera
When using detection systems such as a CCD camera, it is important to note the precision of the
position measurements are limited by the exposure time of the camera [7]. The measured position X m, is
an average of the instantaneous positions X taken over a finite interval, W, which is the exposure time of
the CCD pixels. The simplest model is a step function exposure factor:
(8)
In the application of the equipartition theorem, this blur effect implies that {X2m} is less than or equal to
{X2}, which will lead to an over estimation of the trap stiffness. If we define the dimensionless
parameter,  in terms of the trap relaxation time,  and the exposure time W:
(9)
and the relaxation time, , is given by  = /k. The variance of X and Xm will be related by:
(10)
Where S() is the correction function:
(11)
Using the information above, correct for the blur effect in the equipartition experiment. Can you find a
way to calculate the correction term without knowing the drag coefficient ?
Using the Quadrant Detector
Perform the equipartition and Stokes' drag experiments using the quadrant detector. What are the
advantages?
Analysis Questions
1. Derive the expression for the gradient force for equation (3) in detail.
2. Show that the forces acting on the bead is in the low Reynold's number regime, and that the
assumptions of Stokes' drag are appropriate.
3. Derive equation (7), include an argument for the validity of equation (6).
4. Explain the disadvantages of the second method for determining trapping height.
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ESC471 – Optical Tweezers Preliminary Design Report