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Portable Optical Tweezers Kit

Chapter 7: Experiments

Page 72

MTN012639-D02

Here,

𝜂

𝑒𝑓𝑓

denotes the effective viscosity,

𝑅

is the radius of the PS-bead,

𝑇

is the

temperature of the sample in Kelvin (corresponds to room temperature), and

𝑘

𝐵

is the

Boltzmann constant, which is a natural constant and has a value of

1.38 ⋅ 10

−23 𝐽

𝐾

Exercise

Determine the effective viscosity

𝜂

𝑒𝑓𝑓

of the sample with the 3 µm polystyrene spheres, by

solving the equation (33) according to viscosity and using the gradient

𝑚

of the measured

curve from the previous exercise.

Solution

The equation for the calculation of the effective viscosity

𝜂

𝑒𝑓𝑓

is:

𝜂

𝑒𝑓𝑓

2𝑘

𝐵

𝑇

3𝜋𝑅𝑚

(34)

Here,

is the room temperature,

the Boltzmann constant,

the radius, and

the

previously determined gradient of the PS-beads used.

The determined effective viscosity should be in the range of a few

−3 𝑁𝑠

𝑚

Exercise

After which speed can the PS-bead no longer be held? Determine the maximum holding
force of the optical tweezers.

Solution

If the PS-bead is in the optical trap, two forces act on it. First of all, the frictional force

𝐹

𝑅

which is caused by the suspension in which the PS-bead is located, and thus works against
the other force, the holding force

𝐹

𝐻

of the optical trap. The following equation describes

the frictional force

𝐹

𝑅

𝐹

𝑅

= 6𝜋𝜂

𝑒𝑓𝑓

𝑅𝑣

(35)

Here,

𝜂

𝑒𝑓𝑓

is the effective viscosity of the suspension,

𝑅

is the radius of the bead, and

𝑣

the speed. The maximum holding force is said to have been reached precisely, when the

PS-bead at a certain speed

𝑣

𝑚𝑎𝑥

can just be held. This is the case when both forces are

in balance:

𝐹

𝑆𝑡𝑜𝑘𝑒𝑠

= 𝐹

𝐻,𝑚𝑎𝑥

= 6𝜋𝜂

𝑒𝑓𝑓

𝑅𝑣

𝑚𝑎𝑥

(36)

The holding force is in the range of a few pN.

Содержание EDU-OT2

Страница 1: ...EDU OT2 EDU OT2 M Portable Optical Tweezers User Guide...

Страница 2: ...ander 18 5 3 Right Angle Mirrors 19 5 4 Sample Positioning System 20 5 5 Microscope 21 5 6 Additional Components 23 5 7 Screws Included 24 Chapter 6 Setup and Adjustment 25 6 1 Assembly 25 6 1 1 Trapp...

Страница 3: ...ads 65 7 4 Manipulating a Dairy Cream Particle in a Cream Water Emulsion 66 7 5 The Holding Force of the Optical Trap 69 7 5 1 Brownian Motion 69 7 5 2 The Maximum Holding Force 71 Chapter 8 Teaching...

Страница 4: ...on your device Symbol Description Direct Current Alternating Current Both Direct and Alternating Current Earth Ground Terminal Protective Conductor Terminal Frame or Chassis Terminal Equipotentiality...

Страница 5: ...used in this kit can emit more than 50 mW of optical power which can cause damage to the eyes if viewed directly The laser driver is equipped with a key switch and safety interlock which should be use...

Страница 6: ...ch as geometric optics basic theory of Brownian motion and Stokes friction It is an intriguing experience to be able to control objects with a laser beam and not only for students This Optical Tweezer...

Страница 7: ...table Optical Tweezers Kit Chapter 3 Product Description Page 4 MTN012639 D02 The light path through the optical tweezers experiment Sample Position LED Laser Camera Microscope Beam Path Laser Beam Pa...

Страница 8: ...us is greater than the scattering force which pushes the particle in the direction of the beam away from the focus The various theoretical approaches to describe optical trapping can roughly be divide...

Страница 9: ...al to Therefore according to equation 3 is proportional to 2 and thus to intensity 2 of the incident field The force exerted on the particle by the incident field is proportional to the gradient of th...

Страница 10: ...ow be taken into account namely that light can transfer momentum to an object in the form of photons The force action of a beam on a particle can be explained using Newton s second law the force on a...

Страница 11: ...ains in the sphere while the rest exits the sphere again through transmission The beams which exit the sphere again were thus subject to a change in momentum The force on the sphere is equal to the mo...

Страница 12: ...avily on the angle of incidence of the beam as one can see from the equations This angle becomes larger the more heavily the beam is focused which occurs when a higher numerical aperture objective is...

Страница 13: ...mmetry that the direction of the component would reverse the direction of the Z component would remain the same In short The sphere always moves into the focus or the point of highest intensity In ord...

Страница 14: ...e expressed in terms of and Figure 5 shows a partial beam incident on the sphere with angle from the side The following statements hold true sin sin 19 and sin 2 2 20 roughly corresponds to the focal...

Страница 15: ...in mirrored force vectors and in the right part of the sphere which were not drawn to avoid an overcrowded figure The Contribution of One Ray to the Total Force5 6 When you consider all of the partial...

Страница 16: ...only want to discuss the curve s general form Therefore the forces are given in arbitrary units a u On the horizontal axis 1 corresponds to the focus position on the sphere s outer surface right above...

Страница 17: ...he occurring forces as a function of the focus distance to the sphere s center in units of the sphere s radius Figure 8 shows the gradient force and the scattering force Plotting the sum of both force...

Страница 18: ...at we can have a look at the ratio of and at the point 1 since we have shown that scattering and gradient force are strongest when the laser focus is at near the sphere s surface i e 1 So for a stable...

Страница 19: ...eezing ocurrs or not remains the same see Equation 28 Combining what we know about the numerical aperture and laser power we can note that the increase in trapping strength can be achieved through two...

Страница 20: ...Trapping Laser Source 1 x SR9A DB9 ESD Protection and Strain Relief Cable 1 x L658P040 658 nm 40 mW 5 6 mm A Pin Code Laser Diode 1 x LTN330 A Adjustable Collimator for 5 6 mm Laser Diodes AR Coated...

Страница 21: ...x CP09 M 30 mm Removable Segment Cage Plate 1 x LA1074 A 1 2 N BK7 Plano Convex Lens f 20 mm AR Coating 350 700 nm 1 x LA1509 A 1 N BK7 Plano Convex Lens f 100 mm AR Coating 350 700 nm 1 x SM1A6 Adap...

Страница 22: ...2019 Page 19 5 3 Right Angle Mirrors 2 x KCB1 M Right Angle Kinematic Mirror Mount 30 mm Cage Compatible 2 x PF10 03 P01 1 Protected Silver Mirror 2 x SM1L05 1 Lens Tube 0 5 Long 2 x SM1L10 1 Lens Tu...

Страница 23: ...el7 2 x KDC101 K Cube DC Servo Motor Module 2 x KPS101 K Cube Power Supply 1 x MT402 Right Angle Bracket 1 x MT401 M Mounting Base for Translation Stages 2 x MT405 Side Mounted Actuator Adapter for MT...

Страница 24: ...BG40 Colored Glass Bandpass Filter 335 610 nm 1 x SPT1 M Coarse 1 mm XY Slip Plate Positioner 4 x CP02 M SM1 Threaded Cage Plate 3 x C1498 M Slip On 1 5 Post Clamps 1 x LB1676 1 N BK7 Bi Convex Lens f...

Страница 25: ...eads 1 x Zeiss Microscope Objective 63X 0 8 NA 4 x ER05 6 mm Cage Assembly Rod 0 5 Long 4 x ER3 6 mm Cage Assembly Rod 3 Long 4 x ER1 5 6 mm Cage Assembly Rod 1 5 Long 1 x MCWHL5 Cold White Mounted LE...

Страница 26: ...6 Additional Components 1 x MB1224 MB3060 M Aluminum Breadboard 12 x 24 x 1 2 300 mm x 600 mm x 12 7 mm 1 x RDF1 Rubber Dampening Breadboard Feet 1 x CPA1 30 mm Cage System Alignment Plate with 1 mm A...

Страница 27: ...20 Cap Screw 3 4 Long 4 1 8 x 1 4 Steel Dowel Pin 8 1 4 Washer 22 SD1 8 32 to 1 4 Counterbore Adapter 10 Pack 1 1 x BD 3 16L 3 16 Balldriver 1 x CCHK Imperial Hex Key Set Metric Kit Type Qty Type Qty...

Страница 28: ...e the threaded hole in the breadboard and not the counterbored holes Positions of Components on the Breadboard Teaching Note In the previous version of this kit EDU OT1 M the laser segment had to be a...

Страница 29: ...he orientation depicted to the right note the position of the tip tilt adjusters This orientation is critical because you will not be able to access the cage rod locking screws if the KC1 T M is in a...

Страница 30: ...retaining ring can be tightened using a thin screwdriver Make sure to use the thick retaining ring and not the one you unscrewed in the previous step Also ensure that the laser diode s legs fit throu...

Страница 31: ...tive surface facing away from the knobs Figure 12 Mirror and Right Angle Mount Base Screw the BE1 M base into the PH3 PH75 M post holder as shown in Figure 13 Post Holder Base Lens 1 The elements that...

Страница 32: ...ached to the CP09 M cage plate using two SM1 retaining rings Beam Expander Lens 2 Components Cage Assembly The cage assembly features a removable segment that comprises the two lenses for beam expansi...

Страница 33: ...age rods until the ER1 fill half of the CP09 M s flexure locks Tighten the side located 4 40 setscrews the small lower ones on the CP09 M using a 0 050 1 3 mm hex key The assembly should look like the...

Страница 34: ...cks You may want to leave a small gap between the adjacent cage rods Fix all of the KC1 T s cage rod locking screws You may fix the CP09 M s flexure locks by tightening the 4 40 M3 cap screws with a 3...

Страница 35: ...res that there is sufficient space for manual adjustment between the stage assembly and the mirrors Remove the retaining rings from all four lens tubes Screw an SM1L05 lens tube into the KCB1 M of the...

Страница 36: ...out of its packaging Place the inner piece of the housing on the table in the orientation shown in Figure 19 with the triangular section at the bottom left side Also orient the beamsplitter cube as i...

Страница 37: ...m cap screw Make sure not to mistake the thick SD1 adapter with a thin washer Also the C1498 M s label should face upwards Ensure that you do not touch the bottom of the objective with your fingers in...

Страница 38: ...SM1T2 Connect the SM1L10 lens tube to the CP02 M cage plate Mount the cage plate to the C1498 M post clamp using an SD1 counterbore adapter and an 8 32 1 2 long M4 x 12 mm cap screw Finally install th...

Страница 39: ...r assembling the top part of the camera system First install the two FGB37 filters in the SM1L15 lens tube using retaining rings Screw one retaining ring into the lens tube about half way then insert...

Страница 40: ...s at the side Camera System Components Slip lens 3 from Figure 23 onto the cage rods and secure it with the locking screws on the side Make sure the locking screws do not point towards the side where...

Страница 41: ...tom of the objective should be about 11 5 cm Use a level at the beamsplitter cube to make sure the assembly is vertical If not you have to adjust the angle in which the C1498 M clamp is screwed to the...

Страница 42: ...upporting the cage segment and the laser to the breadboard using the two CF125 clamps and two 1 4 20 3 8 long M6 x 10 mm cap screws with washers Note If the objective microscope was assembled with a h...

Страница 43: ...3 32 hex key from the MT405 Remove the end mount adapter by removing the two inner screws Do not remove the locking plate and attempt to mount an actuator on that side of the stage First screw the two...

Страница 44: ...f the stage Screw the second MT1 M Z8 with side mounted motor onto the first one in the orientation shown in the image to the right using two 1 4 20 3 8 long M6 x 10 mm cap screws Add 2 dowel pins to...

Страница 45: ...washers Screw the adapter assembly to the stage using two 1 4 20 0 315 long M6 x 8 mm cap screws with washers and 4 dowel pins you may need to use the screws to pull the stages together once you have...

Страница 46: ...and washers should be used with the following controllers as well Then place the two KDC101 K Cube Stage controller cubes in their positions mount them to the breadboard and connect them to the compu...

Страница 47: ...lled using the provided CD or downloaded from the Thorlabs website Connect the laser controller to the PC only after you are asked to during the installation Afterwards open the newly installed progra...

Страница 48: ...40 laser diode is 75 mA typical to 110 mA maximum The actual output for a certain current depends on the diode at hand You have two options Set the current to approximately 80 mA and measure the outpu...

Страница 49: ...tup and Adjustment Page 46 MTN012639 D02 More Settings for the Laser Diode Controller Figure 32 shows the Kinesis software with the laser switched on and a current of 95 0 mA Kinesis Software for Lase...

Страница 50: ...DCC Series Compact CMOS and CCD Cameras After finishing the installation reboot and connect the camera to your computer After the driver initialization you can start the ThorCam Software ThorCam Start...

Страница 51: ...ation of your laser spot This can be helpful when you move out of the trapping plane but still want to know the location of the laser focus An example can be seen in Figure 35 There is also the possib...

Страница 52: ...rame rate without changing the pixel clock To set a higher frame rate however the pixel clock might need to be increased For the optical tweezers application we recommend a frame rate of 10 FPS or hig...

Страница 53: ...duct page10 of either the KDC101 or the EDU OT2 M Method 1 Configuration directly via KDC101 display and wheel Power up the controller and open the menu on the KDC101 controller via the menu button se...

Страница 54: ...The recommended Max Velocity is set to 0 03 mm s and Acceleration to 1 2 mm s2 The recommended11 Drive Array Velocities are set to o Velocity 4 0 03 o Velocity 3 0 02 o Velocity 2 0 01 o Velocity 1 0...

Страница 55: ...to this computer they will download the stored settings immediately You can find further information in the KDC101 manual You can operate the motors either by hand via the controllers or by software...

Страница 56: ...rtup This option can be activated via the dropdown menu File Options by checking the box Use device persisted settings see Figure 42 Use Device Persisted Settings In most cases for the optical tweezer...

Страница 57: ...the microscope that includes all parts starting from the camera until the cage plate above the beamsplitter For that unscrew the cage locking screws from the CP02T M and loosen the screw on the C1498...

Страница 58: ...e Screw in the collimation lens retaining ring as far as possible Screw in the collimation lens as far as possible as close to the diode as possible see image to the right Step 2 Collimation Turn the...

Страница 59: ...lt screws on the KC1 T mount until the brightest spot of the laser light distribution hits the hole in the alignment plate Turn off the laser Remove the alignment plate Step 5 Adjustment Mirror Alignm...

Страница 60: ...e laser exits the beamsplitter at its center Turn off the laser Screw the end cap back on Step 7 Insert Beam Expander Adjust the distance between the lenses the distance between the CP09 M cage plates...

Страница 61: ...is not the case After following the instructions above remove the end cap at the beamsplitter and examine the beam shape using a viewing card or piece of paper Notice that it converges at a distance...

Страница 62: ...older Place the sample in the holder with the selected well under the objective Step 3 Approach Raise the sample positioning table with the micrometer screw and pay close attention to the camera image...

Страница 63: ...bad alignment You can move the laser spot closer to the center of the camera image by physically moving the camera The camera s lens tube is mounted on an SPT1 slip plate that allows travel of 1 mm i...

Страница 64: ...lification to maximum when adjusting the live image You can also try dimming the LED If trapping is weak slightly move the sample up or down to find the optimal plane of trapping If the laser spot is...

Страница 65: ...it is necessary to adjust the microscope tube lens shown in Figure 46 in such a way that the focal plane of the observing camera system green curve consisting of the objective the tube lens and the CC...

Страница 66: ...timized for the sample slides and the cover glasses provided with the OTKBTK Content of the OTKBTK Preparation Kit with tools for glass bead sample preparation green highlighting Do not use immersion...

Страница 67: ...trollers to a higher value see Section 6 2 4 Now raise the sample positioning table once again using the micrometer screw and pay close attention to the camera image on the monitor of your computer Af...

Страница 68: ...are not a sign of bad adjustment and can be ignored At this point if the trapped beads move out of the focal plane it indicates that the focal planes of the laser and camera system are not aligned See...

Страница 69: ...ning here Solution In this part of the experiment a sample must first be created out of a cream water emulsion If one attempts to trap the cream particles with the laser it is observed that they disap...

Страница 70: ...s with the z axis screw and thus can clearly be seen on the monitor the laser can be switched off and the particle observed Switching off the laser causes the cream particle to no longer be located in...

Страница 71: ...Chapter 7 Experiments Page 68 MTN012639 D02 A cream particle is pushed down by the laser focus Cream particle is trapped at the laser s focus Once the laser is switched off the fat particle moves bac...

Страница 72: ...e Figure 52 The Brownian motion can be observed in experiments under the optical tweezers The polystyrene beads are located in a medium that consist of molecules These molecules are constantly moving...

Страница 73: ...ate statistically possible deviations of individual particles it is recommended to once again determine the mean value over various particles We recommend doing this for at least 5 particles 2 1 1 2 1...

Страница 74: ...particle in its movement through any liquid This frictional force is directly proportional to the speed with which the spheres move and can be described by the following equation 6 32 Here describes...

Страница 75: ...m the previously determined gradient of the PS beads used The determined effective viscosity should be in the range of a few 10 3 2 Exercise After which speed can the PS bead no longer be held Determi...

Страница 76: ...light This means that at least part of the light has to be transmitted Part of the laser light is reflected off the object s surface while the other part is refracted and transmitted Thereby the laser...

Страница 77: ...ene bead We have to distinguish between two cases The center of the bead is on the beam s main axis The center of the bead is not on the beam s main axis Note The size of the vector arrows in the foll...

Страница 78: ...ntum For example the vector labeled with 1 depicts the momentum of the beam at position 1 It important to note that the magnitude of the momentum i e the length of the arrows does not change However t...

Страница 79: ...the opposite direction of its direction of incidence Momentum conservation then demands a momentum change of the bead in downward direction This means that the bead is pushed away by the beam along t...

Страница 80: ...do not have the same momentum as shown in Figure 60 Unfocused Off Axis Laser Beam Momentum Both partial beams then exhibit the momentum change displayed in Figure 61 Unfocused Off Axis Laser Beam Mome...

Страница 81: ...ensional trap The bead however is still pushed downwards which means that it is not trapped in once place Focused Laser Beam Particle on the Beam s Main Axis Below the Laser Focus We will next conside...

Страница 82: ...cal center both partial beams have the same intensity and therefore the same momentum amplitude The direction off the momentum vectors is different since the incident laser beam is focused Focused Las...

Страница 83: ...ards when the laser focus is beneath it In essence a single laser beam can create an ideal three dimensional optical trap One thing is crucial for functioning optical tweezers in order to trap an obje...

Страница 84: ...pdown menu of Left Analog Y then choose the serial number of the KDC101 that is responsible for a movement of the camera image on the screen in vertical direction Choose the other KDC101 in the Target...

Страница 85: ...Control via Game Controller Page 82 MTN012639 D02 stage will be in one corner of its travel range and should be moved in positive direction for both axes to center the sample under the objective Inpu...

Страница 86: ...Portable Optical Tweezers Kit Chapter 9 Control via Game Controller Rev B July 8 2019 Page 83 Recommended Controller Calibration Settings Homing the KDC101 controllers...

Страница 87: ...PC turn the power of the KLD101 off and back on again All settings are correct but the laser diode still doesn t emit light Switch of the KLD101 then remove the laser diode from its mount and reinser...

Страница 88: ...o Is the objective clean Are you able to find the plane with the beads in their solution If not you may need to carefully clean the objective o Have you used immersion oil Please note that this setup...

Страница 89: ...to other Thorlabs products such as Pure OEM products that means assemblies to be built into a unit by the user e g OEM laser driver cards Components Mechanics and optics Left over parts of units disa...

Страница 90: ...on USA Canada and South America Thorlabs Inc sales thorlabs com le techsupport thorlabs com Europe Thorlabs GmbH europe thorlabs com France Thorlabs SAS SA sales fr thorlabs com Japan Thorlabs Japan I...

Страница 91: ......

Страница 92: ...www thorlabs com...

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