* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download FA15Lec17 Optical Traps.Two
Laser beam profiler wikipedia , lookup
Optical aberration wikipedia , lookup
Birefringence wikipedia , lookup
Super-resolution microscopy wikipedia , lookup
Nonimaging optics wikipedia , lookup
Atmospheric optics wikipedia , lookup
Ellipsometry wikipedia , lookup
Confocal microscopy wikipedia , lookup
Anti-reflective coating wikipedia , lookup
Fiber-optic communication wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Photon scanning microscopy wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Photonic laser thruster wikipedia , lookup
Interferometry wikipedia , lookup
Passive optical network wikipedia , lookup
Optical coherence tomography wikipedia , lookup
Silicon photonics wikipedia , lookup
Optical amplifier wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
3D optical data storage wikipedia , lookup
Harold Hopkins (physicist) wikipedia , lookup
Retroreflector wikipedia , lookup
Optical rogue waves wikipedia , lookup
Announcements Midterm grades: online by 5pm today HW: VMD (primarily) due Thursday Oct 29th. Optical Traps/Tweezers Physics: use lasers and optical traps to control individual molecular motors. Biology: can study how forces operate on these motors. Cartoon of kinesin walking in cell (Optical Traps primarily used for in vitro motion) Optical Traps Hold bead with some force, F. Have the molecular motor pull against it. How does motor act as a function of force? ATP? Mutation? For an Optical Trap to work • Gradient of laser beam (trapping): bead attracted to brightest spot • Generate optical trap force ~ motor force • Laser beam is altered and position measured. Optical Traps (Tweezers) Z Dielectric objects are attracted to the center (x-y) of the beam where light is brightest. (Slight deviation in z-direction due to reflection.) Depends on gradient of beam, index of refraction of bead vs. water. Vary ktrap with laser intensity such that ktrap ≈ kbio (k ≈ 0.1pN/nm) ~ to stiffness of motor. Can measure pN forces and (sub-) nm steps! http://en.wikipedia.org/wiki/Optical_tweezers Lateral (x-y) gradient force (leads to trapping in x-y) (Snell’s law twice: two surfaces) Bright ray Dim ray Z Object feels a force toward brighter light Axial (z-axis) gradient force: leads to trapping in z How so? ΔP Pi Focused light Pf Pi Z Object feels a force toward focus Force ~ gradient intensity What about: Optical scattering forces – reflection (Not of interest, here) Pf Pi = h/λ ΔP θ Pi Z F = ΔP/Δt = (Pf-Pi)/Δt Newton’s third law – for every action there is an equal and opposite reaction Estimate size of trapping force Want: Force (pN) as a function of Laser Power (mW) F= Dp/Dt = 2 pphoton/Dt ≈ Qpphoton/Dt Convert pphoton into Energy/time = Power Photon in vacuum: Energy = f( pphoton ) = pphotonc Photon in index of refraction n: goes with speed v E = pphotonv = pphotonc/n E/Dt = pphotonc/nDt = Power = P F = Qpphoton/Dt = QPn/c pphoton/Dt = Power n/c Incident momentum/sec = Power P in medium of refractive index. Estimating Trap Force/Stiffness F = QPn/c Q spherical particle radius ~ l ~ 0.1 This is approximately correct: Vary ktrap with laser intensity such that ktrap ≈ kbio (k ≈ 0.1pN/nm) How to detect movement of bead? Measuring the position of a trapped bead As bead moves to side, so does trapping light Want a Position Sensitive Detection to measure How you get parallel light? Recall Len’s Maker’s Equation Put object at the focal length of lens. Then image is at infinity. Position sensitive detector (PSD) Out1 Plate resistors separated by reversebiased PIN photodiode P In1 N N In2 P Out2 Opposite electrodes at same potential – no conduction with no light Multiple rays add their currents linearly to the electrodes, where each ray’s power adds Wi current to the total sum. SIGNAL Out1 P In1 N N In2 POSITION P Out2 ΔX ~ (In1-In2) / (In1 + In2) ΔY ~ (Out1-Out2) /(Out1+Out2) Linear signal with position. Can just read off signal, get position Laser Beam expander Photodetector Condenser Objective Optical Traps How small can you see? 1 base-pair (3.4 Å)? • Get rid of (noise) sources of vibration. • Get rid of KBT of thermal vibration Basepair Resolution—Yann Chemla @ UIUC Eliminate (floor) noise Limit BW—noise Take difference & sum. Diff: no shaking of floor! comes in at all frequencies 3.40 1bp = 3.4Å 1 PNAS 2 3 1 2 2.04 4 3 5 4 1.36 5 6 6 0.68 7 7 8 UIUC - 02/11/08 0.00 0 2 Probability (a.u.) Displacement (nm) 2.72 4 6 Time (s) 8 9 9 3.4 kb DNA 8 10 0.00 0.68 1.36 2.04 Distance (nm) 2.72 F ~ 20 pN f = 100Hz, 10Hz What is noise in measurement?. The noise in position using equipartition theorem [For a typical value of stiffness (k) = 0.1 pN/nm; kBT= 4.1pN-nm <x2>1/2 = (kBT/k)1/2 = (4.14 pN-nm/0.1)1/2 = (41.4)1/2 ~ 6.4 nm 6.4 nm is a pretty large number. [ Kinesin moves every 8.3 nm; 1 base-pair = 3.4 Å ] How to decrease noise? Hint: Equipartion Theorem calculates for noise at all frequencies (infinite bandwidth). Reduce bandwidth. Also: Operate at high force less noise due to finite Temp. Also be clever about how to differentiate noise from signal. Solve Langevin’s Equation, Get power spectrum of bead in an optical trap. Noise is not distributed evenly across all frequencies in an optical trap. Most noise at low f. fc k = trap stiffness 2 γ = 6πηr (for sphere) Bandwidth = infinite: limit to ~6 nm. If use BW = 100 Hz ~ 0.4 nm = 4 Angstrom!! Also, know how to cut out noise. Take out frequencies where signal isn’t Class evaluation 1. What was the most interesting thing you learned in class today? 2. What are you confused about? 3. Related to today’s subject, what would you like to know more about? 4. Any helpful comments. Answer, and turn in at the end of class.