20Numerical force calculations All analytical force solutions can not incorporate tightly focused beamsFinite Difference Time Difference method is widely accepted because it is able to formulate arbitrary geometry and laser sourcesSeung-Yong Sung and Yong-Gu Lee, "Calculations of the trapping force of optical tweezers using FDTD Method," Hankook Kwanghak Hoeji, Vol. 19, No. 1, pp 80-83, 2008 Feb (Written in Korean)Seung-Yong Sung and Yong-Gu Lee, “Trapping of a micro-bubble by non-paraxial Gaussian beam: computation using the FDTD method,” Optics Express, Vol. 16, No. 5, pp , 2008
21Position sensing of microscopic beads Part 2Position sensing of microscopic beads
22Physical natureThe position signal measured with a QPD in the BFP is determined by the interference of the unscattered laser beam with the scattered light.The trapped sphere is described as a Rayleigh scatterer (i.e., a dielectric sphere with a radius a much smaller than the wavelength)Ref. Pralle, A. et al, Three dimensional high-resolution particle tracking for optical tweezers by forward scattered light, Microscopy Research and Technique, Vol. 44, pp (1999)Gittes, F. and C. F. Schmidt, Interference model for back-focal-plane displacement detection in optical tweezers. Optics Letters, Vol. 23, pp 7-9 (1998)
23Near to far field transformation Scattering from a spherical bead by a focused Gaussian beam problem is reduced to that by a planar waveScattered field was computed numerically by FDTD and transformed to the far field304 nm diameter polystyrene sphere immersed in water using a 633 nm laser.The spatial and time resolution was nm and attoseconds.(a) Scattering magnitude(b) error as a function of deflection angles (%)Ref. Optical Society of Korea Winter Annual Meeting 2010, 이용구, 시간영역 유한차분법에서 근접장으로부터 원격장으로의 변환
25Movement of a bead under linear spring force 광집게(Optical tweezers)는 피코뉴턴(pN) 단위의 포획 힘을 가짐이때의 포획 힘은 스프링(ktrap)처럼 작용Optical tweezers has a pN range forceOptical tweezers’ force can be thought as a spring forceThis makes the optical stiffness (ktrap)5μm polystyerene bead
26Sx, Sy, Sz signals1QPD(Quadrant Photo Diode) A,B,C,D signal로부터 x, y, z 축방향으로의 변위 signal(Sx, Sy, Sz) 계산
27Calibration factor Laser scanning analysis 커버글래스에 고정(stuck)된 마이크로 비드 이용비드에 조사하는 레이저의 위치를 변화QPD에 측정되는 신호를 수집스캐닝을 이용한 QPD 시그널의 변화 측정(Calibration factor)수집된 신호(Sx, Sy, Sz)에 기울기(Calibration factor) 값을 대입하여 실제 비드의 이동거리 계산
28Force sensing (trap stiffness calibration) Part 3Force sensing (trap stiffness calibration)Ref. Bechhoefer J and Wilson S Faster, cheaper, safer optical tweezers for the undergraduate laboratory. Am. J. Phys. 70:
29Escape force methodThis method determines the minimal force required to pull an object free of the trap entirely, generally accomplished by imposing a viscous drag force whose magnitude can be computedTo produce the necessary force, the particle may either be pulled through the fluid (by moving the trap relative to a stationary stage), or more conventionally, the fluid can be moved past the particle (by moving the stage relative to a stationary trap).The particle velocity immediately after escape is measured from the video record, which permits an estimate of the escape force, provided that the viscous drag coefficient of the particle is known. While somewhat crude, this technique permits calibration of force to within about 10%.Note that escape forces are determined by optical properties at the very edges of the trap, where the restoring force is no longer a linear function of the displacement. Since the measurement is not at the center of the trap, the trap stiffness cannot be ascertained.Escape forces are generally somewhat different in the x,y,z directions, so the exact escape path must be determined for precise measurements. This calibration method does not require a position detector with nanometer resolution.
30Drag Force MethodBy applying a known viscous drag force, F, and measuring the displacement produced from the trap center, x, the stiffness k follows from k=F/x.In practice, drag forces are usually produced by periodic movement of the microscope stage while holding the particle in a fixed trap: either triangle waves of displacement (corresponding to a square wave of force) or sine waves of displacement (corresponding to cosine waves of force) work wellOnce trap stiffness is determined, optical forces can be computed from knowledge of the particle position relative to the trap center, provided that measurements are made within the linear (Hookeian) region of the trap. Apart from the need for a well-calibrated piezo stage and position detector, the viscous drag on the particle must be known.
31Equipartition MethodOne of the simplest and most straightforward ways of determining trap stiffness is to measure the thermal fluctuations in position of a trapped particle. The stiffness of the tweezers is then computed from the Equipartition theorem for a particle bound in a harmonic potential:The chief advantage of this method is that knowledge of the viscous drag coefficient is not required (and therefore of the particle’s geometry as well as the fluid viscosity). A fast, wellcalibrated position detector is essential, precluding video-based schemes.
32Step Response MethodThe trap stiffness may also be determined by finding the response of a particle to a rapid, stepwise movement of the trapharder to identify extraneous sources of noise or artifact using this approach. The time constant for movement of the trap must be faster than the characteristic damping time of the particle
33Trap stiffness measurement 1Trap stiffness measurementPower spectrum methodQPD는 포획된 비드의 위치를 측정푸리에 변환을 거쳐 로렌츠(Lorentzian) 곡선으로 피팅로렌츠 곡선으로 부터 roll-off frequency 도출f: frequency, kb: Boltzmann's constant, T: Temperature,β=6πγa : hydrodynamic drag coefficient, a: radius of the particle, γ: drag coefficientfc : Roll-off frequency주파수 성분이 가지는 파워가 절반으로 떨어지는 지점: Trap stiffness 계산QPD is used to recode the position of the trapped beadThe power spectrum of trapped bead is fitted to the Lorentzian curve to deduce roll-off frequency
34Comparison of methods Viscosity Geometry CCD Thermometer Piezo Stage QPDRemarksEscape force methodTNonlinear regionDrag force methodEquipartition methodLinear region, Need to know Volt,displacement relations (calibration is necessary)Power spectrum methodLinear region, No calibration necessary.Step response methodLinear region
35Optical tweezers as a force measurement device and a monitor Interference pattering detectionQuadrant photo diode10nm resolutiontypically 50pN/μm spring constant100pN~1pN can be measuredMicroscopeBrightfieldFluroscentRef. Pralle, A. et al, Three dimensional high-resolution particle tracking for optical tweezers by forward scattered light, Microscopy Research and Technique,Vol. 44, pp (1999)Sun-Uk Hwang and Yong-Gu Lee, "Influence of time delay on trap stiffness in computer-controlled scanning optical tweezers," Journal of Optics A: Pure and Applied Optics, Vol. 11, No. 8, pp , 2009 Aug
36Summary Scattering and gradient forces Correct optical tweezers geometryDirect manipulationsIndirect manipulationsPosition sensing of microscopic beadsQPDCalibration factorForce sensingPower spectrum method
37Contributors Thank you http://nsl.gist.ac.kr Jong-ho Baek Sun-Uk Hwang Seung-Yong SungJe-Hoon SongSong-Woo LeeIn-Yong ParkMuhammad Tallal Bin NajamIrfan ShabbirPark Yun HuiJung-Dae KimThank you