Optimizing immersion media refractive index …

1 Optimizing immersion media refractive indeximproves optical trapping by compensatingspherical aberrationsS. Nader S. Reihani1,2,*and Lene B. Oddershede1,31 Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark2 Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195-1159, Iran3E-mail: author: January 9, 2007; revised May 8, 2007; accepted May 9, 2007;posted May 18, 2007 (Doc. ID 82291); published July 3, 2007 The efficiency of an optical trap is limited by its axial strength. Light focused by oil- immersion objectivesprovides stronger traps but suffers from spherical aberrations, thus restricting the axial stability and work-ing distance.

2 By changing the refractive index of the immersion media we compensate spherical aberrationsand measure axial trapping strengths at least twice as large as previously reported. Moreover, the sphericalaberrations can be compensated at any desired depth. The improved trapping efficiency implies significantlyless heating of the particles, thus diminishing previously published concerns about using gold nanoparticlesas handles for optical manipulation. 2007 Optical Society of AmericaOCIS , , the past decade optical tweezers have been usedwidely as a tool for micromanipulation [1]. Also, me-tallic nanoparticles can be optically trapped [2], andthese are predicted to have potential asin vivohandles in biological specimens if the laser-heatingeffects [3] can be minimized.

3 Oil- immersion objec-tives can have a higher numerical aperture (NA)than water immersion ones and are therefore favor-able to use for microscopy and optical trapping. How-ever, a common problem with using oil- immersion ob-jective lenses is the presence of the sphericalaberrations (SAs) owing to the mismatch in the re-fractive indices of the immersion and specimen me-dia that widen the focal volume progressively withtrapping depth. Several methods have been sug-gested to improve spherical aberrations, , deform-able mirrors in multiphoton scanning microscopy [4]and in optical tweezing [5]. Implementing deformablemirrors is fairly cumbersome and expensive in com-parison with the methods here presented.

4 Othermethods to correct for SAs include changing the tubelength [6,7].The SAs appear as a phase in the intensity point-spread function [8] (IPSF), and the total SA is a sumof different contributions, all of which depend on thewavelength of the laser light:SAtotal=SAtube+SAobj+SAim/cov+SAco v/sample, 1 whereSAtubeis a contribution that stems from thetube length of the particular thecontribution from the lenses in the objective. Typi-cally, the objective lenses are adjusted to minimizethe SA at visible wavelengths but are not optimizedfor infrared laser the spherical abberations introduced by the pos-sible mismatch in refractive indices of the immersionmedia of the objective, the cover glass, and the mediawithin the sample, respectively.

5 Both these contribu-tions depend on the distance traveled by the lightwithin the various media . MinimizingSAtotalat anygiven depth produces the most focused laser idea is to modify the third term in Eq.(1),SAim/cov, such that it optimally cancels the SA intro-duced by the other terms. The depth at which opti-mal compensation occurs can be adjusted by chang-ing refractive index of the immersion optical tweezer setup [9] is based on aNd:YVO4laser with wavelength 1064 nm and isimplemented in an inverted Leica microscope with aquadrant photodiode back-focal-plane detectionscheme. The objective is from Leica (HCX PL Apo,63 , NA= , , ).

6 The position time series ofthe trapped beads were acquired by using a custom-made LabView program and analyzed by using aMatlab-based power spectrum analysis program [10].The trap constitutes a harmonic potential and ischaracterized by a spring constant,k, which is re-lated to the corner frequencyfcbyk=2 fc, beingthe drag coefficient of the trapped bead that is farfrom the glass perform the most accurate measurements of thespring constant in the axial direction the NA of thecondenser is set to [11]. For measurements ofbead positions in the lateral direction the condenseraperture was fully an objective satisfying the sine condition andilluminated with a linearly polarized Gaussian laserbeam, the effect of the SA on the three-dimensional(3D) IPSF in the second medium can be accounted forby a phase factor [8].

7 In the case where the SAs arecaused by a mismatch between refractive indices oftwo media , the phase factor at depthdwin the secondmedium is given by [8] 1, 2, dw = k0dw n1cos 1 n2cos 2 , 2 where 1, 2,k0, anddware incident angle in first me-dium, refracted angle in second medium, wavenum-1998 OPTICS LETTERS / Vol. 32, No. 14 / July 15, 20070146-9592/07/141998-3/$ 2007 Optical Society of Americaber in vacuum, and the nominal trapping depth, ,the distance traveled by the objective, heredwwill simply be called the depth. Figure1shows these values as well as a schematic diagramof the optical path for marginal is the actualtrapping depth, which is unknown but approximately20% offdw.

8 When the immersion oil and the coverglass are index matched, which occurs for conven-tional immersion oils (dotted line in ), 1and 2can be easily calculated as and 83 , respectively(NA= 1andn1sin 1=n2sin 2withn1= andn2= ). In this case the only componentof the phase factor arising from the glass water in-terface can be written as gw= In the casewhere the immersion oil and the glass are not indexmatched, this introduces an additional phase compo-nent that can be calculated in same manner. Increas-ing immersion oil index of refraction by n= im-plies 0= (see a definition of 0). Thus,the component of the phase factor arising from theoil glass interface can be written as og= ,wheredois the thickness of the oil layer.

9 We mea-sured this thickness to be 115 15 m by measuringthe travel of the objective from the focus of the insidesurface of the coverslip until the objective hit thesample. The optimal depth for optical trapping is thedepth where the various sources of spherical abbera-tions cancel, , where gw+ og=0, which gives achange in optimal trapping depth of dw= m; an increase of in the refractive in-dex of the immersion oil moves the optimal trappingdepth m deeper into the sample. If thismethod is combined, , with changing tube length[7], then the optimal trapping depth can be experimentally show how the optimal trappingdepth depends on the index of refraction of the im-mersion oil, we performed a series of experiments us-ing immersion oils with refractive indices rangingfrom to (Cargille, refractive index liquidsset A).

10 For each immersion oil the axial spring con-stant was measured at different trapping depths( ). Each data point in representative of25 measurements (5 different beads, 5 measure-ments for each bead). The experiment was performedusing a single immersion oil at a time. Between ex-periments with different immersion oils the objectivewas carefully cleaned and the chamber was error bars in the spring constants are less than5% and are not shown. Figure2illustrates that: (1)Using the conventional oil (n= , Leica) providesa maximum trapping strength of only 1/3 of themaximum strength possible. For trapping close to thecover glass an immersion oil with refractive apparently provides the strongest trap.