Aberrations in Confocal and Multi-Photon Fluorescence Microscopy Induced by Refractive Index Mismatch

Transcription

1 PHC2 25/11/25 7:23 PM Page 44 2 beations in Confocal and Multi-Photon Fluoescence Micoscopy Induced by Refactive Index Mismatch lexande Egne and Stefan W. Hell INTRODUCTION Moden optical micoscopes ae so good that many scientists foget that these instuments only povide thei optimal pefomance if they ae used unde cetain opeating conditions. Typical uses may be unawae of the vey existence of such limitations eithe because they may unwittingly wok within the limits o because the fail to ecognize thei effects. It is pobably also coect to assume that the manufactue does not intend to discouage puchase by emphasizing the pitfalls that unavoidably aise fom the physics of imaging. Howeve, advanced micoscopists tend to use thei instuments at the limits of thei pefomance. They wish to use lases fom the ultaviolet (UV) to the infaed (IR), special emission lines fom vey lage ac-lamps, chage-coupled device (CCD) cameas with a dynamic ange of up to 16 bits, photon-counting avalanche photodiodes with unmatched sensitivity, and seveal fast photomultiplie tubes. They want to obseve two o moe dyes simultaneously. They expect the stage to emain in a stable position fo seveal hous, possibly while going though heating and cooling cycles, and sometimes they want to ecod low-level fluoescence emissions fom athe thick specimens mounted in an aqueous medium with high numeical apetue (N) oil-immesion lenses. Is this possible? Can one expect an off-the-shelf poduct to pefom well unde all these cicumstances? The answe is: Within cetain limits, yes, you can. The issue is to specify and ecognize these limits. This chapte descibes the poblems that occu when obseving specimens that ae mounted in a medium whose efactive index is diffeent fom that of the immesion liquid. Classical examples ae live cells kept in a physiological buffe solution o even fixed cells kept in a glyceol-based mountant that ae imaged by an oil-immesion lens of lage numeical apetue. This chapte fist outlines the physics of the situation, both fo confocal and multi-photon micoscopy, then pesents the esults of a theoetical investigation, compaes them with a seies of expeiments, and finally daws conclusions that ae paticulaly elevant to the quantitative obsevation of (living) biological specimens. THE SITUTION Figue 2.1 descibes a common situation encounteed in micoscopy. The sample is mounted between a coveslip and a glass slide, which in fact can be anothe coveslip, and is immesed in a special mounting medium, such as an aqueous buffe o a moe viscous solution based on glyceol. Coveslip glass has a efactive index (RI) n = The immesion oil between the coveslip and the objective lens is assumed to have the same n. The n of the mounting medium aound the sample will usually be diffeent fom that of the glass and of the immesion oil. Wate has an index of n = 1.33 and glyceol has n = The sample itself will have an n that is not much diffeent fom that of the mounting medium and slightly highe than that of wate (see Chapte 18, this volume, fo the RIs of common mounting media). light ay emeging fom an oil-immesion objective lens that is coupled to the coveslip with the appopiate oil will not be efacted until it passes the inteface fom the coveslip into the mounting medium. The light ay is usually only slightly affected by the sample itself and is assumed to cay on staight towads the focal egion once it has passed the inteface between the mounting medium and the coveslip. The discussion can theefoe be esticted to the effects caused by the change in n at the glass medium bounday and to the distance fom this inteface to the focus point somewhee inside the sample. What effects can be expected? light ay is efacted at the glass medium inteface. The angle of the ay is changed; theefoe, the diffeent ays focus at diffeent positions along the z-axis than they would in a pefectly matched optical system. In micoscopy, is usually lage than n 2, and the focus is, theefoe, close to the coveslip than unde ideal conditions. The position of an object will then appea to be futhe away fom the coveslip. If wee smalle than n 2, the focus would be futhe fom the coveslip than it should be and the object would then appea to be close to the coveslip. Wheneve light is efacted, some light is also eflected (Bon and Wolf, 22). s efaction occus only when the angle of incidence is lowe than the angle of total intenal eflection, the N of the immesion system is effectively educed. Pefect imaging is only possible if the wavefont emains spheical. ny deviation fom spheicity esults in a lage spead of the focus and hence in a eduction in both spatial esolution and peak intensity. This speading of the focus means that the image of the focal spot focused back towads the confocal pinhole is also spead. This second defocus effect means that less light penetates the pinhole, and the obseved intensity deceases still moe. THEORY The calculations ae pefomed in a vectoial theoy following Hell and colleagues (1992). The sample object is a laye of fluoophoe immesed in the mounting medium. The immesion oil and the lexande Egne and Stefan W. Hell Depatment of NanoBiophotonics; Max Planck-Institute fo Biophysical Chemisty m Fassbeg 11; D-3777 Goettingen, Gemany 44 Handbook of Biological Confocal Micoscopy, thid edition, edited by James B. Pawley, SpingeScience+Business Media, New Yok, 26.

2 PHC2 25/11/25 7:23 PM Page 45 beations in Confocal and Multi-Photon Fluoescence Micoscopy Induced by Refactive Index Mismatch Chapte 2 45 objective E h = h h ª h cf ill det ill (1) NFP n 2 spheical wavefont focal shift a P = (x, y, z) z-axis FP FIGURE 2.1. Teminology used fo the calculation of point spead functions in optically mismatched systems. spheical wavefont emeges fom the objective lens. The wavefont is descibed by its electic field stength E Æ and its diection k Æ, while the objective lens is descibed by its focal length and its numeical apetue (N) = sin(a). The sample consists of two coveslips, each with a efactive index of and the mounting medium with a homogeneous efactive index of n 2. The immesion medium between the uppe coveslip and the objective lens has the same n as the coveslip. In a pefectly matched system, is equal to n 2 and the geometical focus is a distance NFP (nominal focal position) away fom the glass/mounting medium inteface. In a mismatched system, is not equal to n 2. The focus suffes fom a focal shift and is found at FP (actual focal position). The theoy descibes the calculation of the electic field stength E Æ in a point P(x,y,z) close to both FP and NFP. coveslip have n = and the mounting medium n = n 2. Focusing into the sample is achieved by mechanically vaying the distance between the objective lens and the bottom of the coveslip. The distance between this suface and the geometical focus in a pefectly matched system is efeed to as the nominal focal position (NFP). 1 The diffeence between the NFP and the actual focal position (FP) is efeed to as the focal shift in the optically mismatched system. We wish to calculate the FP and the intensity at a point P(x,y,z) in the vicinity of the FP. The optical system is descibed by the wavelength of the incident light ay (l), the N of the objective lens, and the diamete of the apetue in the lens. In a moden optically pefectly-matched micoscope, the so-called infinity-coected lens is assumed to accept a pefectly plana incoming-wavefont and poduce a pefectly spheical outgoing wavefont that poduces an abeation fee point spead function (PSF) at the focal point. We note that ou consideations apply to any point within the field of view specified fo the lens. In a confocal micoscope, a point souce is used to define the extent and the position of illumination, wheeas a point detecto disciminates against any light emitted outside a cetain egion. In physical tems, the effective PSF (Hell et al., 1992) of the confocal fluoescence micoscope is given by the poduct of the illumination intensity and detection PSF: 1 It should be noticed that the NFP is the actual distance of a featue in the object fom the suface of the coveslip. k k E whee h Æ ill denotes the amplitude of the illumination light in the focal egion and h Æ det is the amplitude distibution fo the detection, which is simila to h Æ ill, but is calculated fo the wavelength of fluoescence emission. So, while h Æ ill is popotional to the light field used fo illumination, and h Æ ill 2 to its intensity, the effective confocal PSF h cf is popotional to the pobability that a given focal coodinate contibutes to the signal at the confocal detecto. If the excitation and emission wavelengths ae athe simila, it follows that h Æ ill 2 ª h Æ det 2. In this case, h cf is popotional to the fouth powe of the illumination amplitude and hence to the squae of the illumination intensity (Wilson and Sheppad, 1984), as indicated on the ight hand side of Eq. 1. This quasi-quadatic signal dependence of the ecoded intensity on the illumination intensity causes a dop of the detected fluoescence fom points away fom the geometical focus and is the actual physical eason why a confocal setup defines a confined ecoding volume in thee-dimensional (3D) space. The z-esponse I(z) to infinitely thin fluoescent planes and the esponse I edge (z) to half-volumes in the z-diection ae of pactical impotance as well because they quantify the ability of a micoscope to distinguish planes that ae stacked in the z-diection: z I( z) = Ú Ú hcf ( ) dx dy and Iedge( z) = Ú I( z ) dz volume confinement can also be achieved by multi-photon excitation of the fluoophoes (Denk et al., 199; Sheppad and Gu, 1992a, 1992b) (Chaptes 28 and 37, this volume). The pobability of two photons being simultaneously absobed by the same molecule is popotional to the squae of the local intensity (Kaise and Gaet, 1961). Theefoe, the effective PSF of a micoscope based on two-photon absoption is descibed by the squae of the illumination PSF, that is, the fouth powe of the field amplitude fo illumination: h The similaity to Eq. 1 indicates that the illumination pocess defines a volume in a manne simila to the combined illumination and detection pocesses in a confocal single-photon excitation fluoescence micoscope (Hell and Stelze, 1992; Sheppad and Gu, 1992b; Stelze et al., 1994). This means that all the poblems discussed fo single-photon confocal micoscopy ae also encounteed in two-photon fluoescence micoscopes. The only eal diffeence is that the latte equies wavelength doubling. dditional confocalization of the system means that the effective PSF is given by h cf 2hv = h Æ ill 4 h Æ det 2 and fo an n-photon confocalized system we obviously have n h = h h cf 2hv ill = h 2hv ill 2 2. det In an abeation-fee system, the calculation of the fields h Æ ill and h Æ det is athe staightfowad because these functions solely depend on the wavelength and the N. By contast, when focusing though RI intefaces, the evaluation of h Æ ill and h Æ det is complicated by the fact that, loosely speaking, it has to be calculated once fo medium and then fo medium n 2 (Hell et al., 1993). The latte publication teated the poblem with specific egad to confocal micoscopy and quantitatively pedicted all the effects 4 (2) (3) (4)

3 PHC2 25/11/25 7:23 PM Page Chapte 2. Egne and S.W. Hell encounteed with efactive index mismatched samples. Theefoe, in this chapte we will follow the agument pesented in that publication. In the meantime, significant advancements in the fomulation of this theoy have been made. These ae consideed late in this chapte (Töök et al., 1995; Egne and Hell, 1999). Stating fom simple tems, the calculation basically equies the solution of a vaiational poblem in optics, that is, the application of Femat s pinciple fom a point of the conveging spheical wavefont to the point of the focal egion in question [Fig. 2.2()]. ccoding to the Huygens Fesnel constuction, each point on the spheical wavefont is a souce of seconday spheical wavelets (Hopkins, 1943; Li and Wolf, 1981). In a matched medium, we have 1 h ( ) = c F ( ) K( c) exp( iks) df s ÚÚ F whee Æ (F) denotes the wavefont amplitude ove the suface F of the spheical wavefont and df is the suface element (see Fig. 2.2); s is the distance between the oigin of the wavelet q and the point P, and c is the angle of inclination between the nomal at q and the diection fom q to P. 1 K( c) =- ( 1 + cos( c) ) (6) 2l In an aplanatic objective lens, the wavefont Æ (F) is given fo in the x-diection polaized light of mplitude i by Richads and Wolf (1959): 2 Êcos( q) + ( 1 - cos( q) ) sin ( j) ˆ F ( ) = i cos( q) Á ( 1 - cos( q) ) cos( j) sin( j) Á Ë sin( q) sin( j) Fo the numeical calculation of h Æ ( Æ ), the tem K(c) can be neglected because it vaies by only a small amount. Because the calculation is esticted to the volume close to the geometical focus, 1/s emains a constant and can theefoe also be neglected. The function h Æ ( Æ ) can be simplified to (5) (7) 2 a Êcos( q) + ( 1 - cos( q) ) sin ( j) 2p ˆ h ( ) = c ( ) Á ( - ( )) ( ) ( ) Ú Ú cos q 1 cos q cos j sin j Á Ë sin( q) sin( j) exp( iks) sin( q) djdq The final poblem is the detemination of s, which, as is pointed out above, is a vaiational poblem and a caeful analysis of the light tansition at the inteface between and n 2, to which one solution has been povided (Hell et al., 1993). If the NFP is small compaed to the focal length of the objective lens, an assumption which is well met in confocal micoscopy, the vaiational poblem can be solved analytically fo the egion nea the NFP (Egne and Hell, 1999). Töök and colleagues deived an identical solution (Töök et al., 1995) using a plane wave expansion of the light field, that is, the Debye appoximation instead of the Huygens Fesnel constuction. In both cases the solution fo h Æ ( Æ ) is given by: Whee the diffaction integals I n ae defined by: a Ú 2 2 I : = cos( q ) sin( q ) t + t cos( q ) J kn x y sin q 1 1 s p 2 1 exp( ik( F( NFP) + n zcos( q ))) dq a Ú I : = cos( q ) sin( q ) t sin( q ) J kn x y sin q p exp( ik( F( NFP) + nzcos( q ))) dq a Ú ÊiI ( ( ) + I( ) ( ) 2 cos 2j ) ˆ h ( ) = cá I ( ) sin( 2j) 2 Á Ë i2i ( ) cos( j) ( ) + ( ) ( ) ( ) + ( ) ( ) ( ) + ( ) 2 2 I : = cos( q ) sin( q ) t - t cos( q ) J ( kn x y sin q ) s p exp( ik( F( NFP) + n zcos( q ))) dq (8) (9) (1) B wavefont q x 2 1 s 1 (x) n 2 s 2 (x) 1 (q, j) p q exit apetue inteface q 1 f f q 2 NFP y x 2 n 2 z z-axis FIGURE 2.2. () The vaiational appoach to the calculation of the electic field stength E Æ at a point P(x,y,z) close to both the FP and the NFP. The geomety is basically the same as descibed in Figue 2.1. The poblem is to minimize the distance s 1 (x) + s 2 (x). It can be shown that this sum depends on the angle and on the oigin of the beam in the pimay spheical wavefont. The calculation, theefoe, has to seach fo those beams that contibute to the field at position P accoding to Femat s pinciple. Fo each point P(x,y,z) in the object, the contibution is found by integating the complex electic field acoss the whole exit apetue. This makes the calculations somewhat tedious. (B) If the NFP is small compaed to the focal length of the objective lens, which is always the case in micoscopy, the calculation becomes much easie as only the tansmission and efaction fo a beam incident upon the bounday with an angle q 1 has to be known.

4 PHC2 25/11/25 7:24 PM Page 47 beations in Confocal and Multi-Photon Fluoescence Micoscopy Induced by Refactive Index Mismatch Chapte 2 47 J n ae Bessel functions of the fist kind and nth ode and t p,s ae Fesnel tansmission coefficients fo s- and p-polaized light (Bon and Wolf, 22). The abeation function F(NFP) = -NFP( cos(q 1 ) - n 2 cos(q 2 )) (11) depends on the nominal focusing position, the azimuth angle q and theefoe on the apetue angle a and the diffeence of the efactive indices and n 2. The diffeences between the calculations of the illumination and the detection PSFs ae the wavelength and the tem cos( q) which is omitted. RESULTS OF THEORETICL CLCULTIONS The theoy descibed above does not esult in an analytical desciption of the PSF. The PSFs have to be calculated numeically as a function of the N, excitation and emission wavelengths, NFP,, and n 2. In ode to illustate how focusing into a mismatched medium affects the PSF, Figue 2.3 shows xz-images of calculated PSFs (logaithmic scale) and the coesponding expeimental though-focus seies (linea scale) fo focusing with a wate-immesion lens eithe 1 mm deep into wate [Fig. 2.3(,B)] o into immesion oil [Fig. 2.3(C,D)]. In the mismatched case, the main maximum is shifted, becomes elatively boade, and dops in peak intensity (Fig. 2.4). In addition, the PSF loses its axial symmety with espect to the main maximum wheeby focusing above the FP leads to a diffeent image than focusing below the FP [Fig. 2.3(D)], an effect that is not pesent in the matched case [Fig. 2.3(B)]. The esults of seveal calculations ae summaized in Figues 2.4, 2.6, 2.7, 2.8, 2.9, and 2.1 and in Tables 2.1 and 2.2 fo wate and fo glyceol mounting media. Figue 2.4 shows the integated intensity fo vaious NFPs using wate as the mounting medium. The fist image indicates the ideal situation encounteed with a fluoophoe mounted in immesion oil. The following images show again that the integated intensity is smeaed along the optical axis, and an additional peak appeas below the main maximum. The main maximum itself is shifted, dops in peak intensity, and becomes elatively boade. These values can be evaluated to obtain the focal shift [(NFP) (FP)], the dop in peak intensity, and the full-width-half-maximum (FWHM) of the main peak. While, because of its convoluted shape (Fig. 2.5), it is difficult to specify a simple metic that quantifies the shapness of a spheically abeated focal spot, the FWHM of the main peak is elatively simple to measue and hence has become the most common measue of the xy o axial esolution. Calculations fo some numbes encounteed in eal situations have been combined with the expeimental esults in Figues 2.6, 2.7, and 2.8. Figue 2.9 shows the focal shift of the excitation PSF of a.6 oil-immesion objective lens diectly as a function of NFP fo vaious efactive indices. Figue 2.1 also plots the focal shift but fo an N 1.4 oil-immesion objective lens. The FP is egaded as the position of the global maximum of the PSF along the optical axis athe than the cente of gavity o some othe measue of this complex shape. n impotant esult of these calculations is that the effects of spheical abeation incease apidly with ( - n 2 ), N, and distance of the object fom the coveslip (NFP). s long as the B C D FIGURE 2.3. Influence of a mismatched medium on the PSF. () and (C) show xz-images of calculated PSFs in logaithmic scale fo focusing with a wateimmesion lens (n = 1.334) 1mm deep into wate and immesion oil (n = 1.518), espectively. The inlets in the lowe left cones show the cental pat of the PSFs in linea scale. (B) and (D) show coesponding expeimental though-focus seies in a linea scale. These seies epesent exactly what one would see when focusing though a point-like object. Focusing into a mismatched medium causes a shift and a boadening of the main maximum. The abeated PSF can be clealy identified in the though-focus seies as focusing above the FP leads to a diffeent image than focusing below the FP. The image seies was made of a mio specimen by J. Pawley using a Zeiss xioskpp 5, with a 4 /N1.2 C-po objective, and ecoded with a Sony TRV-9 camcode using the zoom lens to povide the high magnification.

5 PHC2 25/11/25 7:24 PM Page Chapte 2. Egne and S.W. Hell D E F B C FIGURE 2.4. Integated z-esponses fo vaious penetation depths (NFP) in wate fo an N = 1.3 oil-immesion objective lens. The excitation and emission wavelengths wee 514 nm and 59 nm, espectively. () Ideal situation in oil, penetation depths of (B) 5 mm, (C) 1 mm, (D) 15 mm, (E) 2 mm, and (F) 25 mm. ll cuves ae nomalized to the ideal situation encounteed with immesion oil as the mounting medium. The point spead function is obviously not confined to the minimal volume but instead continues to spead the lage NFP becomes. This causes a decease of the maximal intensity, an incease of the full-width half-maximum, and a focal shift. The intensity is distibuted among seveal axial peaks of which at least two ae clealy visible. Please note that the NFP axis has been offset. = 1,518 cove slips n 2 fluoophoe in mounting medium = 1,518 B FIGURE 2.5. Sample used fo measuing the edge esponse in a confocal lase-scanning micoscope. () The sample consists of two coveslips o a coveslip and a glass slide with a fluoophoe dissolved in the mounting medium (wate, glyceol, immesion oil) in between. The sample thickness (uppe/lowe inteface distance) is at most 1 mm. In this sample, the concentation of the fluoophoe is zeo inside the glass and abuptly eaches a high concentation when moving the pobe along the optical axis. (B) Duing the expeiment, the point spead function penetates the mounting medium though a coveslip. The measued fluoescence intensity signal depends on the penetation depth. The fluoescence emission is maximal when the point spead function is completely inside the sample. Because the point spead function has a finite size, it has a esponse cuve with a finite steepness. The slopes close to the intefaces can, theefoe, be used to detemine the extent of the point spead function along the optical axis, and this is the axial esolution of the instument.

6 PHC2 25/11/25 7:24 PM Page 49 beations in Confocal and Multi-Photon Fluoescence Micoscopy Induced by Refactive Index Mismatch Chapte 2 49 TBLE 2.1. Result of Calculations fo Glyceol a,b xial xial Lateal Edge PSF PSF NFP Focal Shift Nomalized FWHM FWHM FWHM (mm) (mm) (mm) (mm) (mm) a Fo vaious nominal focal positions (NFP), the focal shift, the nomalized intensity, the axial edge esponse, the axial width of the PSF, and the lateal width of the PSF have been calculated fo an N = 1.3 oil-immesion objective lens and excitation and emission wavelengths of 514nm and 59nm, espectively. b The values fo an NFP = ae the ideal values if immesion oil is used as the mounting medium. TBLE 2.2. Result of Calculations fo Wate a xial xial Lateal Edge PSF PSF NFP Focal Shift Nomalized FWHM FWHM FWHM (mm) (mm) (mm) (mm) (mm) a Fo vaious nominal focal positions (NFP), the focal shift, nomalized intensity, axial edge esponse, axial width of the PSF, and lateal width of the PSF have been calculated fo an N = 1.3 oil-immesion objective lens and excitation and emission wavelengths of 514 nm and 59 nm, espectively. The values fo an NFP = ae the ideal values if immesion oil is used as the mounting medium. spheical abeations ae below a cetain theshold, the focal shift depends linealy on the NFP which can be used to coect the appaent thickness of a sample. If the spheical abeations exceed the theshold, the elation between the NFP and the focal shift becomes nonlinea which leads to image distotions along the z- axis and a apid dop in intensity as the excitation and emission PSF will be substantially displaced. This effect is most pominent with high Ns and vey low fo oil-immesion lenses having an N of <.85. EXPERIMENTS To veify these calculations, Rhodamine 6G was dissolved in wate, glyceol, and immesion oil to fom ~1-5 M solutions. The solutions wee mounted between a glass slide and a coveslip using doplets of died nail polish as spaces. The samples wee placed eithe onto a home-built confocal micoscope (Stelze et al., 1991) [Figs. 2.6, 2.7(), 2.8] o a commecial confocal micoscope (TCS SP2, Leica Micosystems Heidelbeg, Mannheim, Gemany) (Matini et al., 22) [Fig. 2.7(B)]. The dye was excited at a wavelength of 488 nm and obseved eithe above 53 nm [Figs. 2.6, 2.7(), 2.8] o between 495 nm and 53 nm [Fig. 2.7(B)]. Fo the data pesented in the Figues 2.6, 2.7() and 2.8, a Zeiss pochomat 1 oil objective with an adjustable apetue (N.8 1.4) was used, wheeas the data of Figue 2.7(B) was ecoded with a 1 adjustable apetue Leica oil-immesion lens (HCX PL PO 1.4.7) and a 1, 1.35 N Leica glyceolimmesion lens (HCX PL PO, GLYC CORR). The instuments wee used to ecod xz-images, that is, images in a plane paallel to the optical axis (Fig. 2.5). These images stated with the focus in the coveslip and ended with the focus in the glass slide. The 1 B Expeiment Theoy Theoy Expeiment Glyc Oil NFP [μm] FNP [μm] FNP [μm] 8 1 FIGURE 2.6. The expeimental and the theoetical edge-esponse cuves fo immesion oil. The theoetical cuve was fitted to the expeimental data set to comply with the appaent sample thickness and the maximum intensity in the sample. The theoetical calculations assume a pefect match of the efactive indices of the immesion oil, the glass, and the mounting medium. s shown, this condition is almost, but not pefectly, fulfilled unde eal conditions. The theoy pedicts a slightly steepe slope. FIGURE 2.7. The expeimental and the theoetical edge-esponse cuves fo glyceol. Focusing with an oil-immesion lens into glyceol leads to a significant dop in image bightness (). The theoetical cuve was fitted to the expeimental data set to comply with the appaent sample thickness and the maximum intensity in the sample. The intensity decease is pefectly epoduced. (B) By using a glyceol-immesion lens the dop in image bightness can be pevented.

7 PHC2 25/11/25 7:24 PM Page Chapte 2. Egne and S.W. Hell FIGURE 2.8. Two edge-esponse cuves in a wate sample. The gaph shows the intensities as a function of NFP fo N 1.4 and.8. Both cuves wee ecoded with the same sample in the same position. This is possible because the objective lens (Zeiss Plan-pochomat 1, N 1.4) has an adjustable N. The figue demonstates that the loss in esolution and the loss in intensity ae due to the effects of high N and not to quenching o bleaching. FIGURE 2.1. Dependence of the focal shift fo an N = 1.4 oil-immesion objective lens on the nominal focal position fo vaious efactive indices betwee.33 and Fo such a high N objective lens, the vaiation is only linea up to cetain maximum NFP, which stongly depends on the diffeence in the efactive index and the apetue angle. fte that, the focal shift stats to show some kind of oscillation. In the linea egime the cuves can be used to coect the appaent thickness of a sample in a mounting medium with a known efactive index by multiplying it by an appopiate facto. 64 cental columns wee then aveaged to geneate the edgeesponse cuves (see Eq. 6) shown in Figues 2.6 though 2.8. These gaphs esemble intensity signals as a function of the NFP. Of inteest is the edge steepness on both sides and the vaiation in peak intensity with depth. The esults ae summaized in Table 2.3. Because it was not possible to systematically vay the thickness of the dye laye (usually between 5 mm and 1mm), the focal shift was not measued diectly. OTHER CONSIDERTIONS Dy Objectives The use of dy, high-n lenses fo the obsevation of wet specimens, o even those sealed behind glass coveslips, causes abeations that ae much wose than fo any of the situations descibed above. Fist, the diffeence between the efactive indices of the immesion and embedding media is lage than fo any othe type of objective. Theefoe, focusing even a few micometes into the sample will esult in a sevee dop of intensity and esolution. Of couse, this can be avoided by adjusting the coection colla. Most high-n dy objectives ae equipped with such a colla but the coect adjustment only woks fo a single plane. Evey change of the NFP will esult in seious degadation of the PSF. Fo the same eason, dy objectives ae vey sensitive to the coveslip thickness. Second, due to total intenal eflection, the maximum angle tansmitted as the emeging light moves fom glass to ai is 41 and 49 as it moves fom wate to ai. The PSF is theefoe dominated by the illumination PSF. The situation is much elaxed when using lenses having an N of.6 o less because the angle inside the wate laye is then 26 and elatively uncitical. On the othe FIGURE 2.9. Dependence of the focal shift fo an N =.6 oil-immesion objective lens on the nominal focal position fo vaious efactive indices betwee.33 and Fo such a low N objective lens, the vaiation is linea fo the whole ange. The cuves can be used to coect the appaent thickness of a sample in a mounting medium with a known efactive index by multiplying it by an appopiate facto. TBLE 2.3. Result of the Expeiments with Wate and Glyceol Wate Wate Glyceol (N =.8) (N = 1.3) (N = 1.3) Uppe edge (mm) Lowe edge (mm) Ratio uppe/lowe

8 PHC2 25/11/25 7:24 PM Page 411 beations in Confocal and Multi-Photon Fluoescence Micoscopy Induced by Refactive Index Mismatch Chapte E B C F G D H FIGURE Optical spheical abeation coection. Images of aqueous PTK2 cells stained with Oegon geen anti-tubulin and made using an N 1.4 oil objective. Replacing micons of glass by wate intoduces distinct spheical abeations [() xy image; (B) xz PSF; (C) aw xz image; (D) deconvolved xz image] that ae not pesent in the coected images [(E) xy image; (F) xz PSF; (G) aw xz image; (H) deconvolved xz image]. The loss in peak intensity and contast is clealy visible in the images of the same xy plane (,E). The zx images of the fluoescent micosphee show the asymmety in the z diection and the loss in axial esolution (B,F). s a esult, afte deconvolution, tubulin fibes lying on top of each othe can be clealy distinguished only in the unabeated case. hand, the axial esolution impovement poduced by confocal micoscopy unde these conditions is so low that it is fai to ask if it makes sense to use such a micoscope unde these cicumstances. Refactive Index, Wavelength, and Tempeatue The efactive index is not a constant but depends on the wavelength (a phenomenon efeed to as dispesion) and on the tempeatue of the medium (especially with liquids). Standad immesion oil has a efactive index of at the n e line of the Hg spectum (486 nm) and a tempeatue of 23 C, but pefomance away fom these standad conditions may vay depending on the manufactue of the oil. Pefect imaging is, theefoe, not staightfowad to achieve. Special immesion oils and gels with many diffeent RI and vaying tempeatue behavio ae available though Cagille Laboatoies (Ceda Gove, NJ). Spheical beation Coection The loss in intensity and esolution caused by RI mismatch induced spheical abeations can highly degade the imaging pocess. Theefoe, it is advisable to educe the RI mismatch as much as possible (see section Consequences). Unfotunately, this is not always possible in a specific expeimental setting. Fo example, when using dipping wate-immesion objective lenses togethe with a coveslip, the spheical abeations caused by the wate glass wate tansitions induce spheical abeations that ae much stonge than those shown in the peceding examples. Fotunately, it is possible to cancel out abeations emeging at one point in the imaging pocess by intoducing negative abeations at anothe point. Fo example, in wate-immesion objective lenses, this is done inside the lens and the spheical abeation can be adjusted using a coection colla. Of couse this balancing can also be pefomed anywhee else in the optical path by eithe using a defomable mio (Booth et al., 22), o a spatial light modulato o alteing the effective tube length (Sheppad and Gu, 1992b). While the fist two appoaches can also coect fo nonspheical abeations, the latte can only be used fo balancing spheical abeations. Figue 2.11 shows an example fo abeation coection by alteing the effective tube length though a commecially available system (SC, Intelligent Imaging Innovations Inc., Denve, CO). Replacing micometes of glass by wate esults in ponounced spheical abeation. One can ecognize the sevee loss in intensity and contast in Figue 11(,E), an xy image of tubulin in PTK2 cells stained with Oegon geen. The axial esolution is also

9 PHC2 25/11/25 7:24 PM Page Chapte 2. Egne and S.W. Hell stongly educed [Fig. 2.11(B,F)], an effect that be compensated fo by deconvolution only appoximately (see Chapte 24, this volume). While in the abeated case, it is difficult to distinguish individual fibes lying nea each othe [Fig. 2.11(C,D)], they ae well sepaated in the abeation-fee images [Fig. 2.11(G,H)]. It is impotant to point out that much of the cham of coecting spheical abeation by moving optical components that ae not mounted in the objective lens comes fom the fact that the motion of such a coecting element can now be diven by a moto. 2 s all optical devices that change the spheical coection of an optical system by tube length alteation also change its focal length, changing the coection implies ceating a shift in the focal plane. Howeve, if the motion of the coecto is diven by a compute, this same compute can also adjust the focus contol in a compensatoy diection to maintain the focus plane. The SC is the fist device to do this automatically. One hopes that such devices may soon be incopoated into micoscope stands as a standad attachment, simila to a magnification shifte o a Betand lens. CONCLUSION The effects mentioned in this chapte ae so impotant that most pacticing micoscopists will have aleady encounteed them. The effects ae mainly visible when using lenses with a high N o, moe coectly, when using lenses whose cone angle is lage than 4. Some of the olde confocal micoscopes did not fill the backfocal plane completely (see Chapte 2, this volume) and the highe angles wee basically not pesent, especially when using high-n objectives of elatively low magnification (-4 ), as such lenses have vey lage entance pupils. Theefoe, it can be assumed that these poblems will become moe obvious as the quality of the instuments impoves and moe scientists wok with aqueous specimens. Consequences The qualitative elevance of these expeiments fo the obsevation of thick specimens mounted in an aqueous medium with a high- N, oil-immesion objective in a confocal micoscope is as follows: Thee is a seious loss of intensity when ecoding optical sections in focal planes away fom the coveslip and this loss becomes geate as the distance fom the coveslip inceases. The PSF suffes fom a seious axial smeaing; consequently, the axial esolution is lowe. The xy-esolution is also lowe because the high-n ays no longe each the focal spot. Less fluoescence intensity is detected behind the confocal pinhole. The distances measued along the optical axis ae smalle than the geometical distances in the object. The benchmak to emembe is that in wate, the focal shift is 13l at a penetation depth of 1l. 2 Othe methods poposed fo the automatic coection of spheical abeations include defomable mios and spatial light modulatos. Like the SC, these devices would be intoduced afte the objective, whee thei opeation could be compute contolled and any adjustments could be coupled with any changes in stage position that might be equied. In a mismatched system, the only pat of the specimen that can be obseved without the sevee effects descibed above is that immediately next to the coveslip. The poblem is encounteed in evey single-photon confocal and two-photon scanning micoscope. The physical elevance of these expeiments is that, in the case of a noticeably mismatched sample, a single PSF, o a single optical tansfe function (OTF) is not valid thoughout the sample. s the PSF o OTF can be defined only locally, a global deconvolution to emove the effect of spheical abeation using the system esponse is unlikely to be successful. This chapte also shows that an abeated PSF can be accuately calculated fom an initial unabeated PSF. The deviations follow an appoximately linea elationship, and a simple linea expansion is likely to be able to descibe the PSF in diffeent locations of the object faily well. Howeve, this does not mean that the effect can be easily coected. If not counteacted optically, the loss in signal level and esolution cannot be ecalled. Pactical Stategies to Reduce Refactive Index Mismatch The biologist can avoid these poblems by adheing to the following guidelines: lways use the appopiate objective lens. High esolving objective lenses like N 1.4 oil-immesion lenses ae usually designed to be used fo thin specimens mounted behind a coveslip. Fo othe expeimental settings, like imaging though the bottom of a peti dish, thee ae othe moe appopiate lenses available, paticulaly those that incopoate a coection colla fo spheical abeation minimization. These should always be popely adjusted. Thick specimens should only be obseved in matched systems. This means the RI of the mounting medium and the immesion medium should be identical at all wavelengths of inteest. Theefoe, wate-immesion and glyceol-immesion lenses should be used fo wate- and glyceol-embedded specimens, espectively. void situations in which the sample is thin but fa away fom the coveslip. This often happens when the object is eithe attached pemanently to the glass micoscope slide o when viewing cells gown on filtes but sepaated fom the potective coveslip by an unknown amount of aqueous medium. If you cannot match the RI of the mounting medium to that of the immesion, ty to get its efactive index as simila as possible. This can be accomplished by pepaing mixtues of glyceol and wate o by adding lage amounts of dextose to the mounting medium. This will at least educe the amount of spheical abeations incident at a cetain focusing depth. Fo unmatched systems, incease the size of the detection pinhole as a function of the penetation depth. This will not impove the PSF, but it will incease the detectable signal without any futhe losses in esolution, and at least the bightness will not decease so much as the image seies extends fathe fom the coveslip suface. If you have to image deepe into unmatched samples and no appopiate lens available, use a lowe N immesion objective. s demonstated in Figue 2.8, fo small mismatches, the loss in intensity is much less below N.85. Howeve, the lowe N has its own disadvantages: lowe light collection and lowe esolution. s shown in Table 2.3, looking though

10 PHC2 25/11/25 7:24 PM Page 413 beations in Confocal and Multi-Photon Fluoescence Micoscopy Induced by Refactive Index Mismatch Chapte mm of aqueous specimen with an N 1.4 oil lens deceases the axial esolution by a facto of 6 and the intensity becomes as low as 11%. If you use instead a N.8 lens, the axial esolution at the suface will be (.8/1.4) 2 = 3 times wose and only 36% of the fluoescence photons of the oil lens will be collected due to the smalle apetue angle. t an imaging depth of 5 mm things will have changed: The peak light intensity will dop to only about 33%, which is about the same signal as we would get with the oil lens (36% * 33% = 12%) and the esolution will be 6 / (3 * 1.3) = 1.5 times that of the oil lens. Clealy, this is an impovement, and the advantage becomes even moe pominent as the sample becomes thicke. On the othe hand, imaging though a 2 mm laye of wate gives about the same image with eithe lens, and any featues close to the coveslip will be imaged bette by the lage N lens. Of couse, one must keep in mind that imaging though ~1mm of wate with an oil immesion lens leads to a seiously abeated PSF. Spheical abeation (and not absoption) is the majo souce of the eduction in fluoescence signal with focus depth commonly noted by most pacticing confocal micoscopists. Optimal obsevation of thick living specimens occus when the sample is obseved using wate-immesion objectives and no coveslip. Upight micoscopes ae best suited fo this pupose because the wate is then less likely to leak into the objective. Howeve, the absence of a coveslip may cause the specimen to move as the focus plane changes to ecod 3D data. Unde these conditions, one may be able to use eithe wateimmesion lenses coected fo use with a coveslip (see Chapte 7, this volume) o CYTOP plastic coveslips, which have n = 1.34, and as a esult can be used with nomal wateimmesion lenses. If the expeimental setting does not allow fo spheical abeation minimization, think about abeation balancing inside the optical light path by intoducing a spheical abeation coection device. CKNOWLEDGMENTS This chapte is in pat based on Chapte 2 of the pevious edition. We acknowledge ealie suggestions and contibutions by Genot Reine and Enst Stelze. We thank Julia König and Nicole Zobiack fom Intelligent Imaging Innovations fo ganting us access to the spheical abeation coecto, Scientific Volume Imaging fo poviding us with thei Huygens deconvolution softwae, ndeas Schönle fo poviding us with his image acquisition and analysis softwae, ndeas Schönle fo poviding us with his image acquisition and analysis softwae Imspecto, Jaydev Jethwa fo caefully poofeading the manuscipt, and all the membes of the Depatment of NanoBiophotonics and James Pawley fo valuable discussions. REFERENCES Booth, M.J., Neil, M..., Juskaitis, R., and Wilson, T., 22, daptive abeation coection in a confocal micoscope, Poc. Natl. cad. Sci. US 99: Bon, M., and Wolf, E., 22, Pinciples of Optics, Cambidge Univesity Pess, Cambidge, New Yok. 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