May 15, 2006 / Vol. 31, No. 10 / OPTICS LETTERS 1477

Resolution enhancement in a light-sheet-basedmicroscope (SPIM)

Christoph J. Engelbrecht and Ernst H. K. StelzerLight Microscopy Group, EMBL Heidelberg, Meyerhofstrasse 1, D-69117 Heidelberg, Germany

Received September 27, 2005; revised January 5, 2006; accepted January 17, 2006; posted February 27, 2006 (Doc. ID 65027)

Light-sheet-based microscopy [single-plane illumination microscope (SPIM)] performs very well at low nu-merical apertures. It complements conventional (FM), confocal (CFM), and two-photon fluorescence micros-copy (2h�-FM) currently used in modern life sciences. Lateral and axial SPIM point spread function (PSF)extents are measured by using fluorescent beads to determine the 3D resolution. The results are comparedwith values derived from an analytical theory and numerical simulations. The discrepancies are found to beless than 5%. The axial extent of a SPIM–PSF �10� /0.3 W� is approximately 5.7 �m. This value is almosta factor of 2 smaller than in CFM, more than 2.5 times smaller than in FM, and more than three timessmaller than in 2h�-FM. SPIM outperforms 2h�-FM and FM, while CFM has a better axial resolution atNAs above 0.8. © 2006 Optical Society of America

OCIS codes: 180.2520, 180.6900, 070.2580, 170.2520, 170.6900.

Microscopy applications in the life sciences requireobjective lenses with low to medium magnificationsand large free-working distances (FWD). Such lenseshave low numerical apertures (NA). The axial resolu-tion of every single-lens fluorescence microscope isdramatically poorer than the lateral resolution at lowNAs. The fundamental principle of confocal thetamicroscopy1 was introduced to overcome the pooraxial resolution of low-NA single-lens systems: thefluorescence light is detected with a second lens at anangle �=90° relative to the illumination axis. Otherimplementations of this principle2–4 take advantageof parallel recording. The illumination system selec-tively excites fluorophores within an entire plane,which coincides with the focal plane of the detectionsystem. The thickness of the illuminating light sheetand the NA of the detection lens determine the axialresolution of the instrument. Our particular imple-mentation of light-sheet-based microscopy (Fig. 1) iscalled a single-plane illumination microscope(SPIM).4 The 3D resolution of a light microscope isdefined by the lateral and axial extents of the inten-sity point spread functions (PSF). We measured thePSFs in a SPIM for three different objective lenses.The results are compared with values derived froman analytical theory and from numerical simulations.

Orange fluorescent latex beads (L-5222, MolecularProbes, USA) with a diameter of 0.1 �m were usedfor experiments. The bead solution (2% solids) wasdiluted 1:10 with distilled water and sonicated in abath sonicator (USR 18, Merck Eurolab, Belgium) for10 min to prevent bead aggregation. The solutionwas mixed 1:1000 with melted agarose solution (1%,A4018, low gelling temperature, Sigma-Aldrich, St.Louis, Missouri) at 40°C. Cylinders of the agarose-bead solution with diameters of 1.2 mm were formedby cooling the solution to room temperature inside aglass micropipette (Blaubrand 7087 44, 100 �l,Brand, Wertheim, Germany) for �30 min. A piece ofwire pushed �1.5 mm of the agarose cylinder intothe immersion medium. The refractive indices of aga-rose and the surrounding water matched ��0.1% �;

aberrations were thus minimized. During image ac-

0146-9592/06/101477-3/$15.00 ©

quisition, six to eight stacks with an axial spacing of0.33 or 0.5 �m were acquired with each objective lens(Zeiss Achroplan 10� /0.3 W, 40� /0.8 W, and 100� /1.0 W). The stacks consisted of 300 or 200 planes,respectively; i.e., all of them had an axial extent of100 �m. The stacks were taken near the edge of theagarose cylinder facing the detection objective lens;deterioration of image quality was thus minimized. APixelfly HiRes CCD camera (PCO AG, Kelheim, Ger-many) with a resolution of 1024�1360 pixels and apixel pitch of 4.65 �m was used for imaging. Fivecuboids with one central bead each were croppedfrom the centers of the image stacks and rescaledalong the z axis by using cubic B-spline interpolation(ImageJ, TransformJ), thus generating isotropicvoxel size. The intensity profiles along any two per-pendicular axes (x and y, x and z, y and z) in thethree central planes �xy ,xz ,yz� of each cuboid weremeasured. The resulting four lateral and two axialintensity distributions of each bead were added andnormalized. The resulting five lateral and five axialintensity distributions (for n=5 different beads perlens) were averaged and fitted with Gaussian-likefunctions y�x��exp�−2x2 /�2� to determine the lateraland axial standard deviations �. An error estimatewas obtained by comparing fits of single beaddatasets with the average fits. The �’s were multi-plied by a factor 1/��2 ln�2�� to calculate the corre-sponding FWHM (Table 1).

Following McCutchen’s5 solution of the Helmholtzequation, and taking polarization effects intoaccount,6 the 3D electromagnetic field distributionh�x ,y ,z� in the focal region can be obtained by Fou-rier transforming a generalized lens aperture A�k�,which can be further separated into the field strengthE0�k�, the transmission T�k�, the polarization P�k�,and the apodization B�k�:

h�x,y,z� =� E0�k�T�k�P�k�B�k� · eikrd3k.

k= �kx ,ky ,kz� is the wave vector with the wave num-

ber �k�=n2� /0, n is the refractive index of the im-

2006 Optical Society of America

1478 OPTICS LETTERS / Vol. 31, No. 10 / May 15, 2006

mersion medium, and 0 is the vacuum wavelength.A detailed treatment of the methods is found in Ref.7. A circular generalized lens aperture with a uni-form illumination intensity (obeying the sinecondition8) is assumed for calculating the detectionPSFs. A linear combination of x- and y-polarized lightaccounts for the unpolarized character of the fluores-cence emission. In contrast, a slit aperture is re-quired for the cylindrical illumination PSFs. Polar-ization does not have noticeable effects on theillumination intensity distribution, as the illumina-tion NAill is very small [ranging from 0.04 to 0.13 andadapted to the field of view (FOV)]. A Gaussian illu-mination of the slit aperture with a beam waist twice

Fig. 1. (Color online) (a), (b) A conventional wide-field mi-croscope (CCD camera, tube lens, filter, and detection ob-jective lens) is used for fluorescence detection. A collimatedlaser beam is focused by a cylindrical lens and generates alight sheet. It excites only fluorophores in the focal plane ofthe detection objective lens, since the illumination axis isrotated by �=90° relative to the detection axis. The samplecan be translated along the three principal axes and ro-tated around an axis perpendicular to both the illumina-tion and the detection axes. The sample is moved along thez axis to acquire stacks; all other parts are spatially con-fined. (c) The detection magnification Mdet, illuminationwavelength ill, refractive index of the immersion mediumn, and the extent of the CCD chip sizeCCD determine theFOV. The illumination numerical aperture NAill is adjust-able by a rectangular diaphragm and is adapted to theFOV. The width of the light sheet in the center of the FOVw0 is 1/�2 the width at the edge wedge. The detection nu-merical aperture NAdet and wavelength combinations det,ill are determined by the experiments, lenses, and dyes.

the slit width is assumed for illumination. We varied

the wavelengths for the detection PSFs due to thefluorescent beads’ emission spectra �565 nm±5 nm�.The central positions of the detection PSFs areshifted by ±0.5 pixels to account for pixilation and/ordigitization effects. The detection PSF is multipliedwith the illumination PSF, since the system PSFof a SPIM is calculated as �hSPIM�x ,y ,z��2= �hill�x ,z ,y��2� �hdet�x ,y ,z��2 (Fig. 2). The resultingsystem PSF is convolved with a spherical object of0.10±0.01 �m diameter to account for size and sizevariations. Five simulated beads were analyzed inexactly the same way as the experimental data to al-low for a comparison avoiding analysis-induced arti-facts. Table 1 provides the FWHM extents obtainedfrom the measurements and from the numerical andanalytical theories. The illumination NAill is calcu-lated with Gaussian beam optics assuming a drop inintensity to a fraction of 1/�2 across the FOV, i.e.,from its center to either edge. The analytical(Stelzer–Grill–Heisenberg, SGH) values are based ona theory derived from Heisenberg’s uncertaintyprinciple.9 It provides estimates for FWHM extents offocused beams. Lateral and axial FWHM extents arecalculated for the cylindrical illumination system and

Table 1. Lateral and Axial PSF Extents andFocal Volumes of Analytical, Simulated,

and Measured PSFs in a SPIMa

LensFWHMlat

��m�FWHMax

��m�Volume

(al)

10� /0.3 W ana 1.10 5.01 3174.1sim 1.06 5.05 2970.4exp 1.06±0.07 5.02±0.36 2953.3±643.7

40� /0.8 W ana 0.40 1.66 139.1sim 0.41 1.66 147.8exp 0.44±0.02 1.57±0.20 159.1±37.0

100� /1.0 W ana 0.32 1.01 54.2sim 0.32 1.00 53.0exp 0.32±0.01 1.02±0.1 54.7±9.6

aThe focal volumes are those of an ellipsoid �V=4/3��FWHMlat /2�2�FWHMax/2�� and specified in attoliters�1 al=10−18 l=10−21 m3��. The parameters are ill=0.488 �m;NAill=0.042, 0.083, and 0.131 for the 10�, 40�, and 100� lenses,respectively; det=0.565 �m; n=1.33; number of pixels=1024�1360; pixel pitch=4.65 �m.

Fig. 2. (a), (b), and (c) show simulated illumination, detec-tion, and system PSFs for a SPIM with a 10� /0.3 W de-tection objective lens. The length of the scale bar is 20 �m.The parameters are camera pixel pitch 4.65 �m, ill=0.488 �m, det=0.565 �m, n=1.33, image size 75�76 pixels, NAill=0.042 (adapted to a FOV of 476.2 �m;only the central part is shown), Mdet=10, NAdet=0.3. A

gamma of 0.4 was applied to images (b) and (c).

May 15, 2006 / Vol. 31, No. 10 / OPTICS LETTERS 1479

for the spherical detection system using Eqs. (1). Theanalytical values in Table 1 and the values in Table 2are obtained by combining the appropriate valuesfrom Eqs. (1) using Eq. (2). The values provided inTable 1 also take additional standard deviations ofpixilation effects and finite bead sizes into account.

rcylindrical�0,n,�� =0��

2n�2� − sin�2��,

zcylindrical�0,n,�� =0�

2n�2�2 − 4 sin2��� + � sin�2��,

rspherical�0,n,�� =0

n�3 − 2 cos��� − cos�2��,

zspherical�0,n,�� =0

n�1 − cos����, �1�

�1+2 =1

��1/�1�2 + �1/�2�2. �2�

0 is the vacuum wavelength of the illumination ordetection system, n is the refractive index of the im-mersion medium, and � is the half-opening angle forthe illumination or detection lens. � are standard

Table 2. Lateral and Axial Extents and FocalVolumes of Simulated PSFs in a SPIM

Compared with Conventional, Confocal,and Two-Photon Microscopesa

Lens TechniqueFWHMlat

�mFWHMax

�mVolume

al

1.0� /0.3 W FM 1.00 15.17 7943.0CFM 0.68 10.38 2513.12h�-FM 1.22 18.57 14472.0SPIM 1.00 5.73 3000.2

40� /0.8 W FM 0.37 1.94 139.1CFM 0.25 1.33 43.52h�-FM 0.45 2.38 252.3SPIM 0.37 1.65 118.3

100� /1.0 W FM 0.29 1.15 50.6CFM 0.20 0.79 16.52h�-FM 0.36 1.40 95.0SPIM 0.29 0.99 43.6

100� /1.2 W FM 0.24 0.69 20.8CFM 0.16 0.47 6.32h�-FM 0.29 0.84 37.0SPIM 0.24 0.65 19.6

aAll calculations do not take pixilation or bead sizes into ac-count. The parameters are ill=0.488 �m; NAill=0.034, 0.068,0.108, and 0.108 for the 10� /0.3 W, 40� /0.8 W, 100� /1.0 W,and 100� /1.2 W lenses in the SPIM; camera pixel pitch 6.45 �m;number of pixels=1024�1344; det=0.520 �m; n=1.33; ill

=0.900 �m for two-photon excitation. These parameters vary fromthose used in Table 1.

1,2

deviations of functions f1 and f2, whereas �1+2 is thestandard deviation of their product f1� f2. Both thenumerical simulations and the values derived fromthe analytical theory are within a 5% range of the ex-perimentally measured values. Thus we continue touse the analytically derived formulas to compare ex-pected lateral and axial PSF extents for different mi-croscope arrangements at parameters suitable for ob-serving green fluorescent proteins (GFP) (Table 2).

SPIM provides a straightforward technology for ob-taining optically sectioned images of live, biologicalsamples, while phototoxic effects are avoided to ahigh degree. The wide-field detection provides fastimage acquisition. We have shown that a SPIM’saxial resolution is always better than that of conven-tional fluorescence microscopy (FM) or two-photonfluorescence microscopy �2h�-FM). It is better thanthat of confocal fluorescence microscopy (CFM) forNA�0.8 (assuming a FOV of 66 �m). At higher NAs,CFM performs slightly better. An optional step forfurther increasing the resolution and obtaining moreinformation is to rotate the sample around an axis or-thogonal to the optical axes of the illumination anddetection systems. Data stacks recorded along differ-ent angles are combined in postprocessing steps toyield high-resolution images of complete samples.10

The isotropic 3D resolution in such a multiview sys-tem is dominated by the lateral resolution of the de-tection system. A multiview SPIM yields a focal vol-ume of about 12.8 al for a 100� /1.0 W objective lens,a more than 3.4-fold improvement over a single-view100� /1.0 W SPIM. A focal volume of 523.6 al isachieved with a multiview 10� /0.3 W SPIM; this isan almost sixfold improvement over a single-view10� /0.3 W SPIM and an almost fivefold improve-ment over a CFM.

J. Swoger, P. Keller, and U. Krzic helped withMATLAB-related problems. K. Greger introduced C.J. Engelbrecht to LabVIEW programming. A. Rohr-bach and H. Kress made valuable comments on thenumerical simulations and critically reviewed themanuscript. Correspondence should be addressed toE. H. K. Stelzer at stelzer@embl.de.

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