May 15, 1995 / Vol. 20, No. 10 / OPTICS LETTERS 1213

Simple binary optical elements for aberrationcorrection in confocal microscopy

Christian K. Sieracki, Christopher G. Levey, and Eric W. Hansen

Thayer School of Engineering, Dartmouth College, 8000 Cummings Hall, Hanover, New Hampshire 03755-8000

Received November 9, 1994

When a confocal fluorescence microscope with a high-numerical-aperture oil-immersion objective is focused deepinto an aqueous medium, aberrations result that degrade image quality. We have designed and fabricated a simpletwo-level binary phase mask that partially corrects these aberrations, improving axial resolution. We present thedesign and some confirming results.

The high axial resolution of confocal microscopy hasmade it a popular tool for constructing detailed three-dimensional images of microscopic structures. Forbiological specimens, this frequently involves imag-ing deep inside an aqueous medium with a high-numerical-aperture (NA) oil-immersion objective lens(Fig. 1). When a portion of the specimen near thecoverslip is imaged, the objective is operating in itsdesign regime, and the index mismatch between thecoverslip and the specimen medium is of little conse-quence. However, as the microscope focuses deeperinto the specimen, a nonnegligible optical path dif-ference (OPD) results between on- and off-axis rays.Gibson and Lanni1 have derived an expression for theOPD that, assuming that the most important sourcesof aberration are specimen–glass index mismatch anddeep focusing, simplifies to

OPDsrd ­ noilstoil 2 toilp d

"1 2

µNA r

noil

∂ 2# 1/2

1 nsts

"1 2

µNA r

ns

∂ 2# 1/2

, (1)

where NA is the numerical aperture of the objectivelens; r is the normalized radius in the lens apertures1 $ r $ 0d; toil, noil and ts, ns are the actual thick-ness and refractive index of the oil and the specimenmedium, respectively; and toilp is the oil thickness forwhich the lens was designed. In practice, noil . ns,and the highest-aperture waves will fail to propagate,effectively limiting the NA of the lens to somethingless than ns.

Aberrations induced by the OPD can exceed severalwaves at the edge of the pupil and include polynomialterms as high as r20.2 This decreases image bright-ness and severely increases the axial width of thepoint-spread function (PSF).3 – 7 Various approachesto correcting these aberrations have been suggested:(1) Water-immersion objectives, designed to operatein an aqueous medium,8 currently are quite expen-sive and may be hard to use in an inverted micro-scope. (2) A lens with lower NA will also have lessaberration, but its collection efficiency is reduced, andthe point spread is broadened. (3) Postdetection digi-tal restoration is characteristically sensitive to noise,particularly at the low light levels characteristic of

0146-9592/95/101213-03$6.00/0

confocal fluorescence microscopy. (4) In some systemsthe objective–detector distance may be adjusted6 to in-troduce balancing aberrations that improve the PSF.The approach taken here also introduces balancingaberrations but allows for more degrees of freedomin design.

We consider a phase mask for the objective pupil ofthe form expf2iksgr2 1 br4dg (i.e., misfocus plus pri-mary spherical aberration), fabricated as a two-levelbinary optical element (0 and p) by wrapping thephase at integer multiples of 2p and quantizing theresult. The minimum feature size of this binary ele-ment, calculated from the local spatial frequency of thephase function, is Ssrd ­ alys4gr 1 8br3d, where a isthe radius of the objective aperture stop. The spheri-cal coefficient b is chosen to correct the third-orderterm of Eq. (1), and the misfocus coefficient g thenis adjusted to produce a practical feature size. Mildresidual focus offsets are removed by a lens in the scan-ning optics. Figure 2 shows the phase profile of idealand two-level correcting elements designed for a 1.4-NA objective lens focusing 40 mm into water.

We simulated the PSF of the confocal microscopewith and without this corrector, using the standardmodel:

hsr, zd ­ jp1sr, zdj2fjp2sr, zdj2 pp P3srdg , (2)

Fig. 1. When a high-NA oil-immersion lens images a spec-imen in an aqueous medium, path differences result fromindex mismatch. Solid ray, noil . ns (exaggerated for pur-poses of illustration); dashed ray, noil ø ns.

1995 Optical Society of America

1214 OPTICS LETTERS / Vol. 20, No. 10 / May 15, 1995

Fig. 2. Phase profiles of continuous and two-levelfourth-order correcting elements designed for a 1.4-NAoil-immersion objective focusing 40 mm into an aqueousmedium.

where p1 and p2 are the PSF’s of the illumination lensand collecting lens, respectively, P3 is the effective de-tector aperture, and pp indicates a two-dimensional(lateral) convolution. The collector lens PSF (propa-gation from the specimen to the detector plane) is ac-curately described by a Hankel transform:

p2sr, zd ­Z 1

0expf2iFsrdgJ0

µkrr

f

∂r dr , (3)

where f is the lens focal length, Fsrd is the pupil phasefunction, including aberrations and corrections, andr ­ sx2 1 y2d1/2. We also used this model for the il-lumination PSF, p1; for our purposes it gives essen-tially the same results as more complex diffractioncalculations.3,7 In the usual epifluorescence mode, thecorrector is traversed in one direction by the illumina-tion light and in the reverse direction by the emittedfluorescence. To model the return path, we scaled thecorrector’s dimensions by lillumylemission (e.g., lillum ­488 nm and lemission ­ 535 nm); no significant degrada-tion arising from the wavelength difference was seen.Figure 3 shows that the FWHM of the image of a pointobject is predicted to improve by 40–50% over a rangeof 20–60-mm depth, while the performance at 10 mm isnow degraded relative to that of the uncorrected case.

An experimental phase mask was designed andprinted from a personal computer and reduced to ac-tual size on microfiche by standard commercial pro-cessing. Photolithography was performed with themicrofiche as a contact mask. The substrate wasa soda-lime glass slide (catalog no. 3051, Becton,Dickinson, Lincoln Park, N.J.) with refractive indexnglass ­ 1.5 at 488 nm. The minimum lateral featuresize was 200 mm, and the step height for a half-wavephase shift was 473 nm (for l ­ 488 nm). A timedwet-etch process that uses a solution of 5% HF in NH4Fetched the soda-lime glass at 180 nmymin with agita-tion. The completed mask was positioned at a planeconjugate to the objective’s aperture stop in a ZeissIM-35 inverted microscope (Carl Zeiss, Oberkochen,Germany) augmented for confocal scanning.

The test objects were 140-nm-diameter polystyrenebeads labeled with fluorescein isothiocyanate (catalogno. 17750, Polysciences, Warrington, Pa.). The beadswere suspended in methanol, deposited onto micro-scope slides, and allowed to dry. Each slide was thenprepared with a layer of water and a #1 coverslip, andthe coverslip was sealed to the slide with fingernail pol-ish (Cover Girl Salon Solutions Antichip Topcoat wasfound to hold up well over time).

The objective’s focal position relative to the stagewas adjusted by a microstepping motor (ModelM061-LF-408, Superior Electric, Bristol, Conn.)attached to the microscope’s fine focus knob and moni-tored with an eddy current sensor (Model KD-2810-1U, Kaman Instrumentation, Colorado Springs, Colo.).The lateral (XY ) scan was created by a galvanome-ter system.9 The focusing system was calibratedfor refractive-index mismatch by means of a slidewith a micro-etched well of known depth, filled withwater, and capped with a coverslip. The change inobserved focus (toil) from the top of the well to thebottom was compared with its known depth. Anempirical scale factor of 0.8 was determined, whichagrees with theory.7 We similarly measured thedepth of the beads by focusing first on the cover-slip–water interface and then on the beads andscaling the observed difference by 0.8. A preparationwith 40-mm bead depth was selected for imaging.

Through-focus image series were taken with 50-nmlateral sampling and 200-nm axial steps at the stage

Fig. 3. Simulated axial point response for a confocalfluorescence microscope at various depths below thecoverslip in an aqueous medium, with (solid curves) andwithout (dashed curves) a binary corrector designed for40-mm depth. Dz is measured at the stage (i.e., toil).Axial FWHM is improved by 40–50% over the range20–60 mm.

May 15, 1995 / Vol. 20, No. 10 / OPTICS LETTERS 1215

Fig. 4. Averaged lateral intensity of ensembles of thirteen140-nm beads at best focus, 40-mm depth, with (solidcurves) and without (dashed curves) the binary corrector.Samples are spaced at 50 nm. Error bars represent 95%confidence intervals; there is no significant difference be-tween the profiles.

Fig. 5. Averaged axial intensity of ensembles of 140-nmbeads at 40-mm depth in water. Optical sections weretaken every 200 nm at the stage (160 nm in water); Dzis measured at the stage (i.e., toil). Solid curve, average of20 beads imaged with the binary corrector; dashed curve,average of 14 beads imaged without the corrector. Errorbars represent 95% confidence intervals. The FWHM isimproved by approximately 50%, from ,1.5 to ,0.7 mm.

(160 nm in water). The 25 mm 3 25 mm fields ofview were scanned with 100-mW input to a Zeiss 6331.4-NA Planapo objective for ,19 msypixel. Measure-

ments taken with the corrector in place were scaled by1.23 to compensate for surface reflection losses. Pro-files of several bead images were measured, aligned,and averaged. Figure 4 shows that the correctormakes little difference in the lateral profile. On theother hand, Fig. 5 shows a significant axial improve-ment. The measured FWHM (at the stage) of theaxial bead images is reduced by approximately 50%from ,1.5 to ,0.7 mm, which agrees with theory (1.58and 0.77 mm, respectively) within the 200-nm axialstep size.

We found that a simple two-level phase mask, de-signed to correct only primary spherical aberration,made significant improvements in the axial responseof a confocal microscope working deep in an aque-ous preparation. The two-level mask was fabricatedwith rudimentary graphics, photolithography, and wetchemical etching; a mask aligner was not required. Aseries of three or four such elements, designed for dif-ferent specimen depths, would be needed to cover awide axial range. We are currently investigating de-signs with more phase levels and higher-order correc-tions.

The support of the National Institutes of Health(grant RO1–GM36594) is gratefully acknowledged.The authors thank Ken Orndorff for his assistance inspecimen preparation.

References

1. S. F. Gibson and F. Lanni, J. Opt. Soc. Am. A 8, 1601(1991).

2. S. F. F. Gibson, “Modeling the three-dimensional imag-ing properties of the fluorescence light microscope,”Ph.D. dissertation (Carnegie-Mellon University, Pitts-burg, Pa., 1990).

3. H. T. M. van der Voort, and G. J. Brakenhoff, J. Microsc.158, 43 (1990).

4. K. Carlsson, J. Microsc. 163, 167 (1991).5. C. J. R. Sheppard and M. Gu, Appl. Opt. 30, 3563 (1991).6. C. J. R. Sheppard and M. Gu, Opt. Commun. 88, 180

(1992).7. S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer,

J. Microsc. 169, 391 (1993).8. M. Brenner, Am. Lab. 26, 14 (1994).9. E. W. Hansen, J. P. Zelten, and B. A. Wiseman, Proc.

Soc. Photo-Opt. Instrum. Eng. 909, 304 (1988).