Optics Letters '95 Paper
The following has been reformatted by the authors for electronic presentation, and is not in archival form. The archival edition has been published in:

Optics Letters, Volume 20, Number 10, page 1213 (May 15, 1995)

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Simple Binary Optical Elements for Aberration Correction 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

When a confocal fluorescence microscope with a high numerical aperture oil immersion objective is focused deep into an aqueous medium, aberrations result which degrade image quality. We have designed and fabricated a simple, two-level binary phase mask which partially corrects these aberrations, improving axial resolution. This letter presents the design and some confirming results.

The high axial resolution of confocal microscopy has made it a popular tool for constructing detailed three-dimensional (3D) images of microscopic structures. For biological specimens, this frequently involves imaging deep inside an aqueous medium with a high numerical aperture (NA) oil immersion objective lens (Figure 1) . When imaging a portion of the specimen near the coverslip, the objective is operating in its design regime and the index mismatch between coverslip and specimen medium is of little consequence. However, as the microscope focuses deeper into the specimen, a non-negligible optical path difference (OPD) results between on- and off-axis rays. Gibson and Lanni [1] have derived an expression for the OPD which, assuming that the most important sources of aberration are specimen-glass index mismatch and deep focusing, simplifies to:


where NA = numerical aperture of the objective lens; [[rho]] = normalized radius in the lens aperture ; toil , noil , ts , ns = actual thickness and refractive index of oil and specimen medium, respectively; and toil* = oil thickness for which 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 something less than ns.

Aberrations induced by the optical path difference can exceed several waves at the edge of the pupil and include polynomial terms as high as [2]. This decreases image brightness and severely increases the axial width of the the point spread function (PSF)[3-7] Various approaches to correcting these aberrations have been suggested: (1) Water-immersion objectives, designed to operate in an aqueous medium [8] are currently quite expensive, do not operate with all specimen mounting media and fluorophores, and are hard to use in an inverted microscope. (2) A lens with lower NA will also have less aberration, but collection efficiency is reduced and the point spread is broadened. (3) Post-detection digital restoration is characteristically sensitive to noise, particularly at the low light levels characteristic of confocal fluorescence microscopy. (4) In some systems the objective-detector distance may be adjusted [6] to introduce balancing aberrations that improve the PSF. The approach taken here also introduces balancing aberrations, but allows for more degrees of freedom in design.

We consider a phase mask for the objective pupil of the form (i.e., misfocus + primary spherical aberration), fabricated as a two-level binary optical element (0 and [[pi]]) by "wrapping" the phase at integer multiples of 2[[pi]] and quantizing the result. The minimum feature size of this binary element, calculated from the local spatial frequency of the phase function, is , where a = radius of the objective aperture stop. The spherical coefficient [[beta]] is chosen to correct the third-order term of (1), and the misfocus coefficient [[gamma]] is then adjusted to achieve a practical feature size. Mild residual focus offsets are removed by an auxiliary lens in the scanning optics. Figure 2 shows the phase profile of ideal and two-level correcting elements designed for a 1.4 NA objective lens focusing 40um into water.

We simulated the PSF of the confocal microscope with and without this corrector using the standard model:


where p1 and p2 are the point spread functions of the illumination lens and collecting lens, respectively, P3 is the effective detector aperture, and ** indicates a 2D (lateral) convolution. The collector lens PSF (propagation from the specimen to the detector plane) is accurately described by a Hankel transform,


where f = lens focal length, [[Phi]]([[rho]]) is the pupil phase function, including aberrations and corrections, and We also used this model for the illumination PSF p1; for our purposes here it gives essentially the same results as more complex diffraction calculations[3,7]. In the usual epi-fluorescence mode, the corrector is traversed in one direction by the illumination light and in the reverse direction by the emitted fluorescence. To model the return path, the corrector's dimensions were scaled by [[lambda]]illum/[[lambda]]emission (e.g., [[lambda]]illum = 488 nm and [[lambda]]emission = 535 nm); no significant degradation due to the wavelength difference was seen. Figure 3 shows that the full width at half maximum (FWHM) of the image of a point object is predicted to improve by 40% to 50% over a range from 20 um to 60 um depth, while the performance at 10 um is now degraded relative to the uncorrected case.

An experimental phase mask was designed and printed from a personal computer and reduced to actual size on microfiche by standard commercial processing. Photolithography was performed using the microfiche as a contact mask. The substrate was a soda-lime glass slide (Cat. No. 3051, Becton, Dickinson and Co., Lincoln Park, NJ) with refractive index nglass =1.5 at 488 nm. The minimum lateral feature size was 200 um and the step height for a half-wave phase shift was 473 nm (for [[lambda]] = 488 nm). A timed wet etch process using a solution of 5% HF in NH4F etched the soda-lime glass at 180 nm/min with agitation. The completed mask was positioned at a plane conjugate to the objective's aperture stop in a Zeiss IM-35 inverted microscope (Carl Zeiss, Oberkochen, Germany) augmented for confocal scanning.

The test objects were 140 nm diameter polystyrene beads labeled with fluorescein isothiocyanate (Cat. No. 17750, Polysciences, Inc., Warrington, PA). The beads were suspended in methanol, deposited on microscope slides and allowed to dry. Each slide was then prepared with a layer of water and a #1 coverslip, and the coverslip was sealed to the slide with fingernail polish (Cover Girl Salon Solutions anti-chip topcoat was found to hold up well over time).

The objective's focal position relative to the stage was adjusted by a microstepping motor (Model M061-LF-408, Superior Electric, Bristol, CT) attached to the microscope's fine focus knob, and monitored with an eddy current sensor (Model KD-2810-1U, Kaman Instrumentation Corporation, Colorado Springs, CO). The lateral (XY) scan was created by a galvanometer system [9]. The focusing system was calibrated for refractive index mismatch using a slide with a micro-etched well of known depth, filled with water and capped with a coverslip. The change in observed focus (toil) from the top of the well to the bottom was compared with its known depth. An empirical scale factor of 0.8 was determined, which agrees with theory [7]. The depth of the beads was similarly measured by focusing first on the coverslip/water interface and then on the beads, and scaling the observed difference by 0.8. A preparation with 40 um bead depth was selected for imaging.

Through-focus image series were taken with 50 nm lateral sampling and 200 nm axial steps at the stage (160 nm in water). 25 x 25 um2 fields of view were scanned with 100 uW input to a Zeiss 63x 1.4NA Plan-apo objective for ca. 19 usec per pixel. Measurements taken with the corrector in place were scaled by 1.23 to compensate for surface reflection losses. Profiles of several bead images were measured, aligned, and averaged. Figure 4 shows that the corrector makes little difference in the lateral profile.
On the other hand, Figure 5 displays a significant axial improvement. The measured FWHM (at the stage) of the axial bead images is reduced by approximately 50% from ca. 1.5 um to ca. 0.7 um, which agrees with theory (1.58 um and 0.77 um, respectively) within the 200 nm axial step size.

We found that a very simple two-level phase mask, designed to correct only primary spherical aberration, made significant improvements in the axial response of a confocal microscope working deep in an aqueous preparation. The two level mask was fabricated using rudimentary graphics, photolithography and wet chemical etching; a mask aligner was not required. A series of three or four such elements designed for different specimen depths would be needed to cover a wide axial range. We are currently investigating designs with more phase levels and higher order corrections.

The support of the National Institutes of Health, grant RO1-GM36594 is gratefully acknowledged. The authors also thank Ken Orndorff for his assistance in specimen preparation.


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

2. S. F. F. Gibson, "Modeling the Three Dimensional Imaging Properties of the Fluorescence Light Microscope," Ph.D. dissertation (Carnegie-Mellon University, 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, et al., J. Microsc. 169, 391 (1993).

8. M. Brenner, American Laboratory 26, 14 (1994).

9. E. W. Hansen, J. P. Zelten and B. A. Wiseman, in Time-Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed. Proc. SPIE 909, 304 (1988).

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