June 15, 1999 / Vol. 24, No. 12 / OPTICS LETTERS 811

Confocal microscopy with a volume holographic filter

George Barbastathis* and Michal Balberg

Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana–Champaign,405 North Mathews Avenue, Urbana, Illinois 61801

David J. Brady

Beckman Institute for Advanced Science and Technology and Department of Electrical and Computer Engineering,University of Illinois at Urbana–Champaign, 405 North Mathews Avenue, Urbana, Illinois 61801

Received February 25, 1999

We describe a modif ied confocal microscope in which depth discrimination results from matched filtering bya volume hologram instead of a pinhole filter. The depth resolution depends on the numerical apertureof the objective lens and the thickness of the hologram, and the dynamic range is determined by thediffraction eff iciency. We calculate the depth response of the volume holographic confocal microscope, verifyit experimentally, and present the scanned image of a silicon wafer with microfabricated surface structures. 1999 Optical Society of America

OCIS codes: 180.1790, 110.6880, 090.7330.

The pinhole preceding the detector in a confocal mi-croscope is a shift-variant optical element. On-axisin-focus point-source objects are imaged exactly insidethe pinhole and give maximal intensity. An out-of-focus object, even when it is on axis, is equivalentto an extended source on the input focal plane. Theoff-axis portion of this extended source is filtered outby the limited aperture of the pinhole. Theoretically,the depth resolution is optimal when an infinitesi-mally small pinhole is used.1 However, such a deviceis an ad hoc f ilter that does not match perfectly theimpulse response of any realistic optical system. Inpractice, the minimum pinhole size, and hence thedepth-resolution limit, are determined by light effi-ciency (i.e., the required dynamic range of the mea-surement) and the broadening of the focal spot by lensaberrations.2 Coupling the dependence of two func-tional requirements (depth resolution and dynamicrange) to a single design parameter (the pinhole size)is a poor design choice.3 This is evident when the col-lected light has low intensity, e.g., in f luorescence andtwo-photon confocal microscopy.

In this Letter we present a new confocal imagingprinciple in which the pinhole is replaced with amatched filter recorded on a volume hologram. Thehologram is recorded such that the field that is gen-erated by an in-focus object is maximally diffracted,whereas objects that are out of focus are filtered outbecause they are Bragg mismatched. Consequently,dynamic range and axial resolution are decoupled; thedynamic range is determined by the diffraction effi-ciency of the volume hologram, and the axial resolutionby the numerical aperture of the objective lens andthe thickness of the hologram. Additional benefits ofpinhole-free confocal microscopy are ease of alignmentand improved aberration performance: Objective-lens aberrations are phase conjugated out during thehologram reconstruction process, and collector-lensaberrations (which increase the collected spot size) areirrelevant in the absence of a pinhole.

The volume holographic confocal microscope isshown schematically in Fig. 1. The volume hologram

0146-9592/99/120811-03$15.00/0

is recorded by the interference of two coherent beamsat wavelength l. The objective lens brings the firstbeam to focus on a reference surface, one focal distanceF away from the objective. The ref lected beam isrecollimated by the same objective and is used asthe recording plane-wave reference beam, with wavevector kR ­ s2pyldz. The signal beam is a planewave that is incident upon the recording medium alongkS ­ s2pyldx (90± recording geometry). The resultinggrating vector is K ­ kS 2 kR . During the imag-ing operation, the signal beam is blocked. The ref-erence surface is replaced by the object surface, andthe ref lected beam reconstructs the volume hologram.The diffracted light is collected by a second objectivelens (focal length F 0) and captured by a photodetector.

Compared with a ref lection-mode confocal micro-scope, the imaging arrangement shown in Fig. 1 con-tains two modifications, in addition to the volumehologram: (a) the objective lens is placed in a Fourier-transform rather than an imaging configuration and(b) the aperture in front of the detector does notcontribute to depth discrimination but only limits scat-ter and other light-noise sources. If the reconstruct-ing object is in focus (dotted lines in Fig. 1), this device

Fig. 1. Volume holographic confocal microscope without apinhole at the detector plane.

1999 Optical Society of America

812 OPTICS LETTERS / Vol. 24, No. 12 / June 15, 1999

operates exactly like a confocal microscope, becausethe volume hologram is Bragg matched (the recordingand the reconstructing reference beams are identical);therefore the diffracted intensity reaching the detectoris maximum.

Consider now an object that is defocused by asmall distance d. The beam that is ref lected fromthe object is no longer collimated by the objectivelens but contains an angular spectrum of plane-wavecomponents, as shown by the solid lines in Fig. 1.Diffraction of the off-axis components by the volumehologram is weaker because of Bragg mis-match. Consider the component with wave vectorkp ­ s2pyld hux 2 vy 1 f1 2 su2 1 v2dy2gzj, shown inFig. 2 sjuj, jvj ,, 1d. Born’s first approximation involume diffraction theory4 requires that the diffractedwave vector kd have the same y and z and compo-nents as the vector k0 ­ kp 1 K and, moreover, thatjkdj ­ 2pyl; therefore

kd ­2p

l

∑µ1 2

v2

2

∂x 2 vy 2

u2 1 v2

2z∏

. (1)

Taking only one diffracted component, kd, into accountin effect neglects the finite extent of the hologramin the y and z dimensions. However, the analysisremains valid because the entire spatial spectrumthat is diffracted in response to kp behaves (in theparaxial approximation) similarly to its central plane-wave component kd, which is the only componentthat we consider here. In other words, the impulseresponse that is due to the finite hologram aperturedoes not affect the depth discrimination of the system.

The diffracted intensity along this central componentkd is proportional to sinc2sDkxLy2pd, where L is theextent of the hologram in the x direction, and sincsjd ;sinspjdyspjd. The quantity Dkx is the deviation of k0

from the k sphere (see Fig. 2):

Dkx ­ jk0 2 kdj ­2p

l

µu 1

v2

2

∂. (2)

To obtain the overall diffraction efficiency summedover an infinite detector area we integrate the dif-fracted intensities from all spatial frequency compo-nents kp that are allowed through the circular objectiveaperture (diameter A; Fig. 1) and normalize them for atotal incident power of 1. The result is

hsdd ­h0

p

Z 2p

0du

Z 1

0dr r sinc2

ΩsNAd2jdjr

2LlA

3

∑cos u 1 sNAd2jdjr

sin2 u

2A

∏æ, (3)

where h0 ; hs0d, sNAd ø Ays2F d is the objectivenumerical aperture, jdjyF ,, 1 is assumed, and polarcoordinates sr, ud are substituted for su, vd in the in-tegral. A microscope without a pinhole in front of thedetector corresponds to the case L ­ 0, when the to-tal detected intensity does not depend on object depth.For finite thickness L . 0, the integral increases withjdj much slower than the denominator d2, and the dif-

fracted intensity decreases rapidly as a result. Theinstrument is optimal if all the light coming out ofthe objective reaches the hologram, i.e., L ­ A.

The Bragg-mismatch effect (expressed through thesinc function in the integrand) effectively acts as amatched spatial filter, discarding the defocused light.This shift-variant filtering operation is similar to thefield-of-view limitation imposed by the pinhole of aconfocal microscope. The passband has an ellipticalshape, with semiaxes umax ­ lyL and vmax ­

p2lyL.

Since vmax .. umax, the depth response is determinedprimarily by the term sNAd2jdjr in the argument ofthe sinc function of Eq. (3). As a measure of depthresolution, we use the FWHM of hsdd. By fittingnumerical data from Eq. (3) at the optimal geometryL ­ A, we obtain

dFWHM ­ 1.09 3l

sNAd2. (4)

By comparison, a confocal microscope with zero pinholesize has dFWHM ­ 0.86 3 lysNAd2, but the FWHM in-creases rapidly with pinhole size in realistic systems.1

We implemented the pinhole-free confocal micro-scope shown in Fig. 1 experimentally. We used anAr1 laser sl ­ 488 nmd as a light source; a 1-cm3

LiNbO3:Fe crystal (45± cut; refractive index, ø2.2) asa holographic medium; a 603, NA 0.85 objective lenssA ø 5 mmd; and a 103, NA 0.25 collector lens. Thereference and the object surfaces were polished siliconwafers with microfabricated features, mounted upon aKlinger translation stage (0.1-mm step size) with threedegrees of freedom. The light collected through a vari-able aperture was measured with a UDT photodetector.To implement a confocal microscope in the same experi-mental arrangement we simply replaced the volumehologram with a mirror oriented at 45±, directing theref lected beam into the collector lens.

The dependence of the normalized diffraction effi-ciency on the depth of the object surface is shown bycurves (a) and (b) of Fig. 3. The depth resolution isthe same for aperture sizes of 25 mm (matched to the

Fig. 2. Bragg mismatch in the k sphere.

June 15, 1999 / Vol. 24, No. 12 / OPTICS LETTERS 813

Fig. 3. Collected intensity as a function of object depthd for the volume holographic confocal microscope with(a) 25-mm and (b) 1-mm pinholes and for the confocal micro-scope (with a 45±-oriented mirror replacing the volume holo-gram) with (c) 25-mm (d) 1-mm pinholes. Location d ­ 0corresponds to the depth of the reference surface (at the fo-cal plane of the objective lens). All curves are normalizedsuch that their peak values equal 1.

Fig. 4. Two-dimensional scanning confocal image (recon-structed intensity map) of the silicon microstructure ob-tained with the volume holographic microscope shownin Fig. 1

collector’s spot size) and 1 mm. The intensity FWHMis s0.8 6 0.1d mm for both curves, in close agreementwith the value of ø0.75 mm predicted by Eqs. (3) and(4). Note, however, that the pedestal of curve (b)is higher because of scattered light that is reachingthe detector (i.e., the dynamic range of the measure-ment is slightly decreased). By contrast, the depth-discrimination capability of the confocal microscope[curves (c) and (d)] is degraded for the 1-mm aperture.

We used the pinhole-free confocal microscope toobtain a scanned image of the silicon microstructure,as shown in Fig. 4. The imaged portion contained atrench 20 mm wide and 5 mm deep. The referencesurface for recording the hologram was outside the

trench. The image of the trench corresponds to thedark region in Fig. 4, because the bottom of the trenchis out of focus. We sampled only five planes along yand one along z to minimize inaccuracies that were dueto the backlash of the translation stage and the decay ofthe hologram. A dense three-dimensional scan couldhave been obtained with a piezoelectric def lector and afixed hologram.

In conclusion, we have demonstrated confocal scan-ning microscopy by use of a volume hologram as ashift-variant element matched to object depth. Thedynamic range of volume holographic confocal imag-ing depends on the holographic diffraction efficiency(in our experiment it was ø1024) and is material lim-ited. Single-hologram efficiencies as high as 100%have been demonstrated,5 albeit with thinner materi-als and, hence, poorer Bragg selectivity. Volume holo-grams also permit the use of other imaging modes, e.g.,color-selective (hyperspectral) tomographic imaging6 orsuperresolution by use of complex filtering,7,8 in combi-nation with the pinhole-free confocal imaging principle.

We are grateful to Bo Kyoung Choi and Chang Liufor fabricating the silicon microstructure, to DanielMarks, Rick Morrison, and Ronald Stack for assistancewith experiment automation, and to Chris Bardeen,Martin Gruebele, Steve Rogers, and Peter So forhelpful discussions and comments on the manuscript.This work was funded by the U.S. Air Force Of-fice of Scientific Research. The authors’ e-mail ad-dresses are gbarb@mit.edu, mbalberg@uiuc.edu, anddbrady@uiuc.edu.

*Present address, Department of Mechanical Engi-neering, Massachusetts Institute of Technology, Room3-461c, 77 Massachusetts Avenue, Cambridge, Massa-chusetts 02139.

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