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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 f iltering by a volume hologram instead of a pinhole f ilter. The depth resolution depends on the numerical aperture of the objective lens and the thickness of the hologram, and the dynamic range is determined by the diffraction eff iciency. We calculate the depth response of the volume holographic confocal microscope, verify it 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 microscope is a shift-variant optical element. On-axis in-focus point-source objects are imaged exactly inside the pinhole and give maximal intensity. An out-offocus object, even when it is on axis, is equivalent to an extended source on the input focal plane. The off-axis portion of this extended source is filtered out by the limited aperture of the pinhole. Theoretically, the depth resolution is optimal when an inf initesimally small pinhole is used.1 However, such a device is an ad hoc filter that does not match perfectly the impulse response of any realistic optical system. In practice, the minimum pinhole size, and hence the depth-resolution limit, are determined by light efficiency (i.e., the required dynamic range of the measurement) and the broadening of the focal spot by lens aberrations.2 Coupling the dependence of two functional requirements (depth resolution and dynamic range) to a single design parameter (the pinhole size) is a poor design choice.3 This is evident when the collected light has low intensity, e.g., in f luorescence and two-photon confocal microscopy. In this Letter we present a new confocal imaging principle in which the pinhole is replaced with a matched filter recorded on a volume hologram. The hologram is recorded such that the field that is generated by an in-focus object is maximally diffracted, whereas objects that are out of focus are filtered out because they are Bragg mismatched. Consequently, dynamic range and axial resolution are decoupled; the dynamic range is determined by the diffraction efficiency of the volume hologram, and the axial resolution by the numerical aperture of the objective lens and the thickness of the hologram. Additional benef its of pinhole-free confocal microscopy are ease of alignment and improved aberration performance: Objectivelens aberrations are phase conjugated out during the hologram reconstruction process, and collector-lens aberrations (which increase the collected spot size) are irrelevant in the absence of a pinhole. The volume holographic confocal microscope is shown schematically in Fig. 1. The volume hologram 0146-9592/99/120811-03$15.00/0 is recorded by the interference of two coherent beams at wavelength l. The objective lens brings the first beam to focus on a reference surface, one focal distance F away from the objective. The ref lected beam is recollimated by the same objective and is used as the recording plane-wave reference beam, with wave vector kR s2pyldẑ. The signal beam is a plane wave that is incident upon the recording medium along kS s2pyldx̂ (90± recording geometry). The resulting grating vector is K kS 2 kR . During the imaging operation, the signal beam is blocked. The reference surface is replaced by the object surface, and the ref lected beam reconstructs the volume hologram. The diffracted light is collected by a second objective lens (focal length F 0 ) and captured by a photodetector. Compared with a ref lection-mode confocal microscope, the imaging arrangement shown in Fig. 1 contains two modifications, in addition to the volume hologram: (a) the objective lens is placed in a Fouriertransform rather than an imaging conf iguration and (b) the aperture in front of the detector does not contribute to depth discrimination but only limits scatter and other light-noise sources. If the reconstructing object is in focus (dotted lines in Fig. 1), this device Fig. 1. Volume holographic confocal microscope without a pinhole 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, because the volume hologram is Bragg matched (the recording and the reconstructing reference beams are identical); therefore the diffracted intensity reaching the detector is maximum. Consider now an object that is defocused by a small distance d. The beam that is ref lected from the object is no longer collimated by the objective lens but contains an angular spectrum of plane-wave components, as shown by the solid lines in Fig. 1. Diffraction of the off-axis components by the volume hologram is weaker because of Bragg mismatch. Consider the component with wave vector kp s2pyld hux̂ 2 v ŷ 1 f1 2 su2 1 v2 dy2gẑj, shown in Fig. 2 sjuj, jvj ,, 1d. Born’s first approximation in volume diffraction theory4 requires that the diffracted wave vector kd have the same ŷ and ẑ and components as the vector k0 kp 1 K and, moreover, that jkd j 2pyl; therefore 2p kd l ∏ ∂ u2 1 v 2 v2 x̂ 2 vŷ 2 ẑ . 12 2 2 ∑µ (1) Taking only one diffracted component, kd , into account in effect neglects the finite extent of the hologram in the ŷ and ẑ dimensions. However, the analysis remains valid because the entire spatial spectrum that is diffracted in response to kp behaves (in the paraxial approximation) similarly to its central planewave component kd , which is the only component that we consider here. In other words, the impulse response that is due to the finite hologram aperture does not affect the depth discrimination of the system. The diffracted intensity along this central component kd is proportional to sinc2 sDkx Ly2pd, where L is the extent of the hologram in the x̂ direction, and sincsjd ; sinspjdyspjd. The quantity Dkx is the deviation of k0 from the k sphere (see Fig. 2): µ ∂ v2 . 2p u1 Dkx jk 2 kd j l 2 0 (2) fracted intensity decreases rapidly as a result. The instrument is optimal if all the light coming out of the objective reaches the hologram, i.e., L A. The Bragg-mismatch effect (expressed through the sinc function in the integrand) effectively acts as a matched spatial filter, discarding the defocused light. This shift-variant filtering operation is similar to the field-of-view limitation imposed by the pinhole of a confocal microscope. The passband has an elliptical p shape, with semiaxes umax lyL and vmax 2lyL. Since vmax .. umax , the depth response is determined primarily by the term sNAd2 jdjr in the argument of the sinc function of Eq. (3). As a measure of depth resolution, we use the FWHM of hsdd. By fitting numerical data from Eq. (3) at the optimal geometry L A, we obtain dFWHM 1.09 3 l . sNAd2 By comparison, a confocal microscope with zero pinhole size has dFWHM 0.86 3 lysNAd2 , but the FWHM increases rapidly with pinhole size in realistic systems.1 We implemented the pinhole-free confocal microscope shown in Fig. 1 experimentally. We used an Ar1 laser sl 488 nmd as a light source; a 1-cm3 LiNbO3 :Fe crystal (45± cut; refractive index, ø2.2) as a holographic medium; a 603, NA 0.85 objective lens sA ø 5 mmd; and a 103, NA 0.25 collector lens. The reference and the object surfaces were polished silicon wafers with microfabricated features, mounted upon a Klinger translation stage (0.1-mm step size) with three degrees of freedom. The light collected through a variable aperture was measured with a UDT photodetector. To implement a confocal microscope in the same experimental arrangement we simply replaced the volume hologram with a mirror oriented at 45±, directing the ref lected beam into the collector lens. The dependence of the normalized diffraction efficiency on the depth of the object surface is shown by curves (a) and (b) of Fig. 3. The depth resolution is the same for aperture sizes of 25 mm (matched to the To obtain the overall diffraction efficiency summed over an inf inite detector area we integrate the diffracted intensities from all spatial frequency components kp that are allowed through the circular objective aperture (diameter A; Fig. 1) and normalize them for a total incident power of 1. The result is hsdd Ω Z 1 h0 Z 2p 2L du dr r sinc2 sNAd2 jdjr p 0 lA 0 ∑ ∏æ sin2 u , (3) 3 cos u 1 sNAd2 jdjr 2A where h0 ; hs0d, sNAd ø Ays2F d is the objective numerical aperture, jdjyF ,, 1 is assumed, and polar coordinates sr, ud are substituted for su, vd in the integral. A microscope without a pinhole in front of the detector corresponds to the case L 0, when the total detected intensity does not depend on object depth. For finite thickness L . 0, the integral increases with jdj much slower than the denominator d 2 , and the dif- (4) Fig. 2. Bragg mismatch in the k sphere. June 15, 1999 / Vol. 24, No. 12 / OPTICS LETTERS Fig. 3. Collected intensity as a function of object depth d for the volume holographic confocal microscope with (a) 25-mm and ( b) 1-mm pinholes and for the confocal microscope (with a 45±-oriented mirror replacing the volume hologram) with (c) 25-mm (d) 1-mm pinholes. Location d 0 corresponds to the depth of the reference surface (at the focal plane of the objective lens). All curves are normalized such that their peak values equal 1. 813 trench. The image of the trench corresponds to the dark region in Fig. 4, because the bottom of the trench is out of focus. We sampled only five planes along ŷ and one along ẑ to minimize inaccuracies that were due to the backlash of the translation stage and the decay of the hologram. A dense three-dimensional scan could have been obtained with a piezoelectric def lector and a fixed hologram. In conclusion, we have demonstrated confocal scanning microscopy by use of a volume hologram as a shift-variant element matched to object depth. The dynamic range of volume holographic confocal imaging depends on the holographic diffraction efficiency (in our experiment it was ø1024 ) and is material limited. Single-hologram eff iciencies as high as 100% have been demonstrated,5 albeit with thinner materials and, hence, poorer Bragg selectivity. Volume holograms also permit the use of other imaging modes, e.g., color-selective (hyperspectral) tomographic imaging6 or superresolution by use of complex filtering,7,8 in combination with the pinhole-free confocal imaging principle. We are grateful to Bo Kyoung Choi and Chang Liu for fabricating the silicon microstructure, to Daniel Marks, Rick Morrison, and Ronald Stack for assistance with experiment automation, and to Chris Bardeen, Martin Gruebele, Steve Rogers, and Peter So for helpful discussions and comments on the manuscript. This work was funded by the U.S. Air Force Office of Scientific Research. The authors’ e-mail addresses are [email protected], [email protected], and [email protected]. *Present address, Department of Mechanical Engineering, Massachusetts Institute of Technology, Room 3-461c, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139. References Fig. 4. Two-dimensional scanning confocal image (reconstructed intensity map) of the silicon microstructure obtained with the volume holographic microscope shown in Fig. 1 collector’s spot size) and 1 mm. The intensity FWHM is s0.8 6 0.1d mm for both curves, in close agreement with 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 reaching the detector (i.e., the dynamic range of the measurement is slightly decreased). By contrast, the depthdiscrimination capability of the confocal microscope [curves (c) and (d)] is degraded for the 1-mm aperture. We used the pinhole-free confocal microscope to obtain a scanned image of the silicon microstructure, as shown in Fig. 4. The imaged portion contained a trench 20 mm wide and 5 mm deep. The reference surface for recording the hologram was outside the 1. T. Wilson and A. R. Carlini, Opt. Lett. 12, 227 (1987); T. Wilson, in Confocal Microscopy, T. Wilson, ed. (Academic, San Diego, Calif., 1990), Chap. 3, pp. 93 – 141. 2. C. J. R. Sheppard and C. J. Cogswell, in Confocal Microscopy, T. Wilson, ed. (Academic, San Diego, Calif., 1990), Chap. 4, pp. 143 – 169. 3. N. P. Suh, A. C. Bell, and D. C. Gossard, Trans. ASME 100, 127 (1978); N. P. Suh, The Principles of Design (Oxford University, New York, 1990). 4. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley-Interscience, Paris, 1977). 5. K. Meerholz, B. L. Volodin, B. S. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994). 6. G. Barbastathis and D. J. Brady, ‘‘Multidimensional tomographic imaging using volume holography,’’ Proc. IEEE (to be published). 7. Z. S. Hegedus and V. Sarafis, J. Opt. Soc. Am. A 3, 1892 (1986). 8. J. G. Walker, E. R. Pike, R. E. Davies, M. R. Young, G. J. Brakenhoff, and M. Bertero, J. Opt. Soc. Am. A 10, 59 (1993).