Download Confocal microscopy with a volume holographic filter

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
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