Efficient Confocal Microscopy with a Dual-Wedge Scanner
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Citation
Warger II, William C. et al. “Efficient confocal microscopy with a
dual-wedge scanner.” Three-Dimensional and Multidimensional
Microscopy: Image Acquisition and Processing XVI. Ed. JoseAngel Conchello, Carol J. Cogswell, & Tony Wilson. San Jose,
CA, USA: SPIE, 2009. 71840M-11. © 2009 SPIE
As Published
http://dx.doi.org/10.1117/12.810527
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Society of Photo-optical Instrumentation Engineers
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Final published version
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Wed May 25 21:54:39 EDT 2016
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http://hdl.handle.net/1721.1/52677
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Detailed Terms
Efficient Confocal Microscopy with a Dual-Wedge Scanner
William C. Warger II (1,3), Stephen A. Guerrera (1,4),
Zachary Eastman (2), Charles A. DiMarzio (1)
(1) Department of Electrical and Computer Engineering
Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115
(2) Lucid, Inc., 2320 Brighton-Henrietta Townline Rd., Rochester, NY 14623
(3) Current Affiliation: Massachusetts General Hospital, Boston, MA 02114
(4) Current Affiliation: Massachusetts Institute of Technology, Cambridge, MA 02139
ABSTRACT
Confocal microscopes achieve high spatial resolution by focusing both a light source and a detector to a single
point with an objective having a high numerical aperture. In order to produce an image, it is then necessary to
scan this common focal spot through the specimen, and it is often important to image the full field of view in a
short time. In order to avoid vignetting, the scanning must be done in or near the pupil of the optical system.
For some fast scanners, this requires the use of multiple relay telescopes to create multiple pupils. Galvanometric
scanners impose a practical limit on the scan speed because of the angular accelerations involved in reversing
direction. Rotating polygons are often used to achieve greater speed. For a scanner consisting of a rotating
polygon and a galvanometric scanner, two relay telescopes are normally used.
We have developed a dual-wedge scanner which has the potential to perform the scan in a configuration which
is very short in the axial direction, thereby eliminating much of the complexity of current high-speed scanners.
We have demonstrated a prototype of the scanner in a reflectance confocal microscope. Transverse and axial
resolution are comparable to those of other scanning systems.
The selection of rotation speeds for the wedges is important to ensuring full coverage of the field of view in
a reasonable time. Various tradeoffs on these parameters will be discussed. The beam behavior in the pupil
will be discussed. Resolution limits and aberrations will be shown from ray-tracing analysis, and compared to
experimental results.
1. INTRODUCTION
There are 1.2 million new cases of basal–cell and squamous–cell skin cancer (BCC and SCC) diagnosed every
year in the US alone, and these non–melanoma skin cancers are increasing in number every year.1, 2 Clinical
screening and diagnosis include some 5.5 million biopsies and histologies performed every year, of which 80% turn
out to be benign and might have been avoided, had better non-invasive screening techniques been in clinical use.
Considering that the cost of a biopsy and histology is approximately $500, the 4.4 million benign biopsies cost US
health-care $2.2 billion and in addition left patients with pain, scarring, and mental anguish that could have been
avoided had better imaging capabilities been available for in vivo diagnosis. Confocal reflectance microscopy
may enable such non–invasive clinical screening and diagnosis, in addition to pre–surgical determination of the
cancer margin, and intra–surgical guidance directly on the patient in real-time, all without the need for biopsy.
Confocal reflectance microscopes have demonstrated excellent success in imaging nuclear and cellular morphology of human skin in vivo.3–11 These microscopes have been cleared by the FDA for use to assist in skin
cancer diagnosis and have led to more than 70 papers by dermatologists at leading academic medical centers in
the USA and Europe. Thus far, confocal reflectance imaging has demonstrated significant promise for clinical
applications such as guiding skin biopsy, determining the margins of skin cancers to guide surgical excision, noninvasive monitoring of the efficacy of laser and topical drug treatments, and sensitivity and specificity studies of
screening and diagnosis of skin cancer.8, 12–34 Depth of imaging is limited to a few hundreds of micrometers,
but most skin cancers originate in the epidermis or near the dermal–epidermal junction which is 50 to 150μm
Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVI
edited by Jose-Angel Conchello, Carol J. Cogswell, Tony Wilson, Proc. of SPIE Vol. 7184,
71840M· © 2009 SPIE · CCC code: 1605-7422/09/$18 · doi: 10.1117/12.810527
Proc. of SPIE Vol. 7184 71840M-1
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01= 00 02
900
01=00 02=180°
01= 00 02
2700
Figure 1. SCANNING CONCEPT. The prisms have apex angles α and rotation angles θ1 and θ2 about the optic axis.
(a) A single prism deviates the beam by the vector, v1 , and (b) two prisms deviate the beam by the vector sum v1 + v2 .
(c) A circle is scanned about the deviation from the first prism when the first prism is stationary and the second prism
was rotated about the optical axis.
deep and easily amenable to imaging with confocal reflectance microscopy. However, the beam scanning mechanism makes these microscopes large and expensive, hindering clinicians from using them on a regular day-to-day
basis to image more lesions, including those which currently are difficult to reach. A small, robust, hand-held,
inexpensive, and user-friendly microscope would make such imaging much easier and more common, and could
expand confocal microscopy into other areas of the body.
2. DUAL–WEDGE SCANNING
The use of two prisms to scan a laser beam was first described by Rosell in 1960 as a prism scanner.35 Since
then, the scanner has been utilized in various applications under a variety of names that include rotating prism
scanner for optical tracking in guidance systems,36 dual-wedge scanner for laser radar,37 Risley prism scanner,38
double-prism scanner for testing the performance of inter-satellite laser communications,39 and a paired-angle
rotation scanner for an OCT scanning probe.40
2.1. Scanning Concept
The concept of the scanner is shown in Figure 1.41 A prism with wedge angle α is oriented such that the second
surface is normal to the incident, collimated laser source and with an angular position θ1 about the optical axis,
where the angular position is measured from the apex of the prism. The incident laser beam is deviated by the
vector v1 in the sample plane in Figure 1(a). As the prism is rotated about the optical axis (θ1 = 0 to 2π), the
beam scans the dotted circle. When an identical prism is placed in the path such that the angular positions
of the prisms are the same (θ1 = θ2 ) and the flat surfaces are parallel and facing each other, the beam will
be deviated by the vector sum v1 + v2 in Figure 1(b). If the first prism is held stationary at θ1 = 0, and the
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second prism is rotated about the optical axis (θ2 = 0 to 2π), a circle with radius |v2 | will be scanned about
the endpoint of v1 in Figure 1(c). When the prisms are rotated in the same direction and at the same speed
(ω1 = ω2 = ω) over time t, the angular positions of the first and second prisms are θ1 = ωt and θ2 = ωt + Δθ,
respectively, where Δθ is the angular offset between the two prism apexes, and the beam scans a circle with
a radius dependent on Δθ. If the prisms rotate in the same direction, but at different speeds (ω1 = ω2 ), the
angular relationship between the two apexes will change with time and a spiral scan will be produced. When the
prisms are rotated in opposite directions and at the same speed, the angular positions of the prisms are θ1 = ωt
and θ2 = −ωt + Δθ, respectively, and the beam scans a line at an angle Δθ. If the prisms rotate in opposite
directions, but at different speeds, the angular relationship between the two apexes will change with time and
a rosette scan will be produced. Various scan patterns are generated by changing the relative rotation speeds
between the prisms and/or the angles of the prisms.36, 38 However, it is important to note that using prisms
with different wedge angles will miss a circular region with a radius ||v1 | − |v2 || within the center of the scan.
Our work involves prisms with equal apex angles.
The analysis is slightly more complicated than it would seem, because the effect of the second prism is slightly
dependent on the angle at which light emerges from the first. An exact ray tracing analysis of the prism rotations
is used to calculate the final refraction vector.36, 37
2.2. Prototype Dual–Wedge Microscope
A benchtop microscope41 which incorporates the dual–wedge scanner, is shown in Figure 2. The optical path
is similar to that of most confocal microscopes except for the scanning technology. The path begins at the
830–nm, linearly–polarized laser diode, and passes through the polarizing beamsplitter with P –polarization.
The P –polarized light continues through the dual–wedge scanner. For experimental purposes, we also include
a relay telescope that places the scanner (P 1 in the figure) conjugate to the pupil of the microscope objective
(P 2), and allows flexibility in changing objectives. The scanner houses two 11–degree prisms (α = 11◦ ) within
two aluminum cylinders, each within a pair of ball bearings and a timing belt pulley. Two timing belts couple
identical pulleys on the shafts of the motors and the prism housings to ensure a one–to–one ratio between the
prism and the motor rotations. The beam passes through a quarter–wave plate, having an axis oriented at 45◦
relative to the linear laser polarization, thereby producing circularly polarized light, which is then focused into the
sample by the custom–built, infinity–corrected, water-immersion 30X objective, with a numerical aperture of 0.9.
Water–immersion provides better correction for aberrations introduced by skin and reduces specular reflection.
The infinity–corrected lens has been specifically designed to image tissue by including a basic tissue model in the
optimization process to minimize aberrations. The tissue model includes multiple surfaces representing index
matching fluid between the disposable window and the stratum corneum and the multiple layers of tissue. Each
layer is assigned optical properties and a thickness. These properties are varied over ranges expected in human
skin, and optimized using a figure of merit which includes the multiple configurations. Optimizing the design for
multiple configurations has yielded a design that has acceptable performance across varying imaging conditions
for different tissue depths and refractive indices within human skin. Unlike standard objective lenses, that
generally are designed to image through either a thin glass cover–slip or none at all, the custom–built objective
was designed to image through a thick (0.762 mm, 0.030inch) polycarbonate window. The thick window is
mounted within a ring that is placed directly on the skin to reduce axial motion and keeps the tissue stable while
imaging a patient with motion caused by respiration and heartbeat.
The backscattered light that is collected within the numerical aperture of the objective passes back through
the quarter–wave plate, telescope, and scanner. On the return path, the light has passed through the quarter–
wave plate a second time converting the incident P polarization into S, provided the backscattered light retains
its state of polarization as it interacts with the sample. Light that has not retained its polarization has likely
been scattered multiple times, and the fact that some of this light is rejected by this technique improves contrast
in optical sections. The S–polarized light is reflected by the polarizing beamsplitter toward the avalanche
photodiode (APD), and is focused by a lens through a pinhole onto the detector.
Data streams are acquired from the two encoders and the APD module. A National–Instruments NI USB–
6251 High–Speed, USB M–Series, multi–functional data acquisition card samples the two encoders that are
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Polarizing
Laser
Plate
Beamsp1itte
I-Il-I
I.P
P
Avalanche
Photodiode
I
Quarter-wave
Prisms
Telescope -
J
'Objective
2
Lens
Figure 2. CURRENT BENCH–TOP LAYOUT. A compact
design is achieved because the dual–wedge scanner eliminates
the folded path and relay telescope of conventional scanners.
Figure 3. PHOTOGRAPH OF BREADBOARD SYSTEM.
The system was designed for benchtop studies to prove the
utility of a dual–wedge scanner.
attached to the motors and the voltage output of the APD (i.e. backscattered light that is detected) simultaneously. A look–up table is used in conjunction with the angular positions to place the intensity value in the correct
pixel location. The look–up table is constructed by modeling the orientation of the prisms and calculating the
refraction vector through each of the four surfaces. Resulting (x, y) coordinates are truncated to the nearest
pixel location. A dot of brightness proportional to the signal amplitude from the APD, digitized in 12 bits, is
placed at the appropriate location on the display.
3. OPTICAL PERFORMANCE
Figure 4 shows the current axial response function, for two different pinhole sizes, as determined by moving a
mirror axially through the focus of the objective. Hair gel is used as an index–matching material between the
objective and the mirror to mimic the refractive index of water in a horizontal configuration. The width of the
axial response function with the 50μm pinhole is 1.8μm, which approaches the expected value42 of
δz = 0.95
1.33 × 830nm
nλ
= 0.95
= 1.3μm.
2
NA
0.92
(1)
The 100μm pinhole was used to collect images, and the measured FWHM is 2.1μm.
After the resolution was determined, we collected an image of excised human skin that is normally discarded
after Mohs surgery, shown in Figure 5. The pixel size is set at 2μm, to acquire a good image with the slower
scan speed of the benchtop instrument. The skin was sandwiched between a microscope slide and a cover–slip
with the epidermis toward the cover–slip, and the cover–slip was coupled to the immersion objective with hair
gel. The image shown, is at a depth of approximately 35μm, and demonstrates the optical sectioning and ability
to resolve features such as hair follicles and cells.
4. SCAN PATTERN ANALYSIS
Current confocal microscopes produce a raster scan with about 500 pixels by 500 lines, and the goals for the
dual–wedge scanner is to achieve the same number of scan points in 1/5 second, with full coverage of a circular
field of view and minimal repetition of points. For analysis of the pattern, it is sufficient to use an approximation:
x = (n − 1)α (cos 2πf1 t + cos 2πf2 t)
(2)
y = (n − 1)α (sin 2πf1 t + sin 2πf2 t) ,
(3)
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1
50
0.9
Signal, Normalized
0.8
0.7
100 μ m Pinhole
2.1μ m FWHM
50 μ m
1.8 μ m FWHM
100
150
0.6
200
0.5
250
0.4
300
0.3
350
0.2
400
0.1
450
0
20
25
30
z, Axial Distance, μ m
35
Figure 4. AXIAL RESPONSE FUNCTION: The width of the
axial response function decreases with decreasing pinhole size,
and is near the expected value.
500
100
200
300
400
500
Figure 5. SAMPLE IMAGE: An image of excised human skin was obtained using the new configuration. The
diameter of the field of view is 1.0 mm.
for the location of the focused spot. The diameter of the field of view in the image plane is thus twice the
maximum of either x or y, or
(4)
DF = 4(n − 1)α.
The diameter in the object plane is this value divided by the magnification of the system Taking derivatives of
Equations 2 and 3 with respect to t, it can be shown that the distance between data points a time δt apart is
δr = δx2 + δy 2 = 2πδt(n − 1)α f12 + f22 + 2f1 f2 cos [2π (f1 − f2 ) t],
(5)
with extreme values of
2πδt(n − 1)α |f1 + f2 |
and
2πδt(n − 1)α |f1 − f2 | .
(6)
The pixel time, δt, is the time between samples. To obtain approximately one pixel between consecutive points,
based on our 5002 –pixel grid, we want,
(n − 1)α
δr ≈
,
(7)
500π
or
(n − 1)α
2πδt(n − 1)α |f1 ± f2 | ≈
(8)
500π
1
δt ≈
.
(9)
2
2 × 500π (|f1 | + |f2 |)
For rotations speeds in the thousands of Hertz, the ideal pixel time will be less than a microsecond. If the ratio
of rotation speeds, f2 /f1 is a rational number, then the pattern will be repeated. Specifically, if the ratio is an
irreducible fraction,
f2 NN
=
(10)
f1 ND ,
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the number of lobes in the rosette scan will be
= NN + ND ,
(11)
and the larger this number, the more dense the data will be. For the 5002 grid, the ideal value is
= NN + ND ≈ 500π.
The pattern will then repeat after a time
trep =
(12)
ND
NN
=
,
f1
f2
(13)
after which no new information will be obtained.
We have examined scans with a variety of possible speed ratios that determine the fill factor, or the fraction
of all points in the 5002 fixed grid that are visited at least once in the frame time. We found a very complicated
behavior, a small part of which is shown in Figure 6. If the number of lobes in Equation 11 is small, the fill
factor becomes very low, and fewer pixels will be sampled. Exploring the whole range of −f1 < f2 < f1 , the fill
factor is relatively constant at a value dependent on the pixel time and frame time. Figure 7 shows the fill factor
as a function of the frame time. We see that it reaches half its maximum value at 1/5 second. Figure 8 shows
the fill factor as a function of the pixel frequency, fp . The fill factor approaches its maximal limit at 1M Hz.,
after which additional increase in frequency results in multiple visits to each pixel. The figure also shows the
number of pixels visited at least twice, and at least five times.
0.45
0.4
0.8
0.7
0.7
0.6
0.6
0.5
Fill
2 or More
5 or More
Fill Factor
0.3
0.25
0.2
0.15
Fill Factor for 5002 Grid
Fill Factor for 5002 Grid
0.35
0.5
0.4
0.3
0.4
0.3
0.2
0.1
0.2
0.05
0
9
9.5
10
10.5
f2, Rotation Rate, kRPM
11
Figure 6. RELATIVE SCAN
SPEED: The fill factor shows local
minima when the ratio of speeds is
an irreducible ratio of small integers,
but is otherwise mostly constant.
A small sample of the whole range
from −f1 to +f1 is shown here.
0.1
0
0.1
0.2
0.4
0.6
tf, Frame Time, Sec.
0.8
1
Figure 7. FRAME TIME: The fill
factor grows with time, slowly approaching a maximum value as the
time approaches the pattern’s repetition time. Most of the possible
resolution is obtained at 1/5 second.
0
0
0.5
1
1.5
2
2.5
fp, Pixel Frequency, MHz.
3
3.5
4
Figure 8. PIXEL FREQUENCY:
The fill factor (X) improves with
pixel frequency, until the point at
which additional samples fill pixels
that have already been filled. Beyond that, the number of pixels with
two or more (+) and five or more (*)
visits increases.
As an analytical demonstration, we use a speed ratio f2 /f1 = −331/1399, with the first wedge rotating at
50,000 RPM, which produces a pattern having 1730 lobes, that repeats every 1.7 seconds. Figure 9 shows the
sampling for three different frame times. The left panel shows that we will obtain a coarse image in 1/20 second
with the center of the image having noticeably better resolution. The center panel shows the sampling at the
nominal frame time of 1/5 second. Even better resolution can be obtained in multiple frame times, but the
improvement diminishes asymptotically as is evident in Figure 7.
This figure suggests a number of ways of using the scan data effectively. After only 1/20 second, a high
density of data is available in the center of the image, while a coarse image is obtained in the peripheral region.
This is suggestive of the foveal vision of the human eye, and could be used for a quick analysis to identify a region
of interest. If this data is used to produce an image, the user can search large areas, and pause when an area
of interest is found. Pausing at any location, the image resolution in the periphery would improve, producing
an image of nearly the same resolution as the raster scan after 1/5 second. Further dwelling on the same region
would lead to slightly improved resolution, and continuous improvement in signal–to–noise ratio.
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Figure 9. SCAN PATTERN FOR ROTATION RATES OF 50,000 AND -11830 RPM. From left to right, the elapsed
times are 1/20, 1/5, and 2/5 seconds. A coarse sampling is obtained quickly, with best resolution in the center. By 1/5
second, the center is completely filled, and after 2/5 second, the fill factor is about 80%, and no further gain in resolution
is expected.
5. SAMPLING
With any digitized image, the data must be sampled. In many confocal microscopes, the sampling is regular,
using a raster scan. It is important to compare the scan patterns generated using the dual–wedge scanner
with those of a raster scan, to determine the extent to which it is possible to reproduce all the relevant spatial
frequencies in an image. The ideal raster scanned image is sampled at least at the Nyquist frequency of a
band–limited image, and then according to the sampling theorem, all the signal information can be recovered.
The limitation on spatial bandwidth is normally the aperture of the objective. In practice, images are often
under-sampled according to this criterion. Satisfactory results are obtained because the image has little energy
at high spatial frequencies and because, in confocal microscopy, the image is partially band–limited by the size
of the pinhole in front of the detector.
In the present implementation of the dual–wedge scanner, data points are assigned to the nearest pixels that
are located in a pre–defined raster pattern. At completion of the imaging process, any pixels that were not
visited by the scanner are filled with the data from the nearest visited pixel. The processing is simple, but does
not make the best use of the data. Analysis of the scan pattern can be used to develop optimal scan patterns
given that the image is band–limited in spatial frequency by the numerical aperture of the objective.
Better means for interpolation of data points will lead to better images, and the ultimate capability is limited
only by fundamental principles of sampling. Just as the Nyquist theorem describes the conditions under which
perfect reconstruction is possible using regularly sampled data, there are other fundamental limitations relating
to irregularly spaced data points. To address these issues, several portions of the 1/5 second image in Figure 9,
were expanded, and examined in detail. One is shown in Figure 10(a). For this example, a 30X objective
was assumed, with a field of view of 1.17 mm. The Fourier transform of the sampling function is shown in
Figure 10(b). For comparison, a raster scan is shown in Figure 10(c,d). The regular sampling in the raster
scan (10c) produces a symmetric pattern in spatial frequency (10d). The bright points are at the inverse of the
sampling frequency, and the remaining points are the result of the finite window around the region of interest.
The sampling rate is 500 pixels per mm.
The sample of the dual–wedge scan shows similar results, with the spacing of sample points in adjacent lines
(10b) of about 1000 cycles per mm. This spacing is about twice as good as the 500–pixel–square images that
are frequently used in confocal microscopy. Variations in line spacing occur (10a) because the pattern has not
completely filled in at this time. The pattern in spatial frequency (10b) is a distorted version of the one for
the raster scan in Figure 10(d). It is interesting to note that very high resolution can be obtained for objects
which are large in a direction perpendicular to one of the scan lines. Thus, with appropriate signal processing,
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60
1500
0.195
50
f , /mm
0.185
0.18
y
y, mm
0.19
1000
40
500
30
0.175
0.17
20
0
0.17
0
0.18
0.19
x, mm
(a)
500 1000
fx, /mm
1500
(b)
50
1500
40
f , /mm
0
y
y, mm
0.01
1000
30
500
20
−0.01
10
0
−0.01
0
x, mm
0.01
0
500 1000
f , /mm
1500
x
(d)
(c)
Figure 10. SAMPLING THE SCAN PATTERN: A small segment of the dual–wedge scan pattern is shown in (a) and
the Fourier transform is shown in (b). A raster scan is shown for comparison in (c,d)
for images which are band–limited in spatial frequency, it should be possible to produce an image equivalent to
that obtained with the raster scan.
6. SUMMARY
Confocal reflectance microscopy has been demonstrated to be useful for imaging skin lesions. A dual–wedge
scanner can result in an extremely compact microscope with the potential to image in areas which are less
accessible, and to do so at a reduced cost.
In summary, the dual–wedge scanner can be implemented with achievable scan speeds, and will produce a
high–resolution image without missing pixels provided that scan frequencies are chosen appropriately. Image
quality may be improved by signal processing to make maximal use of the spatial frequencies being imaged at
each point in the scan.
7. ACKNOWLEDGMENTS
This work was supported in part by the National Cancer Institute of the National Institutes of Health (award
number 1R41CA117187-01), and by CenSSIS, the Gordon Center for Subsurface Sensing and Imaging Systems,
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under the Engineering Research Centers Program of the National Science Foundation (award number EEC9986821).
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