Download Depth of field and improved resolution of slit-scan flow systems

Depth of field and improved resolution of slit-scan flow systems
Michael Hausmann*,+ Martin Crone, Christoph Cremer
Institute of Applied Physics, University of Heidelberg, Albert-Ueberle-Str. 3-5, D-69120 Heidelberg, P.R. Germany
member SPIE;
to whom correspondence should be addressed)
(=
ABSTRACT
In a slit-scan flow cytometer particles specifically labelled by fluorochromes (e.g., cells, chromosomes) are aligned coaxially in
a flow stream. One by another they pass a ribbon-like shaped laser beam with a diameter smaller than the particle length.
Although several slit-scan flow systems have been developed during the last two decades, a complete description of the theory
of optical resolution under the real experimental conditions used as well as a description how to overcome experimental
limitations are missing. Often, resolution values are estimated under the assumption of ideal Gaussian beam propagation. These
estimates suffer from a discrepancy to practical implementation. Here, some of these effects in slit-scan optics will be discussed
from a more theoretical point of view. In order to obtain an acceptable depth of field, a focal width around 2 im appears to be
an optimum under the regime of Gaussian beam propagation. However, in practice, effects due to thick lenses, finite apertures,
chromatic aberrations, or the ellipticity of the laser beam overshadow this result and influence the laser beam shape. To further
improve the resolution with a high depth of field, new concepts are required. Therefore, a combination of an interference fringe
pattern of two coherent laser beams for excitation (fringe-scanning) with a slit-scan detection of the incoherent fluorescence
light is introduced. Preliminary experience of the first experimental realization will be discussed.
1. INTRODUCTION
The slit-scan technique for cell analysis was introduced some 20 years ago1'2. This very early device was a Xenon lamp driven
microscope with a moving slit in the image plane. The resolution was reported to be 5 im (FWHM). The subsequent
development was the application of a flow cuvette in which the cells were moving through the detection volume3. These early
microscope based flow cytometers used microscope objectives with low numerical aperture in combination with a cylinder lens
to obtain an asymmetrical, slit-like shaped focus. In addition, slit-apertures were built into in the detection pathway. An optical
resolution of this system of about 4 jim was reported using an argon ion laser at 488 nm4.
A more widespread interest in slit-scan flow systems came up with the analysis of metaphase chromosomes5'6. With improved
preparation techniques the analyses of several species and cell types were performed612. The fast detection of radiation induced
chromosome rr314 appears to be the most interesting perspective for slit-scan flow cytometry 15
With the development and improvement of the triaxial flow sorter'6 commercially available cell sorters became basic
13, 15, 17-19 Besides
instruments for slit-scan systems
the computer hard- and software'5, the excitation and/or detection optics
of these systems were modified to fulfil the requirements of highly resolved slit-scanning19' 20 Although many articles have
been published on slit-scan flow cytometry, mainly on the appljcation5 9-13)of these systems, some more basic considerations
on the optics of slit-scan systems are still lacking. The following approach will contribute to overcome this shortcoming.
However, since a complete discussion on all resolution influencing effects is not possible due to restrictions of the article
length, we will concentrate ourselves on the excitation optics of triaxial slit-scan systems. We will introduce a new concept
(fringe scan excitation with slit-scan detection) which will combine a small focal width with a high depth of field.
2. EXPERIMENTAL SET UP
2.1. Principle of a slit-scan flow cytometer
In the following the principle of slit-scan flow cytometry will be described for the example of chromosome analysis. However,
this is not a general limitation since the technical principles and problems are nearly the same for all types of particles to be
analyzed and sorted.
O-8194-2328-9196/$6.OO
SPIE Vol. 2926 / 297
Figure 1 schematically shows a slit-scan flow system.
The chromosome suspension is injected coaxially into a
laminar fluid stream. By means of hydrodynamic
probe injection
/ photo.
multiplier
FL
•H
detectorsignal
jet
focussing through an appropriately designed flow cell,
the chromosomes are confined within the core of the
fluid stream. The core typically has a diameter of 10 20 jim. The fluid stream can run as a cylindrical free
flow jet of circular cross- section18 (typical diameter
about 70 - 80 jim) or as a flow stream in a cuvette of
rectangular cross-sectio&9 (typically about 250 x 250
j.tm2). With a velocity of 1 - 10 rn/s depending on the
system, the chromosomes stained with fluorescent dyes,
one by another pass a laser beam (typically an argon ion
laser of UV or visible light). The laser beam direction is
perpendicular to the chromosome flow direction. If the
laser is well focused, the fluorescence of the
deflector
chromosomes can be excited and/or detected in a time
resolved way. For fluorescence detection, a collecting
optics perpendicular to the flow stream and the laser
beam direction is used. Via appropriate optical filters
the fluorescence light is recorded by photomultipliers.
For sorting, the flow stream is acoustically disrupted
into droplets, which can electrically be charged and
deviated into separate vessels (for details see e.g.18 19)
Fig. 1: Schematic representation ofa slit-scanflow sorter (for details
see text).
2.2. Optical requirements
To realize the slit-scan technique, two kinds of systems (object plane or image plane scanning), and the combination of those
are possible. In the case of image plane scanning, the particle is entirely illuminated and the fluorochrome is excited. The
fluorescence is partly detected through an appropriately designed slit aperture in the detection optics. In the case of object plane
scanning, the excitation is spatially resolved using a laser beam that is highly focused in the direction of the flow stream. The
fluorescence detection can be realized by standard equipment for photometric detection. Since object plane scanning is
accomplished at the wavelength of the laser beam, while image plane scanning is accomplished at the higher wavelength of the
fluorescence light, the ultimate resolution of object plane scanning is expected to be better. Furthermore, the fluorescence
contribution of "out of slit" parts of the particles is much higher in the case of image plane scanning due to total illumination.
Using commercially available flow cytometers, optics in a compact form is required which can be more easily realized for
object plane scanning. Thus, this type has become the more often realized instrumental setup17°.
The design for an object plane scanning optics has to fulfil the following requirements:
1. The laser has to be focused into a ribbonlike shape with its short axis in the direction of the flow jet. In the case of
chromosome analysis and sorting, this should experimentally be in the order of 1 pm or less.
298/SPIE Vol. 2926
2. The long axis of the laser focus width should cover the entire core (10-20 jim) of the fluid stream to cover all possible
particle trajectories with about the same intensity.
3. The same demand has to be considered for the depth of focus.
4. In the case of sorters with a free flow fluid jet a working distance between fluid stream and optics of some mm is
necessary'5' 20
5. The system should work for laser intensities of several hundred mW and a variety of laser wavelength from UV (typically
350 nm) to green and red (typically 500 - 600 nm).
The latter two requirements speak against the application of standard microscope objectives. A possible, however expensive,
solution may be to order a specially calculated and fabricated optical system. Such systems can also be designed with a
complex combination of lenses and optical components2' . However, in a more practical way standard flow sorters are modified
into slit-scan systems by only a few and therefore easily to handle lenses. To calculate such lens systems, and to estimate the
focus dimensions, it has been well established to use the theory of ideal Gaussian shaped beams22.
3. CALCULATION OF BEAM SHAPING OPTICS
3.1. Gaussian shaped beams
According to Kogenik and Li22 a laser beam in the TEM-mode (circular cross-section) can be described by:
u(r,z) = c
w expl
(_r22 1.(kr2
exp —ii
w(z)
w(z) )
+ kz
I—
)
2R(z)
with: u(r,z) the solution of the Helmholtz-equation Lu + k2 u = 0 for the electric field; c = const., w0 = beam waist radius, w(z)
= beam radius (defined as distance between the beam axis and the l/e decrease of the intensity), r =coordinate perpendicular to
the beam axis z, k = wave number, R(z) = radius of wave fronts, and 4 = arctan
I
2
I; ((0) =0; (z—°°) = it/2).
1Cw )
z=O
2R
z
Fig. 2: Schematic representation of a diverging Gaussian shaped beam.
SP!E Vol. 2926/299
The beam radius and the radii of the wave fronts (Fig. 2) are given by:
w(z) = w0
R(z) = z •
1 + () , ( R(O) = ; R(zoc)
z),
2
with ZR
the Rayleigh length also describing the depth of focus:
2z (w=l.lwo)=O.9l7zR
=2.88—.
For an argon ion laser typically used in flow cytometry w0 is found on the back plane mirror of the laser resonator. To focus
such a Gaussian beam some assumptions have to be made: The lenses have to be ideal i.e. infinitly thin axially (diens 4 oo) and
cx). The latter assumption is fulfilled experimentally if the lens diameter is more than 1.7 of
the laser beam diameter23. Under these assumptions the lens transformation function T in the Fresnel-Kirchhoff (RayleighSommerfeld) integral can be approximated to
infinitly extended laterally (riens —
.kr , (f
T = exp(—I
= focal length of the lens)
——
and a Gaussian shaped beam is transformed in another Gaussian shaed beam as indicated in Figure 3. The distances of the
beam waists to the lens and the beam waist radius are transformed by
Z=f+
2
W02
z1
1
I______________
W1 _f)2+ZR12
R1
wol
f2(Z —f)
2
2
(z1—f) +ZR1
/R2
w02
z2
Fig. 3: Focussing of a Gaussian shaped beam by an ideal lens.
300 / SPIE Vol. 2926
By means of a subsequent application of these formulas, the transformations by each optical component of the laser beam can
be calculated from resonator back plane mirror to the final focus in the fluid stream of the flow system. On the other hand, with
a given focal diameter the variables of a lens system can be calculated by an appropriate system of equations. For instance for a
focussing optics of just two lenses a non-linear system of four equations with seven variables is obtained. 35 three-tupels of
variables can be given to calculate the remaining four.
In this context, it has to be considered that the worst situation occurs when a lens is placed such that the waist of the original
Wo2 =
beam is in the lens focus. For this case, the focused beam has its new waist at the other bus focus with
w01f
. To
ZR1
minimize the focused beam waist the lens should be placed as far away as possible from the original beam waist. In practical
situation the maximum value for Zi,2 will be dedicated by the lens diameter or the working surface dimension, respectively. In
sum.mary:
Ow12
—
1+ (zRl / 2
Z2 f +
f2
A)
0.5
01
0
a)
8pm
-8pm
0
8pm
c)
b)
B)
-8pm
a)
b)
0
-8pm
8pm
0
8pm
c)
Fig. 4: Computer calculation of a focus of A) 1 pm and B) 2 pm of an ideal Gaussian shaped beam. a) intensity distribution in
gray values (ordinate, abscizza: dimensions in pm; 0 = central axis of the fluid stream), b) relative intensity vs. focal width in
the centre of the focus and c) at a position pm out offocus.
SPIE Vol. 2926/301
Figure 4A shows the computer calculation of an ideal Gaussian shaped focus of a focal diameter of 1 im (=2 w0). Assuming a
mean core value of 12 jim for the fluid stream and thus the possible particle trajectories, a depth of field of jtm has to be
considered. At these positions the focal diameter is increased by a factor of 4. In contrast to this, a focus of only 2 im diameter
shows an increase by a factor of J2 at
im (Fig.4B). This shows that the requirements of depth of field to illuminate all
possible particle trajectories with nearly the same resolution and enough intensity limit the focal width and thus the optical
resolution
3.2 Aberrations from ideal Gaussian conditions
The experimental conditions of slit-scan optics do not fulfil the assumptions of ideal Gaussian shaped beam focusing:
a) The calculations described above are given for spherical lenses. For practical reasons the laser beam is usually focussed by
cylinder lenses. This is necessary to achieve a small focal diameter in the direction of the fluid stream and a large diameter
perpendicularly. In a first order approximation these two focussing directions can be treated independently and with the above
described formulas replacing r by x or y. However, having a more or less elliptical cross-section of the laser beam with an
unsymmetrical Gaussian intensity distribution, further transformations by lenses result in additional focal shift depending on the
ellipticity of the laser beam cross section25. This is especially true in cases where spherical achromatic lenses are used to
overcome aberration effects due to the frequency width of the laser beam20.
b) Another effect is due to the thickness of the lenses. In order to highly focus the laser beam (e.g. from typically 1 mm to
1 i.tm) the geometry of standard flow cytometers require compact optics and thus thick lenses. For these cases the lens
transformation function can no longer be approximated by a second order term. Higher order terms have to be considered26.
With
1.k r+—r
14(1
T=exp—i—
i—+
2f
4 R12 R1R2 R22
(R1,2 are the radii of the lens' surfaces) higher order terms of Fourier optics come into the Fresnel-Kirchhoff integral. This
results in a transformation of a Gaussian shaped beam into a non Gaussian shaped beam by the lens with typical minor intensity
maxima (Fig. 5). Although this effect slightly extends the lateral focal dimensions, it enlarges the depth of focus. In practice,
one can try to find a compromis in suppressing the intensity of the minor side peaks and enlarging the depth of focus20.
c) Further effects are due to the limited working surface diameter of a lens and finite apertures. If these have approx. the same
diameter, truncation effects have to be considered. Such effects are often difficult to calculate analytically and therefore are
often accessible only by numerical computer simulations or detailed experimental measurements.
a) Q.Q
1.0
2.0
3.0
4.0
5.Oys
b)
0.0
1.0
2.0
3.0
4.0
c)
i:o
3.0
4.0
5.Oys
Fig. 5: Example of a measured intensity distribution (scanned by microspheres) of a Gaussian shaped laser beam after
focussing by a thick lens (ordinate: arb. units; abscizza: time of flight in ps, ips corresponds to 10pm) a) between optics and
focus (-250 pin); b) in focus (0 pm); c) out offocus (+250 pm).
302 ISP1E Vol. 2926
4. FRINGE-SCAN OPTICS
4i. Principle
An interesting alternative procedure to overcome limitations of object plane scanning optics (limitation of the focal diameter
due to the depth of field required) was introduced by Mullikin et a!. and called fringe-scanning.
In principle, two coherent laser beams of the same intensity and with plane wavefronts are focused into the fluid stream under a
certain angle to the optical axis. Constructive and destructive interference of the two laser beams result in a fringe pattern
perpendicular to the fluid stream (Fig. 6a). The width of the fringes is independent from the distance to the beam waist. The
intensity distribution is enveloped by a Gaussian curve depending on the laser beam width (Fig. 6b). The width of the fringes Df
is defined by the distance of two intensity minima:
D1=
2sin(/2)
with c1 the angle between the two interfering laser beams. With cb/2
14. 1 0=a fringe width of 1 im can be obtained for 488 nm.
For 350 nm the fringe width is calculated to 0.7 j.im.
To analyze particles excited by a fringe pattern the measured fluorescence intensity distribution has to be deconvoluted by the
28 and Wiener-Filtering29. However, the Fourier
fringe pattern using the well known mathematics of Fourier
transform, i.e. the distribution of spatial frequencies k1 of a typical fringe pattern shows two peaks. One peak for kf —0
decribes the Gaussian shaped envelope of the pattern. The other one around kf =2 ltIDf depends on the individual fringe width.
Spatial frequencies of objects outside these peaks especially between these peaks cannot be resolved by the fringe scan system.
This limits the applicability and may be a reason among others why this approach has not found any more applications, yet.
1(x)
x=Spm.
0
x -5 pm
z=-5pm 0
a)
x=-.5pm
z = 5pm
5pm
b)
Fig 6: Computer calculation of a fringe-scan pattern of two laser beams with ) = 488 nm and a beam waist of 7 pm. The xdirection is the direction of the fluid stream; the z-direction indicates the optical axis. The two laser beams cross the optical
axis at an angle of
a) gray value distribution to indicate the intensity; b) relative intensity 1(x) vs. the x-dimension at
z =0.
4.2 Combination of fringe-scan excitation and slit-scan detection
To close the gap in the frequency spectrum of a fringe pattern, two alternatives are possible. The first one is to increase the
width of the fringes, a drawback for the system resolution. The second one is to reduce the full width of the enveloping
Gaussian curve and thus increasing the full width of the frequency peak around kf = 0. This can be realized by using small
SPIE Vol. 2926 / 303
interfering laser beams. This reduces the number of fringes. However, to deconvolve the object signal, an ideal low noise level
would be required. Furthermore, small laser beams would also reduce the depth of field.
Another solution to overcome the resolution limitations of a fringe pattern can be described by "cutting out one fringe
optically" . For this purpose a fringe excitation pattern is combined with an image plane slit-scan optics as shown schematically
in Fig. 7. Particles passing the fringe pattern are excited by each fringe. This results in a fluorescence fringe pattern which is
detected by an appropriate slit aperture in front of the photomultiplier tube. The slit width is given by the fringe distance Df and
the magnification of the detection optics. The effective depth of field results from the depth of field of the slit-scan detection
optics and the fringe length which depends on the diameters of the interfering laser beams.
image of fringes out of fOcus
slit aperture
image of the excitation fringes
detection optics
Fig. 7: Schematic representation of image plane slit-scan detection to "optically cut out" one excitation fringe.
Taking into account the data of the computer calculation of Figure 6a fringe length of
12 sm is possible. The depth of
field of the detection optics can be calculated from the aperture of the optics and the slit width necessary to acquire enough
fluorescence photons. The aperture angle I of the cone of the detected beams can be calculated using geometrical optics since
the fluorescence light is incoherent. Under the condition that the cone is given by the distance of two side maxima of the central
fringe at r (edge of the central fluid core, see Fig. 7)
= arctan(Df I r)
ForDf= 1pmandr=6tm, f=9.5°.
If the image plane with the slit is a conjugated plane to a plane through the central particle trajectory, particles moving through
the fringe pattern outside the central trajectory are recorded with reduced intensity. In order to achieve a minimal variation in
the image planes of the possible particle trajectories, a magnification of about one is recommended. With
MT(rP) = MT(O) . (1 +
r I f)
(MT = transversal magnification) the differences in the magnification can be neglected for f>> r. With the combination of the
fringe excitation and slit detection, the optical resolution is given by the fringe width and thus can be smaller than the resolution
of the image plane slit-scan detection optics. With a more sofisticated device using a Gaussian shaped detection aperture
(realized e.g., by a gray filter of spherical Gaussian absorption behaviour), the formulas of the above described slit-scan optics
can be applied. In Figure 8 the result of a computer calculation of the light intensity recorded from the fringe pattern by the
photomultiplier after having passed such a detection optics is shown. Only the intensity of the central fringe is contributing to
the fluorescence excitation.
304/SPIEVo!. 2926
The Fourier transform of the detected intensity spectrum shows no considerable gap in the frequency spectrum. With an
appropriate noise filter frequencies of up to k = 9 jtm can be detected. Compared to object plane slit-scanning using the same
optics with 2 pim beam waist diameter this is an increase in resolution by more than a factor of 2.
x=5pm —'
0—
Fig. 8: Computer calculation of the detected intensity
using afringe scan excitation optics (i = 488 nm, D1 =
x=-5pm —
1 Mm)
I
I
z=-Spm
0
z=Spm
and a slit scan detection optics (A = 600 nm, /3 =
5,2 pm, w0 = 2 pm). The x-direction is the
direction of the fluid stream, the z-direction of the fluid
9.5°,
ZR
stream, the z-direction the optical axis of the exciation
optics.
5. DISCUSSION
Although slit-scan flow systems have been applied for more than 20 years'5, a theoretical description of the optics required to
modify flow cytometers into slit-scan systems is lacking. In this article some basic considerations on laser focussing for object
plane scanning are described. Under the regime of Gaussian beam propagation some reasons have been described why slit-scan
flow cytometers do not reach the optical resolution of a fluorescence microscope. Some experimental effects contributing to the
real shape of the laser beam focus are discussed. However, it is anticipated that the spatial resolution that can be achieved by a
slit-scan analyzer and sorter is not only given by the laser focus in air. Some further effects have to be considered: The fluid
stream in the flow cuvette of a rectangular cross-section contributes to minor shifts in the laser beam. However, free flow
streams of circular cross-section have additional focussing effects, which should be considered by calculating an additional
lenslike component with the refraction index of the fluid. Furthermore, slit-scan systems have a detection optics and detection
electronics. Whereas the influence of the first may be of less importance choosing lenses with a numerical aperture which
results in a considerable higher resolution than the laser beam diameter, the electronics may have a practical influence since the
risetime is limited. Finally, profile acquisition and evaluation using special computer hard- and software'5'3° should be
considered, if an estimate of the smallest measurable particle length is given.
Thus, definitions of the resolution just on the calculated laser beam width under ideal conditions may be questionable.
Moreover, the literature shows that these definitions are not always on the basis of the full width at the lie2 intensity points.
Sometimes the full mean half width or the width at the lie intensity points are used. Therefore, for better comparison an
experimental determination of the resolution2° may be suggested as a promising alternative procedure.
The experimental experience has indicated that using standard slit scan optics a considerable increase in optical and
consequenly overall system resolution is not possible. Therefore some years ago the idea of fringe scan flow cytometry was
introduced27. However, as shown here, a fringe pattern for fluorescence excitation has the limitation that not all possible
particle lengths are well resolved. Therefore, the combination of fringe-scan excitation with slit-scan detection is suggested.
SPIE Vol. 2926 I 305
Our preliminary experimental results show that an appropriate fringe pattern for high resolution scanning can be obtained. This
is especially possible for free flow jet devices, which means that the influence of the cylindrical fluid surface may be negligible.
However, in practice, the requirements to quality of the optical components as well as the running conditions are considerably
higher than for standard slit-scan setups. This has to be considered in the case of running such systems in routine medical
laboratories.
6. ACKNOWLEDGEMENT
The authors gratefully acknowledge the financial support of the German Ministry of Education, Science, Research, and
Technology (BMBF). They thank Klaus Aldinger, Dietmar Wolf, Heiko Lentfer, and Olaf Fischer for experimental support and
stimulating discussions. They also thank the mechanics workshop of the Institute of Applied Physics for assistance.
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306 /SP1E Vol. 2926
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