220222 JR
Confocal Laser Scanning Microscopy
Confocal fluorescence image (actin, nucleus, mitochondria) of BPAE cell
J. Rheinlaender
Instruction Manual
Institut für Angewandte Physik
AG Prof. Tilman Schäffer
Universität Tübingen
Assistant room number: C9 A38 / C7 P31
Experiment room number: C9 P13 / H36
Table of Contents
I.
Preparation ........................................................................................................................ 3
II.
Background ........................................................................................................................ 3
1. History of optical microscopy ......................................................................................... 3
2. Basics of wave optics ...................................................................................................... 4
2.1.
Interference ............................................................................................................. 4
2.2.
Refraction ................................................................................................................ 4
2.3.
Diffraction ................................................................................................................ 5
2.4.
The Airy disk............................................................................................................. 6
3. Experimental setup ......................................................................................................... 7
3.1.
Fluorescence microscopy ........................................................................................ 7
3.2.
Confocal microscopy................................................................................................ 7
3.3.
Immersion oil objectives ......................................................................................... 9
4. Resolution in optical microscopy .................................................................................... 9
4.1.
The point spread function (PSF) .............................................................................. 9
4.2.
The Rayleigh criterion .............................................................................................. 9
4.3.
Resolution in confocal microscopy ........................................................................ 10
4.4.
Nyquist–Shannon sampling theorem ................................................................. 11
III. Experiment ....................................................................................................................... 12
1. Laboratory ..................................................................................................................... 12
2. Protocol ......................................................................................................................... 14
References ............................................................................................................................... 15
2
I.
Preparation
The following experiment is an introduction to optical microscopy with focus on confocal
fluorescence microscopy and its application in biology, biophysics and medical research. The
physical background and technical details is kept to minimum. However, the general
principles of optical microscopy are summarized in this instruction manual, while for detailed
information the reader is referred to relevant secondary literature.
In order to conduct this experiment, knowledge of the following topics should be acquired by
reading this instruction manual:
o
o
o
o
Interference, refraction, and diffraction of light
Basics of optical and fluorescence microscopy
Basics of confocal microscopy
Image digitalization
You should be able to answer the following questions before the experiment:






II.
What is interference, what is refraction of light waves?
What is diffraction? How does the interference pattern behind a single slit look like?
What are the main components of an optical / fluorescence microscope?
What determines the physical resolution of an optical microscope? What is the point
spread function?
How does a (laser scanning) confocal microscope work?
What determines the physical resolution of a confocal microscope?
Background
1. History of optical microscopy
Optical or light microscopes (from Greek μικρόν or micron for "small", and σκοπεῖν or skopein
for "to look at") are the oldest type of microscopes and date back into the early 17th century,
when scientists like Galileo Galilei (1564-1642) invented their basic principle. Dutch scientist
Antonie van Leeuwenhoek (1632-1723) introduced them into the field of biology, but the
basic technology did not change until the 20th century, where revolutionary improvements
where achieves such as Köhler illumination, phase contrast or differential interference
contrast microscopy. Since the late 1960s fluorescence microscopy became state of the art,
allowing for functional imaging of the sample. Further improvements were then the confocal
microscope1 and recently super-resolution microscopy techniques2, allowing for higher
resolution and contrast.
3
2. Basics of wave optics
In order to understand the principles of optical microscopy, geometric optics are not sufficient
and light has to be described by wave optics. Some main concepts of wave optics are briefly
noted in the following.
2.1. Interference
As illustrated in Figure 1, two propagating light waves can interfere due to vector properties
of the underlying electromagnetic fields. If the waves have same wavelength or frequency,
interference can be constructive (Figure 1a) or destructive (Figure 1b) depending on their
phase difference with constructive interference for in-phase (even multiple of π or 180°) or
antiphase (odd multiple of π or 180°) superposition, respectively.
a)
b)
Wave 1
Wave 1
Wave 2
Wave 2
Result
Result
Figure 1. Illustration of (a) constructive and (b) destructive superposition of two propagating waves.
2.2. Refraction
Refraction is the change of the propagation direction of a light wave, when passing the
interface between two media (e.g. air and glass) of different refractive index 𝑛, which relates
the speed of light in vacuum 𝑐 to the speed of light in the respective medium, 𝑣 = 𝑐 ⁄𝑛.
According to the phenomenological Snell’s law of refraction (Figure 2a), the ratio of the sines
of the two waves’ angles of incidence, 𝜗1 and 𝜗2 , is given by the opposite ratio of their
refractive indices, 𝑛1 and 𝑛2 ,
sin 𝜗1 𝑛2
(1)
=
.
sin 𝜗2 𝑛1
interface
n1 n2
a)
1
1
normal
interface
v1 v2 sphere
wave
b)
normal
2
wave
front
2
λ1
λ2
Figure 2. Refraction of a light wave at an interfact between two media according to (a) Snell’s law in terms
geometric optics and (b) Huygens-Fresnel principle in terms of wave optics.
4
However, the same result can be obtained using the Huygens-Fresnel principle: From the
incident wave of wavelength 𝜆1 at each point of the interface of a spherical waves of
wavelength 𝜆2 is emitted, forming the propagating wave by superposition (Figure 2b).
Geometrically then follows
sin 𝜗1 𝜆1 𝑣1 ⁄𝑓 𝑛2
(2)
=
=
=
,
sin 𝜗2 𝜆2 𝑣2 ⁄𝑓 𝑛1
since the wave’s frequency 𝑓 is the same in both media.
2.3. Diffraction
The Huygens-Fresnel principle also allows to intuitively describe diffraction, which takes place
when a light wave interacts with structures of size similar to the wavelength. For example, if
a narrow slit is illuminated with coherent light (Figure 3a), the transmitted light exhibits a
typical diffraction pattern of bright and dark regions on a distant screen (Figure 3b).
single slit
b)
screen
c)
intensity I / I0
a)
1.0
0.5
0.0
-4
-2
0
2
angle sin(α) b / λ
4
Figure 3. Diffraction at a single slit. (a) Schematic experiment. (b) Photography of the diffraction pattern and
(c) intensity profile according to Equation (3).
The interference profile of the diffraction pattern can be derived using the Fresnel-Kirchhoff
diffraction formula to calculate the superposition of the individual waves on the screen. For a
slit of width 𝑏 the intensity profile is given by
(3)
𝐼(𝛼) = 𝐼0 sinc 2 [π sin(𝛼) 𝑏⁄𝜆] ,
using sinc 𝑦 = sin(𝑦)⁄𝑦 for the so-called sinc function. While the derivation of the complete
profile is relatively complicated, the location of the intensity minima can be constructed
easily. In a simplified geometric consideration, for the first minima the transmitted wave is
divided into two parts of width 𝑏⁄2 (Figure 4), which interfere destructively, if their path
difference 𝛿 is equal to 𝜆⁄2. Therefore, the first minimum can be observed under an angle of
𝛼 = arcsin(𝜆⁄𝑏 ). For the higher order minima the wave is divided into four, six, etc. parts,
which then interfere destructively on their own. Therefore, the minima can be observed
under the angles
𝛼𝑛 = arcsin(𝑛 𝜆⁄𝑏 ) with 𝑛 = 1, 2, 3, …
(4)
(see Figure 3c).
5
Figure 4. Diffraction at a single slit of width 𝒃 and geometric
consideration to explain the location of the minima under
angle 𝜶. The transmitted wave is divided into two parts with
path difference 𝜹. Usually, the lateral location on the screen
can be apprimated for small angels using 𝐭𝐚𝐧𝜶 = 𝒙⁄𝑳 ≅ 𝜶
in radians.
When the single slit is replaced with a double slit, the diffraction pattern changes, because
now effectively the two beams from the two slits interfere with each other. From similar
geometric considerations (Figure 5) it can be deduced that the path difference between the
beams is 𝛿 = 𝑔 ∙ sin 𝛼. Constructive or destructive interference then occurs if the path
difference is an even or uneven multiple of 𝜆⁄2, respectively. So the angle, under which
maxima and minima can be observed is
𝜆
(5)
𝛼𝑛 = arcsin (𝑛 )
2𝑔
with 𝑛 = 0, 2, 4, … for the maxima and 𝑛 = 1, 3, 5, … for the minima.
Figure 5. Diffraction at a double slit of slit distance 𝒈 and
geometric consideration to explain the location of minima
and maxima under angle 𝜶 with the path difference 𝜹 of the
transmitted waves.
a)
intensity I / I0
2.4. The Airy disk
If the diffraction sample is a circular aperture, the diffraction pattern changes to characteristic
two-dimensional structure (Figure 6), which is commonly denoted as Airy disk or generally
Airy pattern (after George Biddell Airy).
b)
1.0
0.5
0.0
-2
0
2
angle sin(α ) b / λ
Figure 6. Diffraction at a circular aperture of radius 𝒂. (a) Cross section and (b) two-dimensional calculation of
the Airy pattern (logarithmic color scale).
6
3. Experimental setup
Due to the complexity of the topic, only the basic experimental designs of widefield and
confocal fluorescence microscopes are described. For further information, the reader is
referred to relevant secondary literature.
3.1. Fluorescence microscopy
In fluorescence microscopes, not the absorbance or reflectance of the sample is investigated,
but it is stained with specific functionalized dyes to image just certain structures of interest.
The sample is then illuminated not with white light, but with light of a narrow spectrum to
excite the dyes, which then emit light of a certain (generally longer) wavelength. Excitation
and emission light is usually separated with a dichroic mirror and an optional emission filter
(see Figure 7 for details). The dichroic mirror and the filters are often combined in a “filter
cube” to allow for easy change.
Figure 7. Basic experimental setup of a fluorescence
microscope. Light from a broad-spectrum lamp (mercury
vapor or, increasingly, LED lamps) is filtered by an exitation
filter (here shown for green light) and then reflected on the
sample by a dichroic mirror, which is reflecting below and
transmitting above a cerctain wavelength. Sample features
then fluorescently emit light (here shown in red), which is
displayed on the camera. Out-of-focus objects are also
projected onto the camera, but appear blurred.
3.2. Confocal microscopy
Conventional widefield microscopes suffer from the fact that also all light from out-of-focus
regions of the sample are collected by the objective, which massively increases the
background when imaging thick samples (see the two out-of-focus objects in Figure 7). This
problem is solved in the confocal imaging principle, which was invented by Marvin Minsky in
1957,3 by imaging with a diffraction-limited light spot (usually by focusing a laser beam) and
blocking out-of-focus emission with an aperture (usually denoted as “pin-hole”) in the
detector light pass (see Figure 8 for details). This practically eliminates the image background
and slightly improves the optical resolution (see below, section 0).
7
Figure 8. Principle and basic experimental setup of a confocal
microscope. The sample is illuminated with a diffractionlimited spot, often using a focussed laser beam. Excitation of
the sample is then limited to “focal volume”. In the detection
light path a “pin-hole” aperture is placed in the focal plane.
While light emitted from in-focus sample features passes the
pin-hole (dashed light path), light emitted from out-of-focus
sample features is than practically blocked by the pinhole and
does not reach the detector (dotted light path).
However, the confocal imaging principle now results in the expense that imaging now has to
be performed by somehow scanning illumination and detection region through the sample.
In principle, that would be possible by moving the sample relative to the stationary optics,
but is often easier and especially faster to move the confocal volume with respect to the
sample, which is often realized by confocal laser scanning microscopy (CLSM, often simply
named ‘confocal microscopy’) (see Figure 9 for details). The image is then recorded by pixelby-pixel and line-by-line scanning the confocal volume through the sample while recording
the intensity on the detector, which is usually a photomultiplier tube (PMT) or an avalanche
photodiode. Owing to the efficient blockage of out-of-focus light, CLSM is often used for
optical sectioning and recording “stacks” of images through thick samples. For multiple
fluorescence imaging the imaging procedure is sequentially repeated for each channel.
Figure 9. Experimental setup of a confocal
laser scanning microscope, where the
scan movement is realized by scanning
the confocal volume through the sample.
This is often implemented by tilting the
parallel excitation and emission beams
together, for example, using separate
galvano mirrors for the lateral 𝒙- and 𝒚movement. The vertical movement can be
realized by moving the objective with a 𝒛scanner.
8
The instrument used in the practical work is a commercial Nikon C2 confocal microscope with
four separate lasers for illumination (405 nm, 488 nm, 561 nm, and 640 nm) and three
photomultiplier tubes (PMT) for detection, coupled to the scan head with optical fibers. The
scan head contains the 𝑥- and 𝑦-scanning mirrors and is mounted to the microscope at the
camera port, while the 𝑧-scanning is realized by the motorized focus of the microscope body.
3.3. Immersion oil objectives
For achieving high image intensity and resolution (see below), it is advantageous to collect
the light emitted from the sample under an angle as large as possible. If sample and objective
are separated by air, the angle 𝛼, under which the sample is imaged, is effectively smaller
because of refraction of the light at the air/glass interfaces (Figure 10a). Furthermore, the
maximum angle is limited by the critical angle for total internal reflection (typ. 40°). If the
space between sample and objective is filled with a medium of refractive index similar to the
glass, refraction is minimized, which is usually achieved by immersion oil (Figure 10b). The
angle of observation and the refractive index of the separating medium are often combined
in the “numerical aperture”
(6)
NA = 𝑛 sin 𝛼 ,
4
which was introduced by Abbe already.
Figure 10. Difference in light path for
objective (a) without and (b) with immersion
oil with refractive index 𝒏 > 𝟏.
4. Resolution in optical microscopy
If microscopic objects are imaged with optical microscopes, the resolution is ultimately
limited by diffraction, which was first derived by Ernst Abbe in 1873.4 When a sub-wavelength
object is illuminated, its image is not point-like but a diffraction pattern according to the Airy
pattern (see above). Why is that so?
4.1. The point spread function (PSF)
The illuminated object emits light in all directions. However, the objective only collects the
light, which is emitted under an angle of 𝛼 or smaller, given by the opening angle of the
objective, which thereby acts as a circular aperture. The image of the object therefore
corresponds to the Airy diffraction pattern. Hence, every point-like object looks like this
diffraction pattern, which is therefore denoted as “point spread function” (PSF) of the
microscope.
4.2. The Rayleigh criterion
Based on the work of on John William Strutt, 3. Baron Rayleigh, the two objects can just be
separated from each other in the image, the location of the one object is at first minimum of
second particle’s Airy pattern.5 The distance of the objects is then
9
𝜆
𝜆
(7)
= 0.61
,
𝑛 sin 𝛼
NA
for refractive index of the medium 𝑛 and opening angle of the objective 𝛼 or numerical
aperture NA [Equation (6)]. For illustration, images of two objects with distance above, equal
to, and below Rayleigh criterion are shown (Figure 11).
𝑑 = 0.61
a)
b)
c)
Figure 11. Resolution limit according to the Rayleigh critertion. Image of two closely-separated objects
according with distance (a) above, (b) equal to, or (c) below the Rayleigh criterion (logarithmic color scale).
Experimentally, it is complicated to realize the Rayleigh criterion, because for that the position
of sub-wavelength objects would have to be controlled accordingly. For practical reasons the
resolution of optical microscopes is therefore often determined from the width of the PSF by
imaging individual point-like objects such as sub-µm sized fluorescent microbeads (see for
example protocol in 6). The full width at half maximum (FWHM) is very similar to the Rayleigh
criterion and is given in the lateral direction by7
𝜆em
(8)
FWHM𝑥,𝑦 = 0.51
.
NA
In axial direction the FWHM is given by
𝑛𝜆em
(9)
FWHM𝑧 ≅ 1.77
.
NA²
In case of widefield fluorescence microscopy λem refers to the emission wavelength.
4.3. Resolution in confocal microscopy
In confocal microscopy the resolution is slightly improved, both illumination and detection
patterns are now diffraction-limited and the effective PSF is then the multiplication of the
illumination and the detection PSF. If the projected pinhole diameter is equal to the diameter
of the first order minimum in the Airy disk pattern, referred as to 1 Airy unit (or 1 AU), then
the lateral resolution is given by6:
𝜆ex
(10)
FWHM𝑥,𝑦 = 0.51
NA
In confocal microscopy only molecules inside the diffraction limited excitation volume can
emit fluorescence light. Therefore and contrary to widefield fluorescence microscopy, the
excitation wavelength λex is used to calculate the FWHM. In axial direction, a pinhole diameter
of 1 AU will result in a better resolution compared to the widefield setup 6:
𝜆ex
FWHM𝑧 = 0.88
(11)
𝑛 − √𝑛2 − NA2
10
Theoretically, smaller pinhole diameters will further enhance the lateral and axial resolution
slightly, but at the expense of signal intensity, as more light is then blocked by the pinhole.
4.4. Nyquist–Shannon sampling theorem
When converting continuous signals (“analog signals”) into discrete signals (“digital signals“)
the sampling rate must be at least more than two times the maximum frequency of the signal,
in order to represent the signal without loss of information. This criterion is denoted as the
Nyquist-Shannon sampling theorem.8 Figure 12 shows the transformation of an analogue
signal into a digital signal at different sampling rates.
For example, in case of an audio signal with a maximum frequency of 20 kHz the sampling
frequency must be more than 40 kHz. For the compact disc digital audio (“Audio-CD”) the
sampling rate is 44.1 kHz, thus satisfying the theorem.
Output Samples
Input
The Nyquist-Shannon theorem also applies for spatial information. In optical microscopy, to
resolve a structural size of e.g. 250 nm, the pixel size of the detection system has to be less
than 125 nm. To be on the save side, often 1⁄3 of the object frequency is used as pixel size
(e.g. 250 nm⁄3 ≈ 80 nm). A higher sampling rate (smaller pixel size) will not result in a gain
of information (“empty magnification”).
Figure 12. Transformation of analoge signal into digital signal at increasing sampling rate.
11
III.
Experiment
1. Laboratory
The confocal microscope used for the experiment is an expensive research microscope. The
experimental work may therefore be started only after a comprehensive introduction and
together with the instructor. If you are not sure, always ask the instructor first! Before starting
the experiments, read and sign the laser safety form for each of the two setups!
In the experiment the following tasks should be performed:
1. The practical work starts with the diffraction experiments at the optical bench (see
Figure 13). A set of single and double slit samples are provided. The laser wavelength
is 𝜆 = 633 nm.
Figure 13. Schematic setup of the
optical
bench
with
laser
illuminating a slit and the
diffraction pattern projected on a
screen.
a. Adjust the collimator lens to generate a parallel laser beam. Start with the
widest single slit (𝑑 = 0.8 mm). Align the laser to the slit and investigate the
diffraction pattern.
i. Sketch the intensity profile.
ii. Measure the angle between the center maximum and the first order
minimum and compare it with the expected values.
b. Repeat the experiment as in a.i and a.ii with a narrower single slit (e.g. 𝑑 =
0.4 mm) and the narrowest single slit (𝑑 = 0.1 mm). How does the diffraction
pattern change?
c. Replace the sample with the double slit (slit distance 𝑔 = 0.3 mm, slit width
𝑑 = 0.1 mm. Investigate the diffraction pattern and compare it with the last
single slit.
d. Continue the experiment with all other double slits of different slit width vs.
slit distances.
i. How do the diffraction patterns change?
ii. How do slit width and slit distance affect the diffraction pattern?
e. If time allows, insert a collecting lens and the adjustable slit according to Figure
14.
12
Figure 14. Schematic setup of the optical bench modifed by inserting a lense with focal length
𝒇 for demonstrating the contribution of diffraction orders to the image.
i. Move the adjustable slit in such a way that only the 0-order maximum
can pass through. Discuss your observation.
ii. Move the adjustable slit in such a way that only higher order maxima
(1st order and above, 0-order excluded) can pass through. Discuss your
observation.
f. Replace the slit sample with the pinhole and remove the collecting lens and
the adjustable slit. Investigate the diffraction pattern and calculate the pinhole
diameter.
2. In the second part of the practical work the optical microscope in “conventional”
widefield configuration is investigated.
a. Mount the commercial sample with fluorescent microspheres (“beads”) into
the microscope and focus on the sample position 4 (0.2 µm beads) using a lowmagnification air objective (e.g. 20x).
b. Record an image and zoom in onto a single bead to inspect the point spread
function (PSF):
i. Use the microscope software to create a cross section through the PSF.
ii. Compare the shape of the PSF qualitatively with the expected shape.
At home measure the FWHM of the PSF and compare it with the
expected value [see Eq. (8), note that you need the NA of the objective
for that].
c. Now change to a high-magnification oil objective (e.g. 60x). Caution! The
objective is very expensive and must be handled by the assistant only! Change
to position 5 of the sample (0.1 µm beads). Again, focus on the beads and
inspect the PSF:
i. Create a cross section through the PSF.
ii. At home compare the shape and width of the PSF with the result from
section 2.b and with the expected value.
iii. Discuss the different factors affecting the image resolution (optical
resolution, pixel resolution). Discuss whether the pixel size meets the
Nyquist-Shannon criterion. What is “empty magnification”?
13
3. In the third part of the practical work the optical microscope in confocal configuration
is investigated.
a. Use the bead sample to investigate the confocal PSF:
i. Set the pinhole to approx. 1 AU and adjust the imaging parameters.
ii. Zoom in onto a single bead and record the 𝑥𝑦-PSF and create a cross
section. Use appropriate pixel size to meet Nyquist-Shannon criterion.
iii. At home compare the shape and width of the PSF with the expected
value [see Eq. (10) and (11)]. Compare the confocal PSF with the PSF in
conventional mode.
iv. Now record an appropriate 𝑧-stack of the bead and plot the 𝑥𝑧-PSF.
v. Change the pinhole to maximum (approx. 6 AU and compare the 𝑥𝑦and 𝑥𝑧-PSF.
b. Now change to the commercial cell sample. Place the sample into the
microscope and focus on the cells.
i. Record a widefield image of the cells with a single channel, e.g. FITC.
ii. Change to confocal configuration and record a single-channel 𝑥𝑦image. Compare it with the widefield image.
iii. Set up multicolor imaging, e.g. FITC and DAPI, and record an 𝑥𝑦-image.
iv. Finally record an appropriate 𝑧-stack and construct 𝑥𝑧- and 𝑦𝑧-slices, a
maximum-intensity projection and a 3D view of the data.
v. Use the laser power meter to measure the laser power of the 488 nm
laser in the location of the sample with your last used settings. At home
compare irradiance of your 488 nm laser power setting with the
irradiance of the sun in central Europe. Irradiance is the radiant flux
(power) received by a surface per unit area (unit W/m2 ). The
illuminated area can be considered circular with the diameter
estimated by the FWHM of the PSF. In central Europe, the irradiance of
the sun peaks at approx. 1000 W/m2 (summer, midday, clear sky).
Think about possible consequences of your results for live biological
samples.
At the end, clean the oil objective and sample following assistant’s instructions. (Use
high-grade ethanol and Kimwipes and be very careful!)
2. Protocol
The protocol should give a brief description of the basics of optical and confocal microscopy.
Discuss similarities and differences of widefield vs. confocal microscopy. The major part of the
protocol should be the presentation of the results obtained during the experiment and their
detailed discussion and interpretation. Include error analysis for the single slit experiments
and compare your results with expectations from theory.
14
Error analysis:
Estimate how accurate you were able to measure the distance from slit to screen, e.g. 1 cm
accuracy. This will result in a distance of e.g. 550 ± 1 cm. In a similar way, estimate your
measurement error when measuring the distance between minimum and maximum on the
screen. Then estimate, how these two accuracies affect your final results for the calculated
angles, which should be stated in a way such as, e.g., = 0.024 ± 0.002 °.
The protocol must contain a signed declaration that the elaboration of the report was
performed by you and your group (see below):
Name:
..............................
Matriculation number:
..............................
I hereby declare that my elaboration (or that of my group) was made independently and is
not a copy (even partially) of an existing protocol or of the instruction manual. All external
sources (also the instruction manual) have to be cited. I am aware that a violation of this
rules is plagiarism and leads to the experiment being graded as failed (grade 5) and can
result in an exclusion from the labwork.
..............................
Date
..............................
Signature
References
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
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Castello, M.; Diaspro, A.; Cordes, T., The 2015 super-resolution microscopy roadmap. J.
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Minsky, M., Memoir on inventing the confocal scanning microscope. Scanning 1988, 10,
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Abbe, E., Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung.
Archiv f. mikrosk. Anatomie 1873, 9, 413-418.
Rayleigh, L., On the theory of optical images, with special reference to the microscope.
Phil. Mag. 1896, 42, 167-195.
Cole, R. W.; Jinadasa, T.; Brown, C. M., Measuring and interpreting point spread
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Amos, B.; McConnell, G.; Wilson, T., 2.2 Confocal Microscopy A2 - Egelman, Edward H.
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