The Resolving Power
12 ˇ Basics of light Microscopy & iMaging the resolving power
area, spread over the total amount of
sensory cells. More individual sensors
can catch differences and translate them
into a recognised image.
Unfortunately, we can move closer
only up to a certain distance, after which
our flexible optical system is no longer
able to project the image clearly onto the
retina. If the words are typed too small,
like these ["you can not resolve it without
optical help"] "You can not resolve it without optical help", our resolution is
reached.
The wavelength that transports the
information of the image also influences
what we can resolve. Shorter blue wavelengths
carry finer details than longer
ones from the same object. Using a microscope
it would be easy to read the text
and to document it via the sensors of a
camera. But these tools are also restricted
by the resolution of their optical
system and the number and sensitivity of
sensors ­ the pixels.
What is resolution?
Resolution or resolving power of a microscope
can be defined as the smallest distance
apart at which two points on a
specimen can still be seen separately. In
the transmitted light microscope, the xyresolution
R is determined essentially by
three parameters: the wavelength  of
the illuminating light, and the numerical
aperture (NA) of the objective (NAobj) as
well as the condenser (NAcond).
R = 1.22*  / (NAobj
+NAcond
) (1)
When the aperture of the condenser is
adjusted to that of the objective, i.e. the
aperture of the condenser is essentially
the same as the objective aperture, the
equation (1) simplifies to:
R = 0.61*  /NAobj (2)
This equation is used for both transmitted
light microscopy and for reflected
Human vision
For most of us, seeing something is normal
and we are accustomed to evaluate
things by looking at them. But the seeing
act uses many different and complex
structures that enable us not only to
catch images but to process and interpret
them at the same time. Every image
that is projected on the retina of our eye
is transformed into neuronal impulses
creating and influencing behaviour: this
is what we call seeing. Therefore, what
we see is not necessarily what another
person sees.
Compared to these processes within
our brain, the first steps of vision seem to
be much simpler. To create a projection
onto the layer of the retina, where millions
of light sensitive sensory cells are
located, the light passes through an optical
system that consists of cornea, aqueous
humour, iris, pupil, focus lens and
the vitreous humour, see fig. 12. All these
elements together create what the raster
framework of sensory cells can translate
within their capability into neuronal ac-
tivity.
Eagles and mice
Those two different set ups ­ the optical
system and the sensor system ­ restrict
the options of human vision at the very
first step. Details can be found at www.
mic-d.com/curriculum/lightandcolor/
humanvision.html. Having eagle eyed optical
systems alone will not enable us to
see mice from far away. To resolve a
small object (the mouse) against a large
background needs special physical properties
of the optics and also requires a
certain sensitivity and number of sensors
used to translate the information.
If this text is getting too small, you have to come closer to resolve it.
This means your eyes can get light from
the small letters in a wider angle than
before. You are now focusing on a smaller
Fig. 12: Anatomy of the human eye and cross section of the retina.
the resolving power Basics of light Microscopy & iMaging ˇ 13
light microscopy. Note here that resolution
is NOT directly dependent on the
magnification. Furthermore the end
magnification should not be higher than
1000x the NA of the objective, because
then the image will be only enlarged but
no further resolution will be visible. This
is called empty magnification.
What is the numerical aperture of an
objective?
The numerical aperture of a microscope
objective is a measure of its ability to
gather light and thus resolve fine specimen
detail at a fixed objective distance.
The numerical aperture is calculated
with the following formula:
NA = n*(sin ) (3)
n is the refractive index of the medium
between the front lens of the objective
and the specimen cover glass. It is n =
1.00 for air and n = 1.51 for oil.  is one
half the angular aperture, as can be seen
in fig. 13. The bigger , the higher is the
numerical aperture. Working in air, the
theoretical maximum value of the numerical
aperture is NA = 1 ( = 90°). The
practical limit is NA = 0.95.
Numerical aperture in practice
For all microscope objectives the resolving
power is mentioned with the number
for the numerical aperture shown diTable
2: Numerical Apertures (NA) for different types of objectives and magnifications
Magnification Plan Achromat Plan Fluorite Plan Apochromat
4 x 0.1 0.13 0.16
10x 0.25 0.3 0.4
20x 0.4 0.5 0.75
40x 0.65 0.75 0.9
60x 0.8 (dry) 0.9 (dry) 1.42 (oil immersion)
100x 1.25 (oil) 1.3 (oil) 1.4 (oil)
Fig. 13: Angular aperture
of an objective.
Box 2: How to set Köhler illumination
To align a microscope that can change the distance of the condenser to the area of the specimen for Köhler
illumination you should:
1. Focus with a 10x or higher magnifying objective on a specimen, so that you can see at least something of
interest in focus. (If your condenser has a front lens please swing it in when using more then 10x magnifying
objectives.)
2. Close the field stop at the light exit.
3. Move the condenser up or down to visualise the closed field stop. Now only a round central part of your
field of view is illuminated.
4. If the illumination is not in the centre the condenser has to be moved in the XY direction to centre it.
5. Finely adjust the height of the condenser so that the edges of the field stop are in focus and the diffraction
colour at this edge of the field stop is blue green.
6. Open the field stop to such an amount that the total field of view is illuminated (re-centring in xy direction
may be necessary).
7. For best viewing contrast at brightfield close the aperture stop to an amount of 80% of the objective numerical
aperture.
In practice, you can slowly close the aperture stop of your condenser while looking at a specimen.At the moment
when the first change in contrast occurs, the NA of the condenser is getting smaller then the NA of the
objective and this setting can be used. For documentation the condenser NA should be set according to that
of the objective. To visualise the aperture stop directly you can remove one eyepiece and see the aperture
stop working as a normal diaphragm.
rectly following the index for magnification
(fig. 14), e.g. a UPlanFLN 60x/0.9 objective
produces a 60x magnification
with a numerical aperture of 0.9. The
Numerical Aperture strongly differs depending
on the type of objective or condenser,
i.e. the optical aberration correction.
Table 2 lists some typical numerical
apertures for different objective magnifications
and corrections.
To achieve higher NA than 0.95 for objectives
they have to be used with immersion
media between front lens and specimen.
Oil or water is mostly used for that
purpose. Because objectives have to be
specially designed for this, the type of immersion
media is always mentioned on the
objective like on the UPlanFLN 60x/1.25
Oil Iris objective. This objective needs oil
as an immersion media and can not produce
good image quality without it.
For special techniques like the Total
Internal Reflection Fluorescence Microscopy
(TIRFM), objectives are produced
with very high NA leading by the Olympus
APO100x OHR with a NA of 1.65. The
resolution that can be achieved, particularly
for transmitted light microscopy, is
depending on the correct light alignment
of the microscope. Köhler illumination is
recommended to produce equally distributed
transmitted light and ensure the
microscope reaches its full resolving potential
(see box 2).
What resolution can be reached with a
light microscope?
To make the subject more applicable,
some resolution numbers shall be given
here. Using a middle wavelength of 550
nm, the Plan Achromat 4x provides a
resolution of about 3.3 m, whereas the
Plan Apochromat reaches about 2.1 m.
The Plan Achromat 40x provides a resolution
of 0.51 m and the Plan Apochromat
of 0.37 m. The real-world limit for
14 ˇ Basics of light Microscopy & iMaging the resolving power
the resolution which can be reached with
a Plan Apochromat 100x is often not
higher than R = 0.24 m.
To give a comparison to other microscopes
that do not work with visible light,
the resolution reached nowadays in a
scanning electron microscope is about R
= 2.3 nm. In a transmission electron microscope,
structures down to a size of 0.2
nm can be resolved. Scanning probe microscopes
even open the gates to the
atomic, sub Angstrm dimensions and
allow the detection of single atoms.
What are airy disks?
Every specimen detail that is illuminated
within a microscope creates a so-called
diffraction pattern or Airy disk pattern.
This is a distribution of a bright central
spot (the Airy disk or primary maximum),
and the so called secondary maxima separated
by dark regions (minima or rings
of the Airy disk pattern; see fig. 15, 16)
created by interference (More details:
www.mic-d.com/ curriculum/lightandcolor/diffraction.html).
When two details
within the specimen are closely together
we can only see them separated if the
two central spots are not too close to
each other and the Airy disks themselves
are not overlapping. This is what the
Rayleigh criterion describes. Good distinction
is still possible when one Airy
disk just falls in the first minimum of the
other (fig. 15).
The smaller the Airy disks, the higher
the resolution in an image. Objectives
which have a higher numerical aperture
produce smaller Airy disks (fig. 16) from
the same specimen detail than low NA
objectives. But the better the resolution
in the xy direction, the less is the specimen
layer that is in sharp focus at the
same time (Depth of field), because the
resolution also gets better in the z direction.
Like higher magnification, higher
resolution always creates less depth of
field. Also in most cases the increase of
NA means that the objective gets closer
to the specimen (less working distance)
compared to an objective of lower NA but
with same magnification. Therefore,
choosing the best objective for your application
may not only depend on the resolving
power.
Resolution in digital images ­ is it
important?
The next step is to go from the optical
image to the digital image. What happens
here? The "real" world conversion
from an optical to a digital image works
via the light sensitive elements of the
the range of colour values a pixel can
have, and thus determines a kind of a
brightness or colour resolution. Yet it is
the digital sampling which defines the
spatial resolution in a digital image. Both
spatial and brightness resolutions give
the image the capability to reproduce
fine details that were present in the original
image. The spatial resolution depends
on the number of pixels in the digital
image. At first glance, the following
rule makes sense: the higher the number
of pixels within the same physical dimensions,
the higher becomes the spatial resolution.
See the effect of different numbers
of pixels on the actual specimen
structure in fig. 17. The first image (175
x 175) provides the image information as
reasonably expected, whereas specimen
details will be lost with fewer pixels (44 x
44). With even fewer, the specimen features
are masked and not visible any
more. This effect is called pixel
blocking.
Table 3: The number of pixels a 1/2 inch chip should have to meet the Nyquist criterion (2 pixels per
feature) and the optimum resolution (3 pixels per feature).
Objective Magnification NA Resolution Lp/mm CCD resolution 1/2´´ CCD resolution 1/2´´
Nyquist limit Necessary resolution
2 pixel/lp 3 pixel/lp
PlanApoN 2 0,08 4,19 119 1526 x 1145 2289 x 1717
UPlanSApo 4 0,16 2,10 119 1526 x 1145 2289 x 1717
UPlanSApo 10 0,4 0,84 119 1526 x 1145 2289 x 1717
UPlanSApo 20 0,75 0,45 111 1420 x 1065 2131 x 1598
UPlanSApo 40 0,9 0,37 67 858 x 644 1288 x 966
UPlanSApo 100 1,4 0,24 42 534 x 401 801 x 601
Fig. 14: What is what on an objective?
Olympus:Manufacturer
PlanApo: Plan: Flat field correction; Apo:
Apochromatic;
60x: Linear magnification
1,42 Oil: Numerical Aperture (needs oil immer-
sion)
: Infinity corrected optic (can not be
mixed with finite optics that belongs
to the 160 mm optics)
0.17: Cover slip correction. Needs a cover
slip of 0.17mm thickness.
Note: Take care of this parameter. There can
also be a "0" for no coverslip, a "1"
for 1mm thickness or a range of mm.
Wrong usage of objectives will create
"foggy" images (spherical aberra-
tion).
FN 26.5: Field number 26.5 (When using an
ocular and tube that can provide a FN
of 26.5 you may divide this number
with the magnification to achieve the
diameter in your field of view in mm.
26.5/60 = 0,44 mm).
CCD chips in digital cameras, for example.
Or, a video camera sensor may provide
voltage signals that are read out and
digitised in special frame grabber cards.
But what is of more interest here is the
principle which lies behind the actual realisations.
The optical image is continuous-tone,
i.e. it has continuously varying
areas of shades and colour tones. The
continuous image has to be digitised and
quantified; otherwise it cannot be dealt
with in a computer. To do so, the original
image is first divided into small separate
blocks, usually square shaped, which are
called pixels. Next, each pixel is assigned
a discrete brightness value. The first step
is called digital sampling, the second
pixel quantisation. Both convert the continuous-tone
optical image into a two-dimensional
pixel array: a digital image.
Digital resolution ­ what is it for?
The pixel quantisation of the
image intensities depends
on the bit depth or dynamic
range of the
converting system.
The bit
depth defines
the number of
grey levels or
the resolving power Basics of light Microscopy & iMaging ˇ 15
Is there an optimum digital resolution?
Thus, the number of pixels per optical
image area must not be too small. But
what exactly is the limit? There shouldn't
be any information loss during the conversion
from optical to digital. To guarantee
this, the digital spatial resolution
should be equal or higher than the optical
resolution, i.e. the resolving power of
the microscope. This requirement is formulated
in the Nyquist theorem: The
sampling interval (i.e. the number of pixels)
must be equal to twice the highest
spatial frequency present in the optical
image. To say it in different words: To
capture the smallest degree of detail, two
pixels are collected for each feature. For
high resolution images, the Nyquist criterion
is extended to 3 pixels per feature.
To understand what the Nyquist criterion
states, look at the representations in
fig. 18 and 19. The most critical feature
to reproduce is the ideal periodic pattern
of a pair of black and white lines (lower
figures). With a sampling interval of two
pixels (fig. 18), the digital image (upper
figure) might or might not be able to resolve
the line pair pattern, depending on
the geometric alignment of specimen and
camera. Yet a sampling interval with
three pixels (fig. 19) resolves the line pair
pattern under any given geometric alignment.
The digital image (upper figure) is
always able to display the line pair struc-
ture.
With real specimens, 2 pixels per feature
should be sufficient to resolve most
details. So now, we can answer some of
the questions above. Yes, there is an optimum
spatial digital resolution of two or
three pixels per specimen feature. The
resolution should definitely not be
smaller than this, otherwise information
will be lost.
Calculating an example
A practical example will illustrate which
digital resolution is desirable under which
circumstances. The Nyquist criterion is
expressed in the following equation:
R * M = 2 * pixel size (4)
R is the optical resolution of the objective;
M is the resulting magnification at
the camera sensor. It is calculated by the
objective magnification multiplied by the
magnification of the camera adapter.
Assuming we work with a 10x Plan
Apochromat having a numerical aperture
(NA) = 0.4. The central wavelength
of the illuminating light is  = 550 nm. So
the optical resolution of the objective is R
= 0.61* /NA = 0.839 m. Assuming further
that the camera adapter magnification
is 1x, so the resulting magnification
of objective and camera adaptor is M =
10x. Now, the resolution of the objective
has to be multiplied by a factor of 10 to
calculate the resolution at the camera:
R * M = 0.839 m * 10 = 8.39 m.
Thus, in this setup, we have a minimum
distance of 8.39 m at which the line
pairs can still be resolved. These are 1 /
8.39 = 119 line pairs per millimetre.
The pixel size is the size of the CCD
chip divided by the number of pixels.
A 1/2 inch chip has a size of 6.4 mm *
4.8 mm. So the number of pixels a 1/2
inch chip needs to meet the Nyquist criBox
3:
Multiple Image Alignment (mia)
Multiple image alignment is a software approach
to combine several images into one panorama
view having high resolution at the same time.
Here, the software takes control of the microscope,
camera, motor stage, etc. All parameters
are transferred to the imaging system through a
remote interface. Using this data, the entire microscope
and camera setups can be controlled
and calibrated by the software. After defining the
required image size and resolution, the user can
execute the following steps automatically with a
single mouse click:
1. Calculation of the required number of image
sections and their relative positions
2. Acquisition of the image sections including
stage movement, image acquisition and computing
the optimum overlap
3. Seamless "stitching" of the image sections with
sub-pixel accuracy by intelligent pattern recognition
within the overlap areas.
4. The overlap areas are adjusted automatically
for differences in intensity
5.Visualisation of the full view image.
Fig. 15: Intensity profiles of the Airy disk patterns of one specimen detail and of two details at different
distances.
16 ˇ Basics of light Microscopy & iMaging the resolving power
Box 4: Using hardware to increase the resolution in fluorescence microscopy
Several hardware components are available, to enable the acquisition of images that are not disturbed by out
of focus blur. For example, grid projection, confocal pinhole detection and TIRFM.
Since out of focus parts of a specimen produce blur in an image, there is the simple option of eliminating this
stray light from the image. With most confocal microscopes, a small pinhole is located in front of the sensor
and only those light beams that are originally from the focus area can pass through, others are simply absorbed.The
resulting point image only contains information from the focus area.To create an image of more
then just one point of the focus area, a scanning process is needed.
This scanning process can be performed with the help of spinning disks for an ordinary fluorescence microscope
or by a scanning process with a laser beam in a confocal laser scanning microscope (cLSM) set-up.
Each system produces different levels of improvement to the resolution. However, all of them need a professional
digital sensor system to display the images.
TIRFM (Total Internal Reflection Fluorescent Microscopy) uses
a completely different concept. With this method, a very thin
layer of the specimen (around 200 nm) is used to create the
image.Therefore,TIRFM is ideal to analyse e.g. single molecule
interactions or membrane processes. To achieve this target, a
light beam is directed within a critical angle towards the cover
slip.
Because of the higher refractive index of the cover slip compared
to the specimen, total internal reflection occurs. This
means that almost no direct light enters the specimen ­ but
due to the physics of light a so called evanescent wave travels in the specimen direction. This wave is only
strong enough to excite fluorochromes within the first few hundred nanometres close to the cover slip. The
fluorescent image is restricted to this small depth and cannot be driven into deeper areas of the specimen,
and also does not contain out of focus blur from deeper areas. (More information about TIRF can be found at
www.olympusmicro.com/primer/techniques/fluorescence/tirf/tirfhome.html).
Fig. 16: Airy disk patterns of different size as an example of the
resolving power for low NA (left) and high NA (right) objectives.
Fig. 17: Four representations of the same image, with different numbers
of pixels used. The numbers of pixels is written below each image.
terion with 2 pixels per feature, is 1/(R
* M) * chip size * 2 = 119 line pairs / mm
* 6.4 mm *2 = 1526 pixels in horizontal
direction. If you want 3 pixels per line
pair, the result is 2289 pixels. This calculation
can be followed through for different
kind of objectives. Please check out,
which numbers of pixels we need for a
1/2 inch chip in table 3.
What might be astonishing here is the
fact, that the higher the magnification,
the fewer pixels the chip of a CCD camera
needs! Working with a 100x Plan
Apochromat objective combined with an
1/2 inch chip, we need just 800 x 600 pixels
to resolve digitally even the finest optically
distinguished structure. The
higher number of pixels of about 2300 x
1700 is necessary only at lower magnifications
up to 10.
Which camera to buy?
The resolution of a CCD camera is clearly
one important criterion for its selection.
The resolution should be optimally adjusted
to your main imaging objective.
Optimum resolution depends on the objective
and the microscope magnification
you usually work with. It should have a
minimum number of pixels to not lose
any optically achieved resolution as described
above. But the number of pixels
also should not be much higher, because
the number of pixels is directly correlated
with the image acquisition time.
The gain in resolution is paid for by a
slow acquisition process. The fastest
frame rates of digital cameras working
at high resolution can go up to the 100
milliseconds or even reach the second
range, which can become a practical disadvantage
in daily work. Furthermore,
unnecessary pixels obviously need the
same amount of storage capacity as necessary
pixels. For example, a 24 bit true
colour image consisting of 2289 x 1717
pixels has a file size of almost 12 MB, if
there is no compression method applied.
The slow frame rate and the file size are
just two aspects which demonstrate, that
the handling of high resolution images
becomes increasingly elaborate.
High resolution over a wide field
of view
The xy-resolution desired is one aspect
which makes an image `high quality'. Another
partially contradicting aspect is
that we usually want to see the largest
possible fraction of the sample ­ in best
case the whole object under investigation.
Here, the microscope's field of view
becomes important. The field of view is
given by a number ­ the so called field
number ­ e.g. if the microscope is
equipped for the field number 22 and a
10x magnifying objective is in use, the diagonal
of the field of view (via eyepieces
and tube that supports the given FN) is
22/10 = 2.2 mm. Using lower magnifying
objectives will enable a larger field of
view and using large field tubes and oculars
can enlarge the field number to 26.5
(e.g. field number 26.5 and 4x objective
allows a diagonal of 26.5/4 = 6.624 mm),
but unfortunately low magnifying objecthe
resolving power Basics of light Microscopy & iMaging ˇ 17
tives can not reach the same maximum
NA as high magnifying objectives. Even
when we use the best resolving lens for a
4x objective, the N.A of this Apochromat
(0.16) is still lower then the lowest resolving
20x Achromat with a N.A. of 0.35.
Having a lower NA produces a lower resolution.
In a number of applications, a
field of view of several millimetres and a
resolution on the micrometer or nanometre
scale is required simultaneously
(fig. 20). How can we overcome this problem,
especially when we recognise that
the CCD sensor of the camera reduces
the field of view (monitor image) once
more? Some image processing can offer
an alternative. In the first step, these systems
automatically acquire individual
images at the predefined high resolution.
In the next step the software performs
intelligent pattern recognition together
with a plausibility check on the overlapping
parts of the individual image sections
to align them all in one image with
excellent accuracy (better than a pixel).
The computed result shows one combined
image, maintaining the original
resolution. So you get an image which
Box 5: Changing objectives but keeping the digital live image in focus Parfocal
alignment.
High class objectives are designed to be parfocal.That means even when you change from a 4x magnifying objective
to a 40x objective ­ the structure under observation remains in focus.This is especially a need for imaging
with automated microscopy.To use this feature at the microscope the following short guideline will help:
We assume that the microscope in use is in proper Köhler illumination setting, and the digital camera is connected
via a camera adapter (c-mount) that allows focus alignment.
(Some adapters are designed with a focusing screw; some can be fixed with screws in different distance posi-
tions.)
1. Use a high magnifying objective (40x or more) to get well recognisable detail of a specimen into focus
(camera live image), with the help of the course and fine focus of the microscope frame.
2. Change to a low magnifying objective (e.g. 4x), and do not change the course or fine focus at the microscope,
but, align the focus of the camera adapter until the camera live image shows a clear in focus image.
3. Changing back to high magnification ­ the image is still in focus ­ you do not believe? Have a try.
Fig. 18: Line pair
pattern achieved
with 2 pixels per
line pair. Please
refer to the text
for the descrip-
tion.
Fig. 19: Line pair
pattern resolved
with 3 pixels per
line pair. Please
refer to the text
for the descrip-
tion.
Fig 20: Mr. Guido Lüönd, Rieter AG, Department
Werkstoff-Technik DTTAM, Winterthur, Switzerland,
works on fibres using a microscope. For
their investigations they often have to glue the
single images into an overview image. Previously
this was a considerable challenge. Now a
piece of software takes over his job.
has both high resolution and a large field
of view (fig. 21). Please check box 3 for
the description of the image processing
procedure. Additionally, box 7 describes
its sophisticated and extended follower
called Digital Virtual Microscopy.
Physical limits and methods to
overcome them
As described before, the resolution of a
microscope objective is defined as the
smallest distance between two points on
a specimen that can still be distinguished
as two separate entities. But several limitations
influence the resolution. In the
following we cover influence of image
blurring and resolution depth capacity.
Convolution and deconvolution
Stray light from out of focus areas above
or below the focal plane (e.g. in fluorescence
microscopy) causes glare, distortion
and blurriness within the acquisition
(fig. 22.a). These image artefacts are
known as convolution and they limit
one's ability to assess images quickly, as
well as make more extensive evaluations.
There are several sometimes sophisticated
hardware approaches in use which
allow reducing or even avoiding out of
focus blur at the first place when acquiring
the images. Please see the description
in box 4. A different approach is the
so-called deconvolution which is a recognised
mathematical method for eliminating
these image artefacts after image ac-
guidolüönd
18 ˇ Basics of light Microscopy & iMaging the resolving power
quisition. It is called deconvolution. If the
point spread function (PSF) is known, it
is possible to deconvolute the image. This
means the convolution is mathematically
reversed, resulting in a reconstruction of
the original object. The resulting image
is much sharper, with less noise and at
higher resolution (fig. 22.b).
What exactly is the point spread
function?
The point spread function is the image of
a point source of light from the specimen
projected by the microscope objective
onto the intermediate image plane, i.e.
the point spread function is represented
by the Airy disk pattern (fig. 15, 16).
Mathematically, the point spread function
is the Fourier transform of the optical
transfer function (OTF), which is in
general a measurement of the microscope's
ability to transfer contrast from
the specimen to the intermediate image
plane at a specific resolution. PSF (or
OTF) of an individual objective or a lens
system depends on numerical aperture,
objective design, illumination wavelength,
and the contrast mode (e.g.
brightfield, phase, DIC).
The three-dimensional point spread function
The microscope imaging system spreads
the image of a point source of light from
the specimen not only in two dimensions,
but the point appears widened into a
three-dimensional contour. Thus, more
generally speaking, the PSF of a system
is the three dimensional diffraction pattern
generated by an ideal point source
of light. The three-dimensional shapes of
Fig. 21: The analysis of non-metallic inclusions
according to DIN, ASTM and JIS requires the
processing of areas up to 1000 mm2 while the
sulphide and oxide inclusions to be analysed are
themselves are less than micrometres wide. No
camera is available offering such a large CCD
sensor. The image processing solution stitches
single overlapped images to give one high
resolution image together.
Fig. 22: Via deconvolution artefacts can be computed out of fluorescence images. a) These artefacts
are caused by the stray light from non-focused areas above and below the focus level. These phenomena,
referred to as convolution, result in glare, distortion and blurriness. b) Deconvolution is a recognised
mathematical procedure for eliminating such artefacts. The resulting image displayed is sharper
with less noise and thus at higher resolution. This is also advantageous for more extensive analyses.
a)
b)
the PSF create the so-called out-of-focus
blur, which reduces the resolution and
contrast in images, e.g. in fluorescence
microscopy. This blurring or haze comes
from sections within the specimen which
are outside of the focal plane of the actual
image. So, an image from any focal
plane of the specimen contains blurred
light from points located in that plane
mixed together with blurred light from
points originating in other focal planes
(fig. 23).
What is deconvolution used for?
When the PSF of a system is known, it
can be used to remove the blurring
present in the images. This is what the
so-called deconvolution does: It is an image
processing technique for removing
out-of-focus blur from images. The deconvolution
algorithm works on a stack
of images, which are optical sections
through the specimen and are recorded
along the z-axis of the microscope. The
algorithm calculates the three-dimensional
PSF of the system and reverses the
blurring present in the image. In this respect,
deconvolution attempts to reconstruct
the specimen from the blurred image
(fig. 23).
Depth of focus versus depth of field
Two terms ­ depth of focus and depth of
field ­ are often used to describe the
same optical performance, the amount of
specimen depth structures that can be
seen in focus at the same time. However,
the resolving power Basics of light Microscopy & iMaging ˇ 19
only the term "Depth of Field" should be
used for this feature. As we will point out
later the term "Depth of Focus" is needed
for a different optical feature.
An optical system, such as the eye,
which focuses light, will generally produce
a clear image at a particular distance
from the optical components. In a
camera, the ideal situation is where a
clear image is formed on the chip, and in
the eye it is where a clear image is
formed on the retina. For the eye, this
happens when the length of the eye
matches its optical power, and if a distant
object is in focus when the eye is relaxed.
If there is a difference between
the power and length in such a situation,
then the image that is formed on the retina
will be very slightly out of focus. However,
such a discrepancy may be small
enough that it is not noticed, and thus
there is a small amount of "slop" in the
system such that a range of focus is considered
to be acceptable. This range is
termed the "depth of focus" of the eye.
Looking at it the other way round, the
eye might be precisely in focus for a particular
distance ­ for example an object
one metre away. However, because of the
slop in the system, other objects 90 cm
and 110 cm away may also be seen
clearly. In front of, and behind, the precise
focal distance there is a range where
vision is clear, and this is termed the
"depth of field".
Now look at the physical understanding
of depth of focus in microscopy and
the depth of field, respectively. Depth of
field fi in a microscope is the area in
front of and behind the specimen that
will be in acceptable focus. It can be defined
by the distance from the nearest
object plane in focus to that of the farthest
plane also simultaneously in focus.
This value describes the range of distance
along the optical axis in which the
specimen can move without the image
appearing to lose sharpness. Mathematically
fi is directly proportional to
fi ~ /2*NA2
(5)
fi = depth of field
 = wavelength of light (emission)
NA = numerical aperture
fi obviously depends on the resolution
of the microscope. Large lenses with
short focal length and high magnifications
will have a very short depth of field.
Small lenses with long focal length and
low magnifications will be much better.
Depth of focus fo in a microscope is the
distance above and below the image
plane over which the image appears in
focus. It's the extent of the region around
the image plane in which the image will
appear to be sharp. fo is directly proportional
to
fo ~ M2
/NA (6)
fo = depth of focus
M = magnification
NA = numerical aperture
fo refers to the image space and depends
strongly on the magnification M,
but also on changes in numerical aperture
NA.
As a take home message ­ high resolution
will create relative low depth of
field, high magnifications will create a
higher depth of focus ­ this is also why
the procedure for parfocal alignment will
work.
Parfocality
There is a well-known difficulty in conventional
light microscopy which refers
to the limited depth of focus: If you focus
Fig. 23: Stray light originating from areas above and below the focal plane results in glare, distortion
and blurriness (convolution) especially in fluorescence microscopy and histology. Deconvolution is a
recognised mathematical method for correcting these artefacts. The degree to which an image is distorted
is described by what is known as the point spread function (PSF). Once this is known, it becomes
possible to "deconvolute" the image. This means that the convolution of the image is mathematically
reversed and the original contours of the specimen are reconstructed. The greater the precision with
which the degree of distortion ­ i.e., PSF ­ is known, the better the result. What is this result? A
sharper and noise-free version of the image at higher resolution with enhanced image quality.
Fig. 24: The software extracts the focused areas from the component images of an image series and
reassembles them into one infinitely sharp image. The example shown here is the resulting image
computed automatically using 25 images of a Bembidion tetracolum sample.
20 ˇ Basics of light Microscopy & iMaging the resolving power
an image with one objective, e.g. 4x, it
might be out of focus when you change to
a another magnification, e.g. 40x. The
term parfocality describes the situation
when the structures remain in focus.
Parfocality is a characteristic of objectives.
Please read box 5 how to assure
parfocality with high class objectives.
Automated sharp images
Let us come back to restrictions arising
from the limited depth of field. The better
the lateral resolution, the smaller your
depth of field will be. The problem is in
fact physical, and it cannot be circumvented
by any adjustments to the optical
system. Today's standard light microscopes
allow objects to be viewed with a
maximum magnification of about 1000x.
The depth of field is then reduced to
about 1 m. Only in this area the specimen
is perfectly imaged. This physical
limitation of inadequate depth of field is a
familiar problem in microscope acquisitions.
In the metal-processing industry,
when analysing or evaluating two-dimensional
metallographical objects such as,
e.g., a section sample, a section press is
generally used in order to obtain an exact
orthogonal alignment in relation to the
optical axis of the microscope. The sample
to be analysed can then be acquired
totally focused in a single acquisition.
However, objects which have a distinctly
three-dimensional structure or for
investigations of, e.g., 3-D wear, at
greater magnifications no satisfactory
overview image is obtainable via stereo
or reflected-light microscope. The microscope
can only be focused onto limited
areas of the object. Due to the limited
depth of field, it is actually impossible to
obtain a sharp acquisition of the entire
image field. These physical restrictions
can only be transcended via digital image
analysis. The normally wholly-binding
laws of physics are "side-stepped".
What happens is that an image series is
acquired at varying focus levels. Then
special software algorithms are applied
to all the images of the image series and
distinguish between sharply-focused and
unfocused image segments in each image.
The sharp image segments of the
images are then pieced back together to
form a single totally-focused image of the
entire sample (fig. 24). Furthermore,
measuring height differences and generating
three-dimensional images becomes
feasible (fig. 25). For further detail please
see box 6.
Fig. 25:This image shows how far money can go:
This Singaporean coin detail was captured using a
ColorView digital CCD camera and processed
using the realignment, extended focus and 3-D
imaging software modules. Capture and automatically
align multiple component images into a
high-resolution composite using the MIA module.
Extract the sharpest details within the component
images and reassemble into one single image
having infinite depth of focus with the module
EFI. Finally, create incredibly realistic views using
height and texture information attained through
the perspective functions of the 3D module.
Box 7: Virtual microscopy
Light microscopy is one of the classic imaging
techniques used in medical education and for routine
procedures of pathology, histology, physiology
and embryology. Pathology makes use of microscopes
for diagnostic investigation of tissue
samples to determine abnormal changes. Digitisation
has resulted in significant progress in the
field of microscopy. However, digital technology
up until now has presented some decisive limitations.
One problem is that the field of view of any
camera is limited for any given magnification. It is
usually not possible to have a complete overview
of the tissue specimen with just one image at a
resolution that allows further analysis. Digital virtual
microscopy moves beyond this barrier.
Virtual microscopy is the digital equivalent to conventional
microscopy. Instead of viewing a specimen
through the eyepiece of the microscope and
evaluating it, a virtual image of the entire slide (a
'virtual slide`) with perfect image quality is displayed
on the monitor.The individual system components
(microscope, motor stage, PC, software)
are all optimally inter-coordinated and offer speed,
precision and reliability of use. The Olympus solution
.slide scans the entire slide at the resolution
required. Integrated focus routines make sure the
image is always in sharp focus. The single images
acquired are automatically stitched together into
a large montage (the `virtual slide`). The entire
'virtual slide' can be viewed onscreen. Detail image
segments can be selected and zoomed in or
out, the equivalent to working with an actual
glass slide under the microscope with the same
efficiency. With an internet connection, this procedure
can be done from anywhere in the world.
In addition, users have all the advantages of digital
image processing at their fingertips, including
structured web archiving of images, analysis results
and documentation.
Box 6: Extended Focal Imaging (efi)
A lack of depth of field in microscope images is an old and familiar problem. The microscope's own depth of
field is only capable of focusing a limited height range at the same time.The remaining parts of the image are
then blurry. Electronic image processing points the way out of this dead-end street.
For a motorised microscope equipped with a motorised stage the whole process can be automated. The software
takes control of the microscope, camera, motor stage, etc. All parameters are transferred to the imaging
system through a remote interface. Using these data, the entire microscope and camera set-up can be controlled
and calibrated by the software. After having defined the total number of images, and the maximum and minimum
height of the stage, the user can execute the following steps automatically with a single mouse click.
1. In the first step the user defines the number of images in the focus series. Using a microscope with a motor
stage the user has to define the maximum and the minimum lift of the microscope stage as well as the
total number of individual images he intends to acquire.
2. The defined image series at varying focus levels is acquired.
3. Next the composite image of pixel-by-pixel precision will be generated from these images.This is done by
extracting the respective focused image areas of each separate image and assembling these into a focused
composite image. Most of these solutions take into consideration the typical (due to construction)
shift of the optical axis that occurs when focusing stereoscopic microscopes.
4. The "Extended focal image" with practically limitless depth of field is computed.
5. Now the user is able to generate a height map which permits users to reconstruct three-dimensional
views e.g. to measure height differences.
the resolving power Basics of light Microscopy & iMaging ˇ 21