Transcript Optics in Confocal Microscopy

Optics in Confocal
Microscopy
What is a confocal
microscope?
A confocal microscope is one in
which the illumination and detection
are confined to the same diffractionlimited volume in the specimen. A
fully confocal system uses a perfect
lens to form a single illuminated
spot and this spot is focussed on an
infinitely small detector aperture.
After Minsky, 1957
What is the correct
aperture size in a real
confocal microscope?
Short answer: It should be not more than the Airy disk diameter.
Real answer:
To form an image, the detector aperture cannot
be infinitely small. It has to be opened up until
the signal strength (after averaging, if necessary)
is high enough to see the required detail.
So what is an Airy disc?
The image of a single point in the specimen has a characteristic pattern
at the level of the aperture: a bright central spot with bright rings around
it. The central part of this pattern is called the Airy disk.
How big is this
Airy disc then?
The size of the Airy disk is determined by the wavelength of the light, the
numerical aperture of the objective lens and the magnification of the
image at the level of the aperture.
Optical experts use so-called ‘optical units’ when discussing the size of an
Airy disk. The radius of an Airy disk (measuring to the darkest part of the
surrounding ring) is 3.833 optical units. One expert (H.T.M. van der Voort)
has proved theoretically that the aperture radius should be 2 units or less
for near-ideal confocal resolution, but that a radius of 4 units gives the
best compromise between resolution and signal strength for point objects.
A practical approach...
The aperture diameter should be about the same as the Airy disk
diameter under practical conditions, but it should be possible to close it
a little further to get better axial resolution if the signal strength is high
enough. When the object is not a point, but has vertical extent, it is
useful to be able to open up the detector aperture much more.
• Variable apertures are important
• Its better to set it too big than too small
• Often, the fluorescence signal determines the ‘correct’ size
Optimum aperture
sizes in MRC and
MicroRadiance systems
Aperture size (mm)
Objective
MRC
Radiance
10x
40x
60x
100x
0.88
1.25
1.63
2.75
0.92
1.32
1.72
2.90
NA 0.45
NA 1.3
NA 1.4
NA 1.4
Why does Bio-Rad use
a variable iris as the
detector aperture?
Short answers:
1. It allows you to increase the signal strength and get an
image, even when the specimen is too dim to provide a
high enough signal-to-noise ratio for ‘true’ confocal
imaging.
2. It’s a Bio-Rad patent (John White, 1985).
How does the optical
design of the MicroRadiance
compare with the MRC series?
The main difference is the way that the extra magnification at the
aperture is obtained.
In the MRC 500-1024 series it was achieved by having a very long light
path (1.7 metres) from the eyepiece to the aperture, folded inside the
casing of the instrument by means of mirrors.
In the MicroRadiance it is done by placing a telescope between the
eyepiece and the aperture. This telescope, which contains highthroughput achromatic lenses, produces an enlarged image of the
specimen at the level of the iris.
Optical schematics
Why were the MRC 500-1024
series referred to as an
‘infinity optics’ design?
Although often referred to as ‘infinity optics’ this design probably did not
use infinite foci ( i.e. parallel beams). It probably owed its high
performance to the fact that when the image was focussed on the iris (by
a very small adjustment in the focus of the microscope), the iris was then
at a conjugate focus with the beam waist in the laser, which was not
situated at infinity.
The microRadiance is an improved design, in the sense that the focal
positions are under greater control: even the slight variations in beam
waist positions between single-mode optical fibres are compensated for
when the telescope is adjusted during manufacture.
Does a confocal
microscope have better
resolution than a
conventional one?
Short answer:
Yes, it is improved by 40%. However, the big
advantage of a confocal epifluorescence
microscope is not improved resolution, but
the improved contrast due to the elimination
of out-of-focus glare.
What do we mean by
‘resolution’ then?
By far the best-known definition is the Rayleigh criterion. Two points are said to be resolved
if their Airy disks interpenetrate in such a way that the first minimum of one overlaps the
peak of the other (i.e. they are 3.83 optical units apart). This is a rather pessimistic
definition; in fact it is still possible to tell that a point is double by eye when closer than this.
Another definition is the Sparrow criterion, which is the point at which the sum of the two
patterns becomes flat between the two peaks.
Yet another, commonly used, is the FWHM: the resolution is simply the width of the Airy disk
at half its maximum height (this is coincidentally about the same as the radius of the first
minimum).
Which criterion you use makes a big difference to the assessment of optical systems.
Confocal optics do not improve Rayleigh resolution at all, but do improve the Sparrow and
FWHM resolution.
What is a point spread
function?
If an infinitely small object, a geometrical point, is imaged by a
microscope, the image consists of an Airy pattern. If the microscope is
focussed through such an object, the image seems to exist in threedimensions around the original point. The apparent three-dimensional
image of a point is called the ‘point spread function’.
The horizontal section of the PSF for an ideal lens is the Airy pattern.
The axial section is invariably stretched out more than the Airy disk
radius, to an extent that depends on the numerical aperture of the
objective lens. The ratio, always more than 1, is 3.28n / NA, where n is
the refractive index of the medium around the object and NA = numerical
aperture of the objective lens.
What is meant by
numerical aperture?
The numerical aperture of an objective lens is the refractive index of
the medium times the sine of the semi-angle of the included cone.
The latter means the angle to the optical axis of the extreme rays,
those which only just get into the lens.
The expression is normally written:
NA = n sin
The NA of a lens is a measure of both its light collecting and
resolving capabilities.
The relationship between
NA and resolution
For lenses in air NA = 1 / 2F, where F = the F number of the lens.
(i.e. an objective of NA 0.5 has an F number of one).
Ernst Abbe introduced this term because he realised that it is
proportional to the (lateral) resolving power of the lens, according to
the famous equation r = 0.61 / NA, where r = Rayleigh resolution
and  = vacuum wavelength of the light. Experts now dispute this,
for very high numerical apertures, but still do not agree on the
details.
How are the lateral and
axial resolutions
changed by confocal operation?
One way to think about this is to imagine the two stages of confocal
operation as distinct events. The probability of illumination (i.e. of the
arrival of a photon at a particular point in space) is proportional to the
intensity of the point spread function at that point.
The probability of detection (assuming ideal confocal performance) is
also proportional to the point spread function intensity, since this
corresponds to the PSF of the detector aperture projected back into
object space. The resolution (neglecting any effects such a change in
wavelength between illumination and emission) is determined by the
product of the two probabilities, which is the square of the intensity of
the PSF.
What is the effect of
squaring the PSF?
The position of the minima does not change, so the resolution, according
to the strict Rayleigh definition, does not improve. However, the FWHM
improves by a factor of 1.4 (Brakenhoff, 1979). So, the lateral resolution
becomes:
r FWHM = 0.44  / NA
confocal
(1)
r FWHM = 0.61 / NA
conventional
(2)
compared with:
For axial resolution
the corresponding
equations are:
z FWHM = 2  / n (sin 2)
= 2  / n (sin 2sin-1(NA/n) )
(Brakenhoff et al. 1989) (3)
At 488nm, using an oil immersion objective (n=1.515) of N.A. 1.4, the
values for equations (1) , (2) and (3) are 0.15, 0.21 and 0.76 mm.
The plane spread function!
If the microscope is imaging a plane surface (e.g. in reflection) the PSF
may not be the most appropriate measure of the lens performance. A
plane spread function, different from the point spread function, may be
defined as the apparent structure of an ideal planar specimen. Xiao
and Kino give an equation (without derivation) for the FWHM resolution
in reflection imaging as follows:
zref = 0.45  / n (1 - cos)
= 0.45  / n (1- cos (sin-1(NA/n))
This gives a result of 0.23 mm, best measured values being in the
region of 0.35 to 0.4 mm.
Resolution vs. NA
PSF in conventional
and confocal
This shows the computed intensity
pattern for the point spread function
in a conventional microscope (a)
and a confocal microscope (b). The
section is taken along the optical
axis. Distance along the colour
scale (centre) is proportional to the
log of the intensity: this is done in
order to emphasise the low end of
the range. The scale represents 5
lateral optical units.
(From Sandison, Piston, Williams &
Webb, 1995).
How do the wrong mounting
medium, wrong coverslip
and focussing too deep
ruin the image?
Optical performance with
the correct thickness coverslip
The diagram below shows a 20x objective
according to a design given in Zemax, an
optical design software package.
To the right we see the calculated appearance
of the focussed spot at intervals of 50 microns
along the axis, with, below, the intensity
pattern corresponding to the Airy disk at the
focus.
Optical performance with
the wrong thickness coverslip
If the thickness of the coverslip placed
between the lens and the focus is greatly
increased:
The effects are shown in the diagrams to the
right: Top, the focal position has shifted to the
right, and the through-focus series has
become highly asymmetrical, showing that
spherical aberration has been introduced.
Also, the intensity pattern has been
badly messed-up, with many new
peaks or rings appearing.
Refractive Index
mismatch
Using the Zebase software, we can also do another experiment, that of placing a thick water
layer under the coverslip, so that the objective has to focus through a considerable distance
of water. The effect of this on the through-focus series is just as bad.
We have seen how the PSF of an objective lens can be spread and distorted by having the
wrong coverslip thickness or by focussing through a large depth of water. In both cases the
focussed spot expands asymmetrically on either side of focus, indicating spherical
aberration.
Why are they called
‘spherical’ aberrations?
In lens optics, a plane is regarded as a special case of a spherical surface, with
infinite radius. The rays passing from a single point through a planar boundary
into a medium of different refractive index are bent at the interface in such a
way that , when traced back, they no longer intersect in a single point. It is
possible to correct for this by incorporating special spherical surfaces into a
lens system, but this only works for one particular position of the object and the
boundary and for one refractive index.
How can you avoid
spherical aberration
problems?
Start by considering the specimen. If the specimen can be examined dry,
use an objective designed for use without a coverglass. These are often
marked ‘NCG’ or ‘0’ in place of the usual ‘0.17’, which is the coverslip
thickness in millimetres. If the specimen must be examined under fluid,
there are several possibilities:
Homogeneous immersion
with no coverglass
So-called dipping objectives are available, designed for use in
direct contact with physiological salines or even sea water. These
are good for looking at whole animals under saline, but the N.A. is
usually low, so they are usually not considered ‘good’ for confocal
purposes.
Dry lenses with
a coverslip
Those with the highest available N.A. should be used (e.g. for a 10x
objective, an N.A. of 0.45 is desirable, but expensive). Especially for the
highest powers, the correct thickness of coverslip must be used. Coverslips
of number 1 1/2 are often nearly correct, but should be checked with a
micrometer. They are often thicker at one side than another. For 40x dry
lenses, an error of 10 m in coverslip thickness from the standard 0.17 mm
gives an appreciable deterioration in PSF.
Some objectives have correction collars, sometimes for coverslips from zero
to 2 mm. They are designed for looking into glass culture dishes through the
base. Unfortunately the N.A. is usually too low for confocal use. Looking
into a medium of higher index (n) than air introduces an axial distortion of
approximately n-fold compression, which can be compensated for by
entering the refractive index into the Bio-Rad software.
Oil immersion with
a coverslip
These objectives are the ones most often used for high-resolution confocal work. They
have several problems, however. If used with live cells under the coverslip in an aqueous
(i.e. low refractive index) medium such as a physiological saline, the PSF deteriorates
markedly with distance through the aqueous layer.
Beyond 50 mm, the image is poorly resolved and the brightness falls, making quantitation
of fluorescence difficult. Also, the distance through which the focus has to be shifted is
greater than the true height within the specimen, roughly in the ratio noil / nwater, so the zaxis of image datasets has to be compressed. Again, these corrections can be achieved
by entering the medium refractive index and objective type into the Bio-Rad software.
Another important point is that the working distance (i.e. the oil-filled space between the
front of the objective and the coverslip) of immersion objectives varies greatly from one
manufacturer to another. It is essential for researchers to consider this, especially if they
are planning to do deep imaging in whole mounts of embryos, for example. Nikon have the
longest available W.D. for a 60 x N.A. 1.4 lens.
Sample mounting
considerations
The problems of poor PSF, low brightness, distortion of z axis and limited
working distance can all be alleviated if thin preparations can be placed in
close contact with the coverslip: much better images can be obtained from
cells grown on the coverslip than for the same cells grown in multiwell slides,
covered with medium with a coverslip on top. If the cells can be fixed and
permeated with a medium of high refractive index, the PSF remains good at
considerable depth.
Fluoromount (BDH/Gurr) is a suitable low-fluorescence resin mountant, but
prone to large shrinkage as the solvent (xylene) evaporates. Methyl or
Benzoyl salicylate or immersion oils are often used also. Surprisingly, the
coverslip thickness still matters, possibly because neither the refractive index
nor the dispersion of standard coverslip glass matches the corresponding
value for standard immersion oil.
Multi-immersion
objectives
These are available from the main manufacturers in intermediate
magnifications, e.g. 25x, 40x. Often the N.A. is rather low, but new
designs are certainly worth trying for confocal purposes. Water,
glycerol and oil may all be usable with the same objective. There is
invariably a correction collar. If the focus is poor, the collar should
be adjusted and the specimen refocussed, the process being
repeated until an optimum is found. These objectives are invaluable
for low power reflection imaging (reduced reflection off the
coverglass).
Water/ coverglass/ water
objectives of high NA
These objectives are available with N.A. 1.2 from the major
manufacturers, at a cost of approximately 7K sterling. They are truly
remarkable in their ability to preserve the PSF even when focussing
through as much as 200 mm of water. They have become established
as the lenses of choice for use with whole mounts of living tissue, brain
slices, embryos, plant roots etc. However, they should not be
recommended to customers who study only thin monolayers of cells:
there is no significant improvement over the 4 times-cheaper oil
immersion objectives for specimens like this.
Chromatic aberration
When white light is brought to a focus by a simple single-element lens, such as a
magnifying glass, the blue component is refracted more by the glass and comes to
a focus closer to the lens than the red. This separation of colours along the axis is
called longitudinal chromatic aberration. An image of an object illuminated with
white light may also show a chromatic difference in magnification or 'lateral colour'.
This aberration gets worse further from the centre of the image. In a confocal
microscope, chromatic aberration is a disaster. It has two obvious effects:
Firstly, the laser light (e.g. blue) is focussed to a certain off-axis point, but the
detector (sensitive to green or red) looks at a position shifted from the illumination
by an amount that increases with distance from the centre of the image. So, lateral
colour makes the signal strength fall with distance from the centre of the field. The
way to test for this is to examine fluorescent beads distributed all over the field.
Unlike the effect of curvature of focus, the lateral colour effect is much the same at
all positions of focus. Lateral colour can also cause a radial mismatch between the
scanned transmission image and the fluorescence image.
Continued...
Chromatic aberration cont’d.
Secondly, an object which emits over a wide range of fluorescence colours
will, in the presence of longitudinal chromatic aberration, appear as a smeared
or multiple image at a range of depths. The test for this is to image beads
which fluoresce both red and green (available from Polysciences at 1 mm and
2 mm diameter. If you make a z-section through these beads, even the best
objective lenses are likely to show image duplication. In the merged image of
red and green emission channels, the upper part of each bead is likely to be
coloured differently from the lower.
This is quite a problem for researchers who wish to test the colocalisation of,
say, a red and a green-emitting fluorochrome. The aberration may, at a
particular focal level, give a false single positive result for a small object which
is, in reality, doubly positive (i.e. stained with both stains).
What can be done about
chromatic aberration in
confocal imaging?
Use the right type of lens:
Severe chromatic effects may be due to the use of the wrong type of
objective. Do not use old-style non-compensated objectives such as the
Olympus S-Plan series: the Bio-Rad scan head is designed for modern
objectives which give an achromatic intermediate image. The S-Plans
were designed to be used with an equal and opposite chromatic aberration
in the eyepiece to cancel their own.
Collect a 3D data set:
Researchers who are doing colocalisation experiments involving small
intracellular particles, bacteria etc. should test for aberration by collecting
complete 3D datasets. It should then be easy to establish whether apparent
single positives are real or simply a focus artefact.
Set UV correction lens:
Strong chromatic aberration is invariably present in objectives over the range
from ultra-violet to visible. The Bio-Rad UV confocal apparatus contains lenses
designed to counteract this effect. The range of objectives that can be used is
strictly limited.
Use a reflecting objective lens?
Reflecting objectives of the Schwartzchild type (a combination of a convex mirror and a
catadioptric concave mirror (i.e. one with a hole in it) have been suggested as a cure for
chromatic problems. They have the additional appeal that spherical aberration can be
compensated by adjustment of the mirror separation. However, the PSF is badly
disturbed by the central occlusion and they are useless for all high-resolution work.
Buy a 2-photon system!
2-photon imaging with non-confocal detection provides a cure. Here, it does not
matter if the lens is strongly chromatically aberrant, because the resolution is
determined entirely by the (monochromatic) illumination and the emission is collected
but not focussed into an aperture. This will probably become the method of choice for
colocalisation studies in the future. However, this will demand the use of
fluorochromes that can be separated completely by emission windowing alone: FITC
and TRITC will not do!
How do multiphoton
optics differ
from confocal?
In any laser scanning microscope the beam is focused into a cone where the intensity of
illumination above or below the focal plane is proportional to the square of the distance
from focus and absorption is directly proportional to intensity. However, in the 2-photon
case, because of the need for two photons to arrive in a short time interval, absorption is
proportional to the square of the intensity and falls off very rapidly away from the focus
(according to an inverse fourth-power rule).
The fall-off is even more rapid with 3-photon and higher order processes. Analysis
(Williams et al.) yields the perhaps unexpected result that, provided the illuminated volume
is uniformly filled with fluorophores, the total fluorescent emission signal strength is
independent of the numerical aperture of the objective lens. Unlike confocal microscopy,
multiphoton imaging is quite effective with low-magnification lenses of moderate numerical
aperture, provided wide-angle detection is used.
Resolution in
multi-photon - theory
The resolution in a 2-photon microscope is determined entirely by the restriction of excitation
mentioned above. Williams et al (1994) show that the lateral resolution is given by:
rlat = 0.37/ n sin
and the axial by:
rax = 0.32/ n sin2 /2
where  is the exciting wavelength and n sin  is the numerical aperture of the objective lens.
These expressions suggest approximately twice better resolution than a conventional
microscope, but this is counterbalanced by the need to use a twice-longer wavelength.
Resolution in
multi-photon - practice
In practice, the resolution in 2-photon micrographs looks similar to that of conventional epifluorescence, or very slightly inferior if a 1047nm wavelength is used. A combination of
multiphoton excitation and confocal detection is often suggested as a means of improving
resolution, but this is seldom used, because of the loss of signal observed when the confocal
aperture is inserted. The failure of this combination is interesting; it is probably due to
scattering of the emitted light in the specimen or chromatic aberration.
In the Bio-Rad multiphoton system conventional objectives are used; their transmission in
the infra-red is quite good. The reflectors in the scan head are designed to reflect both IR
and visible light (and, sometimes, near UV as well). Special apparatus is used to pick off the
light coming from the specimen before it enters the scan head, and so achieve nondescanned detection. This increases detection efficiency by at least a factor of three and
usually much more (greater for scattering specimens).
References
Amos,W.B. (1995) A note on optical units. Appendix I, pp 579-580. in Handbook of Biological Confocal
Microscopy. J.B.Pawley, ed. IInd Edn. Plenum Press. New York.
Denk, W., Strickler,J.H. & Webb,W.W. (1990) Two-photon laser scanning fluorescence microscopy.
Science 248, 73-76.
Kapitza, H. G. (1986) Oral presentation at Seventh Congress of the International Society for Analytical
Cytology, Cambridge UK.
van der Voort,H.T.M. & Brakenhoff,G.J. (1990) Three dimensional image formation in high-aperture
fluorescence confocal microscopy: a numerical analysis. J. Microscopy
Minsky,M. (1957) U.S.Patent 3013467. Microscopy Apparatus.
Sandison,D. R. Piston, D.W. , Williams, R.M. & Webb, W.W. (1995) Quantitative comparison of
background rejection, signal-to-noise ratio and resolution in confocal and full-field laser scanning
microscopes. Applied Optics 34, 3576-3588.
Visser, T.D., Oud,J.L. & Brakenhoff,G.J. (1992) Refractive index and axial distance measurements in 3D microscopy. Optik. 90, 17-19.
White, J.G. (1985) UK Patent Application 2 184 321 A Confocal Scanning Microscope.
Xiao,G.Q. and Kino,G.S. (1987) A real-time confocal scanning optical microscope. Proc. SPIE 809 ,
Scanning Image Technology. T.Wilson and L. Balk. eds. pp107-113.
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