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James Pawley on
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Re: Objective for confocal
Hi all,
Let's start by saying that I am all in favor of people constantly
monitoring the performance of their confocal microscopes (particularly
z-resolution and photon collection efficiency)...
Yes, strictly speaking, the size of the focus spot is
affected only by the NA and the wavelength (not the
objective lens magnification). While in single-beam confocal, the
magnification is controlled by the size of the scanned raster, in
disk-scanning of normal widefield, it is controlled by the objective
magnification. I won't talk much about disk-scanning/wiidefield today
except to note that when judging "image brightness" using
data obtained from a CCD, one must be fair and always correct for the
effective area of each CCD pixel, referred to the image plane: a pixel
that covers more area on a bright part of the specimen can be expected
to collect more light... This will happen if one uses an objective of
lower magnification unless one compensates by changing the
magnification of the phototube.
In addition, it is also true that the maximum NA that one
can use effectively varies with the refractive index
(RI) of the medium in which the specimen is suspended (or, if the
specimen is a transparent solid, the average RI of the specimen
itself): NA<1.2 for water specimens, NA<1.25 for glycerol
specimens and NA<1.49 for oil-embedded specimens. Using a NA 1.4
oil lens on a watery specimen will only be advantageous if one
confines ones interest to that part of the specimen which is within a
micron or two of the coverslip surface and even then, rays at angles
greater than about NA 1.3 will not contribute to the image because
they totally reflect at the water/glass interface.
To use any objective designed to work with one immersion medium
on a specimen having a different RI will produce spherical aberration:
a circumstance that will not only make the image blurry but will also
make the peak brightness of the image of any point object appear less
intense. In actual fact, the match between specimen RI and lens-design
RI is almost never perfect and this is why having a TIRF objective
with a correction collar is a great advantage (but only for
oil-embedded specimens or those within a micron or two of the
coverglass surface.) This RI-mismatch problem is MUCH more severe at
high NA, particularly for high-NA "dry" objectives (which as
a result, often have correction collars.)
However there are other important factors related to NA and
resolution that have not yet been discussed.
When one considers a laser confocal (single-beam or
disk-scanner), the most important of these is the matter of whether or
not the laser beam "fills" the back-focal plane (BFP) of a
particular objective lens. If you look at a 100x NA 1.4 and a 63x NA
1.4 from the back side, you will see that the diameter of the glass in
the latter is larger. That of a 40x NA 1.3 is larger
still.
A simple way to understand why this should be so is to imagine
that these are "simple" lenses (thin, one-element lenses).
In a thin lens, all the "focusing action" is thought of as
taking place at the principle plane in the middle of this thin lens.
In particular, that any light emerging from a point in the focal plane
on one side of the lens will leave the other side of the lens as a
parallel ray-bundle. If the point is on the optical axis, the emerging
parallel ray bundle will be parallel with this axis.
In round figures, the focal length of the 100x objective will be
about 2 mm and that of the 63x about 3 mm. Because they have the same
NA, they will both accept the same cone of light from a point on the
specimen. However, because of the different focal lengths, the high-NA
rays from the 63x will be ~50% farther from the axis when they reach
the principle plane than those from the 100x. Consequently, the part
of the back-focal plane that is used will have a larger diameter. If
one is to use this lens at its rated NA, the ray bundle in the BFP
must be at least this big.
Now imagine the light from the laser going in the opposite
direction. Clearly the bundle of light from the laser has some
diameter as it reaches the BFP of the objective. This diameter will
depend on the specifics of the beam expander used to convert the light
from the fiber into a ~parallel ray bundle. It is obvious that
if the diameter is large enough to "fill" the BFP of the
63x, then it will overfill that of the 100x (i.e., more than half of
the light will strike the metal around the edge of the glass elements
and so not progress to the specimen. It may be worse than this because
the obstructed light may reflect off components of the optical system
and end up being mistakenly collected as signal.) Although it is
possible to change the parameters of the beam expander in the confocal
scanner to compensate for this change, this is seldom done as it
requires fabricating a diffraction-limited zoom lens.
Consequently, each confocal is characterized by providing a ray
bundle or a certain size at the estimated location of the objective
BFP (An axial location, by the way, that depends on the objective lens
focal length. In the example above, the 63x BFP would be 6 mm from the
focus plane, that of the 100x, 4mm). If the ray bundle is large enough
to fill only the 100x, only this lens will operate at its rated NA
"on the way down" (Light coming back from the specimen will
be accepted by any lens to the full angle of its rated NA.). As a
result, it will produce a smaller spot in the specimen (because the
63x is NOT being operated at its rated NA) that is also has a higher
peak brightness (because it is smaller).
On the other hand, if the ray bundle is big enough to fill the
63x, both the 100x and the 63X will produce a spot of the same size
but much of the power in the laser beam will be strike the metal of
the 100x and consequently the not hit the specimen, making the image
will appear dimmer with the 100x.
So far so good. The bad part is that "the ray bundle"
from the beam expander doesn't actually have a constant brightness
from the center to its edge, and then go to zero. In general, its
intensity varies with distance from the axis in a Gaussian manner. In
other words it doesn't have "a diameter" but its intensity
always drops off away from the axis. The designer can decide how large
to make this Gaussian beam. He/she could design it so that only the
central 10% (in area) goes through the usable part of the 100x BFP (or
the central ~20% goes through the usable part of the 63x BFP). By
using only the central part of the Gaussian distribution in this way,
the intensity will be almost constant across the BFP and this means
that the spot really will be an Airy disk, not the somewhat larger
Gaussian spot that one gets when the BFP is filled by a Gaussian.
However, this will also mean that, 90% of the laser light is being
wasted. As lasers usually put out much more light (5-15 mW) than
one wants to expose a specimen to (1-20 microwatts), this only a
serious loss if one wishes to use the beam for intentional bleaching
or uncaging etc. Still, this is a strategy that few confocal
manufacturers pursue.
It is more common for the designer to set up the optics so that
about 80% of the light will sort-of fill the BFP of a 63x 1.4
(and that therefore a 40x NA 1.3 will be be severely under-filled). If
this is so, then the 100x will be filled with almost constant
intensity and will show slightly better resolution (assuming no
spherical aberration etc.) than the 63x because the latter will
produce an almost-Gaussian spot with a slightly larger
"full-width at half maximum". However, you would have to
look hard to see this change in resolution because, it is a small
change to start with (~10%) and in addition, the NA of the
signal-collection path will be the same on both systems. With a small
pinhole, the measured x-y-z resolution depends on both the
illumination and collection light paths. (i.e., If you want to see
this effect, image a planar array of fluorescent beads and use a large
pinhole size. Don't forget that the pinhole diameter should still be
~50% larger with the 100x.)
All this makes it hard to evaluate the optical performance of any
objective if you don't know the ray bundle diameter at the objective
BFP. The best way to measure this directly is to set up Kohler
illumination using an NA 1.4 oil-immersion condenser (and don't
forget to oil the condenser and use an oiled specimen!). Stop the
scanning beam near to the axis and hold a white card so that you
can see the shape of the light bundle that emerges from the condenser
on the side away from the specimen. You should see a circle of light
that has a sharp edge corresponding to the edge of the aperture
diaphragm. Open this diaphragm until the sharp edge is no longer
illuminated and then note the NA setting of the condenser. That is the
NA to which your objective was illuminated.
If you don't have an oil condenser (most inverted scopes don't),
you can make an approximate measurement using a low-mag dry lens with
an a NA that is high for its mag (say a 10x NA 0.45 or NA. 0.5) but is
still lower than that of the condenser mounted on your scope. Don't
forget to set up Kohler illumination. The active diameter of the BFP
of a 10x NA 0.45 will be about 2x larger than that of a 60x NA 1.4.
(The focal length is about 6x longer but the NA is ~3x smaller.)
However, as the BFP will occur at a plane that is optically about 40
mm from the specimen (rather than 6 mm for the 63x), it may not give a
totally accurate estimate of the size of the ray bundle for the higher
mag lens.
And then there is the matter of whether or not high-NA objectives
are actually diffraction limited. In Chapter 11 of the Handbook,
Rimas Juskaitis actually measures this and reports that he has yet to
test an objective in which diffraction-limited performance extended
beyond NA 1.35. In addition, although imaging performance was
often close to diffraction-limited on the axis, it became much worse
towards the edges of the field of view, especially on lower mag lenses
of a given NA. Although this work was done about 5 years ago and newer
lenses may be better, I think that it is unwise to assume that an
objective will produce optical performance that is limited only by the
NA engraved on the lens barrel.
I hope that this helps explain some of the inconsistencies that
are bound to crop up in measurements of this type, particularly if one
doesn't know what is happening at the objective BFP.
Good luck,
Jim P.
--
**********************************************
Prof. James B.
Pawley,
Ph. 608-263-3147
Room 223, Zoology Research
Building,
FAX 608-265-5315
1117 Johnson Ave., Madison, WI, 53706
[hidden email]
3D Microscopy of Living Cells Course, June 14-26, 2008, UBC,
Vancouver Canada
Info:
http://www.3dcourse.ubc.ca/
Applications due by March 15,
2008
"If it ain't
diffraction, it must be statistics." Anon.