Search the CONFOCAL archive at
http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
Greetings Carl,
For a nice discussion/short review of factors concerning microscope
objective design and optical resolution you may wish to read the recent
article in the October issue of Biotechniques:
Abramowitz et al. (2002). BioImaging: Basic Principles of Microscope
Objectives. Biotechniques, 33,4,772-781.
The rest of this post is a little long winded...
To discuss the resolution of a point scanning microscope we need to
distinguish between lateral (xy) and axial (xz) resolution. The
optical resolution is dependant on the numerical aperture of the
objective, the wavelength of light being used, any index mismatches in
the system, and for a confocal scan head, the pinhole among other
factors related to the scan head optics. I'll outline some simplified
rules of thumb.
Frequently we can make some assumptions (one being that your
system is perfectly index matched) to easily determine the lateral
resolution of an objective in the context of a confocal scanning
system. The formula below is a simplified calculation Leica provides
to model the performance of objectives on the SP-2 platform:
lateral resolution = 0.4 (wavelength) / numerical
aperture
There are different formulas for calculating lateral
resolution, some more sophisticated than others, but this is the one
Leica outlines in their documentation. Most calculations take the form
of ((some constant)(lambda or wavelength))/2(numerical aperture). The
next thing we need to consider is the sampling frequency, in other
words, even with a diffraction limited spot size if you are only
sampling a couple pixels in a large scan raster area then you can only
resolve so much. According to the Nyquist theorem, the smallest
optically resolvable distance can be mapped without loss of information
if it is scanned with about 2 to 3 raster points. This means your scan
resolution has to be high enough that you have at least 50% pixel
overlap; the amount of pixel overlap is dependant on the spot size
(determined above), the zoom (determines the physical dimensions of the
scanning area) and the scan resolution (determines the number of
sampling points/line and number of lines/scan). Using the information
above, we assume that the 10x (NA=0.4) objective using the 488nm
wavelength has a spot size (lateral optical resolution) of about 488nm
in an ideal system (specimen located beneath at least .17mm of material
of a refractive index of 1.514). The scan field size at zoom =1 is
1500um and the maximal scan resolution is 2048 pixels per line. 2048
pixels * .488um spot size = 999um. Clearly this is an example of a
situation where you are limited by the sampling frequency: 1500um -
999um = 501um. 501um/2048= .245um between pixels, so your effective
spot size is .733um. If you need 2 pixels to resolve one unit, your
lateral resolution is .733 * 2 or 1.5um. For maximal resolution, you
would need to zoom in until (scan resolution) * spotsize (or lateral
optical resolution) = 2 * (scan field size). If your scan field size
is 1500um at 10x * (zoom =1) then the scan field size is 750um at (zoom
= 2) etc... Scan field size also decreases proportionally to an
increase in optical magnification.
Describing axial resolution is a little more hairy and people
still argue about it. The optical axial resolution is limited by the
sampling freqency as above, except in the z-axis. The most widely
accepted formula for estimating axial resolution of an objective in a
confocal system (as far as I am presently aware) predicts the FWHM of a
point confocal microscope in reflected mode for a perfect plane mirror
and is given as 0.45*lambda/(n*(1-cos(alpha)) where n = refractive
index, lambda = wavelength and NA = n*sin(alpha). I believe the
primary reference for this formula is R.Ho, Z. Shao (1991). "Axial
resolution of confocal microscopes revisited," Optik 88, 4, 147-154.
If a system isn't index matched, and most thick-section type biological
specimens for confocal microscopy are not, this estimation will be
significantly better than the real situation. For this reason it is
useful to distinguish between modeling axial resolution and determining
it quantitatively. If the refractive index of the sample can be
approximated, the axial resolution can be determined by imaging
sub-resolution fluorescent spheres in an xz line scan.
The scan step increment remains important. For instance, we can
pretend a 10x objective (NA 0.4) has an axial resolution of around 5um.
So in an axial scan or a 3-D stack of images, your z-galvo step size
has to be 2.5um or less to realize maximum resolution with the 10x.
For the sake of comparison, axial resolution of a 63x oil objective in
an index matched system has been measured at about 350nm using 488nm
light on our confocal.
Some pertinent references include:
Hell et al., (1993). Aberrations in confocal fluorescence microscopy
induced by mismatches in refractive index. Journal of Microscopy,
169,3,391-405.
Booth and Wilson. (2001). Refractive-index-mismatch induced aberrations
in single-photon and two-photon microscopy and the use of aberration
correction. J. Biomed. Opt. 6,3,266-272.
Hiraoka, Y et al. (1990). Determination of three-dimensional imaging
properties of a light microscope system. Biophys. J. 57 325-333.
In a conventional confocal or multiphoton rig, you will not be able to
spatially resolve particles smaller than about 200nm in the lateral and
axial dimensions unless the spacing is pretty far apart. Particles
below the resolution limit will appear as spheres the size of the
diffraction limited spot size, so you will still be able to detect
them, you just will not be able to resolve individual particles from
groups of particles.
Workers are developing clever means to break the resolution limit of
confocal and multiphoton microscopes. The smallest excitation spot
volume I am aware of was a sperical spot of 90-110 nm (.67 attoliters):
Klar et al., (2000). Fluorescence microscopy with diffraction
resolution barrier broken by stimulated emission. PNAS,
97,15,8206-8210. There are also the near-field techniques to consider
such as NSOM, and total internal reflectance/evanescent wave
stimulation for thin films.
On Monday, Dec 2, 2002, at 11:21 US/Central, Carl Boswell wrote:
> Search the CONFOCAL archive at
> http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
>
> Hi Andrea,
> This discussion is something I've not found a definitive answer for
> yet.
>> From Inoué, S. (1986) Video Microscopy. Plenum Press, New York,
>> p.114, the
> lateral resolution is calculated using x=(1.22 lamda)/2NA. If your
> numbers
> are plugged into this, it yields 225nm. I'm particularly concerned
> about
> this because I have a web page on this topic
> http://www.mcb.arizona.edu/IPC/zoom_Page.htm, and I'm still not
> comfortable
> with what users might take as the gospel. Another burning question is
> z-resolution, and how the pinhole size effects this, if at all.
> Finally,
> why is there uncertanty about how to determine these values?
> Regards,
> Carl
>
> Carl A. Boswell
> Dept. of Mol. Cell. Biology
> Univ. of Arizona
> (520) 626-8469
> [log in to unmask]
>
> ----- Original Message -----
> From: "andrea manazza" <[log in to unmask]>
> To: <[log in to unmask]>
> Sent: Monday, December 02, 2002 8:39 AM
> Subject: Re: confocal resolution
>
>
> Search the CONFOCAL archive at
> http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
>
> Dear Kathy,
> the maximum resolution for optic microscopy should be 200 nm, according
> to standard physics laws: that means that any higher resolution will
> give you no more information on the sample.
> As for useful formulas:
> - the Nyquist theorem for lateral resolution should be similar to
> X= 0,4*lambda/NA, where NA is numerical aperture of your objective and
> lambda the wavelength. It means that, if you’re working with 63x
> objective and 1,32 as NA, at 488nm, the lateral resolution is 148nm;
> dividing this number by 3, you obtain almost 49 nm. 49 is the raster
> distance you should set in your scan, in order to avoid loss of info
> from the specimen —> it does NOT mean that you will obtain resolution
> higher than 200nm, but only that you’ll obtain good data by scanning
> thrice the 148nm distance obtained before; in order to modify the
> raster distance you should change the electronic zoom and the scan
> format.
> At least, this is what I've found; if anyone else has nice data, I'll
> be interested as you in reading more :)
> Thank you and have a nice time.
> AM
>
>
>
>
> dott. Andrea Manazza
> Dipartimento di Oncologia, Università di Torino
> CeRMS, ospedale Molinette
> Via Santena, 7 - 10126 Torino, Italia
> tel: +39-11-6706522
> lab: +39-11-6336859
> fax: +39-11-6336887
>
> ----- Original Message -----
> From: Kathy Spencer <[log in to unmask]>
> Date: Wednesday, November 27, 2002 9:32 pm
> Subject: confocal resolution
>
>> Search the CONFOCAL archive at
>> http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
>>
>> Hello All!
>> Basic generic question....what is the limit of resolution
>> on a
>> confocal? I'm using an Olympus Fluoview confocal, 60x 1.4NA
>> objective, oil
>> (1.516), pinhole automatically set for 1 Airy disk. For 488nm
>> laser, I
>> calculate 174nm using resolution=wavelength/2NA. But can the confocal
>> resolve more than that? What is a good formula?
>> Thanks!
>> Kathy
>>
>>
>>
>>
>>
>>
>>
>>
>> Kathy Spencer
>> The Scripps Research Institute
>> 10550 N. Torrey Pines Road
>> ICND 202
>> La Jolla, CA 92037
>> 858-784-8437
>>
>
|
