Zeiss LSM 880 Operating Manual page 671

Pixelsize
A quantity of decisive importance in this connection is the
maximum scanning angle set via the scanning zoom. By
varying the scanning angle, it is possible to directly influence
the edge length of the scanned field in the intermediate
image plane (or object plane), and thus the pixel size (at a
given number of pixels per line). The smaller the scanning
angle, the smaller is the edge length of the scanned field,
and the smaller is the pixel (see the example below).
In this way, the user of a ZEISS confocal LSM can control the
sampling rate (pixel size). For setting the suitable scanning
zoom for correct Nyquist sampling, the pixel size d
object plane is important.
b)
150
100
50
0 50 100 150
Pixels
Correct sampling
Pix
c)
150
100
50
0 50 100 150
Pixels
Undersampling
SignalProcessing
seite 15
For a ZEISS confocal LSM, there is a simple formula, based
on the edge length of the scanned field in the intermedi-
ate image:
seite 19
d =
pix
number of pixels
Number of pixels number of pixels per line
Zoom factor (Z) scanning zoom set in the software
(Example: Zoom factor 2 reduces the edge
length of the scanned field by a factor of 2)
3.92
Z ≥
Magnification objective magnification
number of pixels
obj
System constant
LSM 510, LSM 5 PASCAL
in the
LSM 700
LSM 710 with Axio Observer
seite 19
LSM 710 with Axio Imager
LSM 710 with Axio Examiner
d =
pix
number of pixels
The minimum scanning zoom needed to fullfill the Nyquist
theorem can therefore be calculated as follows:
3.92
Z ≥
number of pixels
NA = numerical aperture of objective
λ
= excitation wavelength
exc
As an example, with the LSM 710 / Axio Observer (sideport),
a 40x objective lens (NA=1.2), a wavelength of 488nm and
512 pixels per scanline, the full resolving power (correct
sampling) is achieved with a scanning zoom of 4.38; the
corresponding pixelsize then is 103.8nm. With lower factors
of the scanning zoom the pixel size itself will be the limiting
factor for resolution (pixel resolution). Higher factors will
cause oversampling. Hence, the zoom factor influences not
only the total magnification but also the resolution proper-
ties of the system.
With the more recent LSM systems from Carl Zeiss, the
number of sampling points can also be influenced by an
increase in the number of pixels per scan line.
(With the LSM 710 and LSM 780 the number of pixels
(X/Y) per image can be freely selected between 4 x 1 and
6144 x 6144).
. .
1.77 n 1.77
em
NA 2
2
0.88 .
2 . n . PH
em +
NA
n- n 2 -NA 2
.
0.51
0.51
em
NA
.
n
em
NA 2
. .
1.77 n
em
NA 2
system constant
. .
zoomfactor magnification
.
0.51
em
NA
. .
NA system constant
. .
magnification
obj exc
8.94 mm
6.36 mm
10.08 mm (rearport)
9.31 mm (sideport)
10.08 mm (rearport)
9.31 mm (tube)
system constant
6.85 mm
. .
zoomfactor magnification
. .
NA system constant
. .
magnification
obj exc
. .
n
1.2
PART 2
exc
NA 2
2
.
exc
NA
0.88 .
exc
2 2
(n- n -NA )
. .
1.77 n
exc
NA 2
obj
.
0.51
exc
NA
obj
21