Thus, equations (2) and (3) for the widths of the axial and
lateral half-intensity areas are transformed into:
14
1
For rough estimates, the expression
λ
≈
√λ
em
·
λ
exc
suffices.
Wave-opticalconfocality
If the pinhole is closed down to a diameter of <0.25 AU (vir-
tually “infinitely small”), the character of the image changes.
Additional diffraction effects at the pinhole have to be taken
into account, and PSFdet (optical slice thickness) shrinks
to the order of magnitude of PSF
ill
(Z resolution) (see also
figure 7c).
In order to achieve simple formulae for the range of smallest
pinhole diameters, it is practical to regard the limit of PH = 0
at first, even though it is of no practical use. In this case,
PSF
det
and PSF
ill
are identical. The total PSF can be written as:
In fluorescence applications it is furthermore necessary to
consider both the excitation wavelength
λ
exc
and the emis-
sion wavelength
λ
em
. This is done by specifying a mean
wavelength
1
:
seite 7
PSF
tot
(x,y,z) = PSF
ill
(x,y,z)
.
PSF
det
(x,y,z)
seite 9
FWHM
ill,axial
=
seite 11
FWHM
det,axial
=
0.88 .
em
n- n
2
-NA
2
+
2 . n . PH
NA
2
2
0.88 .
exc
(n- n
2
-NA
2
)
5
1.77 . n .
exc
NA
2
FWHM
ill,lateral
= 0.51
exc
NA
seite 12
PSF
tot
(x,y,z) =
(
PSF
ill
(x,y,z)
)
2
em
.
exc
2
exc
+
2
em
5
2
FWHM
tot,axial
=
0.64 .
(n- n
2
-NA
2
)
5
1.28 . n .
NA
2
FWHM
tot,lateral
= 0.37
NA
(5)
seite 7
PSF
tot
(x,y,z) = PSF
ill
(x,y,z)
.
PSF
det
(x,y,z)
seite 9
FWHM
ill,axial
=
seite 11
FWHM
det,axial
=
0.88 .
em
n- n
2
-NA
2
+
2 . n . PH
NA
2
2
0.88 .
exc
(n- n
2
-NA
2
)
5
1.77 . n .
exc
NA
2
FWHM
ill,lateral
= 0.51
exc
NA
seite 12
PSF
tot
(x,y,z) =
(
PSF
ill
(x,y,z)
)
2
em
.
exc
2
exc
+
2
em
5
2
FWHM
tot,axial
=
0.64 .
(n- n
2
-NA
2
)
5
1.28 . n .
NA
2
FWHM
tot,lateral
= 0.37
NA
(6)
Note:
Withtheobjectbeingamirror,thefactorinequa-
tion7is0.45(insteadof0.64),and0.88(insteadof
1.28)inequation7a.Forafluorescentplaneoffinite
thickness,afactorof0.7canbeusedinequation7.
Thisunderlinesthatapartfromtheparameters(NA,
λ
,n)influencingtheopticalslicethickness,thetype
ofspecimenalsoaffectsthemeasurementresult.
seite 7
PSF
tot
(x,y,z) = PSF
ill
(x,y,z)
.
PSF
det
(x,y,z)
seite 9
FWHM
ill,axial
=
seite 11
FWHM
det,axial
=
0.88 .
em
n- n
2
-NA
2
+
2 . n . PH
NA
2
2
0.88 .
exc
(n- n
2
-NA
2
)
5
1.77 . n .
exc
NA
2
FWHM
ill,lateral
= 0.51
exc
NA
seite 12
PSF
tot
(x,y,z) =
(
PSF
ill
(x,y,z)
)
2
em
.
exc
2
exc
+
2
em
5
2
FWHM
tot,axial
=
0.64 .
(n- n
2
-NA
2
)
5
1.28 . n .
NA
2
FWHM
tot,lateral
= 0.37
NA
(7)
seite 7
PSF
tot
(x,y,z) = PSF
ill
(x,y,z)
.
PSF
det
(x,y,z)
seite 9
FWHM
ill,axial
=
seite 11
FWHM
det,axial
=
0.88 .
em
n- n
2
-NA
2
+
2 . n . PH
NA
2
2
0.88 .
exc
(n- n
2
-NA
2
)
5
1.77 . n .
exc
NA
2
FWHM
ill,lateral
= 0.51
exc
NA
seite 12
PSF
tot
(x,y,z) =
(
PSF
ill
(x,y,z)
)
2
em
.
exc
2
exc
+
2
em
5
2
FWHM
tot,axial
=
0.64 .
(n- n
2
-NA
2
)
5
1.28 . n .
NA
2
FWHM
tot,lateral
= 0.37
NA
(8)
seite 7
PSF
tot
(x,y,z) = PSF
ill
(x,y,z)
.
PSF
det
(x,y,z)
seite 9
FWHM
ill,axial
=
seite 11
FWHM
det,axial
=
0.88 .
em
n- n
2
-NA
2
+
2 . n . PH
NA
2
2
0.88 .
exc
(n- n
2
-NA
2
)
5
1.77 . n .
exc
NA
2
FWHM
ill,lateral
= 0.51
exc
NA
seite 12
PSF
tot
(x,y,z) =
(
PSF
ill
(x,y,z)
)
2
em
.
exc
2
exc
+
2
em
5
2
FWHM
tot,axial
=
0.64 .
(n- n
2
-NA
2
)
5
1.28 . n .
NA
2
FWHM
tot,lateral
= 0.37
NA
(7a)
Axial:
If NA < 0.5, equation (2) can be approximated by:
Lateral:
Summary of Contents for LSM 880
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