Supplement Information for
Tuning Donut Profile for Spatial Resolution in Stimulated
Emission Depletion Microscopy
Submitted to Review of Scientific Instruments for publication
Bhanu Neupane,1 Fang Chen,1 Wei Sun,2 Daniel T. Chiu,2 and Gufeng Wang1,*
1. Chemistry Department, North Carolina State University, Raleigh, NC, 27695, USA
2. Department of Chemistry, the University of Washington, Seattle, WA, USA
*Corresponding Author:
Gufeng Wang, email: gufeng_wang@ncsu.edu
Chemistry Department, North Carolina State University, Raleigh, NC, 27695
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1. Supplementary Figure
Supplementary Figure S1. Donut and cross section profile of obtained by imaging 18 nm
polymer particles. Donut beam size at the objective back aperture is ~6.5 mm so that back aperture
is slightly over filled. Blue curve represents the fit to the center portion of donut with a parabolic
function of slope of 9.0 ×10-5 nm-2.
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2. Theory
2.1. Point spread function (PSF) and STED resolution
In confocal microscopy, the spatial resolution is determined by the confocal PSF, which
is the convolution of the excitation PSF and the detection PSF:
PSFConfocal ( x, y )  PSFExc ( x, y )  PSFDet ( x, y )
(S1)
In practice, the size of the detection PSF is usually larger than the excitation PSF. So the
confocal spatial resolution is determined by the excitation PSF.
Similarly, STED PSF is determined by the spatial excited state population distribution
profile, which is the product of the excitation PSF and the depletion probability:
PSFSTED  PSFExc ( x, y ) Pr( x, y )
(S2)
The depletion probability is a function of the excitation and the depletion laser power.
The theoretical STED PSF can be obtained by solving coupled differential kinetic rate
equations at each position in the focal plane.1 Under continuous wave (CW) excitation/depletion
conditions, the system can be viewed as in steady-state. The rate of the population change at a
particular energy level Ei (i = 0, 1, 2, 3) is zero. Considering a 4-state system (as shown in
Supplementary Figure S2), the equations can be setup according to the 1994 paper:1
dn0
1
(S3)
 0  h( x, y) exc  abs (n1  n0 ) 
n3
dt
 vib
dn1
1
(S4)
 0  h( x, y) exc  abs (n0  n1 ) 
n1
dt
 vib
dn2
1
1
0
n1  h( x, y ) sted  sted (n3  n2 )  (  Q)n2
(S5)
dt
 vib
 fl
dn3
1
1
 0  h( x, y ) sted  sted (n2  n3 )  (  Q)n2 
n3
(S6)
dt
 fl
 vib
where n is the number of molecules; t is time (s); σabs and σsted are the absorption and stimulated
emission depletion cross sections (cm2), respectively; τfl and τvib are the fluorescence and
vibrational relaxation times (s), respectively; h(x,y)exc and h(x,y)sted are the excitation and
depletion intensities (#/cm2/s), respectively; Q is the quenching rate constant (s-1).
Since total population is conserved:
n1  n2  n3  n0  N
(S7)
solving Equations S2-S7, we obtain:
ABN
(S8)
n2 
1  2 B  AB
where
1
 h( x, y ) sted  sted
 vib
(S9)
A
1
h( x, y ) sted  sted  (  Q )
 fl
B
h ( x, y ) exc  abs
h ( x, y ) exc  abs 
(S10)
1
 vib
3
Supplementary Figure S2. Energy levels of a fluorophore, and corresponding
excitation and relaxation pathways under CW excitation and depletion.
The spatial fluorescence intensity distribution function is given by:
1
1
N
(S11)
 ( x, y) fl 
n2 
AB
 fl
 fl
1  2 B  AB
Equation S11 is the basis we calculate STED PSF and estimate spatial resolution for all
the simulations discussed in the manuscript.
2.2. STED resolution under weak excitation approximation
Under weak excitation conditions, it can be assumed that it is only relevant to the depletion
power, as will be discussed below. STED resolution thus can be estimated conveniently when the
donut intensity profile is ideal (0-intensity in the center).
For microscopies with a complicated, non-Bessel function PSF, a popular way to define
resolution is to use their full width at half maximum (FWHM) of their PSF. Assume a perfect
depletion donut profile with the center intensity of zero, the fluorescence intensity in the center
equals to the intensity in the absence of the depletion. According to Equation S11:
1
A' BN
(S12)
 ( x, y ) fl 
 fl 1  2 B  A' B
where
1
 vib
(S13)
A' 
1
Q
 fl
The STED resolution is tightly relevant to the center portion of the donut intensity profile
(several 10s of nanometers). Assume the excitation intensity profile is flat in this range. The
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resolution  is twice the axial distance () where the fluorescence is depleted to the half of that
undepleted:
ABN
 (  ) fl 1 1  2 B  AB
 
(S14)
A' BN
 (0) fl 2
1  2 B  A' B
Under weak excitation conditions (~W), it is easy to find out that terms B, AB, A’B are all
much smaller than 1. For example, when the 488 nm excitation Gaussian beam (15 W) is
focused to the tightest by a NA 1.4 objective, these terms can be estimated as B ~1×10-6, AB
~2×10-4, and A’B ~3×10-12 (all unitless). Equation S14 is thus can be simplified as:
1
 h( x, y ) sted  sted
 vib
 (  ) fl 1 A
 

 (0) fl 2 A'
h( x, y ) sted  sted  (
1
 fl
 Q)
(S15)
1
 vib
1
 fl
Q
When the depletion laser intensity h (power/area) drops to a value that depletes half of the
fluorescence intensity, both h( x, y ) sted  sted (~ 2×109 s-1) much smaller than
1
 vib
(~ 5×1012 s-1),
1
 Q (~ ~3.5×108 s-1) much smaller than h( x, y ) sted  sted (~ 2×109 s-1) can be viewed as
 fl
valid. Above numbers were obtained by assuming the total power of 592 nm depletion beam of
1.0 W was focused to the tightest by a NA 1.4 objective. Ignore the quenching, we can obtain:
2
(S16)
h( x, y ) sted  sted 
 fl
At this position, h(x,y)STED is hSat.
The STED resolution can be estimated as the twice of the radial position  where the
donut intensity drops to hSat for an ideal donut profile as discussed in the manuscript. Given that
we know the donut profile (parabolic profile derived from Equation 5 with small argument
approximation of Bessel functions) and the total depletion laser power (can be measured
experimentally), can be solved conveniently as in Equation 18 in the manuscript. Again, note
above derivation requires the weak excitation approximation and that the donut profile is ideal
(i.e., a zero intensity in the center).
and
3. Total laser power (I) and intensity profile of the donut (h)
The normalized, unitless donut profile g(x,y) was collected experimentally. The donut profile
h(x,y) is:
h( x, y )  h0 g ( x, y )
(S17)
Where h0 is determined by
5
h0 
I Tot
 g ( x, y )dxdy
(S18)
Table 1. Parameters for FITC used in simulation.
Parameters
Psted
Pexc
σsted
σabs
τfl
τvib
Q
Values
1.0 W or specified
15 × 10-6 W or specified
1.0 × 10-17 cm2 (from Ref. 2)
3.0 × 10-16 cm2 (from Ref. 2)
3.7 × 10-9sec (from Ref. 3)
5.0 × 10-12 sec (from Ref. 1)
1.0 × 108 sec-1 (from Ref. 1)
References
1.
Hell, S. W.; Wichmann, J., Opt. Lett. 1994, 19 (11), 780-782.
2.
Ringemann, C.; Schönle, A.; Giske, A.; von Middendorff, C.; Hell, S. W.; Eggeling, C.,
ChemPhysChem 2008, 9 (4), 612-624.
3.
Santra, S.; Liesenfeld, B.; Bertolino, C.; Dutta, D.; Cao, Z.; Tan, W.; Moudgil, B. M.;
Mericle, R. A., Journal of Luminescence 2006, 117 (1), 75-82.
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