Chapter 3 – Making Light Work in Biology  103

window for slow scanning techniques and thus are too blurred to monitor their localization

in a time-​resolved fashion (i.e., it is not possible to track them). To beat the blur time of

biomolecules requires imaging faster than their characteristic diffusional time.

In a sampling time window Δt, a molecule with effective diffusion coefficient D will diffuse

a root mean squared displacement √〈R²〉 of √(2DnΔt) (see Equation 2.12) in n-​dimensional

space. To estimate what maximum value of Δt we can use in order to see a fluorescently labeled

molecule unblurred, we set √〈R²〉 equal to the PSF width. Using this simple assumption in

conjunction with the Stokes–​Einstein relation (Chapter 2) it is trivial to derive:

(3.55)

∆t

r

k nNA T

g

max

peak

Stokes

≈

1 17

2

2

.

ηλ

π

where λpeak is the peak fluorescence emission wavelength through an objective lens of numer­

ical aperture NA of a fluorescent-​labeled molecule of effective Stokes radius rStokes diffusing in

a medium of viscosity η. For typical nanoscale globular biomolecules for a high-​magnification

fluorescence microscope, this indicates a maximum sampling time window of a few hundred

milliseconds for diffusion in cell membranes (2D diffusion), and more like a few milliseconds

in the cytoplasm (3D diffusion). Thus, to image mobile molecular components inside cells

requires millisecond time resolution. Note that if the fluorophore-​labeled biomolecule

exhibits ballistic motion as opposed to diffusive motion (e.g., in the extreme of very short

time intervals that are less than the mean collision time of molecules in the sample), then the

root mean squared displacement will scale linearly with Δt as opposed to having a square

root dependence, thus requiring a shorter camera sampling time window than Equation 3.55

suggests.

However, the normal excitation intensities used for conventional epifluorescence or

oblique epifluorescence generate too low a fluorescence emission signal for millisecond sam­

pling, which is swamped in camera readout noise. This is because there is a limited photon

budget for fluorescence emission and carving this budget into smaller and smaller time

windows reduces the effective signal until it is hidden in the noise. To overcome this, the sim­

plest approach is to shrink the area of the excitation field, while retaining the same incident

laser power, resulting in substantial increases in excitation intensity. Narrow-​field epifluor­

escence shrinks the excitation intensity field to generate a lateral full width at half maximum

of ~5–​15 μm, which has been used to monitor the diffusion of single lipid molecules with

millisecond time resolution (Schmidt et al., 1996), while a variant of the technique delimits

the excitation field by imaging a narrow pinhole into the sample (Yang and Musser, 2006).

A related technique of Slimfield microscopy generates a similar width excitation field in

the sample but achieves this by propagating a narrow collimated laser of width ws (typically

<1 mm diameter) into the back aperture of a high NA objective lens resulting in an expanded

confocal volume of lateral width wc, since there is a reciprocal relation in Gaussian optics

between the input beam width and output diffraction pattern width (see Self, 1983):

(3.56)

w

f

w

c

s

=

λ

π

where f is the focal length of the objective lens (typically 1–​3 mm). Since the Slimfield exci­

tation is a confocal volume and therefore divergent with z away from the laser focus, there is

some improvement in imaging contrast over narrow field in reducing scattering from out-​of-​

focus image planes.

The large effective excitation intensities used in narrow-​field and Slimfield approaches

result in smaller photobleach times for the excited fluorophores. For example, if the GFP

fluorophore is excited, then it may irreversibly photobleach after less than a few tens of

milliseconds, equivalent to only 5–​10 consecutive image frames. This potentially presents a

problem since although the diffusional time scale of biomolecules in the cytoplasm is at the

millisecond level, many biological processes will typically consist of reaction–​diffusion events,