Chapter 3 – Making Light Work in Biology  97

Since the system is in a standard epifluorescence mode with zero angle of inci­

dence, the polarization vector will be parallel to the glass–​water interface; at the

point of attachment of a spherical cell to the coverslip, the cell membrane will lie

parallel to the coverslip, and so the electric dipole axis of the dye will be oriented

normal to this and will thus not be excited into fluorescence, explaining why the

intensity data look similar when the dye is removed. A straight-​line plot of the

intensity points indicates no significant photobleaching above the level of noise,

thus no significant autofluorescence under these conditions, with a mean camera

readout noise of ~110 counts per pixel.

b

Approaching the critical angle, the system is in p-​TIRF mode and so the polar­

ization of the evanescent E-​field will be predominantly normal to glass–​water

interface and will therefore excite the dye into fluorescence. The intensity values

decrease due to stochastic dye photobleaching, converging on the camera noise

level when all dyes are irreversibly bleached. Subtracting the mean camera noise

value from the intensity data and doing a straight-​line fit on a semilog plot, or

equivalent fit, indicates a 1/​e photobleach time of ~115 ms, assuming 33 fps on a

North American model video-​rate camera.

c

The devil is in the detail here! The thinnest evanescent field equates to the min­

imum possible depth of penetration that occurs at the highest achievable angle

of incidence, θmax, set by the NA of the objective lens such that NA =​ ng sin θmax;

therefore

θmax =

(

) =

−

°

sin

/

resulting in a depth of pene

1 1 49 1 515

79 6

.

.

.

,

tration

nm

d =

×

× √

−

(

)

(

) ⁼

561

4

1 49

1 33

66

2

2

/

.

.

π

Thus, the intensity at different x for a 1D (i.e., line) profile will change since z

changes for the height of the membrane above the coverslip surface due to

spherical shape of cell by a factor of exp(−z/​d) where from trigonometry z =​ r(1

− √(1² − (x/​r)²) for a cell radius r assumed to be ~5 μm, but also the dipole axis

of the orientation changes. However, the orientation θd of the electric dipole

axis relative to the normal with the coverslip surface rotates with increasing

x between x =​ 0 − r such that cos θd =​ 1 − √(1² − (x/​r)²) and the absorption by

the dye will thus be attenuated by a further factor [1 − √(1² − (x/​r)²)]². Also, in

the supercritical regime, the excitation p-​polarized vector cartwheels in x with

a sinusoidal spatial periodicity of λp =​ λ/​nw sin θg =​ 561/​(1.33 × 1.49) =​ 283 nm.

In a nonsaturating regime for photon absorption by the dye, the fluorescence

emission intensity is proportional to the incident excitation intensity, which is

proportional to the square of E-​field excitation multiplied by all of the afore­

mentioned attenuation factors. Thus, a line profile intensity plot in x should

look like

I

r

x r

d

x r

x

p

0

2

2

2

2

2

2

1

1

1

1

2

exp

/

/

/

sin

−

−√

−(

)

(

)

(

)



^



^

−√

−(

)

(

)

(

)

π

λ

/

(

)^{+110 counts}

where 110 comes from the camera readout noise and assuming that the cell is

in contact with the glass coverslip at x =​ 0, and there is negligible outer material

on the surface such as a thick cell wall and that changes in intensity due to out-​

of-​focus effects are negligible since the depth of field is at least ~400 nm, greater

than the depth of penetration, namely, a damped sin² x function. A sketch for a line

profile from a “typical” cell should ideally have an x range from −2.5 to +​2.5 μm. The

fluorescence intensity at x =​ 0, I0, assuming nonsaturation photon absorption of

the dye molecules, which is ~0.8/​5.3 of the fluorescence intensity obtained in part

(a) at the critical angle of incidence, multiplied by a factor cos θg/​cos θc ≈ 0.46, since