Fluorescence interference contrast microscopy

Fluorescence interference contrast (FLIC) microscopy is a microscopic technique developed to achieve z-resolution on the nanometer scale. Fluorescence interference contrast (FLIC) microscopy is a microscopic technique developed to achieve z-resolution on the nanometer scale. FLIC occurs whenever fluorescent objects are in the vicinity of a reflecting surface (e.g. Si wafer). The resulting interference between the direct and the reflected light leads to a double sin2 modulation of the intensity, I, of a fluorescent object as a function of distance, h, above the reflecting surface. This allows for the nanometer height measurements. FLIC microscope is well suited to measuring the topography of a membrane that contains fluorescentprobes e.g. an artificial lipid bilayer, or a living cell membrane or the structure of fluorescently labeled proteins on a surface. The optical theory underlying FLIC was developed by Armin Lambacher and Peter Fromherz. They derived a relationship between the observed fluorescence intensity and the distance of the fluorophore from a reflective silicon surface. The observed fluorescence intensity, I F L I C {displaystyle I_{FLIC}} , is the product of the excitation probability per unit time, P e x {displaystyle P_{ex}} , and the probability of measuring an emitted photon per unit time, P e m {displaystyle P_{em}} . Both probabilities are a function of the fluorophore height above the silicon surface, so the observed intensity will also be a function of the fluorophore height. The simplest arrangement to consider is a fluorophore embedded in silicon dioxide (refractive index n 1 {displaystyle n_{1}} ) a distance d from an interface with silicon (refractive index n 0 {displaystyle n_{0}} ). The fluorophore is excited by light of wavelength λ e x {displaystyle lambda _{ex}} and emits light of wavelength λ e m {displaystyle lambda _{em}} . The unit vector ″ e e x ″ {displaystyle ''e_{ex}''} gives the orientation of the transition dipole of excitation of the fluorophore. P e x {displaystyle P_{ex}} is proportional to the squared projection of the local electric field, F i n {displaystyle F_{in}} , which includes the effects of interference, on the direction of the transition dipole. P e x ∝∣ F i n ⋅ e e x ∣ 2 {displaystyle P_{ex}propto mid F_{in}cdot e_{ex}mid ^{2}} The local electric field, F i n {displaystyle F_{in}} , at the fluorophore is affected by interference between the direct incident light and the light reflecting off the silicon surface. The interference is quantified by the phase difference Φ i n {displaystyle Phi _{in}} given by Φ i n = 4 π n 1 d cos ⁡ θ 1 i n λ e x {displaystyle Phi _{in}={frac {4pi n_{1}dcos heta _{1}^{in}}{lambda _{ex}}}} θ 1 i n {displaystyle heta _{1}^{in}} is the angle of the incident light with respect to the silicon plane normal. Not only does interference modulate F i n {displaystyle F_{in}} , but the silicon surface does not perfectly reflect the incident light. Fresnel coefficients give the change in amplitude between an incident and reflected wave. The Fresnel coefficients depend on the angles of incidence, θ i {displaystyle heta _{i}} and θ j {displaystyle heta _{j}} , the indices of refraction of the two mediums and the polarization direction. The angles θ i {displaystyle heta _{i}} and θ j {displaystyle heta _{j}} can be related by Snell's Law. The expressions for the reflection coefficients are: r i j T E = n i cos ⁡ θ i − n j cos ⁡ θ j n i cos ⁡ θ i + n j cos ⁡ θ j r i j T M = n j cos ⁡ θ i − n i cos ⁡ θ j n j cos ⁡ θ i + n i cos ⁡ θ j {displaystyle r_{ij}^{TE}={frac {n_{i}cos heta _{i}-n_{j}cos heta _{j}}{n_{i}cos heta _{i}+n_{j}cos heta _{j}}}quad r_{ij}^{TM}={frac {n_{j}cos heta _{i}-n_{i}cos heta _{j}}{n_{j}cos heta _{i}+n_{i}cos heta _{j}}}} TE refers to the component of the electric field perpendicular to the plane of incidence and TM to the parallel component (The incident plane is defined by the plane normal and the propagation direction of the light). In cartesian coordinates, the local electric field is F i n = sin ⁡ γ i n [ 0 1 + r 10 T E e i Φ i n 0 ] + cos ⁡ γ i n [ cos ⁡ θ 1 i n ( 1 − r 10 T M e i Φ i n ) 0 sin ⁡ θ 1 i n ( 1 + r 10 T M e i Φ i n ) ] {displaystyle F_{in}=sin gamma _{in}left+cos gamma _{in}left} γ i n {displaystyle gamma _{in}} is the polarization angle of the incident light with respect to the plane of incidence. The orientation of the excitation dipole is a function of its angle θ e x {displaystyle heta _{ex}} to the normal and ϕ e x {displaystyle phi _{ex}} azimuthal to the plane of incidence. e e x = [ cos ⁡ ϕ e x sin ⁡ θ e x sin ⁡ ϕ e x sin ⁡ θ e x cos ⁡ θ e x ] {displaystyle { extit {e}}_{ex}=left} The above two equations for F i n {displaystyle F_{in}} and e e x {displaystyle { extit {e}}_{ex}} can be combined to give the probability of exciting the fluorophore per unit time P e x {displaystyle P_{ex}} .Many of the parameters used above would vary in a normal experiment. The variation in the five following parameters should be included in this theoretical description. The squared projection ∣ F i n ⋅ e e x ∣ 2 {displaystyle mid F_{in}cdot e_{ex}mid ^{2}} must be averaged over these quantities to give the probability of excitation P e x {displaystyle P_{ex}} . Averaging over the first 4 parameters gives <∣ F i n ⋅ e e x ∣ 2 >∝ ∫ sin ⁡ θ 1 i n d θ 1 i n A i n ( θ 1 i n ) × ∫ sin ⁡ θ e x d θ e x O ( θ e x ) U e x ( λ i n , θ 1 i n . θ e x ) {displaystyle <mid F_{in}cdot e_{ex}mid ^{2}>propto int sin heta _{1}^{in}d heta _{1}^{in}A_{in}( heta _{1}^{in}) imes int sin heta _{ex}d heta _{ex}O( heta _{ex})U_{ex}(lambda _{in}, heta _{1}^{in}. heta _{ex})} U e x = sin 2 ⁡ θ e x ∣ 1 + r 10 T E e i Φ i n ∣ 2 + sin 2 ⁡ θ e x cos 2 ⁡ θ 1 i n ∣ 1 − r 10 T M e i Φ i n ∣ 2 + 2 cos 2 ⁡ θ e x sin 2 ⁡ θ 1 i n ∣ 1 + r 10 T M e i Φ i n ∣ 2 {displaystyle U_{ex}=sin ^{2} heta _{ex}mid 1+r_{10}^{TE}{ extit {e}}^{iPhi _{in}}mid ^{2}+sin ^{2} heta _{ex}cos ^{2} heta _{1}^{in}mid 1-r_{10}^{TM}{ extit {e}}^{iPhi _{in}}mid ^{2}+2cos ^{2} heta _{ex}sin ^{2} heta _{1}^{in}mid 1+r_{10}^{TM}{ extit {e}}^{iPhi _{in}}mid ^{2}} Normalization factors are not included. O ( θ e x ) {displaystyle O( heta _{ex})} is a distribution of the orientation angle of the fluorophore dipoles. The azimuthal angle ϕ e x {displaystyle phi _{ex}} and the polarization angle γ i n {displaystyle gamma _{in}} are integrated over analytically, so they no longer appear in the above equation. To finally obtain the probability of excitation per unit time, the above equation is integrated over the spread in excitation wavelength, accounting for the intensity I ( λ e x ) {displaystyle I(lambda _{ex})} and the extinction coefficient of the fluorophore ϵ ( λ e x ) {displaystyle epsilon (lambda _{ex})} . P e x ∝ ∫ d λ e x I ( λ e x ) ϵ ( λ e x ) <∣ F i n ⋅ e e x ∣ 2 > {displaystyle P_{ex}propto int dlambda _{ex}I(lambda _{ex})epsilon (lambda _{ex})<mid F_{in}cdot e_{ex}mid ^{2}>} The steps to calculate P e m {displaystyle P_{em}} are equivalent to those above in calculating P e x {displaystyle P_{ex}} except that the parameter labels em are replaced with ex and in is replaced with out. P e m ∝ ∫ d λ e m Φ d e t ( λ e m ) f ( λ e m ) <∣ F i n ⋅ e e x ∣ 2 > {displaystyle P_{em}propto int dlambda _{em}Phi _{det}(lambda _{em}){ extit {f}}(lambda _{em})<mid F_{in}cdot e_{ex}mid ^{2}>} The resulting fluorescence intensity measured is proportional to the product of the excitation probability and emission probability I F L I C ∝ P e x P e m {displaystyle I_{FLIC}propto P_{ex}P_{em}} It is important to note that this theory determines a proportionality relation between the measured fluorescence intensity I F L I C {displaystyle I_{FLIC}} and the distance of the fluorophore above the reflective surface. The fact that it is not an equality relation will have a significant effect on the experimental procedure. A silicon wafer is typically used as the reflective surface in a FLIC experiment. An oxide layer is then thermally grown on top of the silicon wafer to act as a spacer. On top of the oxide is placed the fluorescently labeled specimen, such as a lipid membrane, a cell or membrane bound proteins. With the sample system built, all that is needed is an epifluorescence microscope and a CCD camera to make quantitative intensity measurements.