TIRF Penetration Depth Calculator
Evanescent intensity penetration depth, critical angle, objective angle limit and interface intensity for TIRF microscopy.
Results
Penetration depth vs angle
Evanescent intensity decay
Model
θ_c = arcsin(n₂/n₁); objective limit arcsin(NA/n₁)
I(z) = I(0) exp(−z/d), d = λ/(4π √(n₁² sin²θ − n₂²))
I_s(0) = 4cos²θ/(1 − n²), I_p(0) = 4cos²θ(2sin²θ − n²)/(n⁴cos²θ + sin²θ − n²), n = n₂/n₁
Plane-wave Fresnel optics at one planar interface (Axelrod 2001). d is the 1/e depth of the intensity, which excites the fluorophores; the field decays over 2d. The interface intensity is relative to the incident intensity in the glass and peaks near θ_c (4 for s, 4/n² for p). Real objective-type TIRF also carries some scattered, non-evanescent light, so the measured decay is often longer.
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Plane-wave Fresnel optics at a single planar interface. Objective-type TIRF also carries scattered, non-evanescent light, so measured decays are often longer.
- Axelrod D. (2001). Total internal reflection fluorescence microscopy in cell biology. Traffic 2, 764–774. Penetration depth (eq. 2) and interface intensities for s and p polarisation (eqs. 4–5). doi:10.1034/j.1600-0854.2001.21104.x