Phase Contrast & DIC Calculator
Contrast calculations for phase contrast and differential interference contrast microscopy.
Sample
Phase contrast
DIC
Sample
Phase contrast
DIC
|φ| = 0.286 rad is not small next to the ring amplitude a = 0.500: the contrast is no longer proportional to φ and the small-φ limit is wrong.
Contrast vs object thickness
Model
φ = 2π Δn t/λ
Phase contrast: U = a e^(iδ) + e^(iφ) − 1, C = (|U|² − a²)/a², a² = ring transmission, δ = ∓π/2
DIC: I/I_p = sin²((Γ ± Δφ)/2) + I_c, Δφ = φ·min(s, w)/w
Zernike's (1942) ideal phase contrast: all of the direct light passes the ring and all of the diffracted light misses it, so halos and shade-off from the finite ring width are not modelled. For |φ| ≪ a the contrast is 2φ sin δ/a; the attenuating ring raises it by 1/a, but the image reverses once tan(|φ|/2) > a. DIC follows the sin² law of a de Sénarmont or biased Nomarski system (Salmon & Tran 2007): the phase difference across the shear sets the contrast, so the two edges of an object come out bright and dark. The object edge is a linear phase ramp of width w; blurring by the optics is not included.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Ideal Zernike phase contrast (the ring passes all of the direct light and none of the diffracted light, so no halo or shade-off) and the DIC sin² law across a linear phase edge; blurring by the optics is not included.
- Zernike F. (1942). Phase contrast, a new method for the microscopic observation of transparent objects. Physica 9, 686–698. Direct and diffracted waves and the quarter-wave phase ring. doi:10.1016/S0031-8914(42)80035-X
- Salmon E. D., Tran P. (2007). High-resolution video-enhanced differential interference contrast light microscopy. Methods Cell Biol. 81, 335–364. DIC intensity sin² of the bias plus the specimen retardation, with stray light. doi:10.1016/S0091-679X(06)81016-2