A cell wall in a growing bacterial biofilm produces a phase step rad

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Fourier optics and image formation · Fourier optics and image formation

What an Instrument Can See, Ch Seeing what the transfer function forbids: phase contrast and super-resolution

Problem

A cell wall in a growing bacterial biofilm produces a phase step

\phi = 0.15

rad. A Zernike phase plate is fabricated with the zero order attenuated to amplitude transmittance

A = 0.5

(25 per cent in irradiance) and phase-shifted by a quarter wave, so that the transmitted field is

i(A + \phi)

against a background field of

iA

. ((a)) Compute the linear estimate of the relative irradiance contrast,

2\phi/A

. ((b)) Compute the relative irradiance contrast of this model field,

\left[(A+\phi)^2 - A^2\right]/A^2

. ((c)) The biofilm rearranges its structure on a timescale of about 5 seconds, and the target detail is about 150 nm, over a total observation of 2 minutes. Using the frame counts and times from the super-resolution budget (structured illumination: 9 raw frames, about 0.3 seconds per reconstructed image; localisation: thousands of raw frames, about 30 seconds per reconstructed image), decide which of the two methods is admissible for following this biofilm, and justify the choice in one sentence.

Browse the problem library