A live, dividing yeast cell is being watched under bright field. The septum forming…

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 live, dividing yeast cell is being watched under bright field. The septum forming between mother and daughter cell imposes an optical phase

\phi = 0.090\ \mathrm{rad}

relative to the surrounding cytoplasm, aberration-free imaging, plane-wave illumination. ((a)) A Zernike phase plate places a quarter-wave retarder on the zero order and attenuates its amplitude transmittance to

A

(with

0 < A \le 1

), giving, with

\sin\phi\approx\phi

and

\cos\phi\approx1

, an irradiance contrast

C = \frac{2\phi}{A} + \left(\frac{\phi}{A}\right)^2.

Find the value of

A

(to two significant figures) needed to obtain a contrast

C \ge 0.30

at the septum. ((b)) Division is to be tracked by taking one super-resolved image every

0.5\ \mathrm{s}

for a total observation window of

8\ \mathrm{s}

, to see septum detail at about

120\ \mathrm{nm}

. The camera can record raw frames at

200

frames per second. Structured illumination needs

9

raw frames per reconstructed image (three phase steps at each of three grating orientations); single-molecule localisation needs of order

5000

raw frames per reconstructed image. For each method, compute the time taken to acquire one reconstructed image, and decide whether it is admissible for this

0.5\ \mathrm{s}

cadence.

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