Find the error in: "Using structured illumination on a 1.2 NA objective at 550 nm

PHYSICS · Subjective · 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

Find the error in: "Using structured illumination on a 1.2 NA objective at 550 nm, the illumination pattern itself must pass through the same objective, so its spatial frequency is limited to νi≤2NA/λ\nu_i \le 2\mathrm{NA}/\lambda, the same as the specimen's own cutoff. Each shifted copy of the object spectrum can therefore reach out to 2×(2NA/λ)=4NA/λ2\times(2\mathrm{NA}/\lambda) = 4\mathrm{NA}/\lambda on its own side of the origin, and since this happens on both the positive and negative sides the total recoverable bandwidth is 2×4NA/λ=8NA/λ2\times4\mathrm{NA}/\lambda = 8\mathrm{NA}/\lambda, so the resolution is λ/8NA=550 nm/(8×1.2)≈57\lambda/8\mathrm{NA} = 550\ \mathrm{nm}/(8\times1.2) \approx 57 nm."

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