Circular-Aperture Diffraction and Resolution in Optical Imaging

All flashcards

What pattern does a circular aperture produce?

A bright central maximum surrounded by weaker bright rings, separated by dark regions. The pattern arises from interference among waves from different parts of the aperture.

Why does diffraction limit resolution?

Each point source spreads into a diffraction pattern. Patterns from nearby sources overlap, making it difficult or impossible to identify them as separate sources.

State the Rayleigh criterion.

Two point sources are just resolvable when the center of one source’s diffraction pattern lies at the first minimum of the other’s pattern.

What is the first-minimum angle for a circular aperture?

For aperture diameter $D$ and wavelength $\lambda$, it is approximately $\theta = 1.22\lambda/D$ radians.

How can an optical system improve its diffraction-limited angular resolution?

It can use a larger aperture diameter or shorter-wavelength light. Both reduce the minimum angular separation $1.22\lambda/D$.

Quiz questions

1. What produces the bright and dark rings in the diffraction pattern from a circular aperture?Answer: Interference among waves arriving from different parts of the aperture.
2. For two objects at distance $r$ with a small angular separation $\theta$ in radians, which relation estimates their physical separation $s$?Answer: $s = r\theta$
3. For an objective lens, what does numerical aperture express in terms of refractive index $n$ and cone half-angle $\alpha$?Answer: $\mathrm{NA} = n\sin\alpha$
4. Which source of image distortion does the Hubble Space Telescope avoid by operating above Earth's atmosphere?Answer: Distortion caused by turbulent air along the line of sight.
5. How can super-resolved fluorescence microscopy produce detail finer than the conventional Rayleigh limit?Answer: It controls molecular emission and uses the resulting information to reconstruct finer detail.