IB DP Physics: HL复习笔记9.4.1 The Rayleigh Criterion

Diffracting Aperture

  • A circular aperture allows a cone of light to enter a region behind the aperture
  • Examples of circular aperture include:
    • A lens within an optical device such as a camera
    • The pupil of an eye
  • A circular aperture allows light to act like a point source once passing through
  • Placing two point sources near each other or viewing those sources too far away, will make them appear to be a single unresolved source of light
  • Consider car headlights which are distant on a highway:
    • Initially, when the car is far away, the headlights appear as one point source
    • It is not until the car comes closer that the two individual headlights can be resolved individually
  • Light from any object passing through a circular aperture, including the human eye, will diffract and create a diffraction pattern upon the detector inside
    • In the case of the human eye, for example, the detector is the retina
  • Each of these diffraction patterns need space on the detector to be resolved
    • If they are too close, then they will appear as one single source
  • Resolution is defined as:

The capability of an imaging system to be able to tell if two sources are independent and produce individual images of those two sources

9-4-1-diffraction-pattern-produced-by-circular-aperture-ib-hl

Two light sources outside a circular aperture produce diffraction patterns that have a minimum angle of resolution determined by the Rayleigh criterion

The Rayleigh Criterion

  • The Rayleigh Criterion describes the limit of resolution of a system to separate two sources

9-4-1-intensity-resolution-rayleigh-criterion-ib-hl

Two sources that only just be resolved. The red is a single source, the blue is the other source and the purple line represents their combined intensity

  • The Rayleigh Criterion states that:

Two sources are able to be just resolved if the principal maximum from one diffraction pattern is aligned with the first minimum of the other diffraction pattern

  • Two sources that can be fully resolved:

9-4-1-intensity-resolution-separated-ib-hl

Two sources that can be fully resolved. The red is a single source, the blue is the second source and the purple line represents their combined intensity

  • Visually, two sources that could clearly be resolved would look like the above
  • Two sources that cannot be resolved:

9-4-1-intensity-resolution-unresolved-ib-hl

Two sources that cannot be resolved. The red is a single source, the blue is the second source and the purple line represents their combined intensity

  • Visually, two sources that could not be resolved:

9-4-1-visually-unresolved-ib-hl

Visually, two sources that could not be resolved

  • Visually, two sources that are only just resolved:

9-4-1-visually-just-resolved-ib-hl

Visually, two sources that could only just be resolved

  • This final example is the limiting case of the Rayleigh criterion

9-4-1-visually-resolved-ib-hl

Visually, two sources that could clearly be resolved would look like the above

  • If the two sources are separated further apart than maximum to minimum, they can be resolved
    • If the two sources are brought closer together, they cannot be resolved

 

 

 

 

 

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