experiment 7 - diffraction limited resolution in optical systems and the eye Flashcards
what are we investigating in this experiment ?
- how diffraction and in particular with how the airy pattern limits the final spatial detail a lens can resolve
what is spatial resolution limited by ?
- limited by diffraction , higher order aberrations and scattered light
what does every circular aperture produce ?
- every circular aperture produces a diffraction pattern
when does diffraction affect size of the airy diskc?
- diffraction affects the size of the airy disc produced by the lens when imaging a very small dot object
- it is expected that diffraction takes place only at the edge of the aperture
explain the symmetry of airy disc ?
- the airy disc has radial symmetry and it consists of a centre disc of radius , p , surrounded by a number of progressively larger annuli
- surrounding annuli are much dimmer than the centre disc and appear both dark and bright
what kind of aperture are the pupil and lens ?
- the pupil and the lens diaphragms are also circular aperture
does a rectangular or slit aperture produce same diffraction pattern as a circular aperture ?
- a rectangular or slit aperture produce a different diffraction pattern
- no longer airy pattern
what bit of the aperture is involved in diffraction ?
- only the edge of aperture stop is involved in diffraction
what is the amount of diffracted light proportional to ?
- since only the edge of aperture is involved in diffraction , the amount of diffracted light is proportional to the length of its circumference
2πr
what does the area of aperture increase with ?
the area of aperture increases with the square of the radius πr^2
what is the fraction captured by the lens that is diffracted proportional to ?
1/r
r=radius of aperture
- this ratio changes as you change aperture size
- this is because circumference is 2πr ( light that is diffracted is proportional to 2πr ) and radius is πr^2 -( light that is un diffracted is proportional to πr^2)
- we take ratio of circumference to area we get 1/r
what happens when pupil diameter is 3mm?
- the eye is free from on-axis optical aberrations
- when this happens the spatial resolution of the eye is limited by only diffraction
what is the hypothesis for this experiment ?
- the fraction of the light that is is diffracted when passing through the lens is proportional to the ratio of the circumference to the area of the aperture stop
- fraction of diffracted light = 2πr / πr^2
- ratio determines the size of airy disc which is diffraction pattern
p ∝ 1/r
what is is the equation for fraction of diffracted light ?
- fraction of diffracted light = 2πr / πr^2
- ratio determines the size of airy disc which is diffraction pattern
p ∝ 1/r - the radius (p) of the centre lobe in the airy pattern
how test to test our hypothesis ?
- use diffraction limited object ( i.e. vey small light emitting dot ) and produce an image for this point-like object for each aperture size investigated
- the microscope is viewing the airy disc , and look at image magnified with microscope objective
- what we are measuring is the diameter of the central lobe which is the same as measuring the first dark ring which is the twice the radius as the first dark ring
- we need to vary the aperture size for smallest to largest
- for each aperture size we need to measure size of airy disc