Diffraction Gratings and Resolution Flashcards
what is a diffraction grating
a slab with a periodic modulation on one of its surfaces
what are the three types of diffraction grating
transmission, reflection or phase
How do diffraction gratings let us measure spectra
they diffract different wavelengths in different directions
What is the significance that the modulation of the transmission from a diffraction grating is periodic
we can use a fourier series for it
A(x0,y0)=A0+A1cos( 2ππ₯0/π) + π΄2cos( 4ππ₯0/π) + π΄3 cos(6ππ₯0/π ) +β¦ (only the x integral)
What is the wavelength dependence at order zero diffraction
none
what happens to different wavelengths of light at the +1 diffraction order
because x1 depends on wavelength, the wavelengths are separated x1=zlambda/a
z=distance from grating to screen
a = grating separation
In diffraction, the longer the wavelength
the larger its diffraction angle in nonzero orders
What is the transmission diffraction grating equation
π (sin π β sin ππ) = ππ
How do we understand a transmission diffraction grating from fourier arguments
it is a convolution of a single slit with a comb function so a spectrum is a series of delta functions for each incident wavelength
Describe a blazed diffraction grating
- tilting the facets of the grating so that the desired diffraction order coincides with the specular reflection from the facets, grating efficiency can be increased
- while both diffracted beams would satisfy the grating equation, one is more intense than the other
what does specular mean
angle of incidence = angle of reflection
What happens if two diffraction gratings are superimposed perpendicularly
they form a 2d periodic array of apertures
the observed diffraction pattern isnβt the sum or the product of the individual gratings, the separate patterns repeat to form a 2d array
what are laguerre-gaussian modes
forked patterns due to phase dislocation in spiral phase fronts - donut beams
What is the total intensity for N randomly-distributed apertures
N times the intensity due to a single aperture
What will the diffraction pattern be of randomly places indentical holes
the gross features of the pattern will reveal the shape of the holes
What is Babinetβs Principle
The diffraction pattern of an array of holes is the same as that of its opposite
What is the tendancy of diffraction to expand the smallest structure into the largest pattern key for
x-ray crystallography to diffract rays off atomic nuclei and reveal the crystal molecular structure
explain particle detection and measurement by diffraction
a flow of particles passes through a laser beam
by the fraunhofer diffraction of the laser beam, a cross section of the diffraction ring pattern is captured using a photodiode array
Describe how moon coronas form
moonlight passes through clouds, and diffracts when it passes between water droplets in the atmosphere - produces a coloured ring structure
what is the ultimate limit on image quality
the spreading out of light around each point in an image
As we bring 2 point sources closer and closer, eventually they will overlap - what is the rayleigh criterion
it tells us if we have resolvable images
the sources are just resolved when the centre of one airy pattern falls on the first minimum of the other airy pattern
what is the minimum resolvable angular separation of two objects
Ξπ = 1.22 π/D
if f is the focal length of the lens and D is the diameter of the aperture, what is the radius of the airy disc
1.22 fπ/π·
what are two ways to better resolve an image
decrease the aperture diameter or increase the viewing distance
How can diffraction effects be minimised
keeping the aperture sizes large comared to the wavelengths
Why do astronomical telescopes have such huge apertures
to limit diffraction effects
Why do we replace the objective lens in large reflecting telescopes with a concave mirror
because mirrors are free from chromatic and spherical aberrations and they are easier to correct than a lens
How is modern scanning near-field microscopy able to avoid the rayleigh limit
by sampling the evanescent wave transmitted by the sample through a narrow aperture, the resolution can get to a hundredth of a wavelength
what does sted stand for
stimulated emission depletion microscopy
How does sted work to improve the resolution over a regular microscope
it adds a second laser beam to the scanning process of the image compared to confocal imaging
the normal pulse is followed by a donut shaped pulse (laguerre gaussian beam) which bleaches molecules back to ground state, only molecules in the hole of the donut can emit fluorescence, limiting the point spread function and improving the resolution
What is the abbe limit
NA = nsintheta
what is the dispersion of a diffraction grating
πππ/ππ = π/π πππ π
what is the diffraction grating spectrometer resolution
πΏπ = 4π/πππ where N = no. grating lines = a/d
In a 2 slit experiment, if the spatial coherence length is less than the slit separation, what will happen
the relative phase of light from each slit will vary randomly and fine scale fringes wash out so only a one slit pattern will be observed
What happens if the slit width is period/N
the minima of the slit diffraction correspond to the maxima N, 2N, 3N, of the grating diffraction resulting in missing maxima
