Diffraction Gratings and Resolution

Question 1

what is a diffraction grating

Answer 1

a slab with a periodic modulation on one of its surfaces

Question 2

what are the three types of diffraction grating

Answer 2

transmission, reflection or phase

Question 3

How do diffraction gratings let us measure spectra

Answer 3

they diffract different wavelengths in different directions

Question 4

What is the significance that the modulation of the transmission from a diffraction grating is periodic

Answer 4

we can use a fourier series for it
A(x0,y0)=A0+A1cos( 2𝜋𝑥0/𝑎) + 𝐴2cos( 4𝜋𝑥0/𝑎) + 𝐴3 cos(6𝜋𝑥0/𝑎 ) +… (only the x integral)

Question 5

What is the wavelength dependence at order zero diffraction

Answer 5

none

Question 6

what happens to different wavelengths of light at the +1 diffraction order

Answer 6

because x1 depends on wavelength, the wavelengths are separated x1=zlambda/a
z=distance from grating to screen
a = grating separation

Question 7

In diffraction, the longer the wavelength

Answer 7

the larger its diffraction angle in nonzero orders

Question 8

What is the transmission diffraction grating equation

Answer 8

𝑎 (sin 𝜃 − sin 𝜃𝑖) = 𝑚𝜆

Question 9

How do we understand a transmission diffraction grating from fourier arguments

Answer 9

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

Question 10

Describe a blazed diffraction grating

Answer 10

• 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

Question 11

what does specular mean

Answer 11

angle of incidence = angle of reflection

Question 12

What happens if two diffraction gratings are superimposed perpendicularly

Answer 12

they form a 2d periodic array of apertures
the observed diffraction pattern isn’t the sum or the product of the individual gratings, the separate patterns repeat to form a 2d array

Question 13

what are laguerre-gaussian modes

Answer 13

forked patterns due to phase dislocation in spiral phase fronts - donut beams

Question 14

What is the total intensity for N randomly-distributed apertures

Answer 14

N times the intensity due to a single aperture

Question 15

What will the diffraction pattern be of randomly places indentical holes

Answer 15

the gross features of the pattern will reveal the shape of the holes

Question 16

What is Babinet’s Principle

Answer 16

The diffraction pattern of an array of holes is the same as that of its opposite

Question 17

What is the tendancy of diffraction to expand the smallest structure into the largest pattern key for

Answer 17

x-ray crystallography to diffract rays off atomic nuclei and reveal the crystal molecular structure

Question 18

explain particle detection and measurement by diffraction

Answer 18

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

Question 19

Describe how moon coronas form

Answer 19

moonlight passes through clouds, and diffracts when it passes between water droplets in the atmosphere - produces a coloured ring structure

Question 20

what is the ultimate limit on image quality

Answer 20

the spreading out of light around each point in an image

Question 21

As we bring 2 point sources closer and closer, eventually they will overlap - what is the rayleigh criterion

Answer 21

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

Question 22

what is the minimum resolvable angular separation of two objects

Answer 22

Δ𝜃 = 1.22 𝜆/D

Question 23

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

Answer 23

1.22 f𝜆/𝐷

Question 24

what are two ways to better resolve an image

Answer 24

decrease the aperture diameter or increase the viewing distance

Question 25

How can diffraction effects be minimised

Answer 25

keeping the aperture sizes large comared to the wavelengths

Question 26

Why do astronomical telescopes have such huge apertures

Answer 26

to limit diffraction effects

Question 27

Why do we replace the objective lens in large reflecting telescopes with a concave mirror

Answer 27

because mirrors are free from chromatic and spherical aberrations and they are easier to correct than a lens

Question 28

How is modern scanning near-field microscopy able to avoid the rayleigh limit

Answer 28

by sampling the evanescent wave transmitted by the sample through a narrow aperture, the resolution can get to a hundredth of a wavelength

Question 29

what does sted stand for

Answer 29

stimulated emission depletion microscopy

Question 30

How does sted work to improve the resolution over a regular microscope

Answer 30

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

Question 31

What is the abbe limit

Answer 31

NA = nsintheta

Question 32

what is the dispersion of a diffraction grating

Answer 32

𝑑𝜃𝑚/𝑑𝜆 = 𝑚/𝑎 𝑐𝑜𝑠𝜃

Question 33

what is the diffraction grating spectrometer resolution

Answer 33

𝛿𝜆 = 4𝜆/𝑚𝜋𝑁 where N = no. grating lines = a/d

Question 34

In a 2 slit experiment, if the spatial coherence length is less than the slit separation, what will happen

Answer 34

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

Question 35

What happens if the slit width is period/N

Answer 35

the minima of the slit diffraction correspond to the maxima N, 2N, 3N, of the grating diffraction resulting in missing maxima