Week 3 Flashcards
how do you define constructive and destructive interference?
take 2 identical monochromatic waves, linearly polarized.
if the interference is totally constructive then the phase difference is zero and the electric field’ amplitude is twice the amplitude of one wave
if the interference is completely destructive then the phase difference is pi/2 and the electric field’s amplitude is zero.
what are optical detectors?
optical detectors are not fast enough to measure amplitude’s oscillation that are in the range 10^14 - 10^15 Hz
they measure the intensity= power/surface which corresponds to the magnitude of the time averaged poynting vector
How does the Michelson interferometer work?
you have light input from the left side (it could be a laser or a led), a beam splitter in the middle.
you have 2 mirrors where the light beams are reflected and one of them is moveable.
as soon as the light hits the moveable mirror, the trajectories of the 2 beams impinching onto the 2 different mirrors are no longer the same.
when these 2 beams recombine on output 1 you record some interference.
therefore intensity maxima are observed by moving one of the 2 mirrors.
additionally the different coherence lenghtd of white light and laser light can be demonstrated.
what are the applications of the michelson interferometer?
optical coherence tomography
one possible application is bio imaging
you can use this interferometric configuration to detect at different dephts
the advantage is that here you use visible light and not x rays taht could damage the tissue
Draw the pattern that you would expect (slide 6/85).
you’ll have different intensities depending on the depth you are imaging (tau_i)
to do this measurement you can use red light but even IR to try to minimize the scattering which represents the major issue in this tecnique.
definition of coherence of light.
the coherence of light is the ability of light to interfere.
why don’t we see more interference effects in every day life?
human eye temporal resolution: milliseconds
cycle time of light: femtoseconds
there are 12 orders of magnitude between the cycle time of light and what our eyes can process
orders of magnitude for the coherence for different light sources
unfiltered sunlight 1 femtosecond
LED 10 femtoseconds (LED are normally incoherent as compared to laser light)
single-mode fiber laser 100 microseconds
hydrogen maser 1 s (the maser is for instance used for the atomic clocks)
orders of magnitudes for coherence lenghts
He-Ne laser (monomode) 100 m
He-Ne laser (multimode) 20 cm
laser diodes: below 1 mm
LED: 10 microns
halogen lamp: 16 microns
(going from the top to the bottom: less and less coherence of light)
what is the distinction between temporal coherence and spatial coherence?
temporal coherence: we are considering the ability of light veam to interfere with a delayed (but not spatially shifted) version of itself.
spatial coherence: we are concerned with the ability of a light beam to interfere with a spatially shifted (but not delayed) version of itself.
what type of coherence do you see in the Michelson interferometer?
the michelson interferometer allows the interference of a light beam with a delayed version of itself
the temporal delay is set by the position h of the mirror
as h (delay) increases the detector measures interference fringes
what is the relation between the coherence lenght of a source and the finite bandwidth
light sources have a finite bandwidth which determines a reduced capability to interfere
Lc goes as 1/ (delta_nu)
the larger the bandwidth the shorter the coherence lenght
describe the optical microscopy
For each microscope, even the simplest one, ypu can have different filters, different objectives and different polarizers.
the schematic is as follow: point source–>objective–>tube lens–> airy disk (airy pattern)
you observe this airy pattern whenever you try to image something that is below the resolution limit, you are actually seeing the convolution of the property of the microscope and the point you want to measure
to understand the concept of resoolution is important to understand the point spread function (=response of an imaging system to a point source or point object)
the image of a complex object can be seen as a convolution of the object and the PSF (PSF is a property of your system)
Today in current software you can even deconvolve your image directly.
what is the point spread function PSF?
it is the response of an imaging system to a point source or point object
the point spread function limits the resolution of the imaging system: the capability to distinguish between 2 separate points
what is the rayleigh criterion in the topic of resolution of optical microscopy?
two points can be resolved if the centers of the airy disks are separated by 1/2 the diameter of the airy disk
What happens when we try to image a tiny object with the optical microscope?
If this object is below the resolution limit then you would get the so-called airy disks around the point you want to measure. therefore what you are looking at is actually the convolution of the property of the microscope (point spread function) and the object you want to measure. in today’s software you can have the de-convolution of this image. in prectice the point spread function limits the resolution of the imaging system= the capability to distinguish between 2 separate points.
what determines the final resolution of the optical microscope?
- specific design of the microscope, so the quality of the optical elements, the cost
- a fundamental limit depends on the numerical aperture of the objective NA= n sin (alpha): sketch slide 24/85
what are the different criterion to define resolution?
Raileigh resolution (x,y)=0.61 lambda/NA
Abbe resolution (x,y)= 0.5 lamda/NA
Abbe resolution (z) = 2 lamda / NA^2
the higher NA –> the better resolution
the shorter lambda –> the better resolution
you always have a worse resolution in the z direction, it’s difficult to image in the depth than in the xy plane
How to increase the numerical aperture?
NA=n sin (alpha), n is the refractive index of the medium in between the sample and the objective.
immersion objective NA>1 (n H20= 1.33, n glycerol = 1.47, at 632 nm)
(draw the light rays bending, slide 28/85)
What does NA measure?
the capability of an objective lens to collect/ focus light and resolve the details of a specimen at a fixed distance.
what is the relation between NA and magnification?
there’s no a precise relation, but a rule of thumb is that the higher the NA the higher the magnification
on what does the magnification depends?
on the NA (the higher the NA the higher the magnification)
on the tube lens focal lenght (different tube lens focal lenght for different manifacture)
you really need to know you instrument to get a good imaging
How does the resolution depend on the wavelenght?
The longer the wavelenght thw worse the resolution
typical orders of magnitudes of the different quantities playing a role in optical microscopy?
NA: 1.25 (n*sin(alpha))
resolution: 0.22 microns
plan achromat and plan apochromat are the 2 different objectives that you can have, each of these corrects certain color aberration
what is the distiction between achromat and apochromat objectives?
tzhey consist in the introduction of additional optical elements made of glasses with different dispersion
