Polarization, Diffraction, Fourier Optics Flashcards
Relationship between spatial frequencies and propagation angle?
Theta = lambda * frequency (paraxial approximation) (incident plane wave transmits thru thin optical element). Wave deflection is an interference phenomenon
Basic principle of Fourier optics?
An arbitrary wave in free space can be analyzed as a superposition of plane waves
Fourier transform in the far field
With a sufficiently long propagation distance, the only plane wave contributing to complex amplitude is the Fourier transform of the incident shape. However, the phase is only a Fourier transform over a spherical surface, not a flat plane. Entirely based on angles, so shape does not change as a function of distance.
What is the diffraction pattern off an aperture the further you go?
First: a shadow of the aperture, then a Fresnel diffraction pattern (convolution of aperture function), then a Fraunhofer diffraction pattern (absolute-squared value of Fourier transform)
Purpose of 4f system?
To preserve magnification and propagate beam, Fourier plane is 1f away from lens. If further away it’s still a FT but not unity mag
Shape of low-pass, high-pass, and vertical-pass filter
Low-pass: hollow disk in middle, high-pass: opaque disk in middle, vertical-pass: vertical line
What’s electronic speckle pattern interferometry
Characterizes optically rough surfaces with induced speckle pattern. A speckle pattern is interfered with a reference beam and a speckle pattern is obtained; “correlation” fringes (not interference) are obtained when subtracting one from the other.
As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?
It will get -wider-.
What happens to the diffraction pattern of a single slit when the entire optical apparatus is immersed in water?
The diffraction pattern becomes narrower (higher n)
In our study of diffraction by a single slit, we assume that the length of the slit is much larger than the width. What happens to the diffraction pattern if these two dimensions were comparable?
You get a 2D diffraction pattern.
What’s the Rayleigh criterion?
Theta = 1.22 * lambda / D; theta is smallest possible angle between point sources (best resolution). Smaller theta is, better resolution is. (D = diameter of iris)
Does a red light or blue light give a higher resolution microscope?
Blue light (Rayleigh angle is smaller; Rayleigh criterion)
Why does a beam of light always spread out? Why can’t parallel beam be created?
Because of diffraction; the source is an aperture with fixed diameter. Infinite large diameter aperture is the only way to create perfectly straight beam
What sort of waves do polarization occur with?
Transverse waves (perpendicular to wave advance direction; opposed to longitudinal waves)
Critical angle formula
TIR: theta_c = arcsin(n2/n1)
What’s the Huygens Principle?
The idea that every point on a wavefront is the source of spherical wavelets; secondary wavelets from other points mutually interfere, forming a wavefront.
Does Huygens principle work for all types of waves?
Yes
Brewster angle formula
tan(theta) = n2/n1
Polarization by reflection
Unpolarized light will completely reflect polarized (perpendicular to plane) at Brewster angle
Refractive index of water
1.33
Refractive index of glass
1.52 (crown glass)
Rayleigh scattering wavelength dependence?
1/lambda^4
What’s the Wiener-Khinchin theorem?
For a wide-sense-stationary random process, the autocorrelation function has a spectral decomposition given by the power spectrum.
What is a stationary/wide sense stationary process?
A stochastic process whose mean, variance, and joint PDF does not change with a shift in time. (Important for time series analysis). Wide sense stationary is a bit more general (only mean and autocovariance are time invariant), second moment is finite.
What is an LTI system?
Linear time-invariant system produces an output signal from any input signal given linearity and time-invariance. Use in image processing applications with spatial and temporal dimensions.
Reflectance formula (on incidence)
R = ((n-1)/(n+1))^2
Refractive index of silicon?
3.4
What is the grating equation?
sin(theta_m) = sin(theta) + mlambdaf*10^-6
