Polarization, Diffraction, Fourier Optics Flashcards

1
Q

Relationship between spatial frequencies and propagation angle?

A

Theta = lambda * frequency (paraxial approximation) (incident plane wave transmits thru thin optical element). Wave deflection is an interference phenomenon

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2
Q

Basic principle of Fourier optics?

A

An arbitrary wave in free space can be analyzed as a superposition of plane waves

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3
Q

Fourier transform in the far field

A

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.

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4
Q

What is the diffraction pattern off an aperture the further you go?

A

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)

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5
Q

Purpose of 4f system?

A

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

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6
Q

Shape of low-pass, high-pass, and vertical-pass filter

A

Low-pass: hollow disk in middle, high-pass: opaque disk in middle, vertical-pass: vertical line

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7
Q

What’s electronic speckle pattern interferometry

A

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.

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8
Q

As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?

A

It will get -wider-.

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9
Q

What happens to the diffraction pattern of a single slit when the entire optical apparatus is immersed in water?

A

The diffraction pattern becomes narrower (higher n)

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10
Q

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?

A

You get a 2D diffraction pattern.

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11
Q

What’s the Rayleigh criterion?

A

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)

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12
Q

Does a red light or blue light give a higher resolution microscope?

A

Blue light (Rayleigh angle is smaller; Rayleigh criterion)

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13
Q

Why does a beam of light always spread out? Why can’t parallel beam be created?

A

Because of diffraction; the source is an aperture with fixed diameter. Infinite large diameter aperture is the only way to create perfectly straight beam

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14
Q

What sort of waves do polarization occur with?

A

Transverse waves (perpendicular to wave advance direction; opposed to longitudinal waves)

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15
Q

Critical angle formula

A

TIR: theta_c = arcsin(n2/n1)

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16
Q

What’s the Huygens Principle?

A

The idea that every point on a wavefront is the source of spherical wavelets; secondary wavelets from other points mutually interfere, forming a wavefront.

17
Q

Does Huygens principle work for all types of waves?

A

Yes

18
Q

Brewster angle formula

A

tan(theta) = n2/n1

19
Q

Polarization by reflection

A

Unpolarized light will completely reflect polarized (perpendicular to plane) at Brewster angle

20
Q

Refractive index of water

A

1.33

21
Q

Refractive index of glass

A

1.52 (crown glass)

22
Q

Rayleigh scattering wavelength dependence?

A

1/lambda^4

23
Q

What’s the Wiener-Khinchin theorem?

A

For a wide-sense-stationary random process, the autocorrelation function has a spectral decomposition given by the power spectrum.

24
Q

What is a stationary/wide sense stationary process?

A

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.

25
Q

What is an LTI system?

A

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.

26
Q

Reflectance formula (on incidence)

A

R = ((n-1)/(n+1))^2

27
Q

Refractive index of silicon?

A

3.4

28
Q

What is the grating equation?

A

sin(theta_m) = sin(theta) + mlambdaf*10^-6​