FINAL EXAM REVIEW QUESTIONS
Diffraction Theory :
- What is Huygen's theorem? What was its greatest failure?
- What is meant by the obliquity factor? Who
- What is the usual distance equation that specifies the
requirement for far-field diffraction?
- What is the size of the Airy disk for a small aperture of
diameter a illuminated by light of wavelength l ?
- Explain the following statement: The far-field
diffraction pattern of an aperture is the Fourier
transform of its transmittance function.
- When parallel light passes through a lens at an angle q to the optical axis, where is the
image of the parallel light formed?
- Do small objects in a transparency form data points
closer to or farther from the optic axis than larger
Fourier Transforms :
- When are Fourier frequency terms discrete harmonics and
when are they continuous frequencies?
- What is the Nyquist theorem?
- For an object of 2 cm dimension, what is the minimum
spatial resolution (in cm) when the object is digitized
into an array of 512 samples?
- How many harmonics will be present in the Fourier
transform of the object described in the previous
- What is the lowest (but not dc) spatial frequency
involved in the transform of the object described above?
- Assuming that in physical measurements all data is real,
what is the smallest item in the object mentioned above
that can be resolved ?
- To display a Fourier transform so that the transform is
centered in the display, what must be done to the input
- What is a principal advantage of working in Fourier
- When a lens of focal length f is used to bring
in a far-field pattern to a convenient range, what is the
relation between the radial distance r from the
optic axis of a point in the Fourier transform, and the
spatial frequency this location represents if the
parallel coherent illuminating beam has wavelength l ?
- Link the following aperture types with the appropriate
mathematical form of their Fourier transforms:
rectangular slit, circular aperture, sine wave; Bessel
function, sinc function, Kronecker delta function.
- If an image of dimension 2 cm contains an item of basic
size 0.1 mm, what is the minimum sampling number that
will satisfy the Nyquist condition?
- A grid of small rectangular apertures is illuminated by a
collimated and expanded laser beam. How would you obtain
its Fourier transform optically? Where would you put a
horizontal slit to filter the transform, and how would
you get the transform of the filtered transform? What
would it look like? Draw sketches.
- Describe and sketch an optical low-pass filter. Do the
same for a high-pass optical filter.
Contouring with Moire :
- What is the difference between shadow and projection
- Which requires the higher resolution imaging sensor?
- What are the different requirements as regarding the
necessary size of the master grid?
- Why does one have a geometric term of tan q in its basic equation, while the
other has sin q ?
Holographic Interferometry :
- Give at least five requirements of the experimental setup
for obtaining holographic images.
- What are some of the advantages and disadvantages of
using holography for making measurements?
- What are the three basic types of measurement in
- What is the sensitivity vector and how is it
defined? How is its magnitude obtained?
- What is meant by the sign problem and how can it
- Give a sketch of an experimental setup for
holointerferometry that is suitable for in-plane
- Give a sketch of an experimental setup for
holointerferometry that is suitable for out-of-plane
Speckle Metrology :
- What is the difference between objective and subjective
- What is the difference between speckle photography
and speckle interferometry?
- Which method has the greater resolution, photographic
- Speckle photography is sensitive only to in-plane motion,
while speckle interferometry can be made sensitive to
either in-plane or out-of-plane motion. Draw sketches of
appropriate setups for each case.
- In analyzing specklegrams of speckle photography, what
method of analysis gives point-by-point results? What
analysis method gives full-field results? One method
gives the magnitude and line-of-motion of the
displacement recorded in the specklegram, and the other
gives components of motion along a particular
direction, but neither can give the sign of the
- Draw a sketch of the setups appropriate for each method
Electronic Speckle Pattern Interferometry (ESPI) :
- The basic advantages of ESPI are simplicity and
economy compared to standard speckle pattern
interferometry. What are some of the factors that bring
simplicity and economy?
- Draw sketches showing ESPI setups for in-plane and for
- What is the common way of solving the sign problem
in ESPI ?
- What is meant by phase unwrapping? How is it linked to
the Nyquist requirement and to the periodicity of trig
- If the maximum displacement limitation of ESPI is about
half a speckle size, and the magnification of the optical
system imaging the loaded surface onto the camera sensor
is 1/3, what is the largest measurable motion of
locations in the surface? (Assume speckle size is about 5
List of Equations
a sin q = ml
b sin q = ml
f = x/(lz)
|w = (Dn p)/tan
|w = (Dn p)/sin
k = 2p/l
g = e2 -
g · d = Dn l
g = [0, 2]
|Sobj = 1.22 Ll/D
||objective speckle size
|Ssubj = 1.22 (M + !) l f/a
||subjective speckle size
1/f = 1/s + 1/s'
m = -s'/s
|p = lD/d
||Young: speckle motion
|p = nlf/r
||Fourier: speckle motion
|Dy = p/M
|w = nl/2
||out-of-plane symmetric small angle beams
|u = nl/(2 sin q)
||in-plane motion symmetric beams
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Last Modified on May 01, 1997
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