Download LAB 3 - SPATIAL COHERENCE AND OPTICAL IMAGING

LAB 6 – ROLE OF SPATIAL COHERENCE IN OPTICAL IMAGING
FALL 2016
Objective
To become familiar with the concept of spatial coherence, and its qualitative effects on image
formation.
PRELAB
1)
Explain, in your own words, how it is that an incoherent extended source gains spatial coherence
through propagation.
(1 point)
2)
In Young’s interferometer, two pinholes are illuminated by the same source, and an interference
pattern is observed on the detector. With a sufficiently large coherence area, interference fringes
will be formed. When the coherence area of the illumination is small, the two waves will add
incoherently. In separate boxes, sketch the 1D line profile of the fringes for different degrees of
spatial coherence. Make sure to include the completely spatially coherent and spatially incoherent
cases.
(3 points)
3)
Explain the difference between a random variable and an observation. If we assume that the fields
are statistical in nature, what is recorded on the detector?
(2 points)
PART I
YOUNG'S INTERFEROMETER
Discussion
We will use this part to investigate the coherence of a HeNe and light from a
monochrometer or LED.
Experiment
1)
Construct a pair of slits for a Young's interferometer using a glass slide and any other
creative materials. For example, you can use electrical tape or aluminum foil. A good
method is using a straight edge and an exact-o-knife to scribe a pair of lines into blacktaped slides.
2)
Using any method, you like, determine the slit spacing and slit widths. Hint: You may
need to overlap a calibrated ruled grating with the slits you made…
3)
Set up a Young's interferometer using a CCD camera to view the fringe pattern. First,
calibrate the CCD signal to be able to measure actual distance on the CCD camera as you
did in the past by knowing the CCD dimensions. Be sure to calibrate this distance with
time on an oscilloscope using the TV trigger. See the TA if you are confused.
4)
Having calibrated your apparatus, determine the fringe spacing through your slits at some
distance ~1m from the slits. You will need to expand the HeNe beam in some manner
before impinging on the slits, similar to the previous labs. Be sure to record the distance
1
to the camera. Sketch your setup. What is the wavelength of the HeNe determined using
this method? How does this compare with the known wavelength of a HeNe? Make sure
it compares favorably before continuing.
(3 points)
5)
Wave and spin a glass plate or frosted glass plate both very rapidly and very slowly,
someplace in the beam on the HeNe side of the slits, and describe what happens to the
interference pattern. Explain in terms of spatial coherence concepts.
(2 points)
6)
Repeat steps 3 and 4 for light emerging from an incoherent source (i.e. LED,
spectrometer, or medieval torch). Do you observe any fringes? If you can’t get fringes,
see the TA to confirm. Don’t waste too much time on this if you are unsuccessful.
PART II
THE VAN CITTERT-ZERNIKE THEOREM
Discussion
An extended incoherent source of radiation gains spatial coherence through propagation. This
generally means that either 1) the source is very small compared with the propagation distance or
2) the source is very far from an observation point such that, in either case, the source resembles a
point source over the space of observation. The Van Cittert-Zernike theorem states that there is a
Fourier transform relationship between the mutual intensity function and spatial intensity
distribution of an extended incoherent source (see Eqn. 11.3-25). Obviously, this would imply
that smaller sources would have wider coherence angles.
The coherence radius in the far field for a circular extended source is found from
 c  1.22
l
d
where l is the distance between the source and the observation plane, and d is the diameter of the
extended source. Thus, we can see that the further the observation plane from the source, the
greater the radius of coherence in the observation plane. As long as l is large enough, even
distance stars can closely resemble point sources and have spatial coherence lengths of many
meters. We will investigate case 1) from above using the 200µm core fiber and white light. You
can assume that the light intensity is uniformly distributed in the fiber.
Experiment
1)
Connect a 1-meter 200 m blue fiber patchcord to the Ocean Optics white light source. Secure the
other end of the fiber to a holder and point it down the table. You will probably want darkness
during this exercise.
2)
Place the wire mesh about 1m from the fiber end. Using the fast lens that is provided, form a
focused transform plane. You may observe a rainbow effect, with red on the outside. Is this
consistent with our theory for the diffraction angle as a function of wavelength? A good way to
observe this would be to look down the table at the light source through the wire mesh. Move the
lens out of the way if you use this method.

3)
Place a camera in the focal plane and display it on the TV screen. You may see some streaking,
which is a result of aberrations in the lens, but try to get the focal plane as sharp as you can. This
may require rotating the lens.
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4)
Place the 1-inch narrow-band red interference filter (or similar) in front of the white light source.
How does this affect the transform plane? Does this pattern resemble the transform plane
produced by the HeNe? Record the dot spacing on the TV screen.
(1 point)
5)
Replace the red filter with the green filter (560 nm). Record the new dot spacing.
(1 points)
6)
Repeat (2) with the mesh much closer to the fiber end.
(2 points)
PART III
SPATIAL COHERENCE AND IMAGE FORMATION
Discussion
The role of spatial coherence in image formation is an active area of research. Here you
will note that the qualitative trends when the spatial coherence properties of light are
modified by opening and closing the condenser on the microscope.
Experiment
1)
For this experiment you will use a microscope with Köhler illumination and tunable
condenser aperture. With the help of your TA verify that the microscope is aligned and
producing an ideal image.
2)
The bright field position of the condenser contains an aperture. In our model, each point
in the aperture produces a random wave that contributes a plain wave at the sample plane.
Observe that opening and closing the condenser results in a qualitative change in the
image. Describe what you see.
(1 points)
3)
To quantify this change you will acquire images of two samples at three condenser
positions – “open”, “closed”, and “half-open”.
4)
Switch the light path to the camera port and focus a test sample. Verify that the images
are raw recordings of the pixel sensor (instead of JPEG) and are the expected bit-depth of
the camera (typically 12-bits). If unsure ask your TA.
5)
For the first sample we will attempt to uniformly fill the spatial bandwidth of the imaging
system. Such samples include a fine diffuser or a slide with histopathological prepared
tissue. Now acquire the same field of view at the three condenser positions. Verify your
images before continuing.
6)
Next find a sample with an identifiable structure. For your write up you will draw a line
profile through this structure and note the qualitative changes as the aperture is closed. A
red blood cells or a scratch on the glass will work well. Record three images.
7)
Have a group member send out the acquired images to your partners. You will need them
to answer the lab questions!
QUESTIONS FOR WRITEUP
3
1)
Determine the spectral bandwidth and mean wavelength of the incoherent source used in
Part I. Were there any problems in your setup?
(1 point)
2)
Why might the Young's interferometer be a more practical apparatus for measuring the
spectral characteristics of an LED, rather than using a Michelson interferometer to measure
the coherence function? Answer in terms of the sources of the phase shifts and the relative
practicality of distances involved in the measurements.
(3 points)
3)
What do we mean when we say that the laser is spatially coherent? How can you make it
spatially incoherent?
(3 points)
4)
Determine the coherence radius of the fiber-optic ‘point source’ at 1 meter away. What is it at
2mm away?
(2 points)
5)
Using very rough estimates for the wavelength of the filters, show that the dot spacing measured
in Part II are consistent with Fourier optics principles. What did using the interference filters do to
the spectrum of the light source?
(3 points)
6)
Shows the images you acquired for the first sample in Part III side-by-side with the log magnitude
of the Fourier transform. What conclusions can you draw?
(4 points)
7)
Using a tool such as ImageJ show the line profile of your chosen structure as the condenser
aperture is closed down, side-by-side with the acquired images. What conclusions can you draw?
(4 points)
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