Download Spatial Coherence

LAB 7 - SPATIAL COHERENCE AND OPTICAL IMAGING
FALL 2009
Objective
To become familiar with the concept of spatial coherence.
PRELAB
1)
You have a Young's interferometer with a slit spacing of 1mm. The measured fringe spacing 1m
from the slits is 0.8mm and the visibility (xc) of the fringes is 2.7mm. Determine the wavelength
of the source and estimate its spectral width.
2)
Explain, in your own words, how it is that an incoherent extended source gains spatial coherence
through propagation.
3)
What is the cutoff spatial frequency of a pinhole camera (pinhole and CCD) that has a 100 micron
diameter aperture and a pinhole-to-camera separation of 10 cm for a) a HeNe and b) a
MagLightTM?
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 (i.e. Fourier Optics, setting up a magnified imaging system,
etc.), determine the slit spacing and slit widths. Hint: You may need to overlap a
calibrated ruled grating (1 or 10 lp/mm) with the slits you made, but then maybe not.
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. Be creative. Be sure to record the distance to the camera.
What is the wavelength of the HeNe determined using this method? How accurate are
your results relative to the known HeNe wavelength (632.8nm)?
5)
What is the fringe visibility (xc) of the HeNe? Does your measurement make any sense
when considering your results from the spectroscopy lab?
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6)
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.
7)
Repeat steps 3 and 4 for light emerging from an incoherent source (i.e. LED or
spectrometer). Do you observe any fringes? If you can’t get fringes, see the TA. Don’t
waste too much time on this if you are unsuccessful.
PART II
THE PINHOLE CAMERA
Discussion
We will compare coherent and incoherent imaging using a pinhole camera.
Experiment
1)
Make a pinhole in aluminum foil (or you can use one of the good irises) and place it in
front of the HeNe beam. Try to estimate the pinhole size using Fourier Optics principles.
You can use something of known diameter to make the hole to be sure that you are on the
right track. For example, you may use a buffered piece of optical fiber, whose diameter
is 0.25 mm. If you use the iris, you will have to determine its diameter using Fourier
Optics.
2)
Build a pinhole camera by placing the pinhole right in front of a CCD camera (do not use
a CMOS cameras for this part) and try to obtain an image of the room (it is best if only
the strip of lights on the opposite side of the room are on while the central strip and your
strip are off). Determine whether the image is inverted or upright. Explain. Place the
incoherent light source (white or blue LED) roughly 2 inches away (pointing at the
pinhole) and set the light level so that a bright spot is visible on the TV, but also so that
you are not saturating the CCD (~10 mA into the LED). See the TA if you have
difficulties. Using a slide of your choice, place it between the light source and pinhole
and try to form an image.
3)
Use a ruled grating as an object slide. Measure the grating period using Fourier optics
techniques (unless the value is given on the slide). Illuminate the grating with the light
source and measure the resulting grating period on the CCD camera as a function of
distance between the pinhole and the object. You may just measure features on the TV
using a ruler.
4)
Using a chirped ruled grating (such as the ‘picket fence’ or ‘split grid’), estimate the
maximum spatial frequency that your pinhole camera can resolve at a fixed object
distance.
5)
Keeping the pinhole and object fixed, qualitatively examine how the ‘cutoff’ frequency
varies as you move the camera relative to the pinhole.
6)
Repeat for coherent laser illumination. What problems do you run into? Comment on
the case of spatially incoherent laser illumination (i.e. laser light that has been disturbed
using the frosted glass).
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PART III
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.
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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.
4)
Place the 1-inch narrow-band red interference filter 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.
5)
Replace the red filter with the green filter (560 nm). Record the new dot spacing.
6)
Repeat (2) with the mesh much closer to the fiber end.
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QUESTIONS FOR WRITEUP
1)
Determine the spectral bandwidth and mean wavelength of the incoherent source used in
Part I. Were there any problems in your setup?
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)
What do we mean when we say that the laser is spatially coherent? How can you make it
spatially incoherent?
4)
Describe your results for the pinhole camera and provide all relevant data. What
differences did you observe between coherent and incoherent imaging through the pinhole?
5)
Plot your data showing grating periods as a function of distance between pinhole and
object. Also plot the product of distance and grating period as a function of distance.
Comment on the results.
6)
Determine the coherence radius of the fiber-optic ‘point source’ at 1 meter away. What is it at
2mm away?
7)
Using very rough estimates for the wavelength of the filters, show that the dot spacing measured
in Part III are consistent with Fourier optics principles. What did using the interference filters do
to the spectrum of the light source?
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