Lab 14 – Fiber Optics Principles and Position Sensor
Objective:
Fiber optics represents a large technology market in many areas of optical science and photonics. For example,
fiber optics can be used for telecommunications to transmit data, as a conduit to bring laser light into the human
body for surgery, or as a sensor. In this lab, some of the basic principles of fiber optics will be studied. These
principles will be applied to build and test a simple fiber optic position sensor that measures the position of a surface.
Lastly, this lab will introduce the use of fiber optic imaging using coherent fiber bundles.
1. Introduction
Fiber-optics is an excellent application of Snell’s Law or refraction and more specifically Total Internal
Reflection (TIR). Recall from class that when light interacts with an interface of two different materials, in general a
portion of the light is reflected and a portion of the light is refracted. When light travels from a higher index of
refraction material to a lower index of refraction material, the light will be totally internally reflected if the angle of
incidence at the interface exceeds the critical angle given by
(1)
sin c  n2 / n1 .
In the above equation, n1 is the index of refraction on the incident side of the interface and n2 is the index of
refraction on the refracted side of the interface.
For light to travel down a fiber-optic waveguide, the angle at which the light in the fiber hits the interface must
always exceed the critical angle. A simple illustration of the concept is given in Figure 1. Even as the fiber bends
(provided that the radius of the bend is not too small!), the light will continue to follow the direction of a fiber. A
simple analogy is water flowing in a garden hose. The water is confined to the hose and follows the path of the hose
from one end to the other.
Figure 1: Illustration of light ray light bouncing down an optical fiber due to total internal reflection.
Imaging with fiber optics is fairly simple. If we want to image an object using fiber-optics, we need a bundle of
fibers with each fiber corresponding to a pixel in the image. There are two types of fiber bundles: “incoherent” and
“coherent”. For coherent bundles, the relative position of the individual fibers relative to each other is the same at the
input to the fiber bundle as the output. For an incoherent bundle, the relative positions are mixed in comparing the
input to output. Consequently, if one were to use an incoherent bundle for imaging, the “pixels” of the image would
be scrambled at the fiber output. Incoherent bundles (which are cheaper than their coherent counterparts) are
typically used for delivering high optical power to a location. Coherent fiber bundles are required for imaging since
the order of the fibers (and pixels) is maintained.
2. Procedure
A.
Measure the Numerical Aperture of the fiber
1. Place a ruler or piece of paper in the path of the laser and measure the diameter of the laser beam. Also measure
the end of the large core optical fiber to determine its size.
2. Using a large core (about 1mm) fiber optic cable, couple the light from a He-Ne laser into the fiber as shown in
Figure 2 EXCEPT do NOT put the lens NOR the photodetector into the setup at this point. Optimize the
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position of the fiber optic cable using the x-y-z mount. At this point the laser light should be unfocussed. You
should be able to observe light emerging from the output of the fiber using your eye.
Figure 2: Schematic of coupling laser light into a fiber. The input end of the fiber should be mounted in an x-yz mount. Use a photodetector as the detector (make sure it is linear).
3.
With light coupled in the fiber, measure the numerical aperture (NA) of the fiber. For this measurement you will
use a white piece of paper to measure the diameter of the laser beam D as it exits the fiber at a distance L. The
numerical aperture is defined as
NA  Sin  max 
D/2
(2)
( D / 2) 2  L2
D
B.
1.
2.
3.
C.
1.
Optimizing the coupling into a large core fiber optic cable
Complete setting up the experiment as shown in Figure 2. Using a large area photodetector, measure the power
of the He-Ne laser light that emerges from the end of the fiber. Before proceeding, make sure that the detector is
linear. For this lab, the absolute power of the laser is not important. You can use the "Photodetector Voltage" as
a measure of the detected power and measure the voltage from the detector using a lock-in amplifier.
Optimize the position of the fiber optic cable using the x-y-z mount. Record the optical power which emerges
from the fiber (when optimized).
Compare your measurements from Part 2.A.1 for the size of the fiber relative to the size of the laser beam. If the
size of the laser beam is LARGER than the size of the fiber, use a 100mm lens to focus the laser light onto the
fiber optic cable. DO NOT ADJUST THE position of the fiber. You will only need to adjust the position of the
lens. The distance from the lens to the end of the fiber should be roughly equally to the focal length of the lens.
Optimize the position of the lens to maximize the optical power emerging from the fiber. If you require a lens,
record this optimized power emerging from the fiber.
Bending losses
With the laser light optimally coupled into the fiber, measure the optical power emerging from the fiber. For this
measurement, try to eliminate any bends in the fiber.
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2.
3.
Make a loop in the fiber with a 20cm radius and record the optical power emerging from the fiber. Be careful
that you do not move the ends of the fiber. If you do, this will change the amount of light coupled into the fiber.
Consequently, you would not be measuring the effect of a loop in the fiber, but rather changes in light coupling
due to alignment.
Repeat the voltage measurement with 15cm, 10cm, 5cm, 2cm diameters of fiber. If you do not measure any
reduction in the optical power with smaller loops, decrease the diameter until you do. For each loop diameter,
record the optical power.
D. Build and Evaluate a fiber-optic position sensor
1. Using the large core fiber optic cable, assemble a fiber optic position sensor as shown in Figure 3. One fiber is
used to deliver the light to the mirror surface. The other fiber collects some of the reflected light from the
surface. As the surface moves relative to the ends of the fibers, the power of the light collected by the fiber
optical cable changes.
2. Using some scotch tape, tape the ends of the two fibers together at one end. The instructor will provide the
appropriate mount for holding the fiber ends. Place the fiber ends so that they are roughly perpendicular to the
surface of the mirror and just touching the surface of the mirror.
3. The spare fiber end should be placed in front of the photodetector. The instructor will provide a special mount
for the fiber.
4. Connect the output of the photodetector to the lock-in.
5. Measure the detected power as a function of displacement d of the mirror. Make sure that the displacement is
over a large enough range (0<d<2cm) since a part of the lab is determine the displacement range over which the
position sensor will work.
Figure 3: Schematic of Fiber optic position sensor. The intensity of light which is coupled into the detecting fiber
after reflection from the mirror should depend on the displacement d of the mirror. The lock-in amplifier and
Chopper (not shown) should be set up as shown in Figure 2 above.
Figure 4: Typical image of some writing on a business card as taken with a digital camera and fiber bundle. Picture
on right is enlarged.
E. Observations with a coherent fiber bundle
1. Using a coherent fiber bundle, place the small end of the fiber bundle a few centimeters away from some
printing on a piece of paper or business card. Do you observe a clear image of the printing? If not, you can
change the focusing of the lens that is mounted on the end of the fiber bundle by rotating the lens mount.
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2.
Using a digital camera supplied by the instructor, capture an image from the fiber bundle. The image should
look like the figure below.
3. Discussion
1.
2.
3.
Using Eq. (2) calculate the Numerical Aperture of your fiber.
For Part 2.C, plot the detected optical power as a function of the bend diameter. What is the smallest
diameter of bending before bending losses become noticeable?
Briefly explain (drawing on the diagrams below) WHY there are bending losses. HINT: What draw on the
figure the normal to the surface and illustrate the angle of incidence for the two fibers. What happens if the
angle of incidence EXCEEDS the critical angle?
4.
Based on your results for the fiber optic based vibration sensor (part 2.D), plot the detected optical power
versus displacement of the mirror. Your plot should look something like the following
5.
Starting from zero displacement, why does the detected light intensity first INCREASE from zero (region 1)
in above figure and then decrease (region 2)? HINT: The two fibers are physically separated. If the mirror is
DIRECTLY touching the ends of the fibers, how much light will be detected?
Is there any displacement region where this displacement sensor is linear?
Would you expect the displacement sensor to work on a diffusively reflecting surface (eg. a piece of
cardboard)? Why or Why not?
Include a picture of the fiber bundle image in your report.
 In examining your image, you will observe that there appear to be distinct pixels in the image. Why are
there distinct pixels in the image? Why does the image not appear to be continuous?
 From your image, estimate the number of pixels in the fiber bundle image.
6.
7.
8.
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