Solution: The OBR measures time of flight without knowing what material the light is traveling through. The user has to enter a group index in order for the distance to be calculated correctly from the time of flight. For a case where the index changes throughout the trace (see Figure 1), the user has a couple of options.

Switch between Fiber and Air

Figure 1: OBR measurement of a switch. The material changes from fiber to air and back to fiber, so to measure distance between peaks you must compensate for the change in group index.

Method 1:

First, you can choose to display the x-axis in nanoseconds, instead of distance, using the pull-down menu at the bottom of the graph. Then, use the cursors to mark the two events of interest. Once the delay between peaks in ns is known, the user can calculate the distances using the correct group index.

Peaks measured in nanoseconds

Figure 2: Using the cursors, we can find the time (ns) difference between the two peaks, as shown by dX in the circled area. Use the equation below to convert this to distance.

The equation that governs this measurement is:

OBR material change distance equation

where L is the length (m), c is the speed of light in a vacuum (m/s), t is time (s), and n is the group index of refraction of the device under test.

Using Figure 2, we calculate the following:

c = 299,792,458 m/s
n =1.00027 (index of refraction of air)
t = dX (on the graph) = 53.586E-3 ns = 5.3586E-11 s

Using the numbers above, we find that L = 0.00803017 m for this example. Therefore, the distance between the two events is 8.03 mm.

Method 2:

Another method can be used to find the distance between the two events. First, change the graph to measure length. Then, enter the group index value for the material that is of most interest (for our example, we change it to the index of refraction of air). The absolute distance to each peak will be incorrect, but the relative distance between peaks in that material will be correct (see Figure 3). Notice that the circled measurement shows that dX = 8.030E-3 m, which corresponds to the value found above in method 1.

distance between peaks, measured in meters

Figure 3: Using the group index of air, we can measure the relative distance between the two peaks, as shown by dX in the area circled above.

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Document ID: 0615006002
Last Update: 06/15/2006

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