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Stability and Tempco Issues

                                                                   Stability and Tempco Issues  189

                       This is three orders of magnitude larger than the peak signal from the process
                       liquid, and modulated at the same frequency! In order to resolve even ten refrac-
                       tive index values with this system the total stability of all reflection coefficients
                       and fiber attenuation values would have to be about 20,000:1. This is not impos-
                       sible, but represents an extremely high performance system.
                         Clearly the sensor fiber loss is a big problem, so we might attempt to find an
                       alternative fiber with lower loss. However, even if the sensor fiber loss were
                       reduced to zero, the monitor diode reflection (9.0mW) would still dominate the
                       maximum primary received signal (now 625nW). Hence the next job is to reduce
                       the monitor diode reflection, and we have several options. Antireflection coat-
                       ings in the form of quarter-wave thickness films of geometric-mean refractive
                       index deposited on the fiber end can in principle reduce the reflection to zero.
                       In practice, restricted choice of coating materials, errors in deposition, the
                       refractive index gradient across the fiber core diameter and the spread of prop-
                       agation angles in the coating conspire to reduce the coating performance. We
                       might expect 0.25 percent power reflection coefficient, or about 625nW at the
                       signal photodiode.
                         Better anti-reflection performance can be obtained using carefully matched
                       transparent gels or angle-polished fiber ends (Fig. 8.24), after Ulrich and
                       Rashleigh (1980). By choosing the angle correctly, reflected rays are not recap-
                       tured in the acceptance numerical aperture of the fiber. With single-mode fibers
                                                            -6
                       of N.A. ª 0.1 an angle of 12° can give 10 power reflection coefficient, reducing
                       the spurious reflected power to 0.25nW and give about 20 resolved refractive
                       index values. At last the design looks like it might just measure something, but
                       it is still not exactly robust. With higher N.A. fibers the angle must be increased,
                       making polishing and coupling much more difficult.
                         Perhaps the coupler is the problem. What about asymmetric couplers with
                       only a 1 percent tap-off fraction? The disadvantage here is that although a 99
                       percent cross-over coupling ratio from source to sensor is a big help, returning
                       light also crosses efficiently, propagating back to the LED source. There are
                       ways to use asymmetric couplers to our advantage, but it is usually necessary


                                                 Polish
                                               q  angle
                          Range of
                          incident angles
                                                        Range of
                                                        output angles
                            Range of
                            reflected angles
                       Figure 8.24 Reflections from fiber ends and diode laser
                       windows are routinely reduced by angle-polishing. For
                       good performance the cone of reflected light must not
                       overlap the acceptance cone of the fiber. This becomes
                       more difficult as the numerical aperture increases.


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