The present invention relates generally to level sensors, and more specifically to optical level sensors that generate a measurement based on light escaping from a waveguide over a portion of the waveguide that is submerged in liquid.  In the context of this application, the term liquid will be used to denote any material capable of establishing optical contact with the waveguide (e.g., common liquids such as water, fuels, solvents, process chemicals, acids, bases, and reagents, as well as food stuffs, froths, foams, gels, suspensions, and miscellaneous mixtures, slurries, etc.). 
Currently, there are many different types of liquid level sensors commercially available.  Each different type operates on different physical principles and has particular advantages and disadvantages in specific applications. 
Liquid level sensors for chemical and fuel storage tanks have traditionally employed float-based systems, although in recent years, sensors based on electronic transduction methods have been developed (e.g., capacitance-based sensors).  Float-based sensors continue to be the most widely used in commercial applications due to their low cost and entrenched market position.  Even though capacitive sensors offer higher reliability in demanding environments (e.g., high levels of vibration, shock, etc.),  their relatively high cost has slowed their rate of adoption in applications such as trucks and busses.  Additionally, in demanding liquid storage tank applications such as aircraft fuel, corrosive liquids, solvents, high purity chemicals, and bio-chemical reagents, the relatively limited performance, high cost, and poor material compatibility of both float-based and electronic sensors have restricted the utilization of these level sensing technologies. 
A practical optical level sensor would offer several inherent advantages in the applications described above.  In an optical sensor, no electrical contact is made with the liquid.  Additionally since no electrical conductors enter the liquid storage area, there is no risk that electrical conductors could contact the liquid even if the sensor body were to experience mechanical failure.  Furthermore, optical sensors have no moving parts and therefore exhibit minimal hysteresis.  Moreover, in many cases, due to their simpler construction and no moving parts, optical sensors can be fabricated with materials (e.g., glasses and specialty plastics) that are suitable for use with both high purity chemicals and reagents as well as with aggressive solvents, acids, and corrosives.  An optical sensor can be made at relatively low cost in certain applications due to simplified fabrication methods and the use of inexpensive materials. 
Prior art optical level sensors have suffered from several problems that have made it difficult to produce a low cost, linear, and accurate level sensor that functions reliably in storage tanks of various sizes for a wide range of liquids.  Prior art sensors have been susceptible to fouling from environmental contaminants and the formation of biofilms on their surfaces which spoil their calibration.  Additionally, prior art devices have generally suffered from inherent design limitations which severely compromise accuracy and sensitivity when the sensor's length exceeds six inches to one foot. 
FIG.  1A shows a representative prior art optical sensor 10 of the type that detects the level of a liquid 12 contained in a tank 15 utilizing light propagation in a waveguide.  The sensor exploits the difference in index of refraction between the gas and liquid phases in contact with the probe as the transduction mechanism.  The sensor includes a vertical rod 20 of optically transmissive material (such as plastic) having an index of refraction N1.  The rod is illuminated from the top by a light source 25 with a mirror 27 on the end nearest the bottom of the tank.  A detector such as a photodiode 30 is positioned to measure the light traveling upward after being reflected by the mirror. 
The light launched from the light source propagates inside the rod and will be contained within the rod at the boundary between the rod and the external medium (index of refraction N2) by total internal reflection as long as the angle of propagation of the light relative to the longitudinal axis of the rod is less than the critical angle .theta..sub.c, where:
.theta..sub.c =cos.sup.-1 (N2/N1). ( 1)
At the point where the rod is immersed in the liquid, the index of refraction in the external medium increases dramatically, and a fraction of the light traveling at angles greater than .theta..sub.c will be allowed to propagate into the external medium.  If the tank is empty, most of the light launched into the rod is reflected and returned to the photodetector.  If the tank is full, most of the light is transmitted into the tank if the refractive index of the fluid is relatively well matched to that of the rod. 
FIG.  1B illustrates an inherent problem and limitation with this design, namely that the returned light level drops through about 95% of its range when the liquid level rises above the mirror at the end of the rod by a distance 2 diameters of the length of the rod.  The data of FIG. ( 1B) are taken for the case where the rod is acrylic plastic (index=1.49) having a diameter of 0.5" and a length of 18.375" and is immersed in diesel fuel having an index of refraction of 1.47.  FIG.  1C shows that, for this example, the sensor output will have transitioned through over 90% of its range when the tank is filled to 5% of its capacity. 
Numerous schemes and physical embodiments have been proposed to provide an output that is linearly proportional to the liquid level and thus can be read directly on an output device such as a panel gauge (e.g., silver coating with a tapered slot, contoured surface profile).  Generally, embodiments that include such structural features for providing a linear response result in increased physical complexity (and thus increased manufacturing complexity and cost) as well as increased susceptibility to adverse interactions with the liquid being sensed (e.g., contamination of the liquid, extreme sensitivity to the viscosity of the liquid, failure of the sensor due to action of the liquid, and failure of the sensor due to environmental stresses in the tank, etc.).  Furthermore, provision for linearization alone does not guarantee that the sensor will remain calibrated over its useful lifetime if any significant degree of component drift or fouling occurs.  Fouling refers to the buildup over time of surface contaminants which affect the performance of the sensor by causing absorption of light at the surface or in the bulk materials or by otherwise altering the index of refraction at the sensor/liquid interface or within the bulk materials. 
It should also be noted that the signal does not drop to zero when the tank is full, although a drop to zero would be the ideal situation.  The tank-full background signal arises from several sources: light scattering by imperfections along the rod, back-reflection from refractive index fluctuations at light coupling interfaces, total internal reflection of shallow angle rays when the index of liquid is lower than that of rod, and direct reflection by the mirror of light traveling below the critical angle and/or near parallel to the axis of the rod.  The net effect is that a fraction of the excitation light is reflected back to the photodetector and appears as a background signal which must be subtracted in order to achieve an accurate calibration.  For the data shown in FIG.  1C, the relatively large background signal level compared to the near-full signal and the highly nonlinear change in signal with distance along the probe make this an impractical solution.  Even though the large background signal can be subtracted in principle, unacceptable calibration errors will develop over time if the background signal changes.  Thus it is important to minimize the background signal in order to minimize long term calibration drift. 
In the case where the refractive index of the fluid is equal to or greater than that of the rod, all of the light escapes when the light traveling in the waveguide encounters the portion immersed in the liquid.  This is the most desirable case, although it is difficult to achieve in practice.  In a typical situation, the index of the rod is larger than that of the liquid.  For the case of FIG.  1B, the critical angle is found to be 9.4.degree.  using equation (1).  Light traveling at angles less below 9.4.degree.  will be not propagate into the liquid and will be returned to the detector.  For light traveling at greater than 9.4.degree.,  the fraction of the incident energy which escapes into the liquid increases with the angle of propagation and is also dependent on the polarization of the light relative to the interface. 
Fresnel's equations can be used to calculate the fraction of the energy transmitted by a randomly polarized beam of light traveling an internal medium with index N1 at a given angle of propagation, .alpha.,  into an external medium with index N2 at an angle .beta.. FIG.  2 illustrates the angular relationships between the reflected and refracted beams at a dielectric interface for the cases where N1&gt;N2 and N1&lt;N2.  Fresnel's equations are commonly written in the form: EQU R.sub.par =sin.sup.2 (.alpha.-.beta.)/sin.sup.2 (.alpha.-.beta.) ( 2)
and EQU R.sub.perp =tan.sup.2 (.alpha.-.beta.)/tan.sup.2 (.alpha.-.beta.) ( 3)
where R.sub.par and R.sub.perp refer to the internal reflectance of the parallel and perpendicular polarized components, respectively.  The effective fraction of the energy transmitted is given by: EQU T.sub.effective =1-(R.sub.par +R.sub.perp)/2 (4)
The transmission at the waveguide/liquid interface (T.sub.effective) is plotted in FIG.  3 for a liquid level sensor waveguide with light propagating at several selected angles.  It should be noted that the propagation angle, .theta.,  is measured relative to the optical axis and refers to equation (1).  While ideally the index of refraction of the waveguide should chosen to be equal to or greater than that of the liquid, this may not be possible given available materials.  From FIG.  2, it is clear that if the propagation angle exceeds the critical angle by a sufficient margin, the transmission will be very high.  For example, a liquid level sensor with a waveguide index of 1.49 in water (index 1.33) will transmit &gt;99% of the light traveling at 45.degree.  into the water.  What is important is to insure that the majority of light traveling in the waveguide and/or the fraction thereof coupled to the photodetector from the waveguide is at a relatively steep angle compared to the critical angle.  If a large fraction of the energy received by the photodetector travels at a relatively shallow angle relative to the critical angle, then the signal-to-background ratio and the sensitivity of calibration to changes in operating conditions will be undesirably high.  Prior art sensors have not generally addressed this problem in a fashion that allows the design of practical level sensors with commercially available materials that are compatible with the sensed liquid but have an index of refraction that is greater than that of the liquid.