Abstract:
An algorithm and method for calculating an interferometric gap is disclosed that comprises providing an interferometric sensor having a first gap and an interferometric correlation element having a second gap placed in series with the first gap. A correlation burst waveform is generated having a plurality of features wherein the shape of the burst waveform evolves across the range of the second gap. Means are provided for tracking the features across the entire range of gaps and determining the dominant peak or dominant valley to determine the first gap.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority from U.S. Provisional Patent Application No. 60/716,483 filed on Sep. 13, 2005, which is hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention is generally related to processing signals from sensors, and more particularly, to enhanced signal processing with a tracking algorithm used with a linear array signal processor and a method for using the same to determine the gap of a Fabry-Perot fiber optic sensor. 
     BACKGROUND OF THE INVENTION 
     The invention relates to a method for enhanced processing of signals received from Fabry-Perot sensors. Fabry-Perot sensors have broad utility for applications which require monitoring of absolute, static displacements and small, dynamic vibrations or oscillating changes. For example, their simplicity of design allows these sensors to be embedded into industrial applications, including gas turbines, engines, pressure vessels, pipelines, buildings or other structures, in order to provide information about pressure, temperature, strain, vibration, or acceleration within the structure. Their size, durability, and fast response time make these sensors advantageous. Examples of such sensors or arrangements incorporating such sensors have been developed by the inventor and/or assignee of this application include copending U.S. patent application Ser. No. 11/048,521, which published as U.S. Patent Publication 2005/0244096; Ser. No. 11/105,651, which published as U.S. Patent Publication 2005/0231729; and Ser. No. 11/106,750, which published as U.S. Patent Publication 2005/0231730, each expressly incorporated by reference herein. 
     A Fabry-Perot fiber optic sensor, shown in  FIG. 1 , is generally known in the art. A fiber optic Fabry-Perot sensor is an interferometric sensor. Light passes through optical fiber  10 . The fiber  10  terminates at partially reflective surface  12   a,  which is itself aligned with partially reflective surface  12   b.  Surfaces  12   a  and  12   b  are separated by an air gap G which changes due to vibrations or other movement of at least one of the surfaces  12   a,    12   b.  Preferably, surface  12   a  is fixed while surface  12   b  is affixed to the object being monitored and may therefore move so as to change the length of the gap G. For example, surface  12   b  may be affixed to diaphragms, other fibers, cantilever beams or other such structures in order to monitor the aforementioned parameters. 
     In operation, light travels through fiber  10  and some of this light is reflected back into fiber  10  by surface  12   a.  Additional light is also reflected back into fiber  10  when it strikes surface  12   b.  The light reflected from the two surfaces (i.e., that which is transmitted back into fiber  10  via surfaces  12   a  and  12   b ) interferes to create an interference pattern, also called a modulation pattern. When the interference pattern is monitored over time for changes, these changes are indicative of changes in the length of the gap G and very small changes or oscillations may be detected with this type of sensor. 
     Such Fabry-Perot sensors must be used in conjunction with detection and processing equipment in order to provide quantitative feedback concerning changes in gap G over a given period of time. Notably, these arrangements provide for absolute or static measurements as well as relative or dynamic measurements of the oscillations or vibrations caused by changes in the length of the gap G. 
     In the linear array signal processor (LASP), a cross-correlation pattern is produced when a wedge or Fizeau interferometer is placed in series with a Fabry-Perot sensor (interferometer). The correlation pattern is read out by a linear array of photodetector elements also referred to as pixels. The light source is, for example, a “white light” lamp with a wide output spectrum and the linear array of photodetector elements is, for example, a charge-coupled-device (CCD) made from silicon or InGaAs. Typically, optical fiber runs from the Fabry-Perot sensor to the signal conditioner which is connected to the interferometric correlation element. U.S. Pat. Nos. 5,202,939 and 5,392,117 issued to Bellville et. al. provide a description of a wedge and CCD device and are each also expressly incorporated by reference herein 
     An optical cross-correlation pattern (burst) is shown in  FIG. 2 . The pattern displays the correlation signal as a function of sensor gap. A common simplistic algorithm in the prior art looks for a feature in the burst such as the feature representing “the largest magnitude peak” or “the largest magnitude valley”, and uses this feature to determine the interferometric gap that the feature represents. This simplistic algorithm is not robust enough to be used when the Fabry-Perot gap and the wedge interferometer gap are made of different materials, e.g. air in the Fabry-Perot and transparent oxide in the wedge interferometer. The differences in the refractive index of the gap materials cause the shape of the burst to evolve as the gap in the Fabry-Perot interferometer changes as shown in  FIG. 3 , Graphs  1 - 9 . This evolution in the shape of the burst can lead to serious errors in the accuracy of the measurement of the gap unless a more sophisticated signal-processing algorithm is used. 
     Other algorithms use a statistical method called “statistical correlation” to analyze the entire correlation burst and compare it to reference bursts. Such methods work to reduce noise but in the case of the evolving burst waveform, many reference burst signals are needed to provide reliable gap measurements. A description of one such algorithm is defined in US Patent Publication 2005/0073690 herein incorporated by reference. 
     Another simplistic algorithm analyzes the entire burst and computes an effective center-of-mass of the entire waveform. This method is not subject to discontinuous jumps but limits the dynamic range of the system and has poor resolution compared to the present invention. 
     SUMMARY OF THE INVENTION 
     These and other disadvantages are addressed by the invention disclosed herein. An apparatus and method are provided that more accurately identifies a feature in a burst waveform and tracks that feature across the entire range of gaps with no discontinuous jumps and with predictable repeatability. 
     As such, a method for calculating an interferometric gap is disclosed that comprises providing a first interferometric sensor having an air gap in series with a second interferometer, such as a Fizeau wedge, which has a gap made of a transparent oxide where the gap continuously changes along the wedge direction. The purpose for the Fizeau wedge is to provide an absolute readout of the interferometric sensor gap. Based upon the cross-correlation of the first and second interferometers, a correlation burst waveform is generated having a plurality of features including peaks and valleys. The pattern or shape of the peaks and valleys is a direct function of the dispersion (change in refractive index with light wavelength) of the oxide material in the Fizeau gap. Since there is no dispersion in the Fabry-Perot sensor air gap, there is a relative phase difference between the sensor gap and Fizeau gap, and this phase difference is not a constant for any gap. The phase difference increases with the thickness of the Fizeau gap because of there is no dispersion in the Fabry-Perot sensor air gap. The result is that the shape of the burst waveform evolves across the range of possible Fizeau wedge and Fabry-Perot sensor gaps. In this invention, a means is disclosed for identifying a unique feature (peak or valley) from the pattern of peaks and valleys, and tracking that feature across the entire range of sensor gaps. The dominant peak or dominant valley is used to identify which unique feature to track. The location of this feature with photodetector pixel position on the linear CCD array is used to compute the gap of the Fabry-Perot sensor. 
     The invention is particularly suited for calculating the interferometric gap produced from the cross-correlation of a Fabry-Perot interferometric sensor having an air gap placed in series with a wedge or Fizeau interferometric wedge having an oxide material in the gap. Further, a particular algorithm is provided that accurately identifies and tracks the waveform features across an entire range of the air gaps and determines the dominant peak or dominant valley used to determine the air gap that the dominant peak or dominant valley represents. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       Operation of the invention may be better understood by reference to the following detailed description taken in connection with the following illustrations, wherein: 
         FIG. 1  is a diagram of a Fabry-Perot fiber optic sensor. 
         FIG. 2  is a correlation burst waveform. 
         FIG. 3  shows the modulation of correlation burst. 
         FIG. 4  is a flow chart showing the transition strategy for an embodiment of the invention. 
         FIG. 5  is a flow chart showing an alternate transition strategy.
           FIG. 6  is a diagram of a Fabry-Perot interferometer sensor in series with a second interferometer.       
     
    
    
     DETAILED DESCRIPTION 
     The algorithm and method used for analyzing a correlation burst waveform generated by the cross-correlation of two interferometers is hereinafter disclosed. This application relies on an apparatus such as the ones disclosed in U.S. Pat. Nos. 5,202,939 and 5,392,117, which are hereby expressly incorporated by reference. These sensors measure the gap of a Fabry-Perot sensor using two interferometers in series. 
     The present invention describes a new algorithm that uses the correlation burst generated by such apparati. In particular, the invention analyzes the correlation burst to calculate the gap more precisely over a greater range of gaps than is possible with the existing simplistic algorithm. The new process applies to any apparatus that uses optical cross correlation to determine the gap in a Fabry-Perot interferometric sensor including systems that make absolute and dynamic measurements of the gap. 
     The optical cross-correlation pattern or burst as shown in  FIG. 2  has a number of features that characterize the burst. As seen in  FIG. 6 , when a Fabry-Perot interferometric sensor  14  with an air gap G 1  is placed in series with a second interferometer  16  such as a Fizeau wedge which has a gap G 2  that is made of a transparent oxide material, the shape of the burst evolves as the gap G 1  in the Fabry-Perot interferometer  14  changes as shown in  FIG. 3 , graphs  1 - 9 . The cross-correlation pattern is detected by a detector  20  such as a charged coupled device (CCD). 
     The cross-correlation pattern is then received by a device  22  such as a signal conditioner and analyzed by software. The feature that has the largest magnitude at small gaps does not have the largest magnitude at large gaps. The extent of the evolution of the shape of the burst is a function of the bandwidth of the light source  18  and the variability in the refractive indices of the gap media in the Fizeau wedge  16  over the range of wavelengths used by the system. Note that unlike air, which has uniform refractive index over the range of wavelengths, the transparent oxide material that defines the Fizeau wedge gap G 2  does not have a constant refractive index over the range of wavelengths, and this defines the dispersive properties of the oxide material. It should be noted that the preferred embodiment of the invention is described herein with reference to a Fabry-Perot interferometric sensor having an air (non-dispersive) gap placed in series with a Fizeau wedge having a transparent oxide material (dispersive) gap. However, it should be clear that numerous other materials could be used in the sensor or correlator gaps. However, it is contemplated that while the sensor gap can include a dispersive or non-dispersive material, the correlation gap preferably will have a dispersive material. 
     Note in  FIG. 3  that at small gaps (Graph  1 ) feature (D) has the largest magnitude or is dominant while at large gaps (Graph  7 ) feature (C) is dominant. Simplistic algorithms that use the dominant feature fail to track the gap across its full range of motion because they eventually skip to an adjacent feature when the adjacent feature becomes dominant. For example, an algorithm seeking the largest magnitude peak (D) (Graph  1 ) will be confused when feature (D) modulates to a reduced magnitude and feature (B) modulates to a larger magnitude (Graphs  5 - 8 ). The spacing between adjacent features (A, C, E) or (B, D, F) is approximately lambda/2 where lambda is the center wavelength of the light source. When an adjacent feature becomes dominant, the simplistic algorithm may skip from feature D to feature B or even feature F. The error associated with skipping features is therefore in the range of lambda/2. In a system where lambda is 850 nm, this skip represents an error of 425 nm. An error of 425 nm in a system with a total range of 15,000 nm represents an error in excess of 2% which is unacceptable for most measurement applications. 
     Instead of using the dominant feature to determine the gap, the algorithm described herein identifies a feature in the burst and tracks this feature across the entire range of gaps with no discontinuous jumps and with predictable repeatability. The process selects and tracks this feature by knowing the relationships between the features at various gaps. Therefore, the algorithm can track a feature even though it is not always the largest or the most dominant feature and uses many features of the waveform to select the specific feature to be tracked. 
     Notice in  FIG. 3 , graphs  1 - 9  that for short gaps (graph  1 - 3 ) feature D is dominant and for large gaps (graphs  7 - 9 ) feature C is dominant. At points in between (graphs  4 - 6 ) neither feature C nor D is clearly dominant. Notice also that as the signal evolves there is only one transition from a dominant D to a dominant C and that these two dominant features are always adjacent to one another. 
     Using this knowledge of how the signal evolves, feature C can be selected and tracked. Feature C can always be identified as the feature which is the dominant or the feature adjacent to the dominant feature. 
     How the software characterizes the burst waveform pattern and its features is outlined in the flowchart in  FIG. 4  where “Margin”, “Valley Margin”, and “Peak Margin” are defined. These burst waveform patterns and features are measures of how large a feature (e.g. C) is compared to other features such as V.L2 and V.R2 . And while this software and algorithm are used to calculate the gap of interferometric sensors placed in series, it should be clear that this software and algorithm could be used for tracking and identifying features of any waveform and for any use. The following terminology applies throughout this application:
         min(Value1, Value2) is the mathematic function “minimum of Value1 or Value2”   max(Value1, Value2) is the mathematic function “maximum of Value1 or Value2”   abs(Value1) is the mathematic function “Absolute value of Value1”   Avg is the average intensity through the centerline of the burst waveform measured in the Y-Axis. Typically Avg is zero.   Peak Margin:
           Compute ratio of the second largest magnitude peak to the largest magnitude peak and subtract from 100%.
 
PeakMargin=100%−abs(max( P.L 2,  P.R 2)−Avg)/ C 
   
           Valley Margin:
           Compute the ratio of the second largest magnitude valley to the largest magnitude valley and subtract from 100%.
 
Valley Margin=100%−abs(min( V.L 2,  V.R 2)−Avg)/ C 
   
               

     “BurstType” is defined as BurstType=Peak Margin−Valley Margin+0.5 with values that lie between 0 and 1. When the BurstType is close to zero, it is an indication of a dominant valley. When the BurstType is close to one, it is an indication of a dominant peak. When BurstType is close to 0.5, it is an indication that the burst is near a transition point. 
     Analysis of the margin data shows the following general characteristics:
         In  FIG. 4  example BurstType=Peak, a clearly dominant feature Peak D has approximately 30% margin over features B and F and B and F have margins approaching 0%, i.e. they are about equal.   In  FIG. 4  example BurstType=Valley, a clearly dominant feature Valley C has approximately 30% margin over features A and E and A and E have margins approaching 0%, i.e. they are about equal.   At the transition point, the most dominant peak and dominant valley margins are each approximately 10%.       

     The preferred strategy for selecting and tracking a feature in the burst waveform through the entire range of gaps is defined as the “Automatic Tracking Algorithm” and is also outlined in the flow chart in  FIG. 4 .  FIG. 4  represents an implementation of method “VL” as defined in Table 1 below. Although the description of the algorithm is limited to a condition with a single transition, it may be easily adapted for tracking burst waveforms with multiple transitions. 
     Steps:
         1. Capture the burst waveform   2. Identify the features that are the maxima (dominant peak) and minima (dominant valley) in the waveform.   3. Compute BurstType, Peak Margin, and Valley Margin   4. Determine which feature is to be used to track the burst based on the selection criteria defined in the flowchart in  FIG. 4 .   5. Use the pixel location of the feature being tracked to compute the gap.       

     Note that near transition points it is very likely that the same feature will be selected regardless of whether the BurstType is a peak, valley, or is indeterminate. Thus this algorithm is especially robust near transition points. This is a sharp contrast to simplistic algorithms which are weakest at transition points. For example, refer to  FIG. 3  Graph  4 . Assume strategy “VL” (Valley or Valley Left of dominant Peak) is used, point D is the peak and point C is the valley. Since Valley C is already “left of” Peak D, Valley C will always be chosen. That is, if the calculated valued of BurstType is less than or equal to 0.50, then use Valley C and if the calculated BurstType is greater than 0.50, then use the valley left of the peak which is still Valley C. 
     In the preferred embodiment of the present invention, this new algorithm identifies a feature in the burst waveform and tracks this feature across the entire range of gaps with no discontinuous jumps and with predictable repeatability. The invention selects and tracks this feature by knowing the relationships between the features at various gaps. Notably, the invention is able to track a feature even though it is not always the largest nor the most dominant feature, and many features of the waveform are used to select the feature to be tracked. 
     Alternatively as described in Table 1, multiple features in the burst waveform may be tracked across the entire gap range resulting in smooth tracking through the entire range of gaps with no discontinuous jumps and with predictable repeatability. The selection of these features is based the location of the approximate gap and the characteristics of those features adjacent to those which are most dominant. These methods solve the problems associated with errors introduced by evolving burst waveforms 
     Although the prior description defines the case where the burst waveform evolves from one dominant feature to an adjacent dominant feature, the general form of this algorithm can be used even if the waveform has a consistent dominant feature or evolves to more than two dominant features. For a variety of other reasons, it may be necessary to consider other variations of the preferred tracking strategy using lookup tables and similar techniques to determine which feature to select and track without departing from the principles of the invention contemplated herein. For example, one may determine that a burst waveform may have one or more dominant peaks and valleys as it moves through its full range. By knowing the gap location of the transition points, one may create a lookup table and use the lookup table to select the method and this method is used to select the feature to be tracked. The method is used until the waveform moves into a new transition region. 
     The preferred embodiment of this invention discussed above encompasses sensors with an optical gap from approximately 5,000 nm to 20,000 nm. An air-gap sensor with this operating range cross-correlated with an oxide-based Fizeau wedge produces the modulation progression seen in  FIG. 3 , Charts  1 - 9 . Examination of this progression shows that at low gaps, strategy VLP (Valley Left Of Peak) consistently selects valley “C” and at high gaps, strategy VO (Valley Only) consistently selects the same valley “C”. A single transition between strategies occurs at approximately 14,000 nm. 
     A sensor with an oxide-based Fizeau wedge cross-correlated with another oxide-based Fizeau wedge does not evolve as in  FIG. 3  and strategy VO (Valley Only) would be appropriate for all gaps. See Table 1. 
     A sensor with a different range of gaps, different gap media, or different refractive index could progress in a different manner and the other strategies in Table 1 could be appropriate for these cases. Each sensor could be calibrated with a simple lookup table indicating which strategy to use for a given gap. Any combination of strategies may be used. As a part of the set-up and calibration procedure during manufacturing, the appropriate strategy would be selected for use with a specific sensor for a specific application. 
     For example, using this concept, one variation of this algorithm would work as follows:
         If G MIN &lt;=G APPROXIMATE &lt;G TRANSITION     —     1  then use Method — 8 (VLP)   If G TRANSITION     —     1 &lt;=G APPROXIMATE &lt;G TRANSITION     —     2  then use Method — 1 (VO)   If G TRANSITION     —     2 &lt;=G APPROXIMATE &lt;=G MAX  then use Method — 9 (VRP)   Where
           G MIN  and G MAX  define the range of usable gaps   G APPROXIMATE  is the approximate gap of the waveform   G TRANSITION     —     x  are transition points defined in a lookup table   
           Methods are defined in Table 1 (Note other methods are possible (ex. VLV, VRV, PLP, PRP, as are combinations of these methods).       

     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Methods to select which feature to track 
               
             
          
           
               
                 Method 
                 Abbrev 
                 Description 
               
               
                   
               
             
          
           
               
                 1 
                 VO 
                 Use Largest MagnitudeValley Only 
               
               
                 2 
                 PO 
                 Use Largest Peak Only 
               
               
                 3 
                 PV 
                 Use Peak OR Valley - whichever has largest 
               
               
                   
                   
                 magnitude 
               
               
                 4 
                 VL 
                 Use Valley or Valley-Left-of-Largest Peak 
               
               
                 5 
                 VR 
                 Use Valley or Valley-Right-of-Largest Peak 
               
               
                 6 
                 PL 
                 Use Peak or Peak-Left-of-Largest Valley 
               
               
                 7 
                 PR 
                 Use Peak or Peak-Right-of-Largest Valley 
               
               
                 8 
                 VLP 
                 Use Valley Left of Largest Peak 
               
               
                 9 
                 VRP 
                 Use Valley Right of Largest Peak 
               
               
                 10 
                 PLV 
                 Use Peak Left of Largest Valley 
               
               
                 11 
                 PRV 
                 Use Peak Right of Largest Valley 
               
               
                   
               
             
          
         
       
     
     Steps:
     1. Capture a burst waveform.   2. Identify the features that are the maxima (dominant peak) and minima (dominant valley in the waveform.   3. Compute an approximate gap (G APPROXIMATE ) based on the location of the dominant peak and dominant valley.   4. Look up G APPROXIMATE  in the lookup table and identify the corresponding method. An example lookup table is shown in Table 2. Sample methods are defined in Table 1.   5. Use the identified method to select the feature in the burst waveform to be tracked.   6. Use the pixel location of the feature being tracked to compute a gap.   

     
       
         
               
             
               
               
             
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Example of lookup table 
               
             
          
           
               
                 TRANSITION GAP (nm) 
                 METHOD 
               
               
                   
               
             
          
           
               
                 0 
                 VLP 
               
               
                 5000 
                 VLP 
               
               
                 10000 
                 VO 
               
               
                 15000 
                 VRP 
               
               
                   
               
             
          
         
       
     
     The invention has been described above according to several embodiments and, obviously, modifications and alterations will occur to others upon a reading and understanding of this specification. The claims as follows are intended to include all embodiments, modifications, and alterations whether fully described herein, incorporated by reference, or understood based upon a reading of the specification insofar as they come within the scope of the appended claims or the equivalents thereof.