Abstract:
A method and apparatus for quantitatively measuring the distance of an unknown variable gap is disclosed. Light is provided to two Fabry-Perot interferometers arranged in a series, one spanning the unknown gap and the other spanning a controllably variable gap. Means for verifying the positioning of the Fabry-Perot interferometer having the controllably variable gap work in conjunction with a signal processor, a correlation burst signal detector and means for conveying the light to the various system elements to perform a comparison of detector signals from the two interferometers and quantitatively establish the gap distance. The invention may also be varied to function on a time basis, include more than one source of light, possess filter means to distinguish between light sources and/or include one or more reference interferometers.

Description:
The present invention relates to fiber optic Fabry-Perot interferometers and more particularly to a method and apparatus for quantitatively measuring the absolute length of a static gap in a Fabry-Perot interferometer. This application claims the benefit of application Ser. Nos. 60/562,492 and 60/562,682, both filed on Apr. 15, 2004. 

   BACKGROUND AND FIELD OF INVENTION 
   Fabry-Perot sensors have broad utility for applications where the measurement of the absolute length of an interferometric gap in a Fabry-Perot sensor. These gaps may relate to pressure, temperature, strain or some other physical property of the material which bounds one side of the gap. For example, their simplicity of design allows these sensors to be embedded into large industrial applications including gas turbines, 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. 
   In operation, Fabry-Perot interferometers are capable of spanning a range of gaps to create an interference pattern, regardless of whether via reflected light or transmitted light. Performing an optical cross-correlation of such an interference pattern, by reflecting or transmitting the interference pattern through a second interferometer, produces a distinctive signal that reaches a peak intensity of light when the length of the gap in the optical cross-correlator matches the length of the gap in the Fabry-Perot sensor. This distinctive peak intensity signal forms the basis for measurement of the absolute length of a gap in the Fabry-Perot sensor. Although previous systems known to the inventors use optical cross-correlators to make measurements of the length of gaps in Fabry-Perot sensors, the invention described herein is capable of making quantitative, absolute measurements with better sensitivity, greater dynamic range, greater frequency response, and lower cost than previously known systems. 
   SUMMARY OF INVENTION 
   The invention, at its most basic level, consists of one or more light sources, a first Fabry-Perot sensor spanning a gap which varies in response to changes in the environment (pressure, temperature, strain, etc.) and a second sensor having means for optically cross-correlating modulated light that is reflected by or transmitted through the first Fabry-Perot sensor. This second sensor includes means of controllably varying the length of the gap in the second sensor. A correlation burst signal detector is used, and means for verifying the gap distance of the second sensor are required. Lastly, means for comparing correlation burst signals from the first and second sensor in order to determine the absolute distance of the variable gap in the sensor are also included. Additional light sources may be provided, and the means for verifying the gap distance of the second sensor may comprise a set of known, fixed distance sensors which represent upper and lower limits for the sensitivity of the overall system. 
   The light sources may consist of a broadband light emitting diode (LED), edge light emitting diode (ELED), super luminescent diodes (SLEDs), wideband lasers such as a vertical cavity surface emitting laser (VCSEL), narrow band lasers such as a HeNe, or various tungsten lamps. 
   The means for optical cross-correlation of the modulated light reflected by or transmitted from the Fabry-Perot interferometric sensor preferably comes in the form of an optical cross-correlator placed in series with the Fabry-Perot sensor. As used throughout, the term optical cross-correlator should be understood to mean a system element having a variable gap where the gap is bounded on either side by partial reflectors. Preferably, the reflectivity of these boundary surfaces is between 20% and 50%. This optical cross-correlator is preferably configured as a Fabry-Perot interferometer. The amplitude or percentage of light reflected from or transmitted through the Fabry-Perot sensor and reflected from or transmitted through the optical cross-correlator is defined by the cross correlation product of the classic interferometric equation for each interferometer. For further discussion of such modulation, including the various equations that may be used to perform the calculations contemplated by this invention, refer to  Principles of Optics , Chapter 7, Born and Wolf which is hereby incorporated by reference. This classic interferometric equation defines the intensity of light as a function of both the length of the gap in the interferometer and the spectral distribution of the light that is transmitted from the light source(s). 
   The length of the gap in the optical cross-correlator may be variable by oscillating or moving one or both of the reflectors in the Fabry-Perot optical cross-correlator via a lead-zirconate-titanate (PZT) or some other linear or rotary actuator. The means for controlling the position of the optical cross-correlators can be accomplished with any linear or rotary positioner such as stepper motors, PZTs, magnetostrictive actuators, lever arms or any combination thereof. 
   The resultant correlation may be detected by one or more detectors. The detectors may consist of silicon or InGaAs photodiodes. The detectors may view different light sources with different wavelength bands. The detectors convert the light signals into an electronic output, and an electronic processor converts the electronic signals into representative measures of the Fabry-Perot sensor gap which correspond to the pressure, temperature, strain, vibration, or acceleration of interest. The electronic signals from the detectors are also used to control the frequency and amplitude of the oscillations and/or the length of the gap in the optical cross-correlator. 
   Finally, the invention contemplates the processing of the electronic signals from a microprocessor where software is used to read the electronic signal, control the position of the optical cross-correlators, and generate an output signal indicative of the length of the gap in the Fabry-Perot sensor. 
   One embodiment of the present invention relies upon an optical cross-correlator configured as a Fabry-Perot interferometer with a variable length of gap to make absolute measurements of the length of a gap in a Fabry-Perot sensor at relatively high frequency and at with a higher dynamic range than can be accomplished via other means. In this embodiment, the variable gap optical cross-correlator does not oscillate but is moved via a PZT or similar device through a range of gaps until the length of its gap matches that of the Fabry-Perot sensor. Then the system tracks changes in the length of the gap in the Fabry-Perot sensor by dithering, (oscillating through a very small range of motion). By measuring or otherwise knowing the precise length of gap in the optical cross-correlator where the length of the Fabry-Perot gap is identical to the length of the gap in the optical cross-correlator, one also knows the precise length of the gap in the Fabry-Perot sensor. 
   In an alternate embodiment, the variable gap optical cross-correlator is configured as a Fabry-Perot interferometer using a PZT element that oscillates at a high rate to sweep through a range of gaps at high frequency. Twice in each oscillation or sweep cycle, the length of the gap in the optical cross-correlator precisely matches the length of the gap in the Fabry-Perot sensor and at these moments a peak in the correlation signal is produced. By precisely knowing or mesuring the time of the occurrence of each match and by knowing the amplitude and frequency characteristics of the oscillations of the optical cross-correlators, one also knows the precise length of the gap in the Fabry-Perot sensor. 
   The amplitude and frequency of the oscillations and the precise length of the gap in the optical cross correlator can be controlled and known by applying a known voltage to a PZT element. Further embodiments contemplate the use of one or two reference sensors spanning fixed, known gaps along with two or more light sources to increase the accuracy of the system. 
   In operation, the inventive system comprises a light source, a first Fabry-Perot sensor capable of spanning a range of gaps, an optical cross-correlator configured as a second Fabry-Perot interferometer spanning a gap of a known length and capable of changing the length of that gap in a controllable and known manner, detector means to convert the light signals into electronic signals, and the electronic means to control the length of the gap in the optical cross-correlators and to generate an output signal indicative of the parameter to be measured. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1   a  is a schematic of the invention using a transmissive optical cross-correlator. 
       FIG. 1   b  shows an alternative embodiment for the optical cross-correlator which uses a reflective optical cross-correlator. 
       FIG. 2   a  shows a typical output curve for a fixed sensor gap where the length of the optical cross-correlator gap varies when a narrowband light source such as an ELED is used according to the invention. 
       FIG. 2   b  shows a typical output for a fixed sensor gap where the length of the optical cross-correlator gap varies when a wide bandwidth spectral source is used according to the invention. 
       FIG. 3  shows an alternative embodiment of the optical readout probe used to verify the position of the gap in the optical cross-correlator and improve the accuracy of the invention. 
       FIG. 4  shows alternative schematic for a reflective optical cross-correlator. 
       FIG. 5  shows an electronic schematic of a capacitance bridge that may be employed as a reference sensor in the embodiment depicted in  FIG. 4 . 
       FIG. 6   a  shows an alternate embodiment of the invention which includes the use of three separate light sources to determine the precise length of gap in the optical cross-correlator. 
       FIG. 6   b  shows transmission versus wavelength for cut-off filter F 1 . 
       FIG. 6   c  shows transmission versus wavelength for cut-on filter F 2 . 
       FIG. 6   d  shows output signals from detectors D 1 , D 2 , D 3  that illustrate light intensity versus gap for in  FIG. 6   a.    
       FIG. 6   e  shows a typical output (light intensity versus gap for VCSEL starting from zero gap) for a fixed sensor gap where the length of the optical cross-correlator gap varies when a laser light source is used according to the invention. 
       FIG. 6   f  shows another alternate embodiment of the invention. 
       FIG. 7  shows an embodiment for the invention which includes two reference interferometers to determine the positioning of the optical cross-correlator in transmission mode on the basis of time. 
       FIG. 8  shows a plot of the various signals generated and monitored by the embodiment depicted in  FIG. 7  for two fixed reference sensors that have gaps with lengths of 6000 nm and 25,000 nm respectively, and a sensor with a gap of 15,000 nm over one cycle of oscillation. 
       FIGS. 9   a - 9   d  depict alternative arrangements for the invention, also including signal calculation information. 
       FIG. 10  shows the absolute gap of 12,000 nm in the Fabry-Perot sensor when the peak amplitude of the time difference between the reference interferometer and the Fabry-Perot is 118 microseconds based on the linearization of the sinusoidal function. 
       FIG. 11  shows one possible block diagram of the elements of the invention. 
   

   DESCRIPTION OF PREFERRED EMBODIMENTS 
   A first embodiment of the inventive system  10  is shown in  FIG. 1   a.  Light I o  generated by source L 1  is modulated and reflected from the Fabry-Perot interferometer S 1 , which has an unknown variable gap length of G s , to a Fabry-Perot interferometer S 2  with a controllably variable gap G R  that is mounted on a PZT element  14 . Voltage is applied to PZT element  14  to induce a stretching motion on the Fabry-Perot interferometer S 2  which causes a change in the length of the gap (separation of the parallel Fabry-Perot mirrors), thereby optically cross-correlating the light received by S 2 . The optically cross-correlated light is sensed by detector D. The controllably variable gap can be manipulated so that G R  matches the length of the gap G s . S 1  may be a temperature, pressure, strain, vibration, acceleration, or other similar sensor. The voltage necessary to drive PZT  14  to the position where the length of the gap G R  matches the length of the gap G s  is directly proportional to the length of the gap G s  so that the drive voltage can be directly related to the measure of the output. Notably, detector D converts the optical signal into an electronic signal and is used to determine when the match in the length of these gaps has occurred. As described in more detail below, a positional verification device (not pictured) is associated with the S 2  to confirm the precise positioning of S 2  so as to provide an absolute readout for the system. 
   For a Fabry-Perot sensor with a fixed length of gap, the intensity of the light will vary as a function of the length of the gap in the optical cross-correlator as shown in  FIGS. 2   a  and  2   b  where the length of the gap in the Fabry-Perot sensor is 20 um and the length of the gap in the optical cross-correlator ranges from 15 um to 25 um. The plot in  FIG. 2   a  further assumes the light source is a light emitting diode (LED) with a center wavelength of 850 nm and spectral bandwidth of 50 nm. The plot in  FIG. 2   b  assumes the light source is a tungsten lamp with a center wavelength of 850 nm and an effective spectral bandwidth of 400 nm considering a silicon photodetector. In both  FIGS. 2   a  and  2   b,  the interferometers are made using low finesse reflectors, i.e. approximately 30% reflectors. 
   A second embodiment of the inventive system  10  is shown in  FIG. 1   b.  Light reflected from the S 1  is sent to the detector D after being reflected from an optical cross-correlator configured as a Fabry-Perot interferometer S 2 . This optical cross-correlator is configured by placing an optical fiber with a 30% reflective coating perpendicular to a mirror mounted directly to the PZT  14 . Voltage is applied to PZT element  14  to induce a change in the length of the gap G R . Again, the voltage necessary to drive PZT  14  to the position where the length of the gap G R  matches the length of the gap G s  is directly proportional to the length of the gap G s  so that the drive voltage can be directly related to the measure of the output. Notably, detector D converts the optical signal into an electronic signal and is used to determine when the match in the length of these gaps has occurred. 
   Notably, the signals generated in  FIGS. 2   a  and  2   b  have the same characteristic shape although inverted when viewed in transmission vs. reflectance, i.e. configured as  FIG. 1   a  (transmission) vs.  FIG. 1   b  (reflectance). 
   The PZT actuator  14  may be configured as a stack or as a bimorph as illustrated in  FIG. 4 . The bimorph  30  is a beam fixed at one end, consisting of two layers  30   a,    30   b  of lead-zirconate-titanate material that are excited out of phase. This causes one layer to expand while the other contracts which results in deflection of the beam. The advantage of the bimorph configuration shown in  FIG. 4  is that the desired displacement can be obtained at a lower drive voltage because of the lever arm effect of the beam which comprises bimorph  30 . This configuration is also particularly well suited to the use of secondary readout means (i.e., a means to verify the position of interferometer S 2 ), described below. Another configuration of the optical readout  24  which can be used as a means of verifying the position of the sensors S 2  is shown in  FIG. 3 , with the reference numerals therein corresponding to  FIG. 4 . 
   Overall system accuracy can be improved through variations to the elements shown in  FIGS. 1   a  and  1   b  which provide the means for independent measurement of length of the gap G R . Such means include the use of one or more additional reference sensors to verify the position of the interferometer S 2  and can be configured as but not limited to strain gage, capacitive sensor, or a linear variable differential transformer (LVDT). All of these items are commercially available. A comparison of their characteristics are summarized in Table 1. 
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Comparison of candidate readout 
             
             
               methods for PZT length assuming at range of 15 um 
             
           
        
         
             
                 
               Strain Gage 
               LVDT 
               Capacitance 
             
             
                 
                 
             
           
        
         
             
                 
               Resolution 
               1 nm 
               10 nm 
               0.1 nm 
             
             
                 
               Bandwidth 
               Up to 5 kHz 
               Up to 1 kHz 
               Up to 10 kHz 
             
             
                 
                 
             
           
        
       
     
   
   While each of the items listed in Table 1 can be used in the present invention, it is important to note the limitations of each. The small bandwidth makes the LVDT and the strain gage less attractive than the optical sensor and capacitance sensor. Both the capacitance and the strain gage may have long-term stability problems due to creep of the adhesive needed to bond these sensors to the PZT. Nevertheless, these options, along with others known to those skilled in the art, are available in configuring an enhanced system according to the schematic of  FIG. 1   a  or  1   b.    
   As seen in  FIG. 4 , the optical measurement system  24  used as a positional verification device may also consist of two optical readout devices A, B, one on each side of the PZT which deliver light to the PZT and one on each side of the PZT which receive light reflected from the PZT. Each assembly A, B consists of a light delivery fiber and detector to measure the light intensity. The power delivered to the two detectors is a function of the length of the gap between the ends of the sensor fibers and the PZT. With a probe on either side of the PZT, the signal from one increases while the other decreases. The ratio of the two signals is independent of source intensity fluctuations and gives an indirect measure of the length of the gap in the optical cross-correlator. This optical reference sensor could be improved further by using fiber bundles in lieu of single fibers. Proximity sensors based this principle have been demonstrated for high speed, high-resolution measurement. 
   A capacitance sensor  50  which can be used as the positional verification device is depicted in  FIG. 5 , although this particular arrangement can be relatively expensive. As shown in  FIG. 5 , the particular arrangement of capacitors (C FIX , C gapA , C gapB ) is directed toward a positional verification sensor used with a PZT bender. The fixed capacitors C FIX  act as references in a bridge circuit that measures capacitance differences. With reference to  FIG. 4 , assume that the PZT bender  30  is a capacitor electrode placed between electrodes positioned in place of the optical readout device fibers A and B shown  FIG. 4 . Then as the bender  30  moves closer to A, the capacitance of Capacitor A increases and capacitance of Capacitor B decreases. The capacitance change is detected as a change in voltage V out  from the bridge circuit. A similar arrangement could be devised using a resistive bridge. 
   An alternative to the optical reference sensor would be to make a direct measurement of the length of the gap in the PZT interferometer (rather than the relative position of the PZT as in  FIGS. 3-5  above), thereby eliminating the problems associated with calibration, long term drift, resolution, repeatability and accuracy of the PZT. This alternative employs a reference light source whose wavelength and intensity may slowly vary over time and thus are unknown at any point in time. Through this embodiment, the system self-calibrates the unknown reference light source periodically as explained below and the reference light is used to make an absolute measurement of the length of the gap in the PZT interferometer. 
   Such an alternate embodiment is shown in  FIG. 6   a.  A light source L 1  (preferably a Tungsten lamp) is connected to a 2×2 light splitter C 1  where the light is transmitted to the Fabry-Perot sensor S 1  through one of the output legs of C 1 . The other output leg is connected to a pair of light sources L 2 , L 3  (preferably a VCSEL at 1520 to 1540 nm wavelength and an ELED at 1310 nm wavelength) through a coupler C 4 . Reflected light from the sensor S 1  travels back through splitter C 1  to the interferometer S 2  (which includes PZT  14  for controllably varying the length of gap G R , all not shown in  FIG. 6   a ), which acts as an optical cross-correlator for the modulated light from the sensor. Light transmitted through interferometer S 2  is modulated as the gap G R  is changed by voltage applied to the PZT  14 . The modulation pattern in transmission is similar to the peak-to-valley modulation pattern in reflection from a Fabry-Perot sensor. The cross-correlated light from source L 1  then travels through a splitter C 2  and through a cut-off filter F 1 , which blocks (does not pass) the 1500 nm wavelength light from the VCSEL (see  FIG. 6   b ), but passes all shorter wavelengths. The filtered light then travels through splitter C 3  to detectors D 1  and D 2 . The intensity of the light signal at detector D 1  (silicon) is converted into an electrical current. Notably the light from the ELED source L 3  is not filtered and is transmitted to detector D 1 . Since D 1  is a silicon detector it is insensitive to the ELED wavelength (1310 nm). 
   Light from sources L 2 , L 3  travels through splitter C 1  and the interferometer S 2 , which does not perform a cross-correlation because the light from sources L 2 , L 3  has not been modulated (i.e., it does not come into contact with interferometer S 1 ). However the interferometer S 2  modulates the light from sources L 2 , L 3 . After splitting at C 2 , the light from source L 2  passes through the cut-off filter F 1 , through a second interferometer R 1  with a known, stable fixed gap and then onto detector D 2  (InGaAs). R 1  acts as an optical cross-correlator for the ELED light modulated by the PZT interferometer, and detector D 2  converts the cross-correlated ELED light into an electrical current. Notably the long wavelength light from the tungsten lamp source L 1  is not filtered by F 1  and is transmitted to detector D 2  along with the ELED light. Since the intensity from the tungsten lamp is very low compared to the ELED, the tungsten light has a negligible effect on the signal at detector D 2 . 
   After splitting at C 2 , the light from the VCSEL source  51  travels through a cut-on filter F 2 , which passes the long wavelength VCSEL light but blocks the short wavelengths from the tungsten lamp and ELED (see  FIG. 6   c ). The light is then detected by D 3  (InGaAs), which converts the VCSEL light into an electrical current. 
     FIGS. 6   d  and  6   e  show the signals generated at each detector as the interferometer S 2  is moved through a range of motion corresponding to the gap range ( FIG. 6   d ), and the full range of motion 0 to 30 um in  FIG. 6   e . The output of detector D 1  is a correlation pattern that results from the broadband light from the tungsten source that is modulated and reflected by the sensor and cross-correlated by the PZT interferometer. In the example shown in  FIG. 6   d,  the sensor gap is 12 um. The output from detector D 2  is a different correlation pattern that results from the ELED light modulated by the interferometer S 2  and cross-correlated by the fixed reference interferometer at R 1 . In the example shown in  FIG. 6   d,  the fixed reference interferometer R 1  gap is 28 um. The output from detector D 3  is a signal that is modulated by the interferometer S 2  only and not cross-correlated. The modulation peaks (also called interference fringes or just “fringes”) from the output of detector D 3  are spaced λ/2 apart, where λ is the VCSEL wavelength. Each fringe may be identified by an integer order number, and the light intensity I is described by the relationship
   I =1/[1 +F  sin 2  (2π G   R /λ)]  (1) 
   where G R  is the length of the gap in the interferometer S 2  and F is a constant. When the interferometer S 2  is positioned to zero gap (home position) then as the PZT gap increases, the signal from detector D 3  changes as shown in  FIG. 6   e.  As the voltage continues to increase, software tracks the output from D 3  and counts the number of fringe peaks and the fractional part of the next fringe when the length of the gap in the interferometer S 2  is equal to the length of the gap in the reference interferometer R 1 , i.e. 28 um. The fractional part of the next fringe is a function of the light intensity which can be resolved to 1%. 
   The system operates in two modes, i.e. calibration mode and measurement mode. In calibration mode, the PZT  14  and interferometer S 2  are scanned through the range of motion 0 to 30 um. The signal from detector D 2  reaches a peak when the length of the gap G R  in interferometer S 2  is equal to the length of the gap at reference interferometer R 1 , which has a fixed and known gap of 28 um in the example in  FIG. 6   d . Detector D 3 , which measures light intensity from the VCSEL is monitored during calibration. Refer to Table 2. There is uncertainty in the wavelength of the VCSEL and this uncertainty ranges from 1520 to 1540 nm. When the length of the gap G R  in the interferometer S 2  is scanned through the range of motion 0 to 30 um, the fringes are counted. Zero gap is verified when the VCSEL signal from detector D 3  does not change with applied voltage to the PZT. As shown in  FIG. 6   e,  36.6 fringes are counted when the laser wavelength is 1530 nm (1.53 um). Using Table 2 and Equation (1), the fractional fringe count calibrates the VCSEL wavelength. As shown in Table 2 and verified in  FIG. 6   d,  there are 36.6 VCSEL fringes between the PZT starting position and the R 1  gap, which is known to be fixed at 28 um and is periodically monitored by the ELED source through the output from detector D 2 . 
   In measurement mode, the voltage to the PZT  14  is changed from its value that resulted in a gap of 28 um until the output signal from D 1  reaches its peak as shown in  FIG. 6   d.  As the applied voltage to the PZT is changed, software keeps track of the fringe count from detector D 3 . When the peak value in the correlation pattern is detected by D 1 , the fractional fringe count is recorded and subtracted from the fringe count obtained in calibration mode. Through Equation (1), the sensor gap is calculated in terms of the absolute wavelength of the VCSEL. Thereafter in measurement mode, the PZT voltage is dithered so that the correlation pattern signal from D 1  is tracked by software. Changes in the peak value are tracked by fractional changes in fringe shift at detector D 3 . Recalibration is performed periodically. 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Calibration of the VCSEL Wavelength 
             
           
        
         
             
               VCSEL 
               Known Gap 
                 
             
             
               Wavelength 
               R1 (um) 
               Fringes 
             
             
                 
             
             
               1520 
               28 
               36.84 
             
             
               1521 
               28 
               36.82 
             
             
               1522 
               28 
               36.79 
             
             
               1523 
               28 
               36.77 
             
             
               1524 
               28 
               36.75 
             
             
               1525 
               28 
               36.72 
             
             
               1526 
               28 
               36.70 
             
             
               1527 
               28 
               36.67 
             
             
               1528 
               28 
               36.65 
             
             
               1529 
               28 
               36.63 
             
             
               1530 
               28 
               36.60 
             
             
               1531 
               28 
               36.58 
             
             
               1532 
               28 
               36.55 
             
             
               1533 
               28 
               36.53 
             
             
               1534 
               28 
               36.51 
             
             
               1535 
               28 
               36.48 
             
             
               1536 
               28 
               36.46 
             
             
               1537 
               28 
               36.43 
             
             
               1538 
               28 
               36.41 
             
             
               1539 
               28 
               36.39 
             
             
               1540 
               28 
               36.36 
             
             
                 
             
           
        
       
     
   
   Another alternative to the optical reference sensor relies on making a direct measurement of the length of the gap in the PZT interferometer and thereby again eliminates the problems associated with calibration, long term drift, resolution, repeatability and accuracy of the PZT and the complexities of the embodiment described above. This alternative employs a very stable light source such as a HeNe laser whose wavelength is more stable than other sources. Through this embodiment, the need for system calibration occurs primarily at system startup. 
   This alternative is described in  FIG. 6   f . A light source L 1  (preferably a Tungsten lamp) is connected to a 2×2 light splitter C 1  where the light is transmitted to the Fabry-Perot sensor S 1  through one of the output legs of C 1 . The other output leg is connected to a HeNe laser light sources with a wavelength 633 nm. Reflected light from the sensor travels back through splitter C 1  to the interferometer S 2 , which acts as an optical cross-correlator for the modulated light from the sensor S 1 . Light transmitted through the interferometer S 2  is modulated as the gap is changed by voltage applied to the PZT  14 . The modulation pattern in transmission is similar to the peak-to-valley modulation pattern in reflection from a Fabry-Perot sensor.) The cross-correlated light then travels through a splitter C 2  and through a cut-on filter F 1 , which blocks (does not pass) the 633 nm wavelength light from the HeNe laser but passes all longer wavelengths. The filtered light travels to detector D 1  where the intensity of the light signal is converted into an electrical current. 
   Light from the HeNe source travels through splitter C 1  and the interferometer S 2 , which does not perform a cross-correlation because the light from the HeNe has not been modulated. However the interferometer S 2  modulates the light from the HeNe. After splitting at C 2 , the light from the HeNe travels to detector D 2  (Si). Notably the long wavelength light from the tungsten lamp source L 1  is transmitted to detector D 2  along with the HeNe light. Since the intensity from the tungsten lamp is very low compared to the HeNe, the tungsten light has a negligible effect on the signal at detector D 2 . 
     FIGS. 6   d  and  6   e  show the signals generated at each detector as the interferometer S 2  is moved through a range of motion corresponding to the gap range ( FIG. 6   d ). The output of detector D 1  is a correlation pattern that results from the broadband light from the tungsten source that is modulated and reflected by the sensor and cross-correlated by the interferometer S 2 . In the example shown in  FIG. 6   d,  the sensor gap is 12 um. The output from detector D 2  is a signal that is modulated by the PZT interferometer only and not cross-correlated. The modulation peaks (also called interference fringes or just “fringes”) from the output of detector D 2  are spaced λ/2 apart, where λ is the HeNe wavelength. Each fringe may be identified by an integer order number, and the light intensity I is described by the relationship
   I= 1/[1 +F  sin 2 (2π G   R /λ)]  (1) 
   where G R  is the length of the gap in the interferometer S 2 . When the interferometer S 2  is positioned to zero gap (home position) then as the PZT gap increases, the signal from detector D 2  changes as shown in  FIG. 6   e  (Note the HeNe wavelength is different from the VCSEL but the concept is the same.) In general, the starting point for the light intensity is not zero as shown but can have any value between 0 and 1. As the voltage continues to increase, software tracks the output from D 2  and counts the number of fringe peaks and the fractional part of the next fringe when the length of the gap in the PZT interferometer is equal to the length of the gap in the sensor, i.e. 12 um. The fractional part of the next fringe is a function of the light intensity which can be resolved to 1%. 
   As before, the system operates in two modes, i.e. scan mode and measurement mode. In scan mode, the PZT is scanned through the range of motion 0 to 30 um. The signal from detector D 1  reaches a peak when the length of the gap at the interferometer S 2  is equal to the length of the gap in the Fabry-Perot sensor S 1 . Detector D 2 , which measures light intensity from the HeNe is monitored during scan and software keeps track of the fringe count continuously. Since there is negligible uncertainty in the wavelength of the HeNe, there is no need for a wavelength calibration as there is with a VCSEL or other unstable light source. Once the peak intensity in detector D 1  is found, the system changes into measurement mode. 
   In measurement mode, the sensor gap is calculated in terms of the absolute wavelength of the HeNe using Equation 1. Thereafter in measurement mode, the PZT voltage is dithered so that the correlation pattern signal from D 1  is tracked by software. Changes in the peak value are tracked by fractional changes in fringe shift at detector D 2 . 
   The frequency response is limited by the PZT scan rate and the absolute measurement accuracy is determined by the repeatability of the gap measurement using the reference sensor. 
   Yet another means for improving the resolution and accuracy involves the use of a time-based calculation on the absolute position of the Fabry-Perot sensor. This embodiment eliminates some of the hysteresis and creep in the lead-zirconate-titanate (PZT) modulator. 
   The elements of the time-based system are shown in  FIG. 7 . Light source L preferably a tungsten light source travels through an oscillating interferometer that changes its length of gap at a constant frequency and amplitude. The oscillating interferometer S 2  includes a PZT or other high speed oscillator. The light from L is modulated by the interferometer S 2  and travels through splitter C 1  to the Fabry-Perot sensor on one leg and through a VOA (variable optical attenuator) to a second splitter C 2  where the light travels through reference interferometers R 1  and R 2  which have fixed and known gaps. These reference interferometers R 1 , R 2  and the Fabry-Perot sensor S 1  serve as optical cross-correlators for the modulated light from the oscillating interferometer S 2 . The purpose of the VOA is to reduce the reflected light signal that can interfere with reflected signal from the Fabry-Perot sensor at detector D 3 . 
   The cross-correlated signals from interferometers R 1 , R 2 , and the Fabry-Perot sensor S 1  are monitored continuously by detector D 1 , D 2 , and D 3  respectively (although the invention can be configured for fewer than three detectors as shown in  FIGS. 9   a - 9   d  and described otherwise below). Notably, the reference interferometers R 1  and R 2  and scanned gap G RT  operate in transmission mode, whereas the Fabry-Perot sensor S operates in reflection mode. 
   As oscillating interferometer S 2  travels through its range of motion, the gap G R  provides a range of gaps as a function of time. Each of the three detectors (D 1 , D 2 , D 3 ) sees a peak in the correlation burst pattern when the length of the gap G R  matches the length of the gap in each respective interferometers (R 1 , R 2 , S). The peak detector signals from each interferometer S 1 , R 1 , R 2  are observed as a precise point in time that is a function of the amplitude and frequency of the oscillation gap G R  in the oscillating interferometer S 2 . Refer to  FIG. 8 . The signal from G R  gap. The peak intensity occurs at that moment in time during the oscillation when the gap G R  equals the gap in reference interferometer R 1 , R 2 , and Fabry-Perot sensor S 1 . 
   The Fabry-Perot sensor gap G S  is calculated based on the known precise gap and time of occurrence of the peak intensity of reference interferometers R 1  and R 2  and the sinusoidal functional dependence of the oscillating displacement of the range of gaps from G R . 
   These three signals as described are plotted in  FIG. 8 , with P R1  representing the signal generated by the detector associated with R 1 , P ST  representing sensor S 1  and P R2  representing R 2 . The microprocessor based timing circuit provides the signal plot P T  in the bottom trace of  FIG. 8 . The microprocessor measures the time differences t 1  between the R 1  peak and the Fabry-Perot sensor S 1  peak and time difference t 2  between R 1  peak and the R 2  peak. After linearization of the sinusoidal displacement of G RT , the sensor gap G ST  can be computed from  FIG. 10  and the following equation:
 
 G   S =( t   1   /t   2 )[ G   R2   −G   R1 )+ G   R1 
 
   where G R1  is the gap of R 1  and G R2  is the gap of R 2 . 
   The equation for above assumes a linear change of the scanned gap with time. In fact, the change is sinusoidal and must be modified accordingly to deal with the nonlinearity. Specifically, the scanned gap is driven sinusoidally at frequency co and can be expressed as
 
 G=A+B  cox (ω t )
 
   The correlation peaks of interest occur at the times when:
 
 G   R1   =A+B  cos (ω t   o )
 
 G   S   =A+B  cos (ω t   1 )
 
 G   R2   =A+B  cos (ω t   2 )
 
   where G R1  is the gap of the short reference sensor R 1  (as stated above, a known distance); G S  is the gap of the sensor monitoring the unknown gap; G R2  is the gap of the long reference sensor R 2  (also a known value); and t represents the times of occurrence of the peaks in the correlation burst. 
   Using the equations and information above, it becomes possible to calculate the actual value of G S  through accurate time measurement, as achieved by the aforementioned microprocessor, as follows:
 
 G   S   =G   R1 +( G   R2   −G   R1 )[(cos(ω t   o )−cos(ω t   o ))/(cos(ω t   2 )−cos(ω t   o ))]
 
   Notably, the equation above can be manipulated and used to achieve accurate time-based measurements according to any of the alternative embodiments described below. 
   To maximize the signal the lamp should be a quartz-halogen type that allows high filament temperature while maintaining long life. Exemplary filament temperatures in the range of 2700 K can burn for about 10,000 hours, while temperatures exceeding 3100 K drop that life span to around 100 hours. Notably, manufacturers define the lamp properties in terms of color-temperature, which is approximately 90 degrees higher than the actual filament temperature. 
   Clearly, there is an advantage to using the higher temperature lamp, but the added power comes at a cost of lifetime so there is a trade-off. One possible arrangement would be to use a lower temperature light source, and if there is a signal level problem, the higher temperature lamp can be substituted or integrated into system  10  as an alternative. 
   Additional consideration should be given to the radiance of the light source, which impacts the power delivered throughout the system. Further discussion of these principles can be found in the Photonics Handbook, the relevant portions of which are hereby incorporated by reference. As recognized by those skilled in the art, the radiance of the lamp filament can be determined with the temperature and the emissivity of the filament material (preferably tungsten). The radiance is also a function of wavelength, while the total integrated irradiance over the spectral range from 550 mn to 1050 nm is the quantity of interest for tungsten. Of course, these spectral limits are somewhat arbitrary, but are based on the basic fact that the detector response curve falls to about ½ its maximum value at these wavelengths. 
   The fraction of the input power delivered to the detectors is based on the reflectance from the sensors S 1 , S 2 , R 1 , R 2 . Ideally, this reflectance measured should be approximately 50% of the input light power. 
   Additional alternative arrangements of the optoelectronic components for system  100  are possible, although all of these are fundamentally rooted in the comparative calculation principle set forth in system  10 . For all of the variations discussed below, the previous designations utilized in  FIG. 7  are applicable to all such alternatives unless specifically given a different meaning. By the same token, the denotations for reflectance and input power on  FIG. 7  are for the same purposes as described in  FIGS. 9   a - 9   d.    
   The first such alternative arrangement is presented  9   a.  Light source L is provided to splitter C 1 . Notably, all of the sensors, as well as scanned gap G R  operate in reflection mode. The reflectance from each gap is indicated by r i  and beside the detector is indicated the magnitude of the power delivered through the system arrangement, where Io is the input power. Detector D is used to monitor all three sensors S 1 , R 1 , R 2  through appropriate routing by splitters C 2  and C 3 , and the power delivered to the detector consists of three terms, one from each reference and one from the sensor. In turn, these terms represent the product of two reflectances depending upon the routing of the light (e.g., r RT ×r R1 ) and are not simple products but rather the correlation product that yield individual burst patterns. Adjusting for these variations, further calculations are consistent with the principles described above (also depicted on  FIG. 9   a ). 
     FIG. 9   b  shows another alternate embodiment that employs one 2×4 splitter in place of the three splitters shown in  FIGS. 7 and 9   a.  Only one detector D is required. 
     FIG. 9   c  shows yet another configuration requiring a single 2×2 splitter and a single detector D. Significantly, the first two terms in the expression for the power to the detector are simply the feed-through of half the power input to the splitter. These terms do not contain any correlation information and simply add noise. 
     FIG. 9   d  shows yet another configuration requiring a single 2×2 splitter and a single detector D where the reference interferometers operate in transmission mode rather than reflection. 
   The signal levels provided for each configuration are summarized in Table 3. In some configurations, the signal level for the reference interferometers is different from that for the sensors. In these cases, Table 3 lists the worst case. It is assumed that the reflectance and transmittance of all sensors is the same, so the subscripts that are used for clarity in the Figures are omitted in Table 3. It is also assumed that there is no excess loss in the splitters. 
   
     
       
             
           
             
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               Comparison of optoelectronic configurations 
             
           
        
         
             
                 
               Figure reference 
               Signal Level 
               I/Io 
             
             
                 
                 
             
             
                 
               FIG. 7 
               rr/16 
               .026 
             
             
                 
               FIG. 9a 
               rr/64 
               .006 
             
             
                 
               FIG. 9b 
               rr/64 
               .006 
             
             
                 
               FIG. 9c 
               trtt/4 
               .029 
             
             
                 
               FIG. 9d 
               tr/9 
               .034 
             
             
                 
                 
             
           
        
       
     
   
   To make valid comparisons based on the expressions in Table 3 requires quantification of the cross-correlation terms tt, tr, and rr. Based on 30% reflectance for the separated mirrors that define the gap for each sensor, the cross-correlation products are conservatively estimated to be: tt=0.37; tr=0.31; and rr=0.41. Using these values enables evaluation of the products in column 2 of Table 3 to obtain the fraction of power delivered to the detector, which is given in column 3. The preferred configuration of  FIG. 7  is the best of the first five ( FIG. 7-FIG .  9   d ). 
   It is appropriate to perform a signal-to-noise ratio analysis. Consider, for example a sensor signal update rate of 10 kHz. The scanned gap is sinusoidally driven by the oscillator at 5 kHz, providing the desired 10 kHz update rate. Assuming a total scanning range of 20 μm, the scanned gap is expressed as
 
 g ( t )=10 μm(sin ω t )+ Q    (5)
 
   where Q is the gap in the absence of scanning and ω=2π(5000)rad/sec 
   The scanning rate, dg/dt, is a function of time. The maximum scan rate occurs at the time when sin ωt=0. At this point
 
10 μm(sin ωt)≈10 μm (ωt)
 
So,  dg/dt= 10 μm ω=(10)2π(5000)=3.14×10 5  μm/sec or 314 nm/μsec   (6)
 
   A correlation model can be used to provide results in terms of intensity as a function of correlation element gap. The gap is converted to time using the scan rate Equation (6) above, and the correlation pattern can be viewed as a quasi-sinusoid with a frequency of 0.84 MHz. There are no high frequency features of interest. Accordingly, the photodiode amplifier is designed as a band pass amplifier with a range of 100 kHz to 1 MHz. This is the frequency response of the photodiode signal and not to be confused with the time resolution required to measure the sensor gap with a resolution of 0.1%, (10 nm assuming a full scale range of 10 μm). A 10 nm gap change converted to a time base using Equation (6) reveals a 32 nsec change in time. As a minimum, the time base needs a resolution of 32 nsec. 
   To quantify the effect of noise, consider 1 MHz sine wave with variable amplitude added to the signal. A 1 MHz noise frequency is considered because higher frequencies are filtered out and lower frequencies do not affect the peak. Noise with frequency content comparable to that of the correlation peak, however, does affect both the amplitude and position of the peak. Ideally, the signal processor should be capable of operating with SNR=50. 
   The amplifier noise increases with the capacitance of the photodiode. Thus a photodiode is needed with the smallest capacitance possible. A UDT Sensors PIN-020A has an active area with a diameter of 510 μm and a capacitance of 1.0 pf when reverse biased at 10 V. 
   Other noise sources that need to be considered for systems  10 ,  11  or  12  include: shot noise due to DC signal current plus dark current; Johnson noise from the feedback resistor; noise due to amplifier input current noise; and noise due to amplifier input voltage noise. Conservative calculations show that the combined noise terms can be estimated and expressed as an RMS value of about i T =3.8×10 −10  A. Recall that the estimated light power level delivered to the detector was determined in paragraph 88 to be approximately 5.2×10 −8  Watts. The effective detector responsivity is on the order of 0.3 A/W, and the expected signal current is 1.6×10 −8  amps. Accordingly, the signal-to-noise ratio is 1.6×10 −8 /3.8×10 −10 =42. While this SNR falls slightly below the preferred value of at least 50, it is a worst-case estimate. The SNR can be improved by modifying the arrangement shown in  FIG. 1  so that more light is transmitted through the system. In addition, the SNR can be improved through proper choice of light source. A tungsten filament lamp was assumed but other alternatives are a quartz halogen lamp or super luminescent light emitting diode. Notably, these examples are cited merely as illustrative solutions to improve the performance of the inventive system, and other solutions for improving the SNR and/or the performance of the system will be apparent to those skilled in the art and this disclosure is expressly intended to contemplate such improvements. 
   In the same spirit, the ideal performance ranges for system  10  as shown in  FIG. 7  include gap G ST  which may be anywhere from 5 to 18 μm in length and a visible white light tungsten filament lamp or quartz halogen lamp. Light is delivered to the scanned gap through a 2×2 splitter. Since both splitter outputs illuminate the scanned sensor driven by the oscillator, the light loss budget and SNR can be improved by a factor of 2 compared with the estimated power discussed above. The reflected light from the scanned sensor is modulated by the oscillator, split and transmitted through a 2×2 splitter to the sensor S and also through a 1×2 splitter to two reference sensors R 1 , R 2  and their detectors D 1 , D 2 . The modulated light that is reflected from the sensor S is transmitted back to a third detector D 3 . The two reference interferometers can be designed with gaps of 6 and 18 um, for example. 
   The oscillator for gap G R  changes at a set rate, i.e. 1000 Hz and travels through a range of motion of approximately 20 μm. The ultimate range of motion is approximately 5 to 25 μm for the scanned gap, which consists of a moving mirror that maintains parallelism with the reflective end of an optical fiber. The range of motion and the rate of oscillation may be modified for specific applications. The trade off with increased bandwidth is increased noise and reduced dynamic measurement range of the Fabry-Perot sensor gap to be measured. 
   The detectors D 1 , D 2 , D 3  may be either silicon or InGaAs photodiodes. For short-range applications, i.e. up to 1000 meters, a quartz-halogen lamp provides the best performance. For long-range applications, i.e. 500 meters to 2500 meters the tungsten lamp provides somewhat better performance. 
   The inventive systems  10 ,  11 ,  12  can be easily multiplexed with several channels of optical data sharing a single oscillator and microprocessor, however, each channel requires its own set of reference interferometers and photodiodes. 
   Finally, the system electronics are depicted  FIG. 11 . The power supply board converts 110 VAC to 12 VDC and 5 VDC and is used to power the microprocessor board. The photodiode board generates a voltage proportional to the amount of light that illuminates each photodiode. The output of the photodiode board is the input for the microprocessor board. The microprocessor board digitizes the signal from the photodiode board and determines the sensor gap. The microprocessor also provides a signal to the oscillator driver and provides a digital output, i.e. RS-232, to the control system. The final output of the system can be an analog signal, e.g. 0-5V or 4-20 mA.