Abstract:
A method and apparatus for determining the phase angle of the sensitivity of a hydrophone H to be calibrated. The method comprises positioning in a straight line a transducer P, the hydrophone H, and a reciprocal transducer T that can be used both as a hydrophone and a projector; determining the phase angles of a set of voltages and currents; and finding the phase angle of the sensitivity from the former phase angles. The apparatus includes a framework for positioning P, H and T in a straight line, an electronic system for monitoring the voltages and currents, and a programmed computer for performing a single-point DFT.

Description:
This invention relates generally to hydrophones, and more particularly to systems for obtaining a frequency-calibration of a hydrophone. 
     It is known to use electroacoustic transducers to sense underwater sounds and to produce them as controlled signals. When the transducer is used to sense underwater sounds, it is referred to as a &#34;hydrophone&#34;; when it is used to produce or transmit underwater sounds it is referred to as a &#34;projector&#34;. Electrical and acoustical measurements are required to calibrate, test or evaluate underwater electroacoustic transducers and to enable one, indirectly, to produce or detect and measure an underwater acoustic signal, usually in terms of its acoustic pressure. The end result of most measurements is the value of an electroacoustic parameter; that is, a ratio of an electrical variable to an acoustical one, or the inverse. Typically, the receiving sensitivity (voltage/pressure) or the transmitting response (pressure/current or pressure/voltage) is the electroacoustic parameter computed from measured electrical data and various constants. When the receiving sensitivity (or transmitting response) is measured as a function of frequency, one obtains a frequency calibration of the transducer. 
     Although the receiving sensitivity as a function of frequency is often treated as only an amplitude, it also includes a phase angle. Unless the frequency of measurement is well below the lowest hydrophone resonance, the phase angle of the receiving sensitivity varies considerably (and monlinearly) with frequency. The time waveform of the acoustic pressure of an underwater acoustic signal being detected can only be recovered if the phase shifts for each frequency component of the receiving sensitivity are known. Heretofore, calibration of hydrophones rarely involved the phase angle because of experimental difficulties encountered in its determination when the frequency is not low. One such difficulty is accurately determining the distance between transducers used in the calibration. A very small distance error at higher frequencies can produce a relatively large phase error. Another difficulty encountered is accurately determining the sound speed in the measurement medium. Small errors in sound speed can also lead to large phase errors. 
     Prior art methods of hydrophone calibration are discussed in the text Underwater Electroacoustic Measurements by Robert J. Bobber (1970), especially at pages 28-30. 
     SUMMARY OF THE INVENTION 
     It is therefore an object of this invention to obtain a hydrophone frequency calibration which includes measurement of the phase angle. 
     Another object is to eliminate errors in the phase angle measurement. 
     These and other objects of the present invention are achieved by a system for obtaining a frequency calibration of a hydrophone H, wherein the hydrophone H is positioned together with a projector P and a reciprocal transducer T along a straight line in a substantially free-field water medium. The hydrophone H is positioned so that it lies between the projector P and the reciprocal transducer T, and the projector P and reciprocal transducer T both face thehydrophone H. The output voltage  e  PH of the hydrophone H is measured with the projector being driven by an input current i p  at a desired frequency f=ω/2π; the output voltage  e  PT of the reciprocal transducer T is measured with the hydrophone H removed and the projector being driven by the input current i p  at the desired frequency f=ω/2π; the output voltage  e  TH of the hydrophone H is measured with the hydrophone H replaced and the reciprocal transducer T being driven by an input current  i  T at the desired frequency f=ω/2π; and the input current  i  T is measured. Next, the amplitude and phase angle of the components of the measured output voltages and input current at the desired frequency f=ω/2π are determined, after which the amplitude and phase angle of the receiving sensitivity M H  of the hydrophone H at the desired frequency f=ω/2π are calculated by substitution in the expression 
     
         M.sub.H =[(4πe.sub.PH e.sub.TH d.sub.1 d.sub.3)/(jωρe.sub.PT i.sub.T d.sub.2)].sup.1/2 
    
     wherein 
     j=√-1 
     ρ=the density of the water medium; 
     d 1  =the distance between the projector P and the hydrophone H; 
     d 2  =the distance between the projector P and the reciprocal transducer T; and 
     d 3  =the distance between the hydrophone H and the reciprocal transducer T. 
     Use of the novel in-line configuration of hydrophone, projector and reciprocal transducer, with a corresponding measurement procedure eliminates potential phase error due to experimental uncertainty in both measurement distances and sound speed. This allows the accurate determination of the phase angle of the receiving sensitivity of the hydrophone, even at high frequencies where potential phase errors would likely prevent accurate results using previous methods. 
     A more complete appreciation of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1-4 are block diagrams of an embodiment of the frequency-calibration apparatus of the invention. 
     FIGS. 5-7 are flow charts of a program stored in the microcomputer to implement the invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring now to the drawing, wherein like reference numerals designate identical or corresponding parts throughout the several views and more particularly to FIG. 1 thereof, there is shown an apparatus for obtaining a frequency-calibration of a hydrophone H. The apparatus includes a positioning means 11 for positioning the hydrophone H together with a projector P and a reciprocal electroacoustic transducer T along a straight line in a substantially free-field water medium, so that the hydrophone H lies between the projector P and the reciprocal transducer T within their farfields, and the projector P and reciprocal transducer T both face the hydrophone H. The term&#34;reciprocal transducer&#34; is used herein in its conventional sense to denote a transducer for which the ratio of receiving sensitivity to transmitting response is a constant depending only on the acoustic medium, the frequency and the boundary conditions. Most known conventional transducers (i.e., piezoelectric, piezoceramic, magnetostrictive, moving-coil, etc.) are reciprocal at nominal signal levels. By &#34;free-field&#34; water medium is meant a homogeneous isotropic water medium free from boundaries, and may be, for example, a natural body of water. 
     While the positioning means may take a variety of forms, conveniently it may take the form illustrated in FIG. 1 of a framework 12 having for the hydrophone H a mounting hanger 14 designed so that it can be easily rotated or removed from the framework as desired (FIG. 2 shows a configuration wherein the hydrophone H has been removed from the framework 13). A suitable transducer for both P and T is the USRD type F30 transducer described in Naval Research Laboratory Memorandum Report No. 7735 by I. D. Groves, entitled &#34;Twenty Years of Underwater Electroacoustic Standards&#34;, the disclosure of which is hereby incorporated by reference. The F30 transducer is a piston-type transducer with an active rectangular area about 5.0×3.8 cm that is designed to operate over a frequency range from 10 to 150 kHz. If the distance d 1  between the hydrophone H and the projector P, and the distance d 3  between the hydrophone H and the reciprocal transducer T are both nominally equal to 1 m, the hydrophone H will be well within the sound farfield of either F-30 transducer at frequencies up to 150 kHz (i.e., it will intercept segments of the projected spherical waves that are small enough, or that have radii of curvature large enough, to be indistinguishable from plane waves). 
     The remainder of the calibration apparatus is made up of a driving means 13 which is adapted to be coupled to the input of either the projector P (FIGS. 1 and 2) or the reciprocal transducer T (FIGS. 3 and 4); a measuring means 15 which is adapted to be coupled to the output of either the hydrophone H (FIGS. 1 and 3), the reciprocal transducer T (FIG. 2), or the driving means 13; and a computing means 17 which is connected to the output of the measuring means 15. 
     The driving means 13 is provided to drive the projector P by an input current i p  at a desired frequency f=ω/2π (FIGS. 1 and 2) and alternatively to drive the reciprocal transducer T by another input current i T  at the desired frequency f=ω/2π (FIGS. 3 and 4). While the driving means 13 may take a variety of forms, conveniently it may take the form illustrated in FIGS. 1-4 of a frequency synthesizer 14, such as a Hewlett-Packard model 3320A; a pulse timing generator 21, such as a Scientific-Atlanta Inc. model 1118; a signal gate 23 such as Scientific-Atlanta Inc. model 1111, connected to the frequency synthesizer 19 and to the pulse timing generator 21; a preamplifier 25, such as an H. H. Scott Inc. model 140B, connected to the signal gate 23; a power amplifier 27, such as a Krohn-Hite Corp. model DCA 50(R), connected to the preamplifier 25; and an impedance matching transformer 29, such as a Krohn-Hite Corp model MT 50 whose input is connected to the power amplifier 27, and whose output is adapted to be connected to the input of the projector P (FIGS. 1 and 2), or the reciprocal transducer T (FIGS. 3 and 4). 
     The measuring means 15 is employed to measure the output voltage e PH  of the hydrophone H with the projector P being driven by the input current i P  (FIG. 1); to measure the output voltage e PT  of the reciprocal transducer T with the hydrophone H removed from the framework 12 and with the projector P being driven by the input current i P  (FIG. 2); to measure the output voltage e TH  of the hydrophone H with the latter in place in the framework 13 and the reciprocal transducer T being driven by the input current i T  (FIG. 3); and to measure the input current i T  (FIG. 4). The input current and voltage values are complex; i.e., they include both amplitude and phase. While the measuring means 15 may take a variety of forms, convenienty it may take the form illustrated in FIGS. 1-4 of a current transformer 30, such as a Pearson Electronics Inc. model 110, connected to the driving means 13; a preamplifier 31, such as a Scientific-Atlanta Inc. model 1116; a single pole-double throw switch 33 connecting the input of the preamplifier 31 to either the current transformer 29 (FIG. 4) or to one or the other of the hydrophone H (FIGS. 1 and 3) and the reciprocal transducer T (FIG. 2); and a digital oscilloscope 35, such as a Nicolet Instrument Corporation model 2090 III, connected to the output of the preamplifier 31 and to the pulse timing generator 21. 
     The computing means 17 determines the amplitude and phase angle of the components of the measured output voltages and input current at the desired frequency f=ω/2π, and calculates the amplitude and phase angle of the receiving sensitivity M H  of the hydrophone at the desired frequency f=ω/2π by substituting their values into the expression 
     
         M.sub.H =[(4πe.sub.PH e.sub.TH d.sub.1 d.sub.3)/(jωρe.sub.PT i.sub.T d.sub.2)].sup.1/2 
    
     wherein: 
     j=√-1; 
     ρ=the density of the water medium; and 
     d 2  =the distance between the projector P and the reciprocal transducer T. 
     While the computing means 17 may take a variety of forms, conveniently it may take the form illustrated in FIGS. 1-4 of a microcomputer 37, such as a Hewlett-Packard model 9835, connected to the measuring means 15 by a suitable IEEE interface 39, such as a Hewlett-Packard model HB-IB 98034A. 
     Now, the operation of the frequency-calibration apparatus will be described. Referring to FIG. 1, the hydrophone H and its hanger 14 are placed in the framework 12 and positioned so that the hydrophone H faces towards the projector P. A continuous wave signal at a desired frequency f=ω/2π is generated by the frequency synthesizer 19 and fed to the signal gate 23 which converts the continuous wave signal into a pulsed sinusoid in response to timing signals from the pulse timing generator 21. The duration of each pulse is about 1 millisecond long and the time between pulses about 100 milliseconds, or long enough for reflections to die down between pulses. The pulsed sinusoid is amplified first by the preamplifier 25, and then by the power amplifier 27. The amplified signal is applied to the projector P by way of the impedance matching transformer 29 to drive the projector P by an input current i P  at the desired frequency f=ω/2π. 
     The output voltage e PH  produced by the hydrophone H with the projector P being driven by the input current i P  is fed by way of the switch 33 to the preamplifier 31 for amplification. The amplified voltage waveform is then digitized by the digital oscilloscope 35 to provide a measurement of the output voltage e PH . The digital oscilloscope 35 is triggered by the pulse timing generator 21 at a time corresponding to the arrival of the sound wave at the hydrophone H, i.e., the trigger is delayed from the time that the pulse is applied to the projector. The digitized signal is transferred by way of the IEEE interface 39 to the microcomputer 37. 
     Next, referring to FIG. 2, the hydrophone H and its hanger 14 are removed from the framework 12 and the output voltage e PT  produced by the reciprocal transducer T with the projector P being driven by the input current i P  is fed by way of the switch 33 to the preamplifier 31 for amplification. The amplified voltage waveform is then digitized by the digital oscilloscope 35 to provide a measurement of the output voltage e PT , after which it is transferred by way of the IEEE interface 39 to the microcomputer 37. 
     Next, referring to FIG. 3, the hydrophone H and its hanger 14 are replaced in the framework 12 and positioned so that the hydrophone H faces towards the reciprocal transducer T. The amplified signal from the power amplifier 27 is now applied by way of the impedancematching transformer 29 to the reciprocal transducer T to drive the reciprocal transducer T by another input current i T  at the desired frequency f=ω/2π. 
     The output voltage e TH  produced by the hydrophone H with the reciprocal transducer T being driven by the input current i T  is fed by way of the switch 33 to the preamplifier 31 for amplification. The amplified voltage waveform is then digitized by the digital oscilloscope 35 to provide a measurement of the output voltage e TH , after which it is transferred by way of the IEEE interface 39 to the microcomputer 37. 
     Finally, referring to FIG. 4, the current i T  into the reciprocal transducer T is monitored by means of the current transformer 30 and fed by way of the switch 33 to the preamplifier 31 for amplification. The amplified current waveform is then digitized by the digital oscilloscope 35 to provide a measurement of the input current i T , after which it is transferred by way of the IEEE interface 39 to the microcomputer 37. 
     The microcomputer 37 then uses a conventional discrete Fourier transform to determine the amplitude and phase angles of the components of the measured output voltages e PH , e PT , e TH  and input current i T  at the desired frequency f=ω/2π. After all of the required values have been obtained, the microcomputer then calculates the amplitude and phase angle of the receiving sensitivity M H  of the hydrophone at the desired frequency by substitution of the values into the expression 
     
         M.sub.H =[(4πe.sub.PH e.sub.TH d.sub.1 d.sub.3)/(jωρe.sub.PT i.sub.T d.sub.2)].sup.1/2 
    
     It is important to note that the settings of the preamplifier 31 are left unchanged for all measurements of voltage and current to prevent the introduction of phase and amplitude errors in the calculation of the receiving sensitivity M H . 
     This procedure yields the phase angle relative to the axis of rotation of the hydrophone hanger 14. Because of this and the presence of interference from unavoidable reflections from the hydrophone hanger, the hydrophone H should be calibrated in the same hanger that will later support it when it is being used for measurements. The calibration is representative of both the hydrophone H and the hanger 14. 
     Attached as an Appendix is a listing of the source program stored in the microcomputer 37. The program controls (1) the digitization of the amplified output voltages and input current, (2) the transfer of the digital data to the microcomputer, (3) the analysis of data using the discrete Fourier transform to obtain the amplitude and phase angle of the components of the measured output voltages and input current at the desired frequency f=ω/2π, and (4) the calculation of the receiving sensitivity M H  of the hydrophone H at the desired frequency f=107 /2π. All of the instructions in the source program are in BASIC™. 
     FIGS. 5-7 are flow charts of the source program. 
     Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. For example, if the hydrophone H being calibrated has front-to-back symmetry, a modified procedure slightly different from that described above may be used. The modification involves measuring e TH  with the hydrophone H facing toward the projector P instead of toward the reciprocal transducer T. The received voltage e TH  is then the result of a sound wave incident from the backside of the hydrophone H. In this case the phase angle of e TH  combines with that of e PH  in the expression for M H  to produce a resultant phase angle for M H  which is relative to the center of the hydrophone H rather than to the axis for rotation. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein. ##SPC1##