Abstract:
Acoustic discontinuity responsive echo signals are compressed using special evaluating means for increasing the resolution of pulse-echo test apparatus. The acoustic discontinuity responsive echo signal undergoes mathematical convolution with a predetermined signal which latter signal is selected for providing that the mathematical product of the Laplace transform of the echo signal and the predetermined signal is unity. The mathematical convolution is performed by a computer, a correlator or an arrangement of delay lines.

Description:
BACKGROUND OF THE INVENTION 
     This invention refers to ultrasonic pulse-echo testing in which an ultrasonic search signal is transmitted cyclically from a transducer probe into a workpiece and the probe subsequently senses the receipt of echo signals arising from the search signal intercepting an acoustic discontinuity which reflects a portion of the transmitted acoustic energy. 
     As is well known to those skilled in the art great progress has been made in improving the resolution capability available using pulse-echo test apparatus with respect to small defects and defects disposed at relatively small distances from one another. These improvements are largely due to improved transducer construction and the replacement of electron tube amplifiers by transistorized amplifiers. Nevertheless, there is still a minimum distance in which a defect close to the workpiece surface cannot be resolved. This lack of resolution is due to the ringing of the transducer subsequent to it being pulsed for transmitting the search pulse, such ringing masking the echo signal. Also, if the transducer is excited by the receipt of a defect responsive acoustic signal, an immediately following similar defect responsive signal may be masked by the response of the transducer to the firstoccurring echo signal. Hence, the second defect responsive signal is not recognized. These cases clearly illustrate the lack of resolution still prevalent in currently used pulse-echo ultrasonic test apparatus. 
     In order to stop the ringing of the transducer probe after being excited by the transmit pulse, it has been proposed to immediately apply a pulse of opposite polarity so as to stop the oscillatory motion of the piezoelectric material. This method, by virtue of its complexity, has never been successful. Increased damping of the transducer by mechanical or electrical means obviously reduces its response to small signals and thereby decreases the transducer sensitivity. Similarly, pulse shortening circuits in the form of heretofore used filters decrease the sensitivity of the test apparatus and are of little usefulness in solving the problem of lack of resolution. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention reveals a new method and apparatus for increasing the resolution of pulse-echo test apparatus using special evaluating methods for compressing a pulse signal. In a practical embodiment, computer means or electrical circuit means are used to detect the receipt of a pulse signal and evaluate the signal without the use of suppression means. Resolution capability of pulses received within one period of the transmitted frequency is possible. Particularly, the present invention concerns itself with the detection of the receipt of a pulse in the time domain and the amplitude of the pulse during its first cycle and processing this information in the complete absence of suppression means. Ringing of the transducer as a function of the natural oscillatory decay is also of no consequence in the arrangement described hereafter. 
     For a better understanding of the present invention, reference is made to the following description and the illustrations forming a part thereof. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a representation of a control voltage; 
     FIG. 2 is a graph of a modified video signal; 
     FIG. 3 is a graph of a modified RF signal; 
     FIG. 4 is another graph of a signal; 
     FIG. 5 is a schematic electrical circuit diagram pertaining to RF signal modification; 
     FIG. 6 is a schematic electrical circuit diagram pertaining to video signal modification; 
     FIG. 7 is a graphical representation of an electrical reference signal; 
     FIG. 8 is a schematic circuit diagram for generating the signal per FIG. 7; 
     FIG. 9 is a schematic circuit diagram disclosing delay lines for signal modification; 
     FIG. 10 is another schematic circuit diagram disclosing the use of a single delay line for signal modification, and 
     FIG. 11 is another schematic circuit diagram similar to FIG. 10 applicable to certain signal conditions. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A. Echo Form: 
     An ultrasonic transducer probe comprising a piezoelectric element and a dampening mass contained in an enclosure or housing converts applied electric energy to ultrasonic energy and vice versa. If the probe is energized by a Dirac Delta pulse the effect is an exponentially decreasing wave train whose envelope has the form: 
     
         e .sup..sup.-.sup.αt 
    
     wherein α is the attenuation of the probe and t is time. 
     The Laplace transform of the above function (FOURIER transform with s = iω) is ##EQU1## wherein ω = 2 π f (f = frequency) and i = imaginary component (- 1). 
     If the probe is used as a transmitter and receiver, the Laplace transform of the echo-pulse envelope is the square of the above: 
     
         F(s) = 1/(a s + α).sup.2                             (eq. 1) 
    
     In the time domain, equation 1 corresponds to the echo signal form (envelope): 
     
         f (t) = te .sup..sup.-.sup.α t                       (eq. 2) 
    
     and the high frequency (RF) pulse has the form 
     
         f(t) = te .sup..sup.- .sup.α t cos ω .sub.o t  (eq. 3) 
    
     wherein ω o  = 2π f 0  and f o  = fundamental frequency of the probe. 
     Equation 3 omits ringing of the transducer front protective plate, ringing caused by any electrical matching coils in the transducer, ringing on account of incomplete sound isolation of the probe housing and ringing in the receiver amplifier. 
     B. Reduction of the Echo Signal Shape to Dirac δ-Pulse: 
     In order to obtain the signal reduction, the Laplace transform of the resulting pulse must be: 
     K(s)  .tbd. 1 (Laplace transform of the δ -pulse). 
     To this end, the Laplace transform of the echo-pulse per equation 1 is multipled by a function G(s) so that: 
     
         K(s) = F (s).sup.. G(s)  .tbd. 1                           (eq. 4) 
    
     In the time domain equation 4 corresponds to: ##EQU2## 
     (convolution integral) 
     To realize equation 5 it must be valid that: 
     
         G(s) = 1/F(s) = (s + α).sup.2                        (eq. 6) 
    
     Generally for Laplace transforms, 
     
         H(s + α) corresponds to e .sup..sup.-.sup.αt h(t) (eq. 7) 
    
     substituting p =  s + α, equation 6 then becomes: 
     
         G*(p) = p.sup.2 ; 
    
      in the time domain ##EQU3## (second derivative of a δ -pulse) 
     combined with equation 7, the final result becomes: ##EQU4## 
     The second derivative of a δ-pulse can be described by: ##EQU5## 
     The expression contained in the square parentheses can be represented by a signal shown in FIG. 1. 
     C. Approximation of the Second Derivative of the δ-Pulse 
     For an approximation of the signal g(t) in equation 9 the limit is recalculated with a finite Δt being smaller than the pulse width of f(t); the resulting pulse when using this approximation is derived by inserting equation 9 in equation 5. Then: 
     
         k (t) = te.sup..sup.-.sup.αt *e .sup..sup.-.sup.αt [δ(t) - 2 δ(t-Δt) + Δ (t-2Δt)]. 
    
     Convolution with a δ -pulse reproduces the original function so that the final result will be: 
     
         k(t) = te.sup..sup.-αt - 2e .sup..sup.-.sup.α.sup.δt (t-Δt) e.sup..sup.-.sup.α (t-ΔT) +e .sup..sup.-2.sup.δ (T-ΔT)e.sup..sup.-(T.sup.-2.sup.δT)(eg. 11) 
    
     wherein the second and the third term shall be zero if (t-Δt) and (t-2Δt) are less than or equal to 0. 
     When t is greater than 2Δt equation 11 becomes: 
     k (t) = e.sup. - .sup.αt [t-2 (t-Δt) + (t-2Δt)  .tbd. 0. 
     Conclusion 
     The described approximation shortens the original pulse f(t) = te.sup. - .sup.αt to a time interval less than or equal to 2Δt since when t is greater than 2Δt the ringing is exactly compensated to zero without the use of any non-linear suppression. FIG. 2 shows a graph of the original signal te -  .sup.α.sbsp.o for α = 1 and Δt being equal to the values 0.2, 0.4, 0.6, 1 and 1.6, the original function being shown as dotted. 
     If there are two pulses overlapping with a small transit time difference (two defects in close proximity to one another) they can be completely separated from each other by the present method if the transmit time difference is greater than 2α t. 
     However, the stated method will no longer work if the echo pulse overloads the amplifier, the output signal must be in the linear range of the amplifier which feature is readily achievable by proper amplifier design. 
     D. Compensation of the RF Signal (Equation 3 Using the Described Approximation) 
     The same method described above for the echo signal pulse can be applied also to the RF-signal per equation 3. The only difference is that there is a limited choice of Δt. If ω o  equals 2 π f o , f o  being the fundamental frequency, Δt must be a multiple of the half period 1/2f o . The signal g(t) corresponding to equation 9 must then assume the form: ##EQU6## 
     FIG. 3 shows a graphical representation of the signals for α = 1; f o  = 3; and k = 1.5. In accordance with the present method the long original pulse, shown by the dotted line, is shortened to three cycles. 
     FIG. 4 illustrates the reduction of a heavily, but not aperiodically, damped pulse (where f o  = 1 and α = 2) to an ideal shock wave pulse (k = 0.5) using the described method. 
     The advantage to applying the above method to the RF pulse, in lieu of the envelope (video pulse) resides in the fact that this compensation can be effected in the first amplifier stages or at the transducer probe where the echo pulses do not overload the amplifier. A disadvantage resides in the fact that the value of Δ t must be precisely calibrated to the transducer probe frequency f o . 
     E. Practical Embodiments of Pulse Shortening Method 
     As has been indicated heretofore the pulse shortening method described can be applied to the RF signal or the video signal. 
     Referring to FIG. 5, a pulse generator 20 cyclically applies to a transducer probe 22 a RF pulse electrical signal. The probe converts the electrical signal to an ultrasonic search signal which is transmitted into the workpiece 24 where the search signal intercepts a defect 26. A resultant echo signal sensed by the probe 22 is converted to an electrical signal and is conducted to the pulse shortening circuit 28 having means which will be described below wherein the RF signal wave train is shortened using the principle heretofore described. From the circuit 28, the shortened signal is transmitted to an amplifier 30 and then to a known evaluation circuit, such as a cathode ray tube display or a logic circuit, etc. 
     FIG. 6 depicts a similar arrangement except that the pulse shortening means 28 is coupled to receive the video signal from the receiver circuit 32. 
     Using a digital minicomputer for the embodiment per FIG. 6, the computer replaces the pulse shortening means 28. The received echo signal is conducted to an input connector coupled to an analog to digital converter for converting the analog echo responsive signal into a digital format signal. The computer is programmed to solve the equation 11. This is accomplished by storing the first term, the original non-compensated signal in the computer memory, shifting the argument by Δt and multiplying by a factor of two (zero for negative arguments) and subtracting the value from the memory, then shifting the original signal by 2Δ t and adding that value to the memory. The resulting signal stored in the memory is the solution of equation 11. For high resolution the increment Δt is selected to be small taking into account the resulting lower sensitivity. For increasing the sensitivity Δt is selected to be greater, however, as Δ t approaches unity the resolution is decreased. 
     In the embodiment where the RF signal is processed using the arrangement depicted in FIG. 5, Δt must be selected to be a multiple of 1/f o  or an odd multiple half of 1/f o , see equation 13. In the latter case all of the three terms per the equation must be added together. 
     Another alternative solution comprises the use of a computer which is programmed for solving the convolution integral per equation 5 wherein f(t) is the non-compensated echo signal and the value g(t) is programmed in the computer as per equation 12 or equation 13 (RF signal). Computers for this type of operation are available commercially under the name of &#34;correlators&#34;. Equation 5 is identical with a cross correlation function and the correlator is programmed for solving the equation 5. The signal from the transducer probe is provided as a first input to the correlator comprising the term f(t) and the correlator receives at a second input a reference signal comprising the term g(t) which corresponds either to equation 12 or 13. The electrical signal g(t) per equation 12 must be the triple pulse as shown in FIG. 7. This signal is generated by a circuit as shown in FIG. 8. 
     The transmit pulse is applied to a multivibrator 42 and the output from the multivibrator 42 is conducted to a differentiator 44. The differentiator output is fed to a negative multivibrator 46 and the output from the negative multivibrator to a differentiator 48. A summation network combines the outputs from the differentiators 44 and 48 to provide a signal with two spaced positive peaks and a centrally disposed negative peak of double amplitude. A signal decay circuit 54 receives its input from the pulse generator for charging the capacitor 56 via rectifier 58 to a positive peak value. The resistor 60 adjusts the decay rate. Multiplier 52 receives the signal from the circuit 54 and from the summation circuit 50 to provide the signal of shape per FIG. 7. 
     For equation 13 the negative multivibrator 46 must be a positive multivibrator. 
     Delay Line Circuits 
     If any pulse f(t) is passed through a filter whose impulse response corresponds to g(t) the filter output is given by the convolution integral of equation 5. This means that the output from the filter is identical with the compensated pulse signal k(t) when the filter impulse response corresponds to equations 12 or 13. Such a filter can be inserted readily between the transducer probe receiving the echo signal and the amplifier. 
     A filter having this characteristic can be realized by the use of delay lines. Several possibilities present themselves. 
     A typical embodiment is shown in FIG. 9. The ultrasonic transducer probe 22 is coupled to the input connection 39 of a circuit comprising two delay lines D 1  and D 2 , and three matched amplifiers A 1 , A 2  and A 3 . The delay lines D 1  and D 2  have a travel time k/f o  as shown in equations 12 and 13 (applicable to RF signals) and are matched on the end of an impedance R 0  = Z (Z is the impedance of the delay line) so that no reflection will occur. If the preamplifier A 1  has a gain of g 1 , the gain of the other amplifiers must correspond to ##EQU7## whereby for k = integer, the amplifier A 2  must phase inverting. If k equals odd multiples of 1/2, amplifier A 2  must be non-phase inverting. The outputs of the three preamplifiers A 1 , A 2  and A 3  are added together at output connection 41 and provided to the main RF amplifier. 
     FIG. 10 shows a simplification of the arrangement per FIG. 9. In circuit 42 only one delay line D 1  is used. The delay line D 2  of circuit per FIG. 9 has been replaced in FIG. 10 by a reflection at the end of delay line D 1 . For this purpose the end of delay line D 1  is mismatched by an impedance R o  ≠ Z so that the reflection factor is ##EQU8## but the input of D 1  is matched so R i  = Z to cause the first and third pulse of g (t) per FIG. 7 to be provided at the amplifier A 1 , and the second pulse to be provided to amplifier A 2  as previously. 
     FIG. 11 depicts a further alternative circuit which can be used successfully only if the attenuation of the transducer probe is high. The circuit 44 is a simplified passive filter and operates similar to the circuit per FIG. 10 described above. In circuit 44 the second pulse of g(t) is added by bypassing delay line D 1 . Impedance R 2  is selected to cause the second pulse to have an amplitude ##EQU9## Aside from the desired pulses there are additional pulses caused by multiple reflection in delay line D 1 . However, if the attenuation of the probe is sufficiently high the multiple reflections have a much lower amplitude than the first three desired pulses for providing a sufficiently close approximation of the result.