Abstract:
A transducer device including a housing that encloses a three-layer piezoelectric crystal assembly in contact with a backing block to produce more finely resolved electric and acoustic pulses. The three-layer assembly includes a piezoelectric crystal flanked by a front and back matching layer with a backing block in contact with the back matching layer. In concert with the backing block, the front and back matching layers cooperatively interact to produce more highly resolved acoustic and electrical pulses than by transducers equipped with two-layer crystal assemblies.

Description:
FIELD OF THE INVENTION  
       [0001]     This invention relates generally to acoustic transducers.  
       BACKGROUND OF THE INVENTION  
       [0002]     Acoustic transducers (audible or ultrasound) include a two-layer piezoelectric crystal assembly coupled to a backing block. The backing block is generally made of tungsten powder and rubber in an epoxy resin and serves to dampen the vibrating two-layer piezoelectric crystal assembly when the crystal is no longer electro-stimulated by voltage pulses or mechanically stimulated by received acoustic pulses.  
         [0003]     Backing blocks are used to mechanically dampen vibrations of the crystal assembly and to shorten ultrasonic pulses emitted by the crystal assembly. Accordingly, the backing block is desirably formed from an acoustically absorbent material. To avoid acoustic reflections at the surface of the backing block, the acoustic impedance of the backing block should be approximately matched to the acoustic impedance of the crystal, which is relatively high. The acoustic impedance of the backing block, Z, is the product of a speed of sound, c, and a density, ρ, for the backing block material: 
 
 Z=c·ρ 
 
         [0004]     The density, ρ, can be increased by adding a high density material, such as tungsten powder to the backing block material, but this correspondingly also decreases the speed of sound in the material. Therefore, in two-layer piezoelectric assemblies, limitations are introduced when the acoustic impedance of the backing block is increased in the foregoing manner.  
         [0005]     Thus, there is a need for an acoustic transducer not limited to two-layer crystal assemblies to improve the acoustic energy transmission.  
       SUMMARY OF THE INVENTION  
       [0006]     The preferred embodiment of the invention is a transducer device including a housing that encloses a three-layer piezoelectric crystal assembly in contact with a backing block to produce more finely resolved electric and acoustic pulses. In one aspect, a three-layer assembly includes a piezoelectric crystal flanked by a front and back matching layer with a backing block in contact with the back matching layer. In concert with the backing block, the front and back matching layers cooperatively interact to produce more highly resolved acoustic and electrical pulses than is achievable with transducers equipped with two-layer crystal assemblies. In another aspect, a transducer device has a housing that encloses a three-layer piezoelectric crystal assembly in contact with a backing block. The three-layer piezoelectric crystal assembly includes a piezoelectric crystal flanked by a front and a back matching layer. Along with the backing block in contact with the back matching layer, the combined interaction of the front and back matching layers of the preferred embodiment produces a more highly resolved acoustic pulse than is achievable with conventional two-layer piezoelectric crystal assemblies. Similarly, the three-layer piezoelectric crystal assembly transducer device cooperatively modifies the electrical signal of returning echoes to produce a more highly resolved electrical pulse than a comparable two-layer assembly.  
         [0007]     The foregoing aspect thus maximizes the transmission of acoustic wave energy emanating from a transducer by coupling a three-layer piezoelectric assembly to the backing block. The compositions of the front and back matching layers are formulated to substantially match the impedance of the piezoelectric crystal. The interface location composition maximizes the transmitted wave energy by reducing the reflection from the backing block and results in the reduction of the pulse width of the transmitted wave by reducing waveform tailing to improve the axial resolution of the acoustic wave. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]     The preferred and alternative embodiments of the present invention are described in detail below with reference to the following drawings.  
         [0009]      FIG. 1  is a schematic side view of a prior art acoustic transducer showing a two-layer piezoelectric crystal assembly;  
         [0010]      FIG. 2  is a schematic side view of an acoustic transducer according to an embodiment of the invention having a three-layer piezoelectric crystal assembly;  
         [0011]      FIG. 3A  is a graph of the matching thickness of the back layer as a function of acoustic wavelength between 0 and 0.26λ and axial resolution at −6, −20, and −40 decibels;  
         [0012]      FIG. 3B  is a graph of the matching thickness of the back layer as a function of acoustic wavelength between 0.23 and 0.25λ and axial resolution at −6, −20, and −40 decibels;  
         [0013]      FIG. 4A  is a Hilbert waveform plot from an acoustic transducer with a front layer-piezoelectric crystal two-layer assembly at −20 decibels axial resolution; and  
         [0014]      FIG. 4B  is a Hilbert waveform plot from an acoustic transducer with a front layer-piezoelectric crystal-back three-layer assembly at −20 decibels axial resolution. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0015]     Wave reflection and transmission in multi-layered media governs the relationship between reflection/transmission coefficients and the thickness of middle (matching) layer of acoustic transducers. A design of an acoustic transducer having a two-layer piezoelectric crystal assembly in schematic side view is shown in  FIG. 1 . A transducer  10  is positioned in contact with a human body. The transducer  10  comprises a housing  14  encasing a backing block  18 , a piezoelectric crystal  22 , and a front matching layer  28 . The piezoelectric crystal  22  and the front matching layer  28  define the two-layer piezoelectric crystal assembly. The front layer  28  includes a primary layer  28 A adjacent to the crystal  22 , and a secondary layer  28 B proximal to the human body. Positioned above and in contact with the crystal  22  is a signal collector  34  connected with a signal lead  36  located in the housing  14 . The signal lead  36  is in turn is in contact with a signal terminal  38  extending through the housing  14 . Positioned beneath the crystal  22  is a ground contact  42  connected with a ground lead  44  located in the housing  14 . The ground lead  44  is in turn is in contact with a ground terminal  48  extending through the housing  14 .  
         [0016]     The piezoelectric crystal  22  is stimulated to vibrate with a central frequency or wavelength upon receiving a stimulating or “on” voltage delivered from the signal terminal  38 , through the signal lead  36 , and to the signal collector  34 . The thickness of the piezoelectric crystal  22  generally corresponds to a central frequency wavelength of the crystal  22 . The crystal  22  stops vibrating when the stimulating signal is stopped, i.e., an “off” action, culminating in the release of an ultrasound pulse or bandwidth packet having a range of ultrasound frequencies distributed in a characteristic waveform approximately evenly about the central wavelength. Pulse echoes reflected back impinge upon the piezoelectric crystal  22  and cause it to vibrate and produce electrical signals that are delivered to the signal collector  34  for delivery to the signal terminal  38  via the signal lead  36 .  
         [0017]     Still referring to  FIG. 1 , the backing block  18  serves to dampen the vibrations of the piezoelectric crystal  22  between the “off” and “on” cycles of sequential pulses so that the bandwidth packet resolution is more pronounced or delineated with a minimum of waveform tailing. The backing block  18  is commonly made of tungsten powder distributed in an epoxy resin and liquid rubber to provide enough mass to mechanically dampen vibrations of the crystal  22  and to shorten the transmitted ultrasonic pulse. The tungsten powder and rubber composition of the block  18  is formulated to substantially match the acoustic impedance of the crystal  22  at the interface of the crystal  22  and the block  18  to minimize ultrasonic reflection. The block  18  also dampens “ringing” of the crystal  22  between reception of ultrasound pulse echoes, thereby lowering the noise, so that signals of returning echoes may be more easily and clearly detected and measured.  
         [0018]     The front matching layer  28  is placed on the examination (or human body) side of the transducer  10  to improve the transmission of ultrasound into the body soft tissue. The thicknesses of the front matching layers,  28 A and  28 B, are commonly some fraction of the wavelength of the speed of sound within the layers  28 A and  28 B. For example, layers  28 A and  28 B are commonly configured to be ¼ the wavelength of their respective speed of sound associated with the central frequency wavelength of the pulse echo waveform traversing though the materials within the layers  28 A and  28 B. These ¼λ thicknesses of the proximal layer  28 A and the secondary layer  28 B cancel the small amount of ultrasound that is reflected from the distal and proximal surfaces of the front matching layer  28 . The distance traveled between the surfaces is ½ wavelength and the waves are out of phase and thus cancelled. With this cancellation, the front matching layer  18  serves to increase the ultrasound energy into the body tissue and increases the bandwidth of the ultrasound pulse without any significant reflection. The improved or increase bandwidth similarly improves the axial resolution of the ultrasound pulse by decreasing the spatial pulse length.  
         [0019]     A preferred embodiment of the invention is shown in  FIG. 2  that presents a schematic side view of an acoustic transducer of the instant invention having the three-layer piezoelectric crystal assembly. A transducer  100  is positioned over a human body. The transducer  100  comprises the housing  14  encasing the backing block  18 , a back layer  150 , the piezoelectric crystal  22 , and the front matching layer  28 . Positioned above and in contact with the crystal  22  is the signal collector  34  connected with the signal lead  36  located in the housing  14 . The signal lead  36  is in turn is in contact with the signal terminal  38  extending through the housing  14 . Positioned beneath the crystal  22  is the ground contact  42  connected with the ground lead  44  located in the housing  14 . The ground lead  44  is in turn is in contact with the ground terminal  48  extending through the housing  14 . Positioned next to the signal collector  34  is the back layer  150  that also is in contact with the crystal  22 . The backing block  18  is in contact with the back layer  150 .  
         [0020]     The front layer  28 , the piezoelectric crystal  22 , and the back layer  150  define the three-layer piezoelectric crystal assembly  100 . The front and back layers  28  and  150  are formulated to substantially match the acoustic impedance of the crystal  22 . The front matching layer  28  is placed on the examination (or human body) side of the transducer  100 . The three-layer assembly cooperatively interacts to improve the generation of more highly resolved acoustic pulses when the crystal  22  is stimulated with electrical pulses, and to generate more highly resolved electrical pulses when the crystal  22  receives an acoustic signal pulse. The thicknesses of the front matching layer  28 A,  28 B, and the back matching layer  150  are commonly ¼ the wavelength of the speed of sound within the layers  28 A,  28 B, and  150 . This ¼ wavelength thickness serves to cancel the small amount of ultrasound that is reflected from the distal and proximal surfaces of the front matching layer  28  or the back matching layer  150 . The distance traveled between the surfaces of the front and back matching layers  28  and  150  is ½ wavelength and the waves are out of phase and thus cancelled.  
         [0021]     With this signal cancellation of acoustic reflections, the front matching layer  28  and the back matching layer  150  serve to increase the transmission of ultrasound energy pulses into the body tissue and the backing block without any significant reflection and decreases the spatial pulse length or signal bandwidth of the ultrasound or audible pulse. Thus, the efficiency of electro-to-mechanical conversion (as realized in acoustic pulse generation) is enhanced by the cooperative interaction of the three-layer piezoelectric crystal assembly that generates a shorter and more clearly defined acoustic pulse, either ultrasound or audible depending on the composition and configuration of the piezoelectric crystal  22 .  
         [0022]     Similarly, the efficiency of mechanical-to-electrical conversion (as realized in electric signal generation) is enhanced by the cooperative interaction of the three-layer piezoelectric crystal assembly that generates a shorter and more clearly defined electrical pulse caused by a returning acoustic echo, either ultrasound or audible depending on the composition and configuration of the piezoelectric crystal  22 .  
         [0023]     Axial resolution for a piezoelectric transducer is generally expressed in decibel levels of which −6, −20, and −40 dB levels are used for two-layer vs. three-layer analysis.  FIG. 3  shows a plot of the matching thickness for the back layer  150  of the transducer assembly  100  of  FIG. 2  as a function of acoustic wavelength and axial resolution at −6, −20, and −40 decibels obtained from the simulated values as discussed in the “Theory of Operation” below. Results show that the middle value at approximately 0.244λ represents a suitable matching layer thickness for axial resolution at −6, −20, and −40 decibels that is very close to the ¼λ value.  
         [0024]     Theory of Operation  
         [0025]     Wave reflection and transmission in three-layered media are presented, including the relationship between reflection/transmission coefficients and the thickness of middle (matching) piezoelectric crystal layer.  
         [0026]     Reflection Coefficient on Multiple-Layer media  
         [0027]     The reflection coefficient, R, from a three-layer medium is given by:  
       R   =             Z   2     ⁡     (       Z   3     -     Z   1       )       ⁢           ⁢   cos   ⁢           ⁢     (       k   2     ⁢   L     )       +     j   ⁢           ⁢     (       Z   2   2     -       Z   1     ⁢     Z   3         )     ⁢           ⁢   sin   ⁢           ⁢     (       k   2     ⁢   L     )                 Z   2     ⁡     (       Z   3     -     Z   1       )       ⁢           ⁢   cos   ⁢           ⁢     (       k   2     ⁢   L     )       +     j   ⁢           ⁢     (       Z   2   2     -       Z   1     ⁢     Z   3         )     ⁢           ⁢   sin   ⁢           ⁢     (       k   2     ⁢   L     )               
 
 where, Z 1 , Z 2 , and Z 3  are the respective acoustic impedances of each of the three layers, k 2  is a wave constant and equal to 2π/λ 2  and λ 2  is the wavelength in the medium of the middle layer, and L is the width of the middle layer. 
 
         [0028]     When the thickness of the middle layer, L, is one quarter wavelength, i.e.,  
         L   =       λ   2     4       ,       
 
 the cosine and sine terms in the above equation become  
                 k   2     ⁢   L     =           2   ⁢   π       λ   2       ·       λ   2     4       =     π   2                     cos   ⁢           ⁢     (       k   2     ⁢   L     )       =   0                 sin   ⁢           ⁢     (       k   2     ⁢   L     )       =   1             
 
         [0029]     Therefore the reflection coefficient, R, becomes:  
       R   =         Z   2   2     -       Z   1     ⁢     Z   3             Z   2   2     +       Z   1     ⁢     Z   3               
 
         [0030]     If the numerator of R is set to zero, the reflection coefficient, R, will be zero, too. This means that if Z 2 =√{square root over (Z 1 Z 3 )}, and then there is no reflection from the three-layer medium (of course, in the case of continuous wave).  
         [0031]     Transmission Coefficient in a Three-Layer medium.  
         [0032]     If the ratio of reflection is R, then the transmission ratio, T, is, 
 
 T   2 =1− R   2  
 
         [0033]     In a three-layer medium, the reflection coefficient, R 1 , and transmission coefficient, T 1 , from a first boundary (between layer 1 and layer 2) is:  
           R   1     =         Z   2     -     Z   1           Z   2     +     Z   1           ,           ⁢       T   1     =     1   +     R   1             
 
         [0034]     And, for a second boundary (between layer 2 and layer 3):  
           R   2     =         Z   3     -     Z   2           Z   3     +     Z   2           ,           ⁢       T   2     =     1   +     R   2             
 
         [0035]     Therefore, the overall transmission coefficient, T, is given by:  
       T   =         T   1     ·     T   2       =       4   ⁢     Z   2     ⁢     Z   3           (       Z   2     +     Z   1       )     ⁢           ⁢     (       Z   3     +     Z   2       )               
 
         [0036]     In order to determine a maximum value of the foregoing expression, a derivative of T with respect to Z 2  is set to zero:  
           ⅆ     ⅆ     Z   2         ⁢   T     =           4   ⁢       Z   3     ⁡     (       Z   2     +     Z   1       )       ⁢           ⁢     (       Z   3     +     Z   2       )       -     4   ⁢     Z   2     ⁢       Z   3     ⁡     (       2   ⁢     Z   2       +     (       Z   1     +     Z   3       )       )                 (       Z   2     +     Z   1       )     2     ⁢       (       Z   3     +     Z   2       )     2         =   0         
 
         [0037]     The above equation can be reduced to: 
 
         =4 Z   3 ( Z   2   +Z   1 )( Z   3   +Z   2 )−4 Z   2   Z   3 (2 Z   2 +( Z   1   +Z   3 ))=0 
 
         = Z   3 (− Z   2   2   +Z   1   Z   3 )=0 
 
         [0038]     Therefore, when Z 2   2 =Z 1 Z 3 , the transmission coefficient, T, has its maximum value.  
         [0039]     Simulation  
         [0040]     The ideal matching layer has the quarter wavelength thickness and the impedance of √{square root over (Z 1 Z 3 )}. The sound waves with different thicknesses of the backing matching layer are generated by version 3.02 PiezoCAD base obtained from Sonic Concepts on the following parameters (acoustic impedances). Impedance is expressed in Mrayls, where one Mrayl is defined as 1×10 6  kg/[m 2 s].  
         [0041]     Results for a preferred embodiment of the three-layer transducer  100  of  FIG. 2  when excited at a frequency of 3.7 MHz and having a 0.4162 mm wavelength in water, when adjusted for differences in speed of sound between the piezoelectric crystal  22 , the front matching layer  28  and back matching layer  150  are itemized below.  
         [0042]     The front layer  28  comprises the primary layer  28 A and secondary layer  28 B, as shown in  FIG. 2 . The primary front matching layer  28 A at approximately ¼λ: has an impedance of approximately 8.95 Mrayls (where the material is MF116 obtained from Emerson Cuming, Inc. of Randolph, Mass; or an equivalent) for the primary layer  28 A at its speed of sound. The secondary front matching layer  28 B=¼λ: or approximately 4.22 Mrayls (where the material is also MF110 obtained from Emerson Cuming, or an equivalent). Thickness is approximately 0.14 mm for the secondary layer  28 B at its speed of sound.  
         [0043]     The piezoelectric crystal  22  at approximately ½λ of the crystal  22  at its speed of sound: approximately 34.2 Mrayls (where the crystal material is EBL #3 obtained from Staveley Sensors, Inc., East Hartford, Conn.; or equivalent). The thickness is approximately 0.56 mm for the crystal  22  at its speed of sound.  
         [0044]     The back matching layer  150  at approximately ¼λ. The backing layer  150  is formulated to be approximately 15.13 Mrayls with respect to the speed of sound in the layer  150 . Thickness is approximately 0.16 mm for the backing layer  150  at its speed of sound.  
         [0045]     The backing block  18  is approximately 6.69 Mrayls and approximately 8 mm in thickness. The materials of the backing block  18  are obtained from On-Hand Adhesives Inc., Mt. Prospect, Ill. (Epoxy and hardener), Noveon Inc., Cleveland, Ohio (liquid rubber), and Aldrich Chemical Company Inc., Milwaukee, Wis. (tungsten powder) or another equivalent suppliers.  
         [0046]     The Hilbert envelopes of the two-layer transducer  10  of  FIG. 1  and the three-layer transducer  100  of  FIG. 2  were generated using Matlab to determine a spatial pulse length for the transducers  10  and  100 . The processing includes calculating the spatial pulse length in microseconds (μsec or μs) at a −20 dB axial resolution limit line that intersects the Hilbert rectified waveform. PiezoCAD is also configured to calculate ranges of spatial pulse lengths, converted to mm, as a function of the thickness of the back layer  150  expressed in increments of the sound wavelength transmitting through the back layer  150  for axial resolution levels of −6 dB, −20 dB, and 40 dB.  
         [0047]     The thickness of the back layer  150 , expressed in fractional increments of the wavelength of the speed of sound traversing through the back layer  150 , are plotted as shown in  FIG. 3 . A solid diamond symbol refers to the −6 dB axial resolution level, a solid square symbol refers to the −20 dB axial resolution level, and a solid triangle symbol refers to the −40 dB axial resolution level.  FIG. 3  demonstrates the effectiveness of the three-layer transducer  100  in producing shorter spatial pulse lengths as a function of back layer  150  thickness, especially at −20 dB and −40 dB axial resolution levels.  
         [0048]     The axial resolution plots in  FIG. 3A  demonstrate the simulated results of incrementally varying the thickness of the back matching layer  150  up to 0.260λ. The simulated results demonstrate for the −20 and −40 dB axial resolution levels, square cornered, step-like plateaus matching thickness values from 0 (or no back layer  150 , i.e., equivalent to the two-layer transducer  10  configuration) to 0.260λ thickness for the back layer  150  (or three-layer transducer  100  configuration).  FIG. 3B  shows the detail plot between 0.23 and 0.25λ thickness. At 6 dB axial resolution, there is virtually no change between 0.230λ and 0.250λ. However, at the −20 and −40 axial resolution levels, the backing layer  150  provides improved axial resolution, so that a reduction in the spatial pulse lengths in a centralized region of the −20 and −40 dB plots is evident. The matching thickness value for the back layer  150  having the best axial resolution is 0.244λ that is substantially close to the theoretical 0.250λ (or ¼λ) value.  
         [0049]      FIG. 4A  is a Hilbert waveform plot (as normalized voltage y-axis vs. microseconds μs x-axis) from an acoustic transducer with a front layer-piezoelectric crystal two-layer transducer  10  assembly at −20 decibels axial resolution scanned at 0.77 mm per μs. The waveform plot includes a bimodal tracing  200 ; a rectified Hilbert envelope or tracing line  204  comprising a major peak  204 A, a first minor peak  204 B, and a second minor peak  204 C; a −20 dB limit line  208  from the maxima of the major peak  204 A, a lower limit  212 A of approximately 0.7 μs, a first upper limit  212 B of approximately 1.6 μs, and a second upper limit  212 C of approximately 1.8 μs. The lower limit  212 A and the first-second upper limits  212 B-C are obtained from the intersection of the −20 dB limit line  208  along the Hilbert tracing line  204 .  
         [0050]     The spatial pulse time is defined as a “delta T” or time period obtained as a difference between the lower limit  212 A and the greater or greatest upper limit whenever there is more than one upper limit. In  FIG. 4A  there are three upper limits, the greatest being the second upper limit  212 C obtained by the intersection of the −20 dB limit line  208  with the Hilbert tracing line  204 . The spatial pulse time for the two-layer transducer  10  illustrated in  FIG. 4A  is the absolute difference between the second upper time limit  212 C and the lower limit  212 A, or 1.8 μs-0.7 μs, equivalent to a spatial pulse time of 1.1 μs. With a scan rate of 0.77 mm/μs, the 1.1 μs space pulse time renders an axial resolution of the acoustic pulse emanating from this two-layer piezoelectric transducer  10  equivalent to a spatial pulse length of 0.86 mm.  
         [0051]      FIG. 4B  is a Hilbert waveform plot (as normalized voltage y-axis vs. microseconds μs x-axis) from a three-layer acoustic transducer  100  configured with the back matching layer  150  at −20 decibels axial resolution scanned at 0.77 mm per μs. The waveform plot includes a bimodal tracing  300 ; a rectified Hilbert tracing  304  comprising a major peak  304 A, a first minor peak  304 B, and a second minor peak  304 C; a −20 dB limit line  308  from the maxima of the major peak  304 A, a lower limit  312 A of approximately 0.64 μs and an upper limit  312 B of approximately 1.55 μs. The lower limit  312 A and the upper limit  312 B are obtained by the intersection of the limit line  308  with the Hilbert tracing line  304 .  
         [0052]     The spatial pulse time period is defined as a “delta T” or time period obtained as a difference between the lower limit  312 A and the greater or greatest upper limit whenever there is more than one upper limit. In  FIG. 4B  there is only one upper limit, namely the upper limit  312 B. The spatial pulse time for the three-layer transducer  100  illustrated in  FIG. 4B  is the absolute difference between the upper time limit  312 B and the lower limit  312 A, or 1.55 μs-0.64 μs, equivalent to a spatial pulse time of 0.91 μs. With a scan rate of 0.77 mm/μs, the 0.91 μs space pulse time renders an axial resolution of the acoustic pulse emanating from this three-layer piezoelectric transducer  100  equivalent to a spatial pulse length of 0.70 mm.  
         [0053]     The three-layer transducer  100  having the back matching layer  150  improves the axial resolution by shortening the spatial pulse length. The axial resolution for the two-layer transducer  10  is 0.86 mm and for the three-layer transducer  100  is 0.70 mm. Thus, the spatial pulse length is shortened by 0.16 mm for the three-layer transducer  100 . Thus, the three-layer transducer  100  having the back matching layer  150  improves the axial resolution by approximately 23%.  
         [0054]     The three-layer transducer  100  advantageously exhibits substantially lower energy losses due to reduction or elimination of interface reflections and improved non-signal vibration damping.  
         [0055]     Accordingly, the scope of the invention is not limited by the disclosure of the preferred embodiment. Instead, the invention should be determined entirely by reference to the claims that follow.  
                                                                                                                                                                                                                                                                                                                                             APPENDIX                                Matlab Source Code:                clear all           c = 1540;           directory = ‘e:\work\data\ts0000\PiezoCAD\’;           figure(1), clf           for ii = 1 : 8,                switch ii                case 1                filename = ‘Front0_Back0’;                case 2                filename = ‘Front2_Back0’;                case 3                filename = ‘Front0_Back1’;                case 4                filename = ‘Front2_Back1’;                case 5                filename = ‘Front2_BackPerfect’;                case 6                filename = ‘Front0_BackPerfect’;                case 7                filename = ‘FrontPerfect_BackPerfect’;                case 8                filename = ‘Front2_Back2’;                otherwise                end                fid = fopen([directory, filename, ‘.dat’], ‘rt’);           while feof(fid) == 0                if findstr(fgetl(fid), “‘usec’),                cnt = 1;           while feof(fid) == 0                temp = fgetl(fid);           I = findstr(temp, “”);           beam(cnt,1) = str2num(temp(I(1)+1:I(2)−1));           beam(cnt,2) = str2num(temp(I(3)+1:I(4)−1));           cnt = cnt + 1;                end                end                end           fclose(fid);           beam = beam(1:round(length(beam)/4),:);           Ts = beam(2,1) * 1e−6;           Fs = 1/Ts;           % Axial resolution           H = abs(hilbert(beam(:,2)));           Y = max(H);           threshold = 10{circumflex over ( )}(−20/20) * Y;           I = find(H &gt;= threshold);           AR = I(end)−I(1);           subplot(2,4,ii),                plot(beam(:,1), beam(:,2)), hold on,           plot(beam(:,1), H, ‘g−’, ‘linewidth’, 2),           plot(beam(:,1), ones(length(beam),1) * threshold, ‘r’), hold on,           axis tight, grid on           I = findstr(filename, ‘_’);           title([filename(1:I−1), ‘ ’, filename(I+1:end), ‘, ’,           num2str(round(AR*c/Fs/2 *            1e3 * 1e2)/1e2), ‘ mm’])                end