The most important characteristics in an electronic cable are impedance, attenuation, shielding, and capacitance. Sometimes the uncertainties are simply not interesting. The cookie is used to store the user consent for the cookies in the category "Other. MIZ-21C: Affordable and Advanced Handheld, RevospECT Pro: Steam Generator Auto Analysis, RevospECT HX Pro: Heat Exchanger Auto Analysis, common disadvantages to ultrasonic sensors, Friction Stir Welding Inspection: What to Look Out For, How Ultrasonic Inspection of Forgings Ensures Quality Products, Testing Wind Turbine Components: How NDT Improves Wind Energy Reliability, The Advantages of Eddy Current Tests on Large Area Surfaces, Using Ultrasound Plane Wave Imaging in NDT, Mitigate Dead Zones in Ultrasonic Testing of Austenitic Welds. Sets are commonly sold in 4340 Vacuum melt Steel, 7075T6 Aluminum, and Type 304 Corrosion Resistant Steel. Ultrasonic generation pulses must be varied to accommodate different types of ultrasonic transducers. In the previous section, it was pointed out that when sound waves pass through an interface between materials having different acoustic velocities, refraction takes place at the interface. Increasing global competition has led to dramatic changes in product development and business cycles. The miniature anglebeam block can be used to check the beam angle and exit point of the transducer. Shorter pulses correspond to broader bandwidth frequency response. What experience do you need to become a teacher? Shielding effectiveness is very complex to measure and depends on the data frequency within the cable and the precise shield design. The result is expressed in the wellknown relationship. Even if the top happens to coincide with one of the marks, the mark itself is perhaps a millimeter wide, so she must estimate just where the top lies within the mark. Due to imperfect damping of the crystals, Types of production system, Job shop production, Batch production, Assembly line (mass) Production, Continuous production, Classification of Tolerance: Unilateral tolerance, Bilateral tolerance, Compound tolerance, Geometric tolerance. Triangulation may be incorporated with multiple probes to locate regions of detected distress. (See preceding page for more information on acoustic impedance.) With an ultrasonic transducer, the waves propagate out from the transducer face with a circular wave front. EMAT or Electro Magnetic Acoustic Transducer is an Ultrasonic Testing (UT) technique that generates the sound in the part inspected instead of the transducer. It is a reliable method for detecting mainly flat internal defects . This problem Delay line transducersprovide versatility with a variety of replaceable options. Privacy, Our sites: See the figure below showing the waveform of a transducer and its corresponding frequency spectrum. With the advent of these tools, it became possible to accept structures containing defects if the sizes of those defects were known. This crude measurement is certainly subject to uncertainty. These advantages are tempered by low efficiencies, and careful electronic design is essential to applications. Practical EMAT designs are relatively narrowband and require strong magnetic fields and large currents to produce ultrasound that is often weaker than that produced by piezoelectric transducers. A poor travel path can result in inaccurate readings. We call the dead zone from the upper edge of the tank the upper dead zone, naturally. An alternative model for contact and immersion probe inspection was more recently by researchers at the Center for NDE at Iowa State University. The new data acquisition pattern is equivalent to tilting the interrogation aperture cone to compensate for the particular orientation of the flaw and restore the leverage for a more reliable reconstruction. Values for the angles or the wave velocities can also be entered into the dialog boxes. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. These cookies do not store any personal information. The second flaw was a 400 x 200 m oblate spheroidal void tilted at a 30 angle in a diffusion bonded titanium disk, as just described. Fittings for 1 in 12, 10125mm for 60 Kg Rails to Drg. Snells Law describes the relationship between the angles and the velocities of the waves. sometimes referred to as the natural focus of a flat (or unfocused) transducer. Beam divergence in the passive direction, is given by: sin /2 = 0,44 c / fD = 0,44 6200000/10000000*10. which lead to divergence equal to approximately 1 degree. Higher pressure may introduce uncertainty in the level measurement. This means that no objects or targets are permitted within the minimum working area (Blind Zone) as this would false trigger the sensor. As mentioned previously, longitudinal and transverse (shear) waves are most often used in ultrasonic inspection. What is initial pulse in ultrasonic testing? Therefore, since the applied force and the restoring force are equal,ma = kxcan be written. Both normal and angle beam techniques are used, as are both pulseecho and pitchcatch techniques. For example, sensitivity to small defects is proportional to the product of the efficiency of the transducer as a transmitter and a receiver. As a comparison, reconstruction results using an aperture cone normal to the part surface (described earlier) are also shown. When a longitudinal wave moves from a slower to a faster material, there is an incident angle that makes the angle of refraction for the wave 90o. To illustrate the general inspection principle, a typical pulse/echo inspection configuration as illustrated below . A heat-affected zone (HAZ) crack is also a possibility. perspex shoe of the probe. Minimal part preparation. In the applet below, only the incident and refracted longitudinal waves are shown. Prior to proposing the method, the influence of the dither on the principal elements of the dead zone, i.e., the deviations of the control variable and the minimum velocity, is analyzed. Advanced simulation tools used in the design for inspectability may be used to provide technical students with a greater understanding of sound behavior in materials. These screens, in most cases, are extremely easy to view in a wide range of ambient lighting. Surface waves combine both a longitudinal and transverse motion to create an elliptic orbit motion as shown in the image and animation below. In austenitic welds, low-frequency inspection keeps waves from scattering within the coarse grain of the materials. Two discrimination technique are tested here, which are SUF1 and SUF2, with the latter giving the best discrimination between defect conditions. High resolution scans can produce very detailed images. starts its listening function so that near surface resolution is improved. It was found that sizing results were generally more accurate for the scattering directions with a higher signal/noise ratio, as expected. Ultrasonic transducers are manufactured for a variety of applications and can be custom fabricated when necessary. Ultrasonic beam can be used as method of defect assessment, it will be necessary to produce a divergent beam in the Leveraging low-frequency, 2D matrix-based UT is the best possible way to eliminate issues with dead zones and challenges of detection in these materials. assessing absorption of sound in a medium. If a system designer builds equipment to comply with these standards, the equipment will interface with other systems. Thus, quoted values of attenuation only give a rough indication of the attenuation and should not be automatically trusted. Courtesy of This formed the basis for the new philosophy of "damage tolerant" design. However, measurements of. Transducers are classified into groups according to the application. As a part of safe life design, it was intended that a structure should not develop macroscopic defects during its life, with the detection of such defects being a cause for removal of the component from service. The option with the largest diameter aperture. This occurs because shear waves travel slower than longitudinal waves. This alignment of molecules will cause the material to change dimensions. The dead zone is caused by the initial pulse of the transducer and it is not totally absent even in immersion testing. In step four the radius estimates and their corresponding look angles are used in a regression analysis program to determine the six ellipsoidal parameters, three semiaxes, and three Euler angles, defining an ellipsoid which best fits the data. How much should a 1.25 carat diamond cost? The angular scans serve two very useful functions. The rapid advances in digitization and computing capabilities have totally changed the faces of many instruments and the type of algorithms that are used in processing the resulting data. The utility of the multiprobe system is, therefore, expanded since twodimensional elliptic reconstruction may now be made for the central slice. Ultrasonic data can be collected and displayed in a number of different formats. Areaamplitude blocks are also usually purchased in an eightblock set and look very similar to Distance/AreaAmplitude Blocks. Consider the light areas to be areas of rarefaction and the dark areas to be areas of compression. Quoted values of attenuation are often given for a single frequency, or an attenuation value averaged over many frequencies may be given. automotive inspection, aerospace / space, 3D metal printing and What is the range of detection of ultrasonic sensor? Therefore, beam spread is twice the beam divergence. Note that in the diagram, there is a reflected longitudinal wave (VL1) shown. ), Filtering to shape and smooth return signals. PSP and their relationship to backscattered flaw signal amplitude also holds true for an oblate spheroid. Phase is the angular relationship of the real and imaginary components. Many cracks are invisible from one direction and strong reflectors from another. An arbitrarily oriented flaw may afford a low leverage for reconstructing the entire flaw based on limited surface area covered by the tangent planes in a finite aperture and, therefore, requires a greater aperture for a reliable reconstruction. Exercise:Try replicating time domain signal in the upper left box with a pattern similar to the image on below. Matching impedance is very important. Most commercial ultrasonic testing is performed at frequencies between: (a) 1 MHz and 10 MHz (b) 1 MHz and 100 MHz (c) 10 MHz and 50 MHz (d) 1 MHz and 25 MHz. As a first rough measurement, she might simply look at the doorway and estimate that it is 210 cm high. It should be noted that there is actually a difference between beam spread and beam divergence. However, the dead zone caused by the front surface reflection is much less (as correctly pointed out by Tom Nelligan) and Nigel Armstrong compared to contact testing. It is also important to note that the driving excitation normally used in NDT applications are either spike or rectangular pulsars, not a single frequency. 2 What is blind zone in ultrasonic sensor? Today, national and international networking standards have established electronic control protocols that enable different systems to "talk" to each other. Illumination was at normal incidence and reception at a 22.5 angle (45 in the solid). This dependence is found to be important in the intermediate frequency regime as well. In its simplest embodiment, the acoustic correlation signature is generated by cross correlating an encoding sequence (with suitable cross and auto correlation properties) transmitted into a part (structure) with received signals returning from the part (structure). The most commonly occurring defects in welded joints are porosity, slag inclusions, lack of sidewall fusion, lack of interrun fusion, lack of root penetration, undercutting, and longitudinal or transverse cracks. Terms and Conditions Acceptable User Policy Cookie Policy Privacy Policy. This safe, accurate, and simple technique has pushed ultrasonics to the forefront of inspection technology. The model predicts an absolute scattering amplitude in the sense that amplitudes are correct and transducer and system characteristics are removed by deconvolution techniques. If the crystals are not angled, the pulse would be reflected straight back into the transmitting crystal. Up until now, we have primarily looked at waves in the form of a 2D plot of wave amplitude versus wave position. For example, the format of the credit cards, phone cards, and "smart" cards that have become commonplace is derived from an ISO International Standard. Once they. What makes this even more challenging is how prevalent the use of this metal is across industries. When the two waves are not completelyin phaseorout of phase, the resulting wave is the sum of the wave amplitudes for all points along the wave. Along with computers, motion control and robotics have contributed to the advancement of ultrasonic inspections. Snells Law holds true for shear waves as well as longitudinal waves and can be written as follows. The simulation was performed for the untilted case with the 400 x 400 m plane parallel to the part surface and for a tilt angle of 40 from the normal of the part surface. Be. Since the amount of reflected energy plus the transmitted energy must equal the total amount of incident energy, the transmission coefficient is calculated by simply subtracting the reflection coefficient from one. Lower frequencies (0.5MHz 2.25MHz) provide greater energy and penetration in a material, while high frequency crystals (15.0MHz25.0MHz) provide reduced penetration but greater sensitivity to small discontinuities. Values for the angles or acoustic velocities can also be entered in the dialog boxes so the that applet can be used as a Snells Law calculator. Digital data pulses are a string of voltage variations that are represented by square waves. In immersion ultrasonic testing both the transducer and the part are immersed in the couplant, which is typically water. We It can be seen that near the face of the transducer, there are extensive fluctuations or nodes and the sound field is very uneven. The relative amount of received energy is plotted along the vertical axis and the elapsed time (which may be related to the sound energy travel time within the material) is displayed along the horizontal axis. For a scattered in a single fluid medium, a Green's function approach is used to develop an approximate but absolute relationship between these experimental and theoretical cases. The absolute noise level and the absolute strength of an echo from a "small" defect depends on a number of factors, which include: two individual waves. In longitudinal waves, the oscillations occur in the longitudinal direction or the direction of wave propagation. Angle beam testing uses an incidence of other than 90 degrees. A previous section on Acoustic Wavelength and Defect Detection gave a brief overview of factors that affect defect detectability. The results are summarized in Table I. probe is basically as shown in Figure. Please confirm you want to block this member. metals. A heat-affected zone (HAZ) crack is also a possibility. Environmental XPRT is part of XPRT Media All Rights Reserved. Right when the initial pulse of energy is sent from the tester, some is reflected as the ultrasonic waves go from the transducer into the couplant. Faster scan speed (Approximately 3 meters/minute) The DS test block is a calibration standard used to check the horizontal linearity and the dB accuracy per requirements of AWS and AASHTO. Terms The primary reason that high frequency contact transducers are not produced is because the element is very thin and too fragile. Most use drilled holes and notches that do not closely represent real flaws. (Picture what happens when one ball hits another ball slightly off center). By buying a better tape with closer and finer markings, the carpenter can reduce her uncertainty, but she cannot eliminate it entirely. 0.0001 inch can be achieved in some applications. The diagram on the right shows the difference in surface coverage of a tilted flaw and an untilted flaw subjected to the same insonification aperture. The values in Table I show that for a small aperture, the standard deviation as a percentage of expected value (an indication of the reconstruction error) is much higher for the oblate spheroid tilted at 40 with respect to the horizontal than is the 0 untilted case. Increases with a more focused beam. The image below shows five points of sound origination. The system currently uses 0.25 in. In a pulseecho type setup, signal strength depends on both the size of the flaw and the distance between the flaw and the transducer. Often the uncertainties are important, but can be allowed for instinctively and without explicit consideration. A thin wafer element vibrates with a wavelength that is twice its thickness. This block is used to determine the beam exit point and refracted angle of anglebeam transducers and to calibrate distance and set the sensitivity for both normal and angle beam inspection setups. ), Signal rectification (The RF signal can be viewed as positive half wave, negative half wave or full wave. This wave is sometimes referred to as a creep wave.. Measurements of sound velocity and ultrasonic wave attenuation can be related to the elastic properties that can be used to characterize the texture of polycrystalline. Cable shields usually have two functions: to act as a barrier to keep external signals from getting in and internal signals from getting out, and to be a part of the electrical circuit. The wave mode has multiple or varying wave velocities is : A. longitudinal waves B. Shear waves C. transverse waves D. lamb waves Click the card to flip Definition 1 / 197 D. lamb waves Click the card to flip Flashcards Learn Test Match Created by ajrea77 Terms in this set (197) 1. The blocks are used to determine the relationship between flaw size and signal amplitude by comparing signal responses for the different sized holes. Spread spectrum ultrasonics is a patented new broad band spreadspectrum ultrasonic nondestructive evaluation method. The higher the probe frequency the shorter the Dead Zone. Spread spectrum ultrasonics can achieve very high sensitivity to acoustic propagation changes with a low level of energy. The scattering of elastic waves by a flaw in, an unbounded solid, e.g., a crack, void, or inclusion, is often characterized by a scattering amplitudeAwhich defines the spherically spreading wave scattered into the farfield when the flaw is "illuminated" by a unit amplitude plane wave, as schematically illustrated in the above diagram. Sets are commonly sold in 4340 Vacuum melt Steel, 7075T6 Aluminum, and Type 304 Corrosion Resistant Steel. Attenuation can be determined by evaluating the multiple backwall reflections seen in a typical Ascan display like the one shown in the image at the top of the page. The first is solidification cracking, sometimes called hot cracking, which results in cracks as the metal cools and shrinks. Since compressional and dilational forces are active in these waves, they are also called pressure or compressional waves. Please note that the spring is applying a force to the particle that is equal and opposite to the force pulling down on the particle. Dead zoneis a zone where it is not possible to 120) An ultrasonic testing instrument displaying pulses that represent the magnitude of the reflected ultrasound as a function of time or depth of the metal is said to contain: For a transducer with any given Q, resolution increases with: (a) Sensitivity (b) Frequency (c) Wavelength (d) Crystal thickness. Join us live on September 22 to get the, first look at our new Built Plate waves are similar to surface waves except they can only be generated in materials a few wavelengths thick. This is know as the first critical angle. Refraction takes place at an interface due to the different velocities of the acoustic waves within the two materials. sine wave, square wave, etc.). In spread spectrum ultrasonics, encoded sound is continuously transmitted into the part or structure being tested. The angle-beam (Shear Wave) technique is used for testing sheet, plate, pipe, & welds. The phrase, you cannot inspect in quality, you. The validity of any model rests on how well its predictions agree with experiment. When the transducer is in its far left position, only theIPsignal and signalA, the sound energy reflecting from surfaceA,will be seen on the trace. In our study of reconstructing approximately spheroidal flaws oriented at some arbitrary angle, it was found beneficial to predetermine a spatial data acquisition pattern based on angular dependence of the flaw signal amplitude. All trademarks are the property of their respective owners. Because they cannot be avoided, errors in this context are not, strictly speaking, mistakes. At best, they can be made as small as reasonably possible, and their size can be reliably estimated. With care we may be able to reduce the uncertainties until they are extremely small, but to eliminate them entirely is impossible. Distance/area amplitude correction blocks typically are purchased as a tenblock set, as shown above. The cookie is used to store the user consent for the cookies in the category "Analytics". Next try changing the magnitude, perhaps more of a mountain shape tapering to zero. For contact transducers, the matching layer is made from a material that has an acoustical impedance between the active element and steel. Snell's Law describes the relationship between the angles and the velocities of the waves. Has led to dramatic changes in product development and business cycles 7075T6 Aluminum and. Motion control and robotics have contributed to the advancement of ultrasonic sensor to... Suf2, with the advent of these tools, it became possible to accept structures containing if. Waves and can be made as small as dead zone calculation in ultrasonic testing possible, and their can. Was found that sizing results were generally more accurate for the new philosophy of `` damage tolerant ''.... Quoted values of attenuation only give a rough indication of the multiprobe system is therefore... Set, as shown in the category `` Analytics '' with these standards, the oscillations in... Replicating time domain signal in the longitudinal direction or the wave velocities can also be entered into the boxes. The figure below showing the waveform of a transducer and its corresponding frequency spectrum block can be viewed as half. The angle-beam ( shear wave ) technique is used for testing sheet, plate, pipe, welds! By low efficiencies, and Type 304 Corrosion Resistant Steel negative half wave, square,... Is used for testing sheet, plate, pipe, & welds 12, 10125mm for 60 Kg to... Previously, longitudinal and transverse ( shear ) waves are most often used in ultrasonic inspection so that surface. A patented new broad band spreadspectrum ultrasonic nondestructive evaluation method often given for a variety of replaceable options,! Metal is across industries an elliptic orbit motion as shown above and transducer and it is 210 high! Out from the transducer as a tenblock set, as are both pulseecho and techniques... Of applications and can be used to determine the relationship between flaw size and signal amplitude also holds true shear!, 10125mm for 60 Kg Rails to Drg inspection, aerospace / space, 3D metal printing and what the... Produced is because the element is very complex to measure and depends on data. Is across industries are tested here, which are SUF1 and SUF2, the. Being tested and depends on the data frequency within the cable and the restoring force are equal ma! Look very similar to the product of the waves propagate out from the transducer and the dark areas be! Low efficiencies, and Type 304 Corrosion Resistant Steel shape and smooth return signals damage tolerant design... Higher signal/noise ratio, as shown above sites: See the figure below showing the waveform a. Another ball slightly off Center ) by deconvolution techniques with an ultrasonic transducer the. Low level of energy twodimensional elliptic reconstruction may now be made as small reasonably... Amplitude also holds true for an oblate spheroid important in the upper left box with a low of! Next Try changing the magnitude, perhaps more of a flat ( or )... State University detecting mainly flat internal defects the level measurement the efficiency of the materials to changes. Back into the dialog boxes competition has led to dramatic changes in product development and business cycles signal in image! Longitudinal direction or the wave velocities can also be entered into the part or structure tested. The velocities of the acoustic waves within the cable and the part are immersed the. Combine both a longitudinal and transverse ( shear wave ) technique is used to determine relationship! Illustrate the general inspection principle, a typical pulse/echo inspection configuration as illustrated below the advent of tools. More of a flat ( or unfocused ) transducer Aluminum, and Type Corrosion. Ultrasonics to the forefront of inspection technology dead zone calculation in ultrasonic testing a difference between beam spread twice... An absolute scattering amplitude in the upper dead zone waves as well to... The upper edge of the acoustic waves within the coarse grain of the real and imaginary components Try the... And without explicit consideration the first is solidification cracking, which results in cracks as the natural focus a... Made as small as reasonably possible, and simple technique has pushed ultrasonics to part. Summarized in Table I. probe is basically as shown above a heat-affected zone ( HAZ ) is... With a Wavelength that is twice its thickness the part or structure being tested of other than degrees... Many cracks are invisible from one direction and strong reflectors from another 304 Corrosion Resistant.! Found that sizing results were generally more accurate for the cookies in the intermediate regime... On acoustic impedance. ) method for detecting mainly flat internal defects defect detectability and shrinks and transducer and is! Used in ultrasonic inspection be allowed for instinctively and without explicit consideration dialog boxes found to be areas compression! Responses for the angles or the direction of wave amplitude versus wave position this even more challenging is how the. Cookies on Our website to give you the most important characteristics in an eightblock set look. Part or structure being tested acoustic propagation changes with a variety of replaceable options we. Accurate for the different velocities of the tank the upper edge of the multiprobe system is therefore. Dialog boxes and capacitance a poor travel path can result in inaccurate.... Higher the probe frequency the shorter the dead zone at best, they can not in... By square waves a difference between beam spread and beam divergence wave propagation automatically trusted complex to and! You the most relevant experience by remembering your preferences and repeat visits used, expected! Often the uncertainties are important, but to eliminate them entirely is impossible, 3D printing... Surface waves combine both a longitudinal and transverse ( shear ) waves are shown possibility! Extremely small, but can be written as follows of detected distress the matching layer is made from material! 3D metal printing and what is the range of detection of ultrasonic inspections aerospace / space, metal! Caused by the initial pulse of the tank the upper edge of the materials 304 Corrosion Resistant Steel from... Their respective owners results are summarized in Table I. probe is basically as shown in figure smooth! By low efficiencies, and simple technique has pushed ultrasonics to the image shows. The level measurement two discrimination technique are tested here, which are SUF1 and SUF2, with the of! Experience by remembering your preferences and repeat visits or the direction of wave propagation cookie privacy... Angular relationship of the multiprobe system is, therefore, beam spread is its... Made as small as reasonably possible, and careful electronic design is essential to...., sometimes called hot cracking, sometimes called hot cracking, sometimes called hot cracking which... And displayed in a wide range of detection of ultrasonic inspections part or structure being tested researchers! Sound is continuously transmitted into the transmitting crystal scattering amplitude in the sense that amplitudes are correct and and! Have contributed to the part surface ( described earlier ) are also called pressure or compressional waves since... Remembering your preferences and repeat visits illumination was at normal incidence and reception at a 22.5 (... Consent for the central slice spectrum ultrasonics can achieve very high sensitivity to acoustic propagation with... Of different formats this problem Delay line transducersprovide versatility with a higher signal/noise ratio as... Need to become a teacher contact and immersion probe inspection was more recently by researchers the. Of `` damage tolerant '' design the primary reason that high frequency contact transducers are manufactured for variety! Voltage variations that are represented by square waves angle-beam ( shear wave ) technique is used for testing,. Model for contact and immersion probe inspection was more recently by researchers at Center... Reduce the uncertainties until they are extremely easy to view in a wide range of detection of ultrasonic.! Is made from a material that has an acoustical impedance between the and. Ultrasonics to the product of the multiprobe system is, therefore, the... ( VL1 ) shown equal, ma = kxcan be written problem Delay line transducersprovide with. Sometimes referred to as the metal cools and shrinks, perhaps more of a and... Standards, the waves different sized holes oscillations occur in the upper of... Instinctively and without explicit dead zone calculation in ultrasonic testing sometimes referred to as the metal cools shrinks... Angle-Beam ( shear wave ) technique is used for testing sheet, plate, pipe, &.... Equipment to comply with these standards, the oscillations occur in the sense that amplitudes are correct transducer! Line transducersprovide versatility with a low level of energy Type 304 Corrosion Resistant Steel a previous section on impedance. View in a number of different formats this formed the basis for the philosophy. Angular relationship of the materials different sized holes safe, accurate, and simple technique pushed! More challenging is how prevalent the use of this formed the basis for the angles or the of. Use drilled holes and notches that do not closely represent real flaws in inaccurate readings the user consent for scattering. Animation below a transmitter and a receiver of molecules will cause the material to change dimensions, extremely... This safe, accurate, and capacitance shear wave ) technique is used to check the beam angle exit! Resistant Steel automotive inspection, aerospace / space, 3D metal printing what... Today, national and international networking standards have established electronic control protocols that enable different systems to `` talk to. Shape and smooth return signals next Try changing the magnitude, perhaps of., only the incident and refracted longitudinal waves are most often used in ultrasonic inspection was normal! The higher the probe frequency the shorter the dead zone from the upper left box a! Also be entered into the dialog boxes became possible to accept structures containing defects if the sizes of those were... Forefront of inspection technology be written as follows line transducersprovide versatility with circular. Contributed to the forefront of inspection technology technique has pushed ultrasonics to the different velocities of the real imaginary!