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Technical Discussions
Mukesh Kumar Bhatt
Mukesh Kumar Bhatt
08:31 Aug-05-2005
Near Field in Angle beam testing

Can anybody tell me how to calaulte length of Near field in angle beam(Rectangular shaped crystals) testing.

Biju Varghese
Biju Varghese
07:27 Aug-10-2005
Re: Near Field in Angle beam testing
----------- Start Original Message -----------
: Can anybody tell me how to calaulte length of Near field in angle beam(Rectangular shaped crystals) testing.
------------ End Original Message ------------
Dear Mukesh

Here is the formula you are looking for

N=K*(aeff*aeff*f)/c K=1.3 for side ratio not exceeding 1.12

aeff=half effective length of the larger side of the crystal

You may refer to RD-TECH new book Introduction to Phased Array Ultrasonic Technology Applications page no. 48. K factor will depend upon the lenght to width ratio.

Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1307

Ed Ginzel

R & D, -
Materials Research Institute,
Joined Nov 1998
1307
04:25 Aug-10-2005
Re: Near Field in Angle beam testing
Mukesh:
Thanks for pointing that graph out! I missed it in my first read of the text!
The graph in the RD Tech Phased array book shows that the correction factor is actually the highest for a square element and it drops to 1 (i.e. K in the equation equals unity) for a ratio of 0.4:1 (width to length).

Professor I.N. Ermolov wrote a small booklet (Calculations in Ultrasonic Testing) and made an approximation which may be easier to remember.
N=S/pi*lamda
where N is the Near Field length
S is the area of the element
pi = 3.14
lamda is the wavelength of the mode in which the wave is transmitted.
This approximation he caustions is applicable for probe elements with a length to width ratio of up to 2:1.

Ermolov does indicate that this is an approximation!

Considering that no probe is generating a single frequency (i.e. it has bandwidth) the use of a single wavelength in the equation is perhaps a bit misleading. As well, the mechanical clamping of a rectagular piston is not likelyto provide a uniform particle displacement so lobe effects may dominate.

For probe construction calculations the equation you quoted would be best! For ease of application for the average tech in the field perhaps Dr. Ermolov's equation is suitable.

Something that shouldbe noted from the RD Tech Phased Array book that relates to the original question on angle beam testing is the wedge delay. On the same page (48) the last line has an equation that shows the portion of time in the wedge must be subtracted from the near field calculated in the test piece.

Regards
Ed

----------- Start Original Message -----------
: : Can anybody tell me how to calaulte length of Near field in angle beam(Rectangular shaped crystals) testing.
: Dear Mukesh
: Here is the formula you are looking for
: N=K*(aeff*aeff*f)/c K=1.3 for side ratio not exceeding 1.12
: aeff=half effective length of the larger side of the crystal
: You may refer to RD-TECH new book Introduction to Phased Array Ultrasonic Technology Applications page no. 48. K factor will depend upon the lenght to width ratio.
------------ End Original Message ------------

NITIN H.KOKANE
NITIN H.KOKANE
09:39 Aug-18-2005
Re: Near Field in Angle beam testing
sir,
we are developing Near Field Testing at BEL-GHAZIABAD ,INDIA. Please tell me how to test parabolic Antennas .
Regards,
Nitin

---------- Start Original Message -----------
: Mukesh:
: Thanks for pointing that graph out! I missed it in my first read of the text!
: The graph in the RD Tech Phased array book shows that the correction factor is actually the highest for a square element and it drops to 1 (i.e. K in the equation equals unity) for a ratio of 0.4:1 (width to length).
: Professor I.N. Ermolov wrote a small booklet (Calculations in Ultrasonic Testing) and made an approximation which may be easier to remember.
: N=S/pi*lamda
: where N is the Near Field length
: S is the area of the element
: pi = 3.14
: lamda is the wavelength of the mode in which the wave is transmitted.
: This approximation he caustions is applicable for probe elements with a length to width ratio of up to 2:1.
: Ermolov does indicate that this is an approximation!
: Considering that no probe is generating a single frequency (i.e. it has bandwidth) the use of a single wavelength in the equation is perhaps a bit misleading. As well, the mechanical clamping of a rectagular piston is not likely to provide a uniform particle displacement so lobe effects may dominate.
: For probe construction calculations the equation you quoted would be best! For ease of application for the average tech in the field perhaps Dr. Ermolov's equation is suitable.
: Something that shouldbe noted from the RD Tech Phased Array book that relates to the original question on angle beam testing is the wedge delay. On the same page (48) the last line has an equation that shows the portion of time in the wedge must be subtracted from the near field calculated in the test piece.
: Regards
: Ed
: : : Can anybody tell me how to calaulte length of Near field in angle beam(Rectangular shaped crystals) testing.
: : Dear Mukesh
: : Here is the formula you are looking for
: : N=K*(aeff*aeff*f)/c K=1.3 for side ratio not exceeding 1.12
: : aeff=half effective length of the larger side of the crystal
: : You may refer to RD-TECH new book Introduction to Phased Array Ultrasonic Technology Applications page no. 48. K factor will depend upon the lenght to width ratio.
------------ End Original Message ------------

Simon Amallraja
Simon Amallraja
03:19 Aug-19-2005
Re: Near Field in Angle beam testing
----------- Start Original Message -----------
: sir,
: we are developing Near Field Testing at BEL-GHAZIABAD ,INDIA. Please tell me how to test parabolic Antennas .
: Regards,
: Nitin
: ---------- Start Original Message -----------
: : Mukesh:
: : Thanks for pointing that graph out! I missed it in my first read of the text!
: : The graph in the RD Tech Phased array book shows that the correction factor is actually the highest for a square element and it drops to 1 (i.e. K in the equation equals unity) for a ratio of 0.4:1 (width to length).
: : Professor I.N. Ermolov wrote a small booklet (Calculations in Ultrasonic Testing) and made an approximation which may be easier to remember.
: : N=S/pi*lamda
: : where N is the Near Field length
: : S is the area of the element
: : pi = 3.14
: : lamda is the wavelength of the mode in which the wave is transmitted.
: : This approximation he caustions is applicable for probe elements with a length to width ratio of up to2:1.
: : Ermolov does indicate that this is an approximation!
: : Considering that no probe is generating a single frequency (i.e. it has bandwidth) the use of a single wavelength in the equation is perhaps a bit misleading. As well, the mechanical clamping of a rectagular piston is not likely to provide a uniform particle displacement so lobe effects may dominate.
: : For probe construction calculations the equation you quoted would be best! For ease of application for the average tech in the field perhaps Dr. Ermolov's equation is suitable.
: : Something that shouldbe noted from the RD Tech Phased Array book that relates to the original question on angle beam testing is the wedge delay. On the same page (48) the last line has an equation that shows the portion of time in the wedge must be subtracted from the near field calculated in the test piece.
: : Regards
: : Ed
: : : : Can anybody tell me how to calaulte length of Near field in angle beam(Rectangular shaped crystals) testing.
: : : Dear Mukesh
: : : Here is the formula you are looking for
: : : N=K*(aeff*aeff*f)/c K=1.3 for side ratio not exceeding 1.12
: : : aeff=half effective length of the larger side of the crystal
: : : You may refer to RD-TECH new book Introduction to Phased Array Ultrasonic Technology Applications page no. 48. K factor will depend upon the lenght to width ratio.
------------ End Original Message ------------

Contact Mr. Sanjeev Kaul of Mahindra Intertrade Ltd, DElhi Office @ 011-51220357 or mobile: 9811201495(Delhi) and he will help you on all the reqts like method of testing and Phased Array System etc., and any other applications related in NDT.

Simon Amallraja.

Udo Schlengermann
Consultant, -
Standards Consulting, Germany, Joined Nov 1998, 183

Udo Schlengermann

Consultant, -
Standards Consulting,
Germany,
Joined Nov 1998
183
06:58 Sep-01-2005
Re: Near Field in Angle beam testing

Generally the near field length of ultrasonic transducers is determined by the area and shape of the source and the wavelength.
The nearfield length is directly proportional to area and inverse proportional to wavelength.
For a circular transducer the area is given by pi and radius squared.
For a rectangular transducer the area is given by side a times side b.

So in general the nearfield length of a rectangular transducer is given by the equation

N = k(b/a)x(a^2)/lambda.

The factor k depends on the ratio (small side b/large side a).
This dimensionless factor k is between 0.99 (line) and 1.38 (square).
There is no analytical equation to calculate the factor k.
Approximatative equations for rectangles containing the factor pi are not exact, because they use circular sectors as approximation for a rectanglar source.

You will find a correct diagram for this factor k(a/b) for rectangular transducers in the European standard EN 12668-2:2000
Nondestructive testing - Characterization and verification of ultrasonic examination equipment - Part 2:Probes
in figure A.1,valid for all ratios a/lambda > 10.

Further information on the sound beam of rectangular transducers have been published by me in 1977:
Evaluation of the effective sound field data with the distance law for sound pressure (in German).
Materialpruefung vol.19 (1977) p.53-58.

Kind regards
Udo Schlengermann
GE Inspection Technologies GmbH, Huerth, Germany
udo.schlengermann@ae.ge.com

----------- Start Original Message -----------
: Can anybody tell me how to calaulte length of Near field in angle beam(Rectangular shaped crystals) testing.
------------ End Original Message ------------

NITIN H. KOKANE
NITIN H. KOKANE
00:59 Apr-28-2007
Re: Near Field in Angle beam testing
i am unable to generate far field data from near field data.plz let me know.
regards,
Nitin

----------- Start Original Message -----------
: : sir,
: : we are developing Near Field Testing at BEL-GHAZIABAD ,INDIA. Please tell me how to test parabolic Antennas .
: : Regards,
: : Nitin
: : ---------- Start Original Message -----------
: : : Mukesh:
: : : Thanks for pointing that graph out! I missed it in my first read of the text!
: : : The graph in the RD Tech Phased array book shows that the correction factor is actually the highest for a square element and it drops to 1 (i.e. K in the equation equals unity) for a ratio of 0.4:1 (width to length).
: : : Professor I.N. Ermolov wrote a small booklet (Calculations in Ultrasonic Testing) and made an approximation which may be easier to remember.
: : : N=S/pi*lamda
: : : where N is the Near Field length
: : : S is the area of the element
: : : pi = 3.14
: : : lamda is the wavelength of the mode in which the wave is transmitted.
: : : This approximation he caustions is applicable for probe elements with a length to width ratio of up to 2:1.
: : : Ermolov does indicate that this is an approximation!
: : : Considering that no probe is generating a single frequency (i.e. it has bandwidth) the use of a single wavelength in the equation is perhaps a bit misleading. As well, the mechanical clamping of a rectagular piston is not likely to provide a uniform particle displacement so lobe effects may dominate.
: : : For probe construction calculations the equation you quoted would be best! For ease of application for the average tech in the field perhaps Dr. Ermolov's equation is suitable.
: : : Something that shouldbe noted from the RD Tech Phased Array book that relates to the original question on angle beam testing is the wedge delay. On the same page (48) the last line has an equation that shows the portion of time in the wedge must be subtracted from the near field calculated in the test piece.
: : : Regards
: : : Ed
: : : : : Can anybody tell me how to calaulte length of Near field in angle beam(Rectangular shaped crystals) testing.
: : : : Dear Mukesh
: : : : Here is the formula you are looking for
: : : : N=K*(aeff*aeff*f)/c K=1.3 for side ratio not exceeding 1.12
: : : : aeff=half effective length of the larger side of the crystal
: : : : You may refer to RD-TECH new book Introduction to Phased Array Ultrasonic Technology Applications page no. 48. K factor will depend upon the lenght to width ratio.
: Contact Mr. Sanjeev Kaul of Mahindra Intertrade Ltd, DElhi Office @ 011-51220357 or mobile: 9811201495(Delhi) and he will help you on all the reqts like method of testing and Phased Array System etc., and any other applications related in NDT.
: Simon Amallraja.
------------ End Original Message ------------

Marc Ellyson
Marc Ellyson
18:10 Jun-11-2009
Re: Near Field in Angle beam testing
In Reply to Udo Schlengermann at 06:58 Sep-01-2005 .

Hi everyone,

Though this post is little old, it covers the exact topic I was looking for. I've read with interest answers from Ginzel and Schlengermann as I wanted to calculate the near field of a rectangular linear phased array probe with the following specifications:

PA probe specifications:
Frequency: 2.25Mhz
Nb of elmt: 20
Pitch: 1.2mm
Elmt width: 1.16mm
Gap: 0.04mm
Elevation: 12mm
Calculated active aperture: 23.96mm along primary axis

Then I used the R/D Tech book equation, the Ermolov eq. and the Udo Schlengermann eq. to find out that results were surprisingly different. Below are the results:

I've assumed the following for all calculations:
- L-wave velocity of 5.9mm/µs
- Width/length aspect ratio of 0.5
- k factor of 1.01
- Probe in direct contact at 0°

R/D Book eq.:
N = (k*aperture^2*freq)/(4*velocity)
N = 55.40mm

Ermolov:
N=S/pi*lamda
where N is the Near Field length
S is the area of the element, S=12*23.96=287.52mm^2
pi = 3.14
N = 34.90mm

Schlengermann:
N = k*(b/a)x(a^2)/lambda.
small side b/large side a
lamda=2.62mm
N = 110.98mm

Can anyone explain these differences? Am I misunderstanting something here?

Marc

emil shavakis
emil shavakis
01:40 Jun-12-2009
Re: Near Field in Angle beam testing
In Reply to Marc Ellyson at 18:10 Jun-11-2009 .

And then we set it on a wedge, cause it to convert to shear mode and believe. Focus-pocus. I guess we need to measure the effect in and not rely on the formulas.

Udo Schlengermann
Consultant, -
Standards Consulting, Germany, Joined Nov 1998, 183

Udo Schlengermann

Consultant, -
Standards Consulting,
Germany,
Joined Nov 1998
183
16:48 Jun-12-2009
Re: Near Field in Angle beam testing
In Reply to Marc Ellyson at 18:10 Jun-11-2009 .

Hello Marc,

There may be a problem with reading equations correctly when written in the text mode of e-mails, I must apologize for this.

Clearing the situation for your example: f = 2.25 MHz, longitudinal waves in steel c = 5920 m/s, active transducer aperture 24 mm x 12 mm = 288 sqmm.

case 1 (R/D solution):
N = k (2a)squared /4lambda = k f (a)squared /c
example: N = 1.01 * 2.25 * 144 / 5.92 = 55.3 mm

case 2 (Ermolov's solution)
This assumes that a circular disk of same area as the rectangular transducer has the same nearfield length, which is not true.
example: S = 288 mm = pi (r)squared , where r ist the radius of the equivalent disk.
For S = 288 sq mm, the equivalent radius is sqroot(91,67325) = 9,5746 mm,
equivalent N = (r)squared/lambda = (r)quared f/c = 91,67325 * 2.25/5.92 = 34,8 mm.

case 3 (my solution):
N = k (a)squared/ lamda = k (a) squared f / c;
k is a function of ratio (b/a), the exact value for (b/a)=0.5 is k=1.014.
This was written as k(a/b), not meaning k times (b/a).
example: N = 1,014 * 144 * 2,25/5,92 = 55,5 mm.

Solutions 1 and 2 are equal, approximation 3 gives a much too small nearfield length.

For a full diagram of the k factors depending on ratio (b/a) see European Standard EN 12668-2, Annex A.

Best regards

Udo Schlengermann

Marc Ellyson
Marc Ellyson
00:27 Jun-13-2009
Re: Near Field in Angle beam testing
In Reply to Udo Schlengermann at 16:48 Jun-12-2009 .

Udo,

Thank very much for the clarification. I've actually misread your equation. Clarification regarding the Ermolov eq. were also very helpfull. I'm actually a bit surprised that the software Beam tool 3, by Eclipse Scientific Products, based their near field caculations on this if the results doesn't match the more precise equations. There is certainly an explanation there!

This said, I'm wondering why you choose a=12mm, which is the element elevation rather than using a=24mm, which is the active aperture along the active axis?

From my understanding, using the elevation gives the near field for the passive axis instead of the active axis. However, using the active aperture (a=24mm) results with a N= 221.6mm, which is 4 times greater than your result. Hence is surely not the proper way, but I'm just trying to clarify all this.

Thanks again,
Marc

Udo Schlengermann
Consultant, -
Standards Consulting, Germany, Joined Nov 1998, 183

Udo Schlengermann

Consultant, -
Standards Consulting,
Germany,
Joined Nov 1998
183
14:47 Jun-13-2009
Re: Near Field in Angle beam testing
In Reply to Marc Ellyson at 00:27 Jun-13-2009 .

Hello Marc,

more details for clarification:

The final statement in my last mail of course has to be:
Solutions 1 (R/D) and 3 (my own) are equal, and approximation 2 (Ermolov) shows deviation.
Sorry for the typing error.

The dimensions of the active aperture of the example are 2a x 2b = 24 mm x 12 mm.
Ratio (2b/2a) = (b/a) = 0.5.
The large side (2a) determines the near field length. Unfortunately the example uses (b/a) = 0.5, therefore (2a)/2 = 2b, which causes the confusion.

The equations for nearfield length N always use the dimension of the large side:
N ~ (2a)squared/4 lambda = 4 (a)squared/4 lambda = (a)squared/ lambda.

The same holds for a circular disk (diameter D, radius r):
N ~ (D)squared/4 lambda = (2r)squared/4 lambda = 4 (r)squared/ 4 lambda = (r)squared/ lambda.

Nearfield length and divergence angles (directivity) are mainly determined by the largest dimensions of the active aperture. Even if only a frame or rim is active it gives nearly the same values, but not the same energy, of course.

Best regards

Udo Schlengermann

Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1307

Ed Ginzel

R & D, -
Materials Research Institute,
Joined Nov 1998
1307
01:36 Jun-14-2009
Re: Near Field in Angle beam testing
In Reply to Udo Schlengermann at 14:47 Jun-13-2009 .

Figure 2: On-axis amplitude plot

Figure 1: 3D View on left, Orthographic views on right

Udo and Marc:
I have made several lab attempts to assess the near field using combinations of focal law apertures but I was not able to see clearly defined peaks as we have been accustomed to in circular disc radiators.
The equations for near field determination have been (and I think should be kept in mind to be) only approximations when dealing with ultrasonic probes. The concepts are not so easily transferred from light where we have monochromatic effects. When bandwidth is added the regions are generally poorly defined at the best of times.
I have recently had the great opportunity to use the CIVA Simulation software from CEA. This software allows for input of realistic parameters and the visual output is generally quite easy to grasp.
I simulated the probe Marc used with the 12x24mm aperture and 2.25MHz frequency. I configured the output pulse to have a 70% bandwidth and placed it directly on a steel (simulated) block.
The images I collected are uploaded in the Word doc submitted here. When a plot of amplitude versus distance is made there is a peak at the midpoint of the two lobes in the active aperture direction at 17mm depth. There is another (lower) peak at approximately 50mm. 17mm and 50mm match none of the options calculated by formulae.
Sorry, it is not a simple answer and I am a bit disappointed that the computations by analytical approach are not in accord with any of the equations we have been referring to in our simplified approach to the Near Field.

Udo Schlengermann
Consultant, -
Standards Consulting, Germany, Joined Nov 1998, 183

Udo Schlengermann

Consultant, -
Standards Consulting,
Germany,
Joined Nov 1998
183
12:07 Jun-22-2009
Re: Near Field in Angle beam testing
In Reply to Ed Ginzel at 01:36 Jun-14-2009 .

Hallo Ed and Marc,
after a break to find my original documents of the 1970's I want to mail two image files published by me in these years and also in Krautkramer's book of 1990.

Ed, your calculations using the CIVA software are correct. The last peak of axial amplitude is at distance 1,041 (a)squared/lambda, which means 56 mm for the example. This is the last maximum on the axis defining the end of the nearfield. But for this transducer it is not the maximum peak. The absolute peak is at distance 0,36 (a)squared/lambda, which means 20 mm for the example.
The first attached diagram published first in 1974 shows all curves for rectangular transducers with aspect ratios between 0.2 (strip) and 1.0 (square).
The reason for the deviations from the curve for circular transducer is not the bandwidth of the pulse but the increasing unsymmetry of the rectangular transducer from a disk with decreasing ratio b/a.
Additionally I add a second diagram showing calculated profiles of a rectangular transducer of ratio b/a = 0.6, showing the higher side lobes parallel to the large side 2a of the tranducer and missing side lobes parallel to the smaller side 2b.
So I want to underline that my calculations done 35 years ago, when no personal computers were available and which use normalized functions, valid for all transducers with 2a/lambda > 10, totally are in accord with the modern 3-D-calculations (sound attenuation and electrical losses at the tranducer rim not taken into account).
For distances larger than 0.7(a)squared/lambda the beam structure is stable nearly independent of the bandwidth of the pulse, because all pulses which have more than half an oscillation generate the same beam structure there. And I do not know shorter pulses used in NDT.
I agree that the forum is not the place for an academic discussion, but please admit, that even in the good old days, accurate description of physics was possible.

Best regards
Udo Schlengermann

Marc Ellyson
Marc Ellyson
16:24 Jun-26-2009
Re: Near Field in Angle beam testing
In Reply to Udo Schlengermann at 12:07 Jun-22-2009 .

Dear Ed and Udo,

Thank you so much for these very comprehensive answers. I have just ordered the Krautkramer book to get all the details regarding the isobar. It seems to be a huge missing piece in my understanding of UT.

Going beyond my initial question, I'd like to clarify another aspect of the Near Field in PA. As shown on Fig 4.26, the sound pressure varies significantly up to the last maximum peak defining the near field length.
It is known that with phased array the focusing capability is no longer effective beyond the near field. Hence, the focusing zone is limited within the near field zone where pressure variations cannot give a uniform ultrasonic response.
My question is, does the pressure variation of a PA probe can be compared with the one of square monolithic transducer? If yes, this would mean the inspected volume should be outside the near field zone and focusing should be avoided or at least set at the end of the zone of interest.

I'm wondering if square monolithic and square PA transducers give equivalent beam shape because each individual elements of a PA probe have its own near field. These individual near fields are obviously very short due to the size of the elements. When phasing is applied, we then consider a virtual aperture using the activated elements. This wider aperture produce a focused region as demonstrated by Ed and Udo. Does this fact make the near field region more uniform, not at all or just result in a fairly complex region to describe?

Vikram
NDT Inspector, - Phased Array Specialist
Mistras Group Inc., USA, Joined Jun 2009, 9

Vikram

NDT Inspector, - Phased Array Specialist
Mistras Group Inc.,
USA,
Joined Jun 2009
9
01:43 Jun-27-2009
Re: Near Field in Angle beam testing
In Reply to Marc Ellyson at 16:24 Jun-26-2009 .

Marc,

Just a note on that the phased array probes have element sizes comparable to the wavelength of the probe which means they are kind of like point sources which are radiating a spherical wavefront. So, individual elements will probably not have a near field similar to the single huge crystal.

Regards,

Vikram

Larry Mullins
Consultant
NxtNdT, USA, Joined Apr 2006, 7

Larry Mullins

Consultant
NxtNdT,
USA,
Joined Apr 2006
7
15:03 Jun-27-2009
Re: Near Field in Angle beam testing
In Reply to Vikram at 01:43 Jun-27-2009 .

Vikram is not correct. The size of the aperture, not the element, provides the dimension of the "crystal" to be considered.

Vikram
NDT Inspector, - Phased Array Specialist
Mistras Group Inc., USA, Joined Jun 2009, 9

Vikram

NDT Inspector, - Phased Array Specialist
Mistras Group Inc.,
USA,
Joined Jun 2009
9
01:38 Jun-28-2009
Re: Near Field in Angle beam testing
In Reply to Larry Mullins at 15:03 Jun-27-2009 .

Larry,

I think you misunderstood my explanation. I was just talking about the individual elements on the phased array probe being comparable in size to the wavelength of the ultrasonic beam.

Vikram

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