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- since 1996 -

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Technical Discussions
Stan
NDT Inspector,
Canada, Joined Jan 2009, 31

Stan

NDT Inspector,
Canada,
Joined Jan 2009
31
21:27 Oct-20-2010
Sound Beam Focal Region

Hi:
Does any one know of a formula to measure or approximate the length of the focal region of a sound beam.
Stan

    
 
 
Gerhard Splitt
R & D, -
Private, Germany, Joined Nov 1998, 38

Gerhard Splitt

R & D, -
Private,
Germany,
Joined Nov 1998
38
21:47 Oct-20-2010
Re: Sound Beam Focal Region
In Reply to Stan at 21:27 Oct-20-2010 (Opening).

Hi Stan,
as a rule of thumb, the focus range (-6 dB) is roughly 1/3 in front of the focus and 2/3 behind the focus. For an exact calculation see the web site of imasonic: http://imasonic.com/Industry/IM_Design.php.

Gerhard

    
 
 
Tom Nelligan
Engineering,
retired, USA, Joined Nov 1998, 390

Tom Nelligan

Engineering,
retired,
USA,
Joined Nov 1998
390
22:30 Oct-20-2010
Re: Sound Beam Focal Region
In Reply to Stan at 21:27 Oct-20-2010 (Opening).

You may also find useful the beam equations on page 43 of the Panametrics-NDT transducer catalog, which you can download through the link below.

http://www.olympus-ims.com/panametrics-ndt-ultrasonic/pdf/

    
 
 
Carlos Correia
R & D, - -
UCV & EGROUP, Venezuela, Joined Oct 2008, 120

Carlos Correia

R & D, - -
UCV & EGROUP,
Venezuela,
Joined Oct 2008
120
03:29 Oct-21-2010
Re: Sound Beam Focal Region
In Reply to Tom Nelligan at 22:30 Oct-20-2010 .

Hello Stan, the following equation was extracted from AUTOMATIC ULTRASONIC TESTING FOR PIPELINE GIRTH WELDS (chapter 2) an excellent book from our friend Ed Ginzel.
d=0.2568xDxSf
Where
Sf=F/N
F: Focal length
N: Near field
D: transducer diameter
Sf: Normalized focal length
d: beam diameter at -6dB

    
 
 
Gerhard Splitt
R & D, -
Private, Germany, Joined Nov 1998, 38

Gerhard Splitt

R & D, -
Private,
Germany,
Joined Nov 1998
38
09:23 Oct-21-2010
Re: Sound Beam Focal Region
In Reply to Stan at 21:27 Oct-20-2010 (Opening).

Hi Carlos,
your formula calculates the beam diameter (beam width) at the focus point; not the length of the focal region, which Stan has asked for.

Gerhard

    
 
 
Stan
NDT Inspector,
Canada, Joined Jan 2009, 31

Stan

NDT Inspector,
Canada,
Joined Jan 2009
31
01:45 Oct-22-2010
Re: Sound Beam Focal Region
In Reply to Gerhard Splitt at 09:23 Oct-21-2010 .

Gerhard:
If my understanding is correct, then for a flat unfocused transducer, where Sf = F/N, Focal Length and Near Field Length should be equal and therefore Sf should equal 1. Is this correct?

Stan

    
 
 
Gerhard Splitt
R & D, -
Private, Germany, Joined Nov 1998, 38

Gerhard Splitt

R & D, -
Private,
Germany,
Joined Nov 1998
38
09:33 Oct-22-2010
Re: Sound Beam Focal Region
In Reply to Stan at 01:45 Oct-22-2010 .

Stan,
that's right!
For N we have as a good approximation the well known formula:
N=D²*f/(4v)
with D= transducer diameter
f=frequency
v= sound velocity in the material under test, e.g. steel.

Regards,
Gerhard

    
 
 
Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1254

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1254
14:29 Oct-27-2010
Re: Sound Beam Focal Region
In Reply to Stan at 21:27 Oct-20-2010 (Opening).

Stan, it sounds like you are looking to calculate the depth of field for the 6dB working range of the soundpath.
There is a nice application avaialble on the Immasonic website at http://www.imasonic.com/Industry/IM_Design.php
You enter the appropriate values (for a single element round probe) and then press Calculation to see the values filled in. It is interesting to see how the radius of curvature and the focal distance are not the same! Focusing quickly reduces the useful working range (depth of field) of the beam.

    
 
 
Stan
NDT Inspector,
Canada, Joined Jan 2009, 31

Stan

NDT Inspector,
Canada,
Joined Jan 2009
31
22:22 Oct-29-2010
Re: Sound Beam Focal Region
In Reply to Ed Ginzel at 14:29 Oct-27-2010 .

Thanks Ed:
I played around with this, and I am wondering how the Radius of Curvature is related to the Focal distance programmed into the focal laws for a PA instrument. Are they the same number?
Stan

    
 
 
Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1254

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1254
22:40 Oct-31-2010
Re: Sound Beam Focal Region
In Reply to Stan at 21:27 Oct-20-2010 (Opening).

Stan, the ROC (radius of curvature) is not really related in any direct way to the PA focusing in the focal laws. They use the Fermat principle to compute the shortest travel "time" to the desired focal point.
You can now order a curved passive plane on a linear array (helps reduce over-sizing of length in a linear scan). This would use the equation seen on the Imasonic site. It is intersting to see that the optical focal point and the acoustic focal point are not identical! For the focal point defined by the ROC to equal the distance in the test material, the velocity of the test material must be 1m/s. E.g. if the 5MHz 10mm diameter probe had a 50mm ROC the beam would focus at 50mm from the probe only if the material velocity was 1m/s.

    
 
 

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