09:59 Sep-04-1996 Robert A. Day Engineering Milky Way Jewels, USA, Joined Nov 1998 40
Re: Depth of Field Marty -
I have good new and bad new. First the bad. There are no equations for the depth of field of a transducer (that I know off) and as far as I know there is no definition of depth of field. The whole concept of depth of field in optics is acceptable sharpness which is kind hard to get a grasp on in NDT. I suspect every application is different and you need to define your terms. I worked on a program to NDT closure welds for radioactive spent fuel containers several years ago. I defined acceptable sharpness as 1 mm. Other applications would use other numbers.
The good news is that once you have a definition you can calculate the diffraction field of a transducer and from that determine the depth of field. The same rules prevail in ultrasound as optics, i.e. you want the diameter of the transducer (lens) to be much smaller than the focal length (large f/number). You generally want to get depth of field in the part and the focus changes. Calculating the actual depth of field in the part is much more difficult even for straight beam. The depth of field decreases to a value similar to what would be obtained if the focal length is entirely in the faster material. This means if you get 2 cm of less than 1 mm focus in water the actual depth of field is about 5 mm. It does vary a bit with ratio of water path to metal path but because the effective focal length in steel is shorter and the wavelength increases you wind up with a shorter depth of field and almost the same focal diameter (usually a little larger).
Equations are available but solving them is not straight forward. The following are good starting points:
Exact general solution for right circular piston: D.G. Crighton, et. al., "Modern Methods in Analytical Acoustics", 1992, Springer-Verlag, pp 530 - 536. The talk about the high frequency limit which is the approximation commonly used.
A more classical and less useful discussion is in Richardson's "Ultrasonic Physics" on page 43. This is the usual on axis only solution but he shows his work.
A more accessible but still not for focused transducers discussion is in Timken's " Elements of Acoustics." This has the solution in Bessel functions and is more easily calculated.
There are many approximate solutions for focused transducers published in the literature, and a few exact numerical approaches. I have copies of most of them and am planning to put together a program someday soon. Moving my office to San Francisco has most of this in boxes and it's not clear when I will get back to unpacking them. As soon as I get that organized, I'll send you a list of papers that discuss this.
Getting the depth of field from these is still not easy since you still have to decide how to measure focal size. The old FWHM is good but not always the most appropriate, do you do 6 or 12dB or do you do something more sophisticated. Once you have a diffraction code that can do focused transducers, and have a definition if focal size, and decide what acceptable focus is, then off course it's easy.
Hope That helps.
: Can you tell me of a good textbook or paper that develops the equations for depth of field of focused transducers?