# I Like To Look At The OceanNearfield Lyrics

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#### samter

Side lobes and apodization? More like "Stupendous lectures and great appreciation!" Thanks again so much for putting this series together.

#### D H

Awesome lectures developing an ultrasound demonstration as an engineering project very interesting and useful information

#### samter

I know it's been a very long time, but I just came across your comment and was intrigued. How did the engineering project go?

#### Ken Rolt

theta, as shown in the figures, is supposed to be the FULL width angle. The artwork shows it incorrectly as the half angle. The math is correct for a circular aperture (a disk). Also note that d is the diameter of the transducer disk. The beam diameter depends on the measurement distance from the transducer:
1. At the transducer surface, the beam diameter is d.
2. At the NZL distance, the beam diameter is assumed to be d/2, and
3. (well) beyond the NZL the beam diameter is approx distance*wavelength/d

#### samter

For what it's worth I tried looking things up and I came across a distinction between the beam divergence angle and the beam spread angle. Based on this resource ( https://www.nde-ed.org/NDETechniques/Ultrasonics/EquipmentTrans/beamspread.xhtml ), I think that theta as shown in the diagrams in this video would be the divergence angle, and then the spread angle would just be twice of that. But I'm sure that there are different conventions and subtle differences based on context...

#### Ken Rolt

Another comment: flat transducers have natural focus for pulsed ultrasound, and it occurs at a distance of 0.25*(d^2)/wavelength --- which is exactly the NZL. This is sometimes called the "last axial maximum" because the nearfield has many partial focal points (that are seldom mentioned), but the last one is the strongest (and why it's the most useful in ultrasound). The focus distance can be made smaller than NZL by using either a concave PZT or by adding a concave lens to the PZT. (a convex lens would diverge or spread the beam)

#### samter

That's really interesting and thanks for pointing it out!

#### Ken Rolt

Last comment on the summary slide:
1. NZL is proportional to diameter (d), but inversely proportional to wavelength.
2. beam diameter and divergence are proportional to wavelength, but inversely proportional to diameter d.

The author used the proportion symbol to mean "related to", but I am being more specific to avoid reader confusion.
If you can remember the simple algebra for these (as shown in these slides), then proportional, and inversely proportional, become obvious.

#### samter

I had the same exact thought. Thanks for pointing this out!