Hi

The linear array directivity index (DI) can be calculated as 10log10(n) or 10log10(2L/lemda) where n is no of sensors in linear array, L is acoustic length/aperture of array and lemda is wavelength.

If we have a uniform linear array whose elements have spacing greater than lemda/2 among them then what formula is more accurate for DI calculation?

For that particular question I would check Harry van Trees book series (estimation, modulation techniques) volume 4. It is devoted to radio waves, but math is the same for mechanical waves as well.

Thanks. I will try to get this book series

Maybe this will help:

https://www.usna.edu/Users/physics/ejtuchol/docume...

Thanks for literature

Why would you want array spacing greater than half wavelength?

It would create Grating Lobe, Unwanted Lobe in undesired direction.

That is why all literature keep the spacing equal or less than half wavelength.

Best regards,

Shahram

https://ortenga.com/

Dear Shahram

Thanks for reply. You are rigth but some times at higher frequencies, it is difficult to maintain lemda/2 spacing in an array due to sensors physical dimensions. This will of course limit the useful scanning area of the array but it is trade of b/w individual sensors sensitivity and scanning area

You can look up equation 3.92 in Antenna Theory and Design by Warren Stutzman and Gary Thiele for directivity of linear array, equally spaced elements.

Keep in mind that, grating lobe is present for greater than half wavelength, and good portion of the energy/power is lost in the grating lobe.

You can contact me directly if there is any question.

Best regards,

Shahram

https://ortenga.com/about-2/