Dear Craig:

Sorry to be slow responding. It seems to me that your calculation indeed shows that your proposed array spacing is good. I'm writing detailed comments below. Some of them apply to side issues, so let me first state the main point as I see it:

For backscatter measurements, the figure of merit of an antenna is its backscatter gain, the average value of G^2. Backscatter gain is not simply proportional to G(0,0), the ordinary on-axis gain. Hagen and Baumgartner showed that when an array antenna is

used for backscatter, it should be a filled array. (They found that the backscatter gain of a sparse array is less than when its elements are moved inwards to form a filled array - even though the sparse arrangement and the filled arrangement have equal on-axis gains). It is therefore important to check that the element spacing proposed for the RAO avoids this degradation. The backscatter gain of the proposed array was computed numerically and was found to be equal to the backscatter gain of a uniformly illuminated aperture-type antenna of the same size.

Detailed comments:

page 2: You've shown that Equation 8 is an appropriate

figure of merit. Why then even mention "A slightly different

figure of merit", Equation 9? The point of the Hagen and

Baumgartner paper was not that Gbs is different from G(0,0)

but that Gbs is not, in general, even proportional to

G(0,0). The "slightly different figure of merit" is an

incorrect figure of merit (extremely incorrect for the case

of an sparse array). You write, correctly, at the top of

page 3 that this figure of merit "can yield large errors

when used for widely disparate antenna types". Yes, such as

when a dish antenna is compared to an array antenna - which

is the purpose of your memo. But then you say "As a result,

we need to modify this figure of merit somewhat....". Why

do you reject the correct figure of merit (Equation 8) in

favor of modifying a defective figure of merit (Equation 9)?

I guess you've answered that on page 6, citing a "long

tradition" of using Equation 9. But the integral that

defines Gbs is right there in the original 1969 review by

Evans.

As for modifying the defective figure of merit, you state

"This modification will be made in a future section, after

the relationship between backscatter gain and on-axis gain

has been defined". But both backscatter gain and on-axis

gain have precise definitions and, in general, one is not

proportional to the other. How can you "define" a

relationship between them when they are not strictly

related? You carry on through the paper implying this proportionality. I'd recommend that you use only the FOM of Equation 8 and not even mention Equation 9. (The backscatter gain of the Sonderstrom antenna is specified by your Equations 11 and 12 without the need to introduce the alternate FOM).

On page 5 you mention a "surprising and non-intuitive

conclusion... that the

individual element gain has very little impact on the

overall antenna gain." I may be missing the point but, for

any array that isn't filled, decreasing the element gain

should indeed decrease the overall gain. The main beam will

retain its shape, i.e. beamwidth, but the gain in the main

beam will decrease as more power is makes its way into side

lobes.

Best wishes, Jon