To reiterate chromatic, you should generally "declare" your my variables as late as possible so that they are scoped in the appropriate BLOCKs.

Let's take $sig for example. When you declared

my ($r, $rad, $twopi, $sig, $pi, $a0, $c0);
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what you're saying is $sig is available for the rest of the entire program (file-scoped). That works, but it's good practice to only scope $sig where it is used.

Hence, remove my (..., $sig, ...); above and rewrite your if-statement like:

    if ($r>20)
        {
        my $sig = $twopi*($rad**2);
        push (@sigs, $sig);
        }
    else
        {
        my $sig = $pi*($rad**2)*$a0*(1-exp((-$c0)*$rad));
        push (@sigs, $sig);
        }
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Now $sig is lexically scoped to either of those two BLOCKs. Try using $sig outside those blocks and you'll trigger a warning. This is a good thing.

Why? This approach leads to cleaner code in the long run:

• Less confusion, easier debugging.
• It allows you to structure your thoughts better when variables are "compartmentalized".
• Plus, it's way easier to declare when-you-need-it rather than maintaining a huge list at the very beginning of the program.