Access cell in sheet named in another cell

I have sheet names in A1:a10 I want to get the b20 cell for each of these sheets into the current sheet's b1:b10. I know I'm close as this:

="[My excel file.xls]'"&$A1&"'!b20"

produces this (with A1=Sheet 1):

[My excel file.xls]'Sheet 1'!b20

but I can't figure out how to have excel evaluate the string.

Ideas?

Thanks!