Can Double Slit Experiment Results Differ with Two Separate Light Sources?

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If you were to take Youngs original Double Slit Experiment, with this slight variation, would you get the same results you would usually expect, i.e. an interference pattern?

The variation is as follows: Instead of one source of light, there are two sources of light, positioned next to each other each aimed directly at independent single slits. Between the slits, there is a barrier running all the way down to separate the two sources of light from each other, resulting in; Source A can only travel through Slit A, and Source B can only Travel through Slit B.

A crude diagram of what I'm trying to explain:

0 = Slit
x =Light Source
| = Solid Barrier Between Light Sources
_ = Detector Screen
. = Ignore (Purely for spacing purposes)

__________

-----0|0-----
|...|...|
|...|...|
|...|...|
|...x | x...|
 
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Interference effects depend upon the coherence of the light; this is usually done by using a single source passed through a pinhole - this improves the spatial coherence of the beam. This improved beam then goes through the double slit.

See http://www.rp-photonics.com/coherence.htmlAnd for some history see: http://en.wikipedia.org/wiki/Young's_interference_experiment

Of course it is possible to use two independent sources to show interference; this was first done in 1967 using two lasers: Pfleegor and Mandel "Interference of Independent Photon Beams". This experiment is much easier to do today.
 
Thanks for your informative reply, much appreciated.