phase from FFT of autocorrelation

This question is confusing. Autocorrelations generally produce real-valued functions; as such, they should contain no phase information.

You should give more explicit details and examples of how your data sets are produced.

The data is produced by a variation of the "interferometric autocorrelation" described here: https://en.wikipedia.org/wiki/Optical_autocorrelation . In my situation, there is a phase shift in the data caused by the relative orientation of the material that generates the signal. I am trying to resolve the relative phase differences between measurements by FFT of the signals. 

I guess my question is more general though: Why do the FFTs of functions such as the following 

make/d/o/n=1000 test= 2*sin(0.5*x)*exp(-((x-500)/200)^2)

or even the FFT of a sine function with a window applied produce a phase which seems to alternate? Attached is a graph of the FFT result of a sine using a Bartlett window.

I interpret that as being the periodic sign change of a real-valued amplitude. Be careful of the centering, or initial conditions. Any temporal shift of a real sinusoid will alter the position of the sign-reversals (i.e. the apparent phase of the sinusoid). I would recommend reading carefully the Igor help files on how it handles Fourier Transforms, and finding a good text book on the general topic. Your projected interferometric auto-correlation produces waveforms considerably different from your test cases. It is also hard to see the purpose of applying an FFT to those symmetric, real-valued time-delay data to extract further phase information.