Re: [ccp4bb] Why Do Phases Dominate?

[Eleanor Dodson]

It is quite instructibe to draw the 2-d vector representing the 
amplitude and then the error vector when you assume certain things...
Change the magnitude by 50% and see the error vector, then change the 
phase by a random shift - say 90 degrees and draw the error vector. In 
general it is much more severe for case 2 than case 1..

 eleanor


Edward A. Berry wrote:
This bias is exacerbated by the convention that phases go from 0 to 360*
while amplitudes go from zero to Plus.
Thus the phase decides where to put it, and whether to add or take away,
while the amplitude only decides how much.

If phase was 0 to 180* and amplitude was Minus to Plus,  then
amplitude would decide whether to add or take away as well as how much.



Lijun Liu wrote:
Does anybody have a good way to understand this?
=========
There are a lot of good ways to understand this. The amplitudes
determines how much
to put, while the phases tell you where to/how to correctly put. For
example, treating San
Francisco as a cell, the heights of buildings and lines of streets
determine the landscape.
Moving all buildings along some streets separately will change more the
landscape than
just changing some buildings' height along the street. Another example,
taken at different
lighting/darkness conditions, the photos from the same face could be
easily recognized
and compared. However, with the same light condition, when the position
of nose, eyes,
mouth, etc., are dislocated from their original positions, the face will
be very different.

One possible answer is "it is the nature of the Fourier Synthesis to
emphasize phases." (Which is a pretty unsatisfying answer). But, could
there
be an alternative summation which emphasizes amplitudes? If so, that
might
be handy in our field, where we measure amplitudes...
==========
It does have. For example, Patterson function.

Lijun


Regards,

Jacob Keller

*******************************************
Jacob Pearson Keller
Northwestern University
Medical Scientist Training Program
Dallos Laboratory
F. Searle 1-240
2240 Campus Drive
Evanston IL 60208
lab: 847.491.2438
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email: j-kell...@northwestern.edu <mailto:j-kell...@northwestern.edu>
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Lijun Liu
Cardiovascular Research Institute
University of California, San Francisco
1700 4th Street, Box 2532
San Francisco, CA 94158
Phone: (415)514-2836