"The treatment of errors in the isomporphous replacement method"

Date:
[1958]
Reference:
PP/CRI/H/2/28
Catalogue details

Licence: In copyright

Credit: "The treatment of errors in the isomporphous replacement method". Source: Wellcome Collection.

    8/13
    Sfpfps í To deal with errors te have to consider as represnetd by by probabiltiy functions. In drawing these on the diagram we shall consider the vertex 0 of the triangle as a fixed point (figure^b). The two probability functions may now be combined into one., showing the probability that the point marked P falls at that point in the diagram, This distribution is the convolution of the two previous ones; if ^ is much smaller than F , F~ k the result is close to a Gaussian of elliptical contour with major axis \<0ey><SVand minor axis <?-> (figure 5c). Moving P along the minor axis of the ellipse has little eff - ct on the phase of relative to that of which is what we are trying to determine. So f qxJL s this phase is concerend, the probability function mey be represented by its projection on its major axis, which is very nearly ass siiipss Gaussian of breadth \)<£>%-<>£> = (figure 5d). This is clearly equivalent to regarding the whole error as residing in the gas-suéter I~u- __ In practice, errors will occur in the determination of both I abd F. To show that an error in F has an effect of the same magnitude as an H error in % ,(0l9a) may be differentiated with respect to these two quantities. So long as is small compared to 1 , ^Hwe find cL^ ^ . d-P j j~- Thus the assumption that all the error,/lies in the determination of r H does not affect the magnitude of the phase error. All these approximations are most accurate when i 7 and Ç are large, which is when estimation of error is most important. We can be satisfied with a much cruder estimate for the weaker terms. Using the approximate result given above, we can now estimate the probability, from the observations, of a particular phase, fi) , being the true phase. This is done by finding the error ;3C ^^)needed to be added to the, F observed to close the triangle when ^is given some phase cfi . Using the cosine law we {jave