User Interaction with the program

A FEW WORDS ABOUT NUMERICAL RESPONSES BY THE USER

If you respond to a numerical question with a “zero”, the default answer will be used. That is the way this program works to give you default answers. If you want to set a parameter to be “zero”, use an infinitesimal value such as 1.0E-25.

All floating point responses should include a decimal point somewhere in the mantissa of the response, otherwise the results are unpredictable and very system dependent!

EXPLANATION OF QUESTIONS ASKED BY THE PROGRAM

Q: Input file? <Quit>

The input file contains the SAS intensity data as ordered triples of Q-vector (in 1/A units), Intensity (in arbitrary units), and statistical error of intensity (same as intensity units). Note that there are no initial header lines in the input file. No more than the first 300 data points (ordered triples) will be read from the input file.

If you were to press {CR} without typing in a file name, the program would quit (as indicated by the default).

If the input file does not exist, the program will happily proceed to ask you all the remaining questions it has. Then and only then will it find out that the file you named does not exist. This will generate a program crash.

A suggestion for input file name extensions is ”.SAS” but this only a suggestion. The input file name may be up to 80 characters long.

Q: Output file?

This is the only question which has no default answer. You must answer this question with something. If your answer is the same as the input file name, the program will start over asking you for the input file name. This may be used as an easy exit if you specified the wrong name.

The program does not check to see if the named output file already exists. On some systems (Macintosh and MS-DOS), the old file will be erased and a new file created. On other systems (VAX), a file with the same name but a new version number will be created. Forewarned is forearmed.

My suggestion for MaxSas solution file name extensions is ”.MAX” or ”.DIS”. The output file name may be up to 80 characters long.

Q: Minimum (Maximum) q-vector? [1/A]

Use Q-vector (actually Q-vector magnitude) in units of 1/Angstrom. The user is allowed to exclude data points from the ends of the input data. Only those data points satisfying qMin <= Q-vector <= qMax will be analyzed. The program is designed to only handle positive Q-vectors.

Initially, qMin is set ridiculously low so that even the lowest data point will be used. Correspondingly, qMax is set high enough to include all typical SAS Q-vectors.

The user should generally cut off the data when the signal-to-noise ratio becomes poor. Truncating earlier than this will lose information about the smallest particles present in the sample. Users might note that it is not neccessary for all the intensity values to be positive, although it is probably inadvisable to include more than five negative ones.

Q: Scattering contrast? [10^28 m^-4]

The scattering contrast is the squared difference between the scattering length density of particle and matrix. If the contrast is 1.27E30 1/m**4, then enter the value 127.0. By the way, 1.E28 1/m**4 = 1.E20 1/cm**4.

The user can either enter the true contrast here or reply {CR}, in which case the final “volume fractions” obtained will have to be divided by the contrast (in units of 1.E28 1/m**4) in order to obtain genuine volume fractions. The program is coded to accept scattering contrast values no larger than one million units of 1.0E28 (1.0e34) 1/m**4.

Q: Factor to convert data to 1/cm?

If the intensity values in the input file were not in units of 1/cm, enter the constant to convert them into such units. If they were already in 1/cm units, good for you, so just press {CR} to accept the default. The program is coded to accept conversion values no larger than 1000.0.

Q: Error scaling factor?

Here is an opportunity for you to try analyzing your data with different ratios of signal to noise. If you think that the errors in the input file were underspecified, you may multiply them by this constant. More on this later as this will have a major influence upon the analysis.

Q: Background?

This program has left you the opportunity to subtract a constant intensity value. A good initial approximation will put you on the road to a good analysis of the data. Remarkably, the background may take any value, positive or negative. If you want to set the background back to zero, use infinitesimal (such as 1.E-25) rather instead. More on background later.

Q: Spheroids: D x D x vD, Aspect ratio (v)?

The scattering form factor currently implemented is that discussed by [Roess, 1947]. A special case of this ellipsoid of revolution, whose outside dimensions are D x D x vD, is the sphere whose form factor is described in [Culverwell, 1986] and [Potton, 1988a].

It is possible to select any aspect ratio (within reason) using this model and the program only checks to see that you have entered a positive value. Special care has been taken to ensure that the volume fractions determined by this model are correct.

For a full explanation of the coding of this model (from eq. 4, 5, & 6 of [Roess, 1947]), see the source code listing. Look for the routine named “Spheroid.”

Remember that the distributions that are output are in terms of the dimension “D”. The volume of this type of spheroid is (4Pi/3) v r**3.

Q: Bin step scale? (1=Linear, 2=Log)

“Linear” binning means that the diametral bins will increase in size according to an algebraic series (e.g. 1, 2, 3, ...). The other method currently available is “logarithmic” binning where the increase is according to a geometric series (e.g. 1.0, 1.05, 1.1025, ...). Use whichever method gives you a sufficient number of points over all the peaks in the distribution. Be aware that the calculated volume fractions and number densities for the first few bins on the “log scale” are likely to be artificially high because of the small bin width and small particle volume corresponding to that bin (both these terms divide the quantity that MaxSas derives to give you the volume fraction”).

The width of each bin indexed by “i” is dD(i) = D(i+1) - D(i) so that the number density of scatterers whose size is between D and D + dD is truly N(D) dD. The bin width appears in the output file as “dD.”

Q: Number of histogram bins?

This is an integer between 2 and 100, limited by computer memory and execution CPU time. Use as few bins as you think you need to adequately describe the distribution or as many bins as you want, up to the maximum of 100.

Q: Maximum (Minimum) value of D? [A]

Use Angstrom units. Because each intensity is a statistical representation of ALL dimensions D in the sample, weighted by a particular form factor (model function), the choice of maximum and minimum D is left to the user. You may specify values that are beyond the “peripheral vision” of your data to see if there is any statistical support for such sizes in your data. Usually, one knows something about the size distribution to be solved and a maximum particle diameter can be estimated. Ideally Dmax should be an over-estimate; if too small a diameter range (Dmin to Dmax) is specified, the program will likely fail.

The largest value for Dmax is something unreasonable for most SAS data (1 million Angstroms). If you try to exceed this limit, the program will patiently ask you again for the maximum D value. The smallest Dmin value you may enter is 1.0 Angstrom. The program will always suggest Dmin = Dmax / (number of bins).

If Dmin >= Dmax, the program will start asking you questions all over. You can use this as an easy way to correct a bad input prior to this question, without having to stop and restart the program.

Q: Maximum number of iterations?

The number of iterations is best estimated by experience. Skilling and Bryan [Skilling, 1984] suggest that one should re-consider the model if more than about 20 iterations are required for convergence within the Maximum Entropy routine (MaxEnt). The largest allowed number of iterations is 200 but if you require this, your model is probably not representing the data well. The MaxEnt routine may not require as many iterations as you specify. That just means the job was easier than you “thought”.

If, while the MaxEnt routine is iterating, you see that a few more iterations will be required to achieve a satisfying solution than you have specified here, all is not lost. If the limit specified is reached with no satisfying maximum entropy solution yet in hand, the program will ask you if you want to iterate more. You can then extend the process. For this reason, it is suggested that you specify a lower value (rather than higher) so that you may check the program’s progress. A low limit allows the MaxEnt routine to escape should the fitting process fail to converge. In such an event, one or more of the input parameters should be adjusted to achieve a more harmonius solution.

A good general suggestion for the number of iterations is the maximum number that you are willing to see the MaxEnt routine perform and not converge. If the MaxEnt routine needs more iterations, it will ask you for permission.

Q: The change in ChiSquared should be < 5%.

Run the Stability Check? (Y/<N>)

The Stability Check will perform the same analysis on the data set with all the same parameters except that the suggested background will be used. If the answer is stable, then all the results should be the same. If the answer is unsteady, then things will look different in some way. The prompt for a stability check will not appear unless the program calculates that the shift should produce less than a 5% change in the ChiSquared.

Q: Maximum iterations have been reached.:

How many more iterations? <none>

This question occurs inside the MaxEnt routine when the maximum number of iterations that you specified have been reached. If you want the MaxEnt routine to keep trying, specify a positive integer, otherwise take the default which will generate the following output:

No convergence! # iter. = "IterMax"
File was: "InFile"

The program will then start over at the first question.