Parab user's manuel

When you first run Parab and you are starting from scratch, you should use [Edit > Mirror] and enter the mirror description and knife-edge readings. Next click [Edit > Horizontal Scale]. This applies to the graph only and should be a nice even number. For example, for a 12.5 inch, a good number would be 14. For a 15 inch it would be 16. Next, you need to enter the vertical scale. Unlike the horizontal scale, the vertical scale applies only to the current graph. The recommended approach is to click [Edit > Auto Scale Vert] and then use [Edit > Vertical Scale] and round the numbers up to some nice whole numbers. This sounds tedious, but you have to do it only once. You don't have to do this at all. It does make for better looking graphs. Later on, when the errors are getting small, you may want to [Edit > Vertical Scale] again.

Piecewise cubic splines were used for drawing most of the graphs. The exceptions being the "best fit" parabola and the "perfect" parabola which are true parabolas.

Below the graph are two columns that pretty much reflect the mirror description that was entered. Below that is the zone data showing zone number and the knife edge measurments. Before further processing, X measured is adjusted to a more meaningfull value. There will be a littlle more discussion on this later. "X best" is from a parabola that passes through the vertex and the X at the highest numbered zone. The "perfect" parabola matches the vertex and the input ROC. Note that if there is no knife edge reading at Y = 0, the vertex itself is determined by the spline fit. "X diff" is just the difference between an "adjusted" X measured and X best fit.

"RTA" is Relative Transverse Aberration. Texereau has it as lamdaf/rho, line 12 of his test data sheet on page 95. "Slope e6" is the slope error. See Texereau line 13. It is a tiny number. The e6 means it has been multiplied by 10**6. Finally, the slope is integrated to get the Waveform error. It also is a tiny number and is displayed in nanometers. To get the RMS (Root Mean Square), a spline fit of the Waveform error was performed and then sampled at 100 evenly spaced points between 0 and R. I think using just the input points would have been enough, but I have a computer. The Strehl ratio follows using the Mahajan approximation. I suggest you Google Strehl ratio.

As for the "adjusted" X measured, clearly (I hope) you can add any arbitrary constant you want to X measured. After all, Texereau adjusted his by more than 1/2". First, I added a constant that centered the X (x min = -x max). Then I changed that constant such that X[zone 1] = X[highest zone]. You can see that in the Waveform error graph and tabulated results. The final value is output as "X KE shift". This whole process is a lengthy iteration, but that is what computers are good at.

P-V is just Waveform error max - min. You can eyeball that from the graph. It is expressed in units of wave length which is 560 nanometers.