1. MONALISA Compact Straightness Monitor Simulation and Calibration
Week 6 Report
By Patrick Gloster

2. Where We Stood Last Week
Using fmincon to solve the bowtie problem we were only getting solutions accurate to 0.1mm
Increasing the number of target positions did not improve the accuracy of the results
My function wasn’t working at all

3. Reformulation of the Problem
We wanted to use lsqnonlin before, but to apply constraints we needed to use fmincon
The solution – reformulate the problem so that we could solve it without constraints
Instead of working with 4 coordinates for each position of plate 2 and constraining the distance between them to be the same in each case…
…we work with 2 coordinates (the mid point of plate 2), an angle and the distance between reflectors on a plate

4. BEFORE
AFTER
(x2,y2)
(x1,y1) d α
(x,y)
With this set up we can use lsqnonlin

5. Results With this new set-up we can achieve nanometre precision
However, to do this we have to set a parameter of the lsqnonlin function called TolFun to 10-15
Time was also an issue at first, but removal of for loops  a huge decrease in time taken

6. A Slight Extension
I am also working on a more realistic problem where the launch pairs are separated by a finite distance and are no longer modelled as a point source
This is not a point source

7. What I’ve done…
For both set-ups I have written a function which plots histograms of the difference between the measurements and the ‘predicted’ values
All information and the histograms are saved automatically
As well as choosing the number of plate positions we would like to be able to repeat the minimization any number of times for the same set of ‘true’ plate positions

8. 40 targets, 500 repeats

9. …and what I’m doing I have now incorporated this into the functions
The functions work out the differences between measured and ‘predicted’ values for all of these points including data from each repetition and plot more histograms
I am currently working through different numbers of targets and different numbers of repeats to find how many of each we need