1. LIGO-G09xxxxx-v1 Form F0900043-v1 The Viewfinder Telescopes of Advanced LIGO’s Optical Levers Michael Enciso Mentor: Riccardo DeSalvo Co-Mentor: Tara Celermsongsak ‘Unofficial’ Mentors: Fabian Pena Rich Abbott

2. LIGO-G09xxxxx-v1 Form F0900043-v1 LIGO Laboratory2 Optical Levers for Advanced LIGO 1. What are aLIGO’s optical levers and what do they do? 2. What progress on the optical levers did you make? 3. How did you make that progress? »Why is that guy always in the hallway? The questions I will try to answer:

3. LIGO-G09xxxxx-v1 Form F0900043-v1 Answer to Question #1 Goal of Optical Levers: To keep the interferometer aligned until lock is acquired and the interferometer’s angular feedback system can take over. Possible secondary function of Optical Levers: Monitor the radius of curvature of test masses (if beam splitters and additional CCD cameras are added). LIGO Laboratory3 Primary function of pre-alignment telescope: To pre-align the optical elements in the interferometer. Secondary function of pre-alignment telescope: Monitor scattered light from the test masses.

4. LIGO-G09xxxxx-v1 Form F0900043-v1 Basic Components of the Pre- Alignment System LIGO Laboratory4 Why are they called “levers”?

5. LIGO-G09xxxxx-v1 Form F0900043-v1 Floor Occupancy Plan Front view of optical lever system. “Looking into the barrel.” LIGO Laboratory 5

6. LIGO-G09xxxxx-v1 Form F0900043-v1 Floor Occupancy Side view of optical lever system LIGO Laboratory6

7. LIGO-G09xxxxx-v1 Form F0900043-v1 Viewfinder and Launching Telescope Setup LIGO Laboratory7 Viewfinder Launching The viewfinder telescopes are our eyes for aligning the launching telescope. A helpful analogy 

8. LIGO-G09xxxxx-v1 Form F0900043-v1 A Much More Helpful Analogy LIGO Laboratory8

9. LIGO-G09xxxxx-v1 Form F0900043-v1 The Real Thing LIGO Laboratory9 Viewfinder Launching

10. LIGO-G09xxxxx-v1 Form F0900043-v1 Answer to Question #2 “What progress did you make?” Main Project: Design, build, and characterize the viewfinder telescopes. What needed to be done: 1. Build the telescopes from the designs made in collaboration with Fabian Pena. 2. Find the best focus for the telescopes at the necessary distances (what distances?) in both visible and IR light (why both?). 3. At this focus, characterize the stability of the focus with respect to varying distances and the angular resolution of the image. 4. Write a manual describing exactly how to focus the telescope so that it can be quickly focused on site by anyone. LIGO Laboratory10

11. LIGO-G09xxxxx-v1 Form F0900043-v1 What Distances? 4 different distances need to be accounted for in the design of this system: 33.1 m, 28.2 m, 5.7 m, and 3.3 m. 2 different designs of the viewfinder were made in collaboration with Fabian Pena. »The “long” viewfinder design will be able to focus in visible and IR at 33.1 m and 28.2 m. »The “short” viewfinder design will do the same at 5.7 m and 3.3 m. LIGO Laboratory11

12. LIGO-G09xxxxx-v1 Form F0900043-v1 Viewfinder Telescope Designs Long Viewfinder LIGO Laboratory12

13. LIGO-G09xxxxx-v1 Form F0900043-v1 Viewfinder Telescope Designs Short Viewfinder LIGO Laboratory13

14. LIGO-G09xxxxx-v1 Form F0900043-v1 Why both IR and Visible? The primary function of the viewfinder is to align the launching telescope to the optical component. »Therefore, the viewfinder must be able to focus in visible wavelengths. In order to avoid the viewfinder having a one-and-done function, it will have a secondary function as a monitor of scattered 1064 nm light from the test masses. »Therefore, the viewfinder must also be able to focus in IR. LIGO Laboratory14

15. LIGO-G09xxxxx-v1 Form F0900043-v1 Answer to Question #3 “How did you go about doing it?” Well, I’ll tell you. LIGO Laboratory15

16. LIGO-G09xxxxx-v1 Form F0900043-v1 Building the Telescopes LIGO Laboratory16 Model of the long viewfinder telescope.

17. LIGO-G09xxxxx-v1 Form F0900043-v1 Building the Telescopes LIGO Laboratory17 Model of short viewfinder telescopes

18. LIGO-G09xxxxx-v1 Form F0900043-v1 Focusing the Telescopes To find the best focus these telescopes could achieve, a system had to be created to quantitatively describe the focus of an image. “Looks good” doesn’t cut it. Moreover, a systematic approach to finding this focus needed to be created for the sake of writing the instructions for focusing on site. LIGO Laboratory18

19. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus The lenses in the telescope are moved closer to or farther from each other by turning the adjustment thread in or out. I defined point where the thread is all the way in as “zero turns” and divided each revolution into 1/30 th of a revolution, or π/15 radians. LIGO Laboratory19.23 in

20. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus Images were taken as the adjustment thread was twisted out, thus moving the front lens farther away from the back. Several dozens of images were taken as the focus continuously moves from bad to good to great, then back to good and back to bad. LIGO Laboratory20

21. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus Mathematica program analyzes a single row or column. 1 = completely white, 0 = completely black, 256 bins total. When vertical lines were used as target, rows were analyzed. Columns were analyzed in some tests and also used as a cross check. LIGO Laboratory21

22. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus For example, the following image: LIGO Laboratory22

23. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus Produces the following plot: LIGO Laboratory23 These are the results from the swath of a single row. The only results of interest, however, are in the 600-800 range, i.e., the large dip corresponding to the black line that is being tested. The values of interest stay constant over all the rows of a given image.

24. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus After isolating the data pertaining to the line, the following plot can be obtained: LIGO Laboratory24

25. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus This curve can then be fitted by two inverse tangent functions. To be precise: m1 + m2 *invtan((x-m4)/m3) + m5 *invtan((x-m6)/m3) where m1-6 are all parameters to be adjusted for each fit. LIGO Laboratory25 The most important of these 6 parameters is the m3 parameter, which is in pixels, as it characterizes the speed of the curve in moving from white to black and back to white again. The lower m3, the better.

26. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus Each curve was fitted and the m3 parameter from each was extracted and plotted as a function of turns from the reference point zero. LIGO Laboratory26 The point where m3 has the lowest value corresponds to the number of turns that produces the best focus. It is shown here that to focus in visible light, one should turn the adjustment thread 7.9 turns.

27. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus This method was repeated at each distance for IR light as well. The same target line was used but instead of visible light falling on the target, and IR LED was pointed at the line. LIGO Laboratory27 Which produced this image:

28. LIGO-G09xxxxx-v1 Form F0900043-v1 Method for Quantifying the Focus The same analysis was done and the focus in both visible and IR light was quantified. The minimums of these curves (33.1 m and 28.2 m) overlap at the number of turns that give maximal focus in IR and visible simultaneously. LIGO Laboratory28

29. LIGO-G09xxxxx-v1 Form F0900043-v1 Stability of Focus wrt Distance Once the best focus was found, we needed to know what these telescopes can do at that focus. Distances may not be precise so we need to understand our room for error. 33.1, 28.2, 5.7, and 3.3 ± 1 m by.1m intervals. “Snap and move”. LIGO Laboratory29 “1.2192” meter stick

30. LIGO-G09xxxxx-v1 Form F0900043-v1 Calculating the Resolution 1. Map each pixel of the CCD to its corresponding point on the image. LIGO Laboratory30 1360 pixels 1024 pixels => 43.18 cm (at 33.1 m) 32.51 cm 1 pixel.1 mm 2

31. LIGO-G09xxxxx-v1 Form F0900043-v1 Calculating the Angular Resolution LIGO Laboratory31 # of pixels corresponds to physical distance. d 2. Compare the continuous change of an arctan function, which measures the actual resolution, with the jump of a perfect step function, which represents infinite resolution. 3. Calculate the derivative of the arctan function at its maximum and convert from pixels to mm. 4. To define an effective resolution in mm, we plot the corresponding linear function and find where it overlaps with the step function.

32. LIGO-G09xxxxx-v1 Form F0900043-v1 Calculating the Angular Resolution 5. Calculate the lateral displacement in mm. 6. Using the given distance to the target and this lateral displacement, calculate the angular resolution. LIGO Laboratory32 d 33.1 m

33. LIGO-G09xxxxx-v1 Form F0900043-v1 Lather, Rinse, Repeat…Almost This process was repeated for all the necessary distances with a few minor adjustments. »For the short telescopes, the entire derivative, not just the m3 parameter had to be used. »The stability of the focus wrt distance for the short telescope was not tested. »The visible and IR focus for the short telescopes did not overlap. The IR focus was prioritized as these telescopes will be primarily used as scatterometers. LIGO Laboratory33

34. LIGO-G09xxxxx-v1 Form F0900043-v1 When All Was Said and Done LIGO Laboratory34

35. LIGO-G09xxxxx-v1 Form F0900043-v1 More to be Done Consolidate as many parts as possible. Actually write the manual! LIGO Laboratory35