1. Mucool meeting April 26, 2002 presentation Donna Kubik

2. The FEA sensitivity analyses emphasize the need to accurately determine the thickness of the window:

3. --------330um --------345um

4. Burst at 117psi for 330um Burst at 123psi for 345um Radius = 0.5mm Radius = 2.0mm Stress (MPa) Room temp

5. If the window is machined to 345um instead of the design thickness of 330um, the burst pressure is increased by 5%.

6. How to determine the window thickness via photogrammetry Need for a surface model What we have done: VANGO’s TIN Small patch sphere fit (SPSF) What we might do next: Extended application of SPSF Modified TIN

7. How to determine the window thickness via photogrammetry Need for a surface model What we have done: VANGO’s TIN Small patch sphere fit (SPSF) What we might do next: Extended application of SPS Modified TIN

8. Need for a surface model Do not need to model the surface to compare the window shape with design. Calculate design z for the x,y of each target & compare to measured z.

9. Setup to measure window shape Measure the concave and convex sides in same coordinate system, moving projector and camera from one side to the other

10. Difference between measured shape and design Concave Convex Whisker = z(measured)-z(design)* *Given the design radius of curvature of the concave and convex surfaces, z(design) was calculated for the (x,y) position of each target

13. Need for a surface model A surface model is needed to determine the thickness It is necessary to determine z for matching pairs of x,y on the concave and convex surfaces or the window. The required positions may be different from the target locations.

14. Problem of convex and concave alignment convexconcave

15. Problem of alignment convex concave This makes it difficult to determine the window thickness

16. How to determine the window thickness via photogrammetry Need for a surface model What we have done: VANGO’s TIN Spherical patch surface fit (SPSF) What we might do next: Extended application of SPSF Modified TIN

17. VANGO VANGO uses a TIN (Triangular Irregular Network) to create a surface model.

18. VANGO Point on triangle is always < true point. This is important to interpret any periodicities seen in the data; period of an oscillation caused by the TIN would be ~6mm ~6mm

19. VANGO error d R r d = f(radius of curvature, size of triangle)

20. D’ D Errors in thickness due to VANGO TIN worst case geometry* D’=D-14.6um D’=D+15umIDEAL *Assumes 6mm chord and design radii 30.000cm and 30.844cm Note: Nominal thickness (D) = 330um

21. D’ D Errors in thickness due to VANGO TIN: intermediate and best case* D’=D-0.4umD’=D IDEAL *Assumes 6mm chord and design radii 30.000cm and 30.844cm Note: Nominal thickness (D) = 330um

22. D’ D’=D+(~10um) D IDEAL TIN geometry for center of Window 4

23. VANGO TIN Result for the center: Thickness = 341.0um ( 5.5um) + (- ~10um) Convex RMS = 3.6um Concave RMS = 4.1um The difference (thickness) should have an RMS of about 5.5um

24. VANGO error bars Each point requires a unique error bar. Error = f(phase between concave & convex triangles, size of triangles, radius of curvature)

25. N W E S

26. Error bars Error for North and South is greater for large radii due to location of alignment slots. Here a typical triangle has sides of 6x20x20 mm

27. How to determine the window thickness via photogrammetry Need for a surface model What we have done: VANGO’s TIN Small patch sphere fit (SPSF) What we might do next: Extended application of SPSF Modified TIN

28. Small patch sphere fit (SPSF) Fit a sphere to the points near the point in question. The sphere fit gives the equation of the sphere:

29. Small patch sphere fit (SPSF)

30. To find the thickness at the center of the window, solve for z choosing x=0 and y=0.

31. Small patch sphere fit (SPSF) errors Intrinsic precision of the points used in the fit. The basic assumption is that the intended shape was a sphere

32. Small patch sphere fit (SPSF) Result for the center: Thickness = 331.6um 5.5um Error of spherical fit: Convex RMS = 3.6um Concave RMS = 4.1um The difference (thickness) should have an RMS of about 5.5um

33. Other info from SPSF Design radius of curvature = 308.44mm

34. 0_000

35. 1_xxx

36. 2_xxx

37. 3_xxx

38. R_xxx

39. Other info from SPSF Design radius of curvature = 308.44mm

40. Summary of what we’ve done so far to determine thickness Obtained two window thickness measurements at the center: VANGO TIN 341.0um ( 5.5um) + (- ~10um) SPSF 331.6um 5.5um

41. Additional support for the thickness value derived from SPSF:

42. 152psi

43. The predicted burst pressure (162psi) was greater than the observed burst pressure (152psi). This implies that thickness assumed in the FEA (345um) was greater than the true thickness. This would be consistent with a measured thickness of 331um.

44. What next? We haven’t found the thinnest part of window yet, only the thickness at a chosen point…which we chose to be the center.

45. How to determine the window thickness via photogrammetry Need for a surface model What we have done: VANGO’s TIN Small patch sphere fit (SPSF) What we might do next: Extended application of SPSF Modified TIN

46. Small patch sphere fit (SPSF) We haven’t found the thinnest part of window yet, just the thickness at a chosen point. BUT, we could do SPSF for many points and search for minimum.

47. Pseudo code to determine thinnest part of window using SPSF Chose number of points in “Small Patch” Choose r=design or r=f(measurement) Choose (x,y)’s Do sphere fit Now do the same for the other surface Calculate differences Search for minimum to find thinnest part of window

48. How to determine the window thickness via photogrammetry Need for a surface model What we have done: VANGO’s TIN Small patch sphere fit (SPSF) What we might do next: Extended application of SPSF Modified TIN

49. Use a sphere to approximate the triangular surface between measured points. What to use for radius of curvature? ~6mm

50. Is the measurement repeatable? Yes. Measurements were repeated 3 times over ~1 week Two of those times the MET-L-CHEK was very thin and some points were rejected. HOWEVER, those points that were measured agreed well For only one of the three was the TIN created (the one without rejected points - Sasha’s MET-L-CHEK) So check repeatability by z-plane fit to flange

51. Targets on flange Many projected targets fall on the flange

52. Is the measurement repeatable? Yes.

53. How else can improvements be made? Upgrade the camera: Refined calibration (one GSI’s most dearly guarded secret, second to how they achieve 1/50 pixel resolution!) New lenses Faster processor Network capability

54. How much would we gain? Result in 30% (maybe 50%) improvement in RMS So for determining the window thickness, this would result in change RMS=5.5um to RMS=3.85um