Opacity Correction (1/20/09) Schumacher, Ovchinnikov Materials: Copper (1/e absoption length taken as 22  ), Aluminum (72.4  ). Targets: Slab sandwich, Cone, Thick cone/wire, Cone/foil. Detectors: HOPG, Single Hit, DC HOPG front, DC HOPG back. Correction factor  S NA / S A w/ S A = signal with absorption, S NA = signal with no absorption Outline: (1) Coordinate system. Algorithm. (2) Target description and detector orientation. Discussion of selected results.

Coordinate System The coordinate system used in the following discussion is tied to the target, not the laser or the detector. yis along a symmetry axis of the detector. If the laser hits the target at normal incidence, it is propagating in the -y direction. xis along an orthogonal symmetry axis +zis up, as usual. (0,0,0) is at TCC. y z x

Algorithm A pinhole is placed at the location of the detector (HOPG, Single Hit, etc), and the target is imaged through it onto a virtual detector. The integrated signal on the virtual detector yields S A or S NA. Examination of the image itself is not necessary, but can be useful in understanding the behavior of S NA /S A. y z x Suppose the HOPG is here at (X,0,0). This is where the code would place the pinhole, then. Virtual detector would go here at (2X,0,0) for unity magnification. The image is inverted, of course. For this discussion, all of the images are “un-inverted” so that the view is what you would see if you removed the pinhole and simply placed your eye at the virtual detector.

Slab Targets Example: 10um Al/30um Cu [ s01] 1 mm x 1 mm cross-section (not to scale). Correction factor calculation assumed: Only the central 100x100  m of the copper is illuminated (red). y z x Here is the view from (20 cm, 0, 0) at low magnification with the “cold” Cu and Al both illuminated so they can be seen. No absorption. Al is blue, “cold” Cu is in outline, “hot” Cu is red.

Slab - HOPG view (15.5 cm, 2.5 cm,13.2 cm) Cold Cu & Al illuminated. Low mag. No absorption. Like (A), high mag.Cold Cu & Al dark. High mag. No Absorption. (A)(B)(C)(D) Like (C), absorption. Looking down on target. x y HOPG y z Looking along x-axis HOPG This is the face of the hot Cu closest to the front. Rear portion of hot Cu is blocked by the cold Cu. Note, all pictures are normalized so the peak signal is displayed at max brightness.

Slab - Single Hit view (103 cm, 44 cm, 0 cm) Cold Cu & Al illuminated. Low mag. No absorption. Like (A), high mag. (A) (B)

Slab - Results HOPG correction: 33.6 Single Hit correction: 5.12 HOPG correction: effect of background If the “cold” copper is 1/10 as bright as the hot copper, instead of being dark. Correction = 22.7 Reference case: Looking normal to the target. Eg. If the HOPG were placed on the +y axis looking towards the origin (Al and Cold copper dark, only the 100  x 100  is bright) Correction = 2.10(exact analytical result = 2.10)

Cone Target, Results Correction factor calculation assumed: The entire cone is illuminated, the washer is dark. View from HOPG ( 12.5 cm, 9.5 cm, 13.2 cm) with no absorption. y z x Like above, but absorption turned on. Brightness is shown relative to above. Correction factor: 4.32 (HOPG) If the cone illumination starts bright at the tip and falls to zero by the middle… Correction factor: 4.11 (HOPG)

Cone/wire Targets, Results Correction factor calculation assumed: From the tip of the cone, the wire faded to dark in 150 . (For calculational convenience, the wire was only 400  long.) View from HOPG ( 15.0 cm, 4.7 cm, 13.2 cm) with no absorption. Cone is illuminated so you can see it. y z x Like above, but absorption turned on. Brightness is normalized to maximum. Correction factor: 3.35 (HOPG) If the wire illumination fades to dark in only 50  Correction factor: 12.6 (HOPG)

Why the sensitivity to wire illumination? The zero-absorption views can be misleading. The base of the wire is actually obscured by the cone tip. This is the edge of the cone tip closest to the HOPG. This is the edge farthest from the HOPG, seen through the body of the cone. Top: No absorption. Illuminated wire region is 150  long. Cone is dark. Bottom: Absorption on. Note how wire near cone is darkened. Similar to pics on the left, but with 50  illumination length. Bottom image normalized consistent with top.Bottom/top normalized for brightness.

Cone/foil Targets Correction factor calculation assumed: Illuminated region is a 50  x 50  copper patch just past cone tip. View from HOPG ( 15.0 cm, 4.7 cm, 13.2 cm) with no absorption. Cone and Al slabs are illuminated so you can see them. Cold Cu is not illuminated. y z x Like above, but absorption turned on. Brightness is normalized to maximum. Cone Foil: 20um Al/10um Cu/50um Al (Target ID: Bur-20 #1) Green = copper slab. The “hot” spot is at the center of the copper.

Cone/foil - Results HOPG [ detector location = ( 15.0 cm, 4.7 cm, 13.2 cm)] Correction dependence on hotspot size 30  x 30  =  x 50  =  x 100  = 7.84 DC HOPG (front) [ detector location = ( 6.3 cm, 19.5 cm, 4.6 cm)] Correction dependence on hotspot size 30  x 30  =  x 50  =  x 100  = 5.20 The DC HOPG (front) is more sensitive to the size of the hotspot because it is looking up the backside of the cone. DC HOPG (front) view of the cone with the cone illuminated.