This article [Opt. Eng. 51, 073607 (2012)] was originally published on 17 July 2012 with errors on p. 2 and in Tables 2 and 4. On p. 2, the last sentence has been changed from “Therefore, taking the value of the distance point to point from to we get:” to “Therefore, taking the value of the distance point to point from to we get:”
Also, on the left side of Table 2, row 6, the value of should be negative. On the left side of Table 4, row 5, should be . In the right side of row 6, should be . The corrected tables appear below.
Geometric parameters, rotation angles, and translations for zrta and zref.
|Test surface (zrta)||Reference surface (zref)|
|r=−44.9507 mm||rb=−44.95 mm|
|A1=2.9001×10−6 mm−3||B1=2.9×10−6 mm−3|
|A2=1.1107×10−10 mm−5||B2=1.1106×10−10 mm−5|
|A3=−1.0380×10−14 mm−7||B3=−1.0379×10−14 mm−7|
|A4=2.4396×10−17 mm−9||B4=2.4395×10−17 mm−9|
Solutions found by minimizing Eq. (14), and the RMS error on zkr.
|Solution found when the test surface fitted by R2 is analyzed, RMS error on zkr||Solution found when the test surface fitted by R1 is analyzed, RMS error on zkr|
|r=-44.9546 mm||r=-44.9442 mm|
|A1=2.9002×10−6 mm−3||A1=2.9001×10−6 mm−3|
|A2=1.1103×10−10 mm−5||A2=1.1102×10−10 mm−5|
|A3=-1.0369×10−14 mm−7||A3=−1.0388×10−14 mm−7|
|A4=2.4392×10−17 mm−9||A4=2.4391×10−17 mm−9|
|Percentage difference in r=0.010%||Percentage difference in r=0.012%|
|Percentage difference in k=0.45%||Percentage difference in k=0.89%|
|Percentage difference in A1=0.0069%||Percentage difference in A1=0.0064%|
|Percentage difference in A2=0.0270%||Percentage difference in A2=0.0315%|
|Percentage difference in A3=0.0963%||Percentage difference in A3=0.0915%|
|Percentage difference in A4=0.0123%||Percentage difference in A4=0.0164%|
|RMS error on zkr=0.011 mm||RMS error on zkr=0.016 mm|
In addition, the first line of the caption of Fig. 13 has been changed to read, “Behavior of the ES (black) and the HGA (blue) when both...”
The manuscript was corrected online on 5 October 2012.