12 October 2012 Errata: Measuring the profile of a convex aspherical surface by solving a bi-objective optimization problem
Abstract
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 z rta+ trans   to z rta   we get:" to "Therefore, taking the value of the distance point to point from z rot+ trans   to z rta   we get:" Also, on the left side of Table 2, row 6, the value of A 3 should be negative. On the left side of Table 4, row 5, mm −7 should be mm −5 . In the right side of row 6, mm −9 should be mm −7 . The corrected tables appear below.
Escobar: Errata: Measuring the profile of a convex aspherical surface by solving a bi-objective optimization problem

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 ${z}_{rta+\text{\hspace{0.17em}}\text{trans}}\text{\hspace{0.17em}}$ to ${z}_{rta}\text{\hspace{0.17em}}$ we get:” to “Therefore, taking the value of the distance point to point from ${z}_{\text{rot}+\text{\hspace{0.17em}}\text{trans}}\text{\hspace{0.17em}}$ to ${z}_{rta}\text{\hspace{0.17em}}$ we get:”

Also, on the left side of Table 2, row 6, the value of ${A}_{3}$ should be negative. On the left side of Table 4, row 5, ${\mathrm{mm}}^{-7}$ should be ${\mathrm{mm}}^{-5}$. In the right side of row 6, ${\mathrm{mm}}^{-9}$ should be ${\mathrm{mm}}^{-7}$. The corrected tables appear below.

## Table 2

Geometric parameters, rotation angles, and translations for zrta and zref.

Test surface (zrta)Reference surface (zref)
r=−44.9507  mmrb=−44.95  mm
k=−1.0007kb=−1
A1=2.9001×10−6  mm−3B1=2.9×10−6  mm−3
A2=1.1107×10−10  mm−5B2=1.1106×10−10  mm−5
A3=−1.0380×10−14  mm−7B3=−1.0379×10−14  mm−7
A4=2.4396×10−17  mm−9B4=2.4395×10−17  mm−9
tx=−50  mm
ty=50  mm
tz=100  mm

## Table 4

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 zkrSolution found when the test surface fitted by R1 is analyzed, RMS error on zkr
r=-44.9546  mmr=-44.9442  mm
k=-1.0045k=-0.9911
A1=2.9002×10−6  mm−3A1=2.9001×10−6  mm−3
A2=1.1103×10−10  mm−5A2=1.1102×10−10  mm−5
A3=-1.0369×10−14  mm−7A3=−1.0388×10−14  mm−7
A4=2.4392×10−17  mm−9A4=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  mmRMS 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.

© 2012 Society of Photo-Optical Instrumentation Engineers (SPIE)
Juan Jaime Sanchez Escobar, Juan Jaime Sanchez Escobar, } "Errata: Measuring the profile of a convex aspherical surface by solving a bi-objective optimization problem," Optical Engineering 51(10), 109801 (12 October 2012). https://doi.org/10.1117/1.OE.51.10.109801 . Submission:
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