Implementation of sine condition test to measure optical system misalignments: erratum

Sara Lampen; Matthew Dubin; James H. Burge

doi:10.1364/AO.52.008518

Abstract

One mathematical error from [Appl. Opt. 50, 6391–6398 (2011)] is corrected in this erratum.

There is one error in [1] that is corrected here. In the simplification of Eq. (4) to Eq. (5), it was incorrectly assumed that the object wavefront radius of curvature could be related to the image wavefront radius of curvature through the magnification, $m$ . As the derivation progressed, this led Eq. (8),

W_{PME} = {\hat{S}}_{o} \cdot ε_{o} - \frac{1}{m} {\hat{S}}_{i} \cdot ε_{i},

to have an extraneous

1 / m

. A more straightforward derivation starts with Eq. (2) in [1] where the object wavefront phase difference at

O

is defined as

W_{o} = {\hat{S}}_{o} \cdot ε_{o} .

The same relationship holds for the image wavefront phase difference at

I

,

W_{I}

, where

W_{I} = {\hat{S}}_{i} \cdot ε_{i} .

Using Fermat’s principle again, it is known that the phase between point

B

and point

C

must be stationary. Therefore, the pupil mapping error

W_{PME}

is

W_{PME} = W_{o} - W_{I} .

After substituting Eqs. (2) and (3), the correct relationship for

W_{PME}

is

W_{PME} = {\hat{S}}_{o} \cdot ε_{o} - {\hat{S}}_{i} \cdot ε_{i} .

The incorrect form of

W_{PME}

also appeared in the summary of the background material in [2].

References

1. S. Lampen, M. Dubin, and J. H. Burge, “Implementation of sine condition test to measure optical system misalignments,” Appl. Opt. 50, 6391–6398 (2011). [CrossRef]

2. S. Lampen, M. Dubin, and J. H. Burge, “Design and optimization of the sine condition test for measuring misaligned optical systems,” Appl. Opt. 52, 7099–7108 (2013). [CrossRef]

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Equations (5)

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W_{PME} = {\hat{S}}_{o} \cdot ε_{o} - \frac{1}{m} {\hat{S}}_{i} \cdot ε_{i},

W_{o} = {\hat{S}}_{o} \cdot ε_{o} .

W_{I} = {\hat{S}}_{i} \cdot ε_{i} .

W_{PME} = W_{o} - W_{I} .

W_{PME} = {\hat{S}}_{o} \cdot ε_{o} - {\hat{S}}_{i} \cdot ε_{i} .

Abstract

References

Cited By

Equations (5)

Applied Optics