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Test surface imaging distortion and its consequences for optical testing

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#1 BGRE

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Posted 13 October 2019 - 04:56 PM

Any optical test method that relies on the mapping between a point in the image of the test surface and the corresponding point on the test surface needs to take distortion into account.
In interferometry for example uncorrected radial distortion results in an SA component that depends on defocus.
Sources of distortion are the camera lens and the geometry of the test surface. When corrected for distortion (either optically or in software) the displacement of a point in the image from the centre is proportional to the tangent of the field angle.
This works well when mapping a flat surface to a flat image surface. Unfortunately most test surfaces of interest aren't flat.
For a spherical test surface a radial displacement of a point proportional to the sine of the field angle is better. Zygo define distortion as departure from such a mapping in their spherical wave Fizeau interferometers.
If a distortion corrected camera lens is used to image an aspheric surface then the variation of the tangent of field angle due to the finite length of the caustic and the sagitta of the test surface.

For a paraboloid measured with a distortion (rectilinear) free lens the fractional distortion is
(3/8)*(D/R)^2*(rho)^2 + (9/64)*(D/R)^4*(rho)^4 + .
1/3 of this is due to the finite sagitta 2/3 due to the finite length of the caustic (in effect SA of the entrance pupil of the camera lens).

Edited by BGRE, 13 October 2019 - 04:57 PM.


#2 BGRE

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Posted 13 October 2019 - 05:07 PM

Distortion will affect both Ronchi testing (defocus dependent component of SA due to distortion will alter the Ronchi pattern) and Foucault unmasked (relies on mapping between surface image and test surface to determine the position of zones on the test surface)

#3 BGRE

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Posted 13 October 2019 - 05:26 PM

Some modern DSLR lenses correct distortion in the camera firmware. Unfortunately this correction is only valid for the stop in the location the lens designer intended.
In interferometry (including Ronchi testing) and Foucault testing the effective stop is located external to and in front of the camera lens not at the design location (at the internal iris) but at the image of the test source formed by the test surface.
In the Seidel approximation lens distortion in invariant with stop shift only if SA, coma, astigmatism and field curvature are zero. Thus in general distortion should be measured with the stop at the actual location defined by the test setup.
The finite length of the caustic when testing an aspheric surface at its CoC introduces SA of the stop location complicating the issue.
In general te distortion of the lens as a function of stop location along the caustic would need to be known to allow accurate correction.
Fortunately some lenses are well corrected (e.g. some Double Gauss lenses and their variants) so that their distortion is very low and independent of stop location.

#4 BGRE

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Posted 13 October 2019 - 09:34 PM

Amongst a host of "interesting" effects if the test surface image isn't centered over the camera lens distortion center and the test surface exhibits SA at the test conjugates then a form of induced decentering coma appears if the camera lens distortion isn't corrected.

Edited by BGRE, 13 October 2019 - 09:37 PM.


#5 BGRE

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Posted 17 October 2019 - 07:57 PM

The existence of imaging distortion and its relative importance are readily established with an interferometer using the method detailed in:
https://patentimages...070201035A1.pdf

This method is perhaps most useful in verifying the correctness of the somewhat indirect multistep methods which are more practical for most.
It is also useful in verifying the effect of a finite length caustic when measuring large highly aspheric surfaces.

#6 BGRE

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Posted 22 October 2019 - 10:28 PM

In a spherical wave interferometer uncorrected geometric imaging distortion produces an "induced" aberration about 4x larger than the change in measured OPD due to defocus. Camera imaging distortion may also be significant as 1% pure second order radial distortion results in an induced SA equal to 2% of the defocus.
For high accuracy especially with large fast aspheres calibration and correction of distortion induced aberrations is critical especially if the defocus is significant.


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