In lens metrology, how do people measure a double-sided thick aspherical lens optically? By "optically" I mean for example, using wavefront sensing, interferometry or the interferogram methods.

I searched a little but only found mirror surfaces measurement.

To me, the difficulty is, there are two sides to be measured, but we only get one "accumulated phase" from our measurement. For example, from Shack-Hartmann wavefront sensors we only get one single phase for the lens, but we need the surfaces from both sides. It is mixed.

So is it possible to do double-side lenses metrology optically?

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    $\begingroup$ Is the lens assumed to be mirror-symmetric? That could allow the normal approach to work. $\endgroup$ – probably_someone May 1 '18 at 0:29
  • $\begingroup$ @probably_someone Unfortunately not. The lens assumes to be a freeform, an asymmetric one. And could you hint more on the "normal approach"? $\endgroup$ – WDC May 1 '18 at 0:32
  • $\begingroup$ What do you want to measure? Do you want to know the curvature of each surface? $\endgroup$ – S. McGrew May 1 '18 at 0:39
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    $\begingroup$ There are probably several different ways to do that, but I would do it by measuring the wavefront of a collimated beam reflected off the front surface, then measure the wavefront of a collimated beam reflected off the back surface. One surface at a time makes it MUCH simpler. $\endgroup$ – S. McGrew May 1 '18 at 0:42
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    $\begingroup$ Don't know if there is a straightforward way to measure the curvature of both surfaces by sending a beam all the way through the lens. Possibly it could be done by using several different incident beams (e.g., collimated, diverging, and converging by known amounts), measuring the resulting wavefront for each, and solving the parallel equations made by plugging in the wavefront values to a thick-lens equation. It could be a messy calculation. $\endgroup$ – S. McGrew May 1 '18 at 0:57

Measuring the surface of both sides of an aspheric lens is difficult. You don't say if both sides are aspheric, or only a single side is aspheric. Whether it is one or both sides, many of the problems are identical. There are two primary methods that are used in the industry be people who make such lenses. 1) Surface profilometer 2) Aspheric interferometer. 1) A surface profilometer uses a precision stylus to physically trace over the part. Typically two scans are done at 90 degrees to each other, and software fits the result. See, for example, www.mahr.com.

2) Aspheric interferometer - Zygo and others make interferometers that can measure the surface of an asphere. Most of these work by taking multiple measurements, then "stitching" the results together to construct the surface. There are limitations on the asphericity departure that they can measure.

Neither of these methods address possible phase errors within the lens (caused by inhomogeneity or birefringence). To measure those, you need an optical measurement that looks at the final output wavefront. If your lens does not form a good image by itself, you can construct a null lens that, when added to your biasphere, produced a good image. The good image can be tested interferometrically or via incoherent methods (star test, for example). Note you have to make the null lens very well, or you will incorrectly test the asphere.

With any lens, relating the opposite surfaces to each other can be tricky. For a biasphere lens (aspheres on both sides), each surface has an optical axis, which represents a line in space. These two axes can be displaced with respect to each other or not parallel, or some combination thereof. To quantify how the two surfaces relate to each other is likely beyond the scope of your question. It requires measurements on both surfaces that can somehow relate the two measurements in a shared coordinate system. For molded optics, a flange can often be molded into the part that makes this relative measurement easier.

  • $\begingroup$ Thanks for such an elaborative answer. So the conclusion for my question is "hard and probably impossible". Could you expand a little more on 2) aspheric interferometers? How can we measure surfaces solely? By reflecting lights from the surfaces? When the lens is just a piece of glass (without coatings), how to decide which wavelength to use to shine light onto the surfaces? $\endgroup$ – WDC May 6 '18 at 17:55
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    $\begingroup$ Aspheric interferometers look at the reflection from (usually) uncoated surfaces. They commonly use He-Ne lasers at 632.8 nm, as these lasers are cheap and have a long coherence length. Other wavelengths don't provide significant advantage for measuring uncoated optics - the reflection coefficient is usually close to 4% and not that sensitive to wavelength. For more information, look on websites of companies that make these interferometers, like Zygo, Wyko, ESDI, or 4D. $\endgroup$ – JB2 May 7 '18 at 2:45

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