AT-WAVELENGTH METROLOGY FOR OPTICAL SYSTEMS AND SURFACES

AT-WAVELENGTH METROLOGY
FOR OPTICAL SYSTEMS
AND SURFACES
WHITE PAPER

by Rafael Porcar, Diego Ormaechea
November 2022

Fixed-Wavelength Metrology Needs to be Fixed
   Traditional laser interferometers rely on temporally coherent light sources to
   produce interference. Most of the metrology is therefore done at 632.8 nm, the
   emitting wavelength of HeNe lasers.

   But the operating wavelength of an optical component or system is not
   necessarily 632.8 nm. In fact, it can be purposely designed for a specific
   wavelength that differs from common laser lines. Alternatively, the to-be-tested
   optics can be designed for a broad spectral range. In this case, it would be useful
   to test additional wavelengths, especially those at the extremes of the range.

   Of course, a real measurement can be completed by extrapolations from a
   chromatic model based on simulations. This requires a specific skill set, access to
   the information necessary to model the optics, not to mention a nontrivial time
   investment, and there will still be discrepancies between the model and the real
   optics or system as mounted.

   Even relying on this modeling, some optics are simply not compatible with
   a characterization at common laser line. This is the case for some filters or
   dichroics: how can we measure the reflected wavefront of a standard dichroic at
   632.8 nm if it has been designed to transmit at this particular wavelength?

Achromaticity: the True Colors of Wavefront
Sensing
   An alternative to traditional interferometry consists of wavefront sensing (WFS)
   solutions. One particular implementation, and probably the most frequently
   adopted, is Shack Hartmann-based wavefront sensing. In this setup, a matrix
   of microlenses is placed in front of a camera detector so that each microlens
   focuses a centroid onto it. By tracking the lateral position of each centroid, the
   wavefront slopes (tilt) can be calculated. Integrating them on the whole pupil
   then results in a phase map.

   Recently, an innovation called LIFT (1, 2, 3) - for Linearized Focal Plane Technique
   - has been commercialized. Using LIFT, intensity distribution of the centroids is
   analyzed along with their lateral position in order to reconstruct a phase map in
   front of each individual microlens. This new approach leads to a 16-fold increase
   in resolution without compromising the other specs of the WFS.

   In both Shack-Hartmann wavefront sensing and LIFT, the signal to be analyzed
   (including centroid lateral position and intensity) is not compromised by
   chromaticity, that is, the same slopes will be retrieved. To demonstrate this,
   one microlens of similar features as the ones embedded in a Shack-Hartmann
   wavefront sensor has been simulated with Zemax rray trace software.
   Illumination configuration consists of three incoming beams with different

                       AT-WAVELENGTH OPTICAL METROLOGY © Imagine Optic 2022

angles: 0°, 1° and 3°, simulating various wavefront slope configurations. For
each angle, 3 different wavelengths have been selected in order to observe
the effect of chromaticity on the centroids focused by the microlens onto the
camera detector. Spot diagrams corresponding to the described simulation are
represented in Fig. 1 below.

 Fig. 1 Spot diagrams of a Shack-Hartmann wavefront sensor microlens for different wavefront slope
   values: normal (top left), 1° or ~17.5 mrad (top right) and 3° or ~52.4 mrad (bottom center) with
wavelengths represented by color: green for 450 nm, blue for 630 nm, and red for 850 nm. The size of
            the Airy disk symbolizing the diffraction limit is represented by the black circles.

We can, as expected, observe the effect of chromaticity on the size of the spot
diagrams. The centroids’ diameters change as a function of the wavelength
because the best focal plane of the microlens moves along the optical axis with
wavelength. (In other words, if the position of the detector has been optimized
for the central wavelength, then smaller wavelengths focus slightly before and
longer wavelengths slightly after the detector).

Nevertheless, the lateral position of the centroid is not affected by the
wavelength – blue, green and red centroids keep centered with respect to each
other. Note that for scale purposes, the airy disk representing the best focused
spot of light that a perfect lens with a circular aperture can make, limited by the
diffraction of light, is represented as a black circle.

For the most extreme case illustrated here, a slope as steep as 50+ mrad, the
centroid moves from its original position by 52 mm, which represents half a
microlens (!), but the relative displacement of the colored centroids is barely
noticeable.

                        AT-WAVELENGTH OPTICAL METROLOGY © Imagine Optic 2022

At-wavelength metrology with MESOTM
   An illustration of at-wavelength metrology is reported below using the MESOTM
   instrument. MESOTM allows for the characterization of surface shapes and
   wavefront measurements for up to a 6’’ diameter. It embeds up to 4 wavelengths
   adapted to a real working optics setup, which can be selected from the following
   list: 405 nm, 488 nm, 520 nm, 635 nm, 785 nm, 830 nm, 1064 nm. All sources are
   controlled automatically by the hardware and software user interface.

   For the purpose of this experiment, the instrument has been equipped with 402
   nm, 635 nm, and 785 nm wavelengths. MESOTM with 4’’ output testing diameter
   has been aligned in double pass onto the optics to be tested, a plane mirror.
   References have been taken at each testing wavelength on a flat reference
   mirror. It allows taking into account residual chromatic aberrations of the
   instrument optical path (mainly the collimator expanding the beam from the
   detector pupil up to 4’’).

   Each measurement has been averaged 20 times to improve stability, and
   integration times vary from 7.5 ms to 3 s depending on the power of the optical
   test instruments available. Each wavefront map in Fig. 2 below is reconstructed
   in Modal on the Zernike coefficients and plotted on a circle of 5.09 mm on the
   detector, corresponding to 101.8 mm on the test optics. Tilts X and Y are filtered,
   curvature is not.

                   Fig. 2 Surface shape (Reflected Wavefronts) of a flat mirror tested at
                             402 nm (left), 635 nm (center) and 785 nm (right)

   We can observe MESOTM is able to measure on the whole visible range and
   on a large dynamic of exposure times allowing accommodation of the optics’
   characteristics, such as the spectrum of its coating or its reflectance.

   If we analyze the RW values more closely (see Table 1 below), we can observe the
   accuracy of MESOTM on the whole visible range: RMS values vary from 53 nm to
   57 nm, that is, 4 nm or l/158 which is within the accuracy and repeatability of the
   instrument.
     Table 1. Variation of the Reflected Wavefront measured with MESOTM on a flat mirror across the
                                    detector range is less than 5 nm RMS.
   Wavelength                      402 nm                     635 nm                        785 nm
   RW (RMS)                         53 nm                      57 nm                         57 nm

                          AT-WAVELENGTH OPTICAL METROLOGY © Imagine Optic 2022

In Summary
   Most optical metrology is performed at 632.8 nm even if the optics to be tested
   is designed and will operate at a different wavelength. This is due to historical
   and technological reasons, as metrology gold standards were operating at laser
   lines.

   Nowadays, wavefront sensing solutions are no longer constrained by these
   limitations. In particular, Shack-Hartmann wavefront sensor are achromatic and
   can perform at any wavelength desired by users within the spectral range of the
   detector they rely on.

   This can open up new possibilities to users who need to test their optical
   components or systems at design/operating wavelength

References
   1
    S. Meimon and al ONERA, “Sensing more modes with fewer sub-apertures:
   the LIFTed Shack–Hartmann wavefront sensor”, May 15, 2014 / Vol. 39, No. 10 /
   OPTICS LETTERS.
   2
    C. Plantet, S. Meimon, J.-M. Conan and T. Fusco, “Experimental validation of LIFT
   for estimation of low-order modes in low-flux wavefront sensing”, 15 July 2013 |
   Vol. 21, No. 14, OSA.
   3
    R. Gonsalves, “Small-phase solution to the phase-retrieval problem”, Opt. Lett.,
   Vol. 26, No 10, pp. 684-685 (2001).

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