What is mWFS? 

Figure: mWFS mounted at the f/10 Cassegrain focus of the UH88” telescope on Mauna Kea.  The five WFSs (top) and the field acquisition camera (bottom) are seen.

Photo credit: Doug Toomey

The mWFS experiment deploys five Shack-Hartmann wavefront sensors (WFS) over a half-degree field of view to quantify the atmospheric wavefront correlations over extremely large fields of view.  Each WFS samples the wavefront from one star from a constellation of stars with 23x23 9-cm subapertures at a rate of 25-50Hz.  The wavefront phase correlation as well as the optical turbulence profile are extracted from the telemetry data.  The data from this project is feeding several design studies for ground-layer AO on Mauna Kea.

What kind of data do we get?

Figure: A single mWFS image from on of the five wavefront sensors (LEFT) along with its corresponding pupil image (RIGHT).  Note the two pupil masks placed just in front of the telescope primary mirror as references.

We stream the synchronized Shack-Hartmann images to disk and post-observation extract the centroids and phase aberrations from each WFS.  To ensure we have all five WFSs aligned with respect to each other we have a pupil imaging mode within each WFS.  The lenslet array (LLA) that divides the pupil into subapertures has a circular mask on each lenslet.  In the pupil imaging mode we see the telescope pupil superimposed on the lenslet array grid.  This allows us to unambiguously align all WFS back to the telescope pupil.

A typical data set consists of 10,000 measurements from each WFS taken at a rate of 25Hz.  This corresponds to a sample of 400 seconds (nearly 7 minutes).

What can be learned from the data?

  1.   Distribution of optical turbulence within the first 10s of meters

  2.   Wavefront correlations versus angle

  3.   PSF reconstruction

  4.   GLAO control algorithms

As an example of what can be extracted from this data, the following figure shows the cross-covariance of each WFSs derived x-slope with all the others as a function of offset in time.  Each frame of the animation is the average of the covariance of one time-steps x-slopes with the x-slopes from a time step (or two, or three, etc.) later.    The two movies below are from the same data (12_09_01_23_31_10_947) but in the second I’ve subtracted the auto-cross-covariance (e.g. dt=0) map from each time step. This quite effectively subtracts out the long-lived/static covariances and highlights the changing component.   It is clear from this data set that the cross-covariance changes very slowly (with a lifetime longer than the 8 frame offset calculated here).  This strong and long-lived component is the dominant source of optical turbulence and arises (as seen in the cross-covariance) from right at the ground.  A much weaker layer is seen in the animations moving from the center of the frame to the right.  This layer only shows up in the auto-cross-covariances (e.g. a single WFS cross-covariance with itself a time later) so we infer that this layer arises from within the upper atmosphere (e.g. above where the five WFSs have any overlap).  

Figure: The cross-covariance maps derived of each of the five wavefront sensors from a single data set.  Each step in the animation displays a different offset in time in increments of the 50Hz sampling rate.  The figure on the right is the same cross-covariances but with the first time step subtracted from each frame to highlight the dynamic component.

image credit: Olivier Lai (CFHT)