Wavefront sensing from a saturated PSF
A well AO-corrected PSF is a highly contrasted object. The proper simultaneous sampling of the core of the PSF and its diffraction rings therefore requires a detector with a large dynamical range, which is rarely compatible with a fast readout. The SCExAO internal science camera has an effective dynamical range of ~10 000 counts so that, in practice, an exposure time has to be chosen that either gives access to a non-saturated PSF core (the normal operating mode of the wavefront sensing approach described thus far) or over-expose the PSF core to better see the fainter diffraction structures that surround it.
In its general form, the linear model of Eq. (2) only holds when working on non-saturated images that otherwise result in a non-translation invariant PSF. Pixels that are saturated by the bright core of the PSF can be treated as zeros, so that the effect of saturation can be modeled as a multiplication by a top-hat function that cuts off anything higher than a level imposed by the characteristics of the detector. This multiplication in the image space results in a convolution by an Airy-like function whose characteristic size is inversely proportional to the size of the saturated part of the PSF.
The effect of this convolution is expected to be most prominent in the outermost region of the Fourier plane where the phase will experience a change of sign. Figure 11 illustrates this effect by comparing the Fourier-phase signature of a specific aberration for a non-saturated PSF to that of a mildly saturated one. We can see that, while the outermost part of the Fourier-phase is obviously affected by the saturation, the innermost part of the PSF (highlighted by the smaller dashed circle) does resemble the original non-saturated case.
| Fig. 11 Comparison of the UV-phase signature of the same amount of aberration (here coma) for a non-saturated PSF (on the left) and a saturated one (on the right). The saturation primarily affects the higher spatial frequencies of the image, corresponding to the outermost parts of the Fourier plane. In the inner region of the saturated case (within the highlighted smaller circle), the Fourier-phase signature of the aberration is similar to its non-saturated counterpart. |
| Open with DEXTER |
Figure 12 further makes this obvious by representing in a 1D plot the values of the Fourier-phase of the saturated image against the Fourier-phase of the non-saturated image. Whereas considered as a whole, the Fourier-phase of the saturated data appears as non-usable (the blue points are widely scattered), the inner part of this same saturated data set is strongly correlated (the red points) with the non-saturated data, suggesting that some of the wavefront information can be recovered in the saturated case, assuming that we can filter out the information coming from the largest baselines.
| Fig. 12 1D comparison of the phase (in radians) extracted from the Fourier plane, featured in Fig. 11, in the non-saturated case (along the horizontal axis) and in the saturated case (along the vertical axis). The blue points include the data at all spatial frequencies while the red ones correspond to the inner part of the Fourier plane only. The strong correlation observed in the latter case suggests that some of the wavefront information can be recovered from the analysis of mildly saturated data. |
| Open with DEXTER |
To account for this filtering, the Fourier-phase model can be modified, and the parts of the phase transfer matrix A can be discarded along with the parts of the Fourier-phase vector Φ that are filtered out. The model we tested only preserves baselines that are 70% or less than the longest baseline in the model, which corresponds to the area inscribed within the inner circle plotted in the right panel of Fig. 11. Out of the 675 original distinct UV-phase samples, 330 remain with this configuration, which is still of the order of the number of modes necessary to recover the full theoretical pupil phase information (291 modes).
For the computation of the pseudo-inverse A+ of this new system, 50 modes are kept. With less constraints from the UV-plane, the Zernike modes are less well reconstructed, but are nevertheless recognizable, as shown in Fig. 13.
| Fig. 13 Experimentally recovered Zernike modes after discarding the phase associated with the longest baselines, which are affected by saturation effects. This new series of experimental modes should be compared to the non-saturated case presented in Fig. 6. |
| Open with DEXTER |
The calibration procedure introduced in Sect. 2.4 can be repeated with this new model, after which the APF-WFS is effectively able to operate in closed-loop from the analysis of saturated data, albeit with lower performance. To see how this saturation affects the sensor, the study presented in Sect. 3.3 was repeated in this new operating mode. The outcome of this study is presented in Fig. 14.
| Fig. 14 Study of the response of the sensor in the saturated case to Zernike modes of varying amplitude. This series is to be compared to the case presented in Fig. 10 in the non-saturated case. |
| Open with DEXTER |
In this peculiar saturated mode, the sensor is able to operate linearly over a limited range of aberrations. As previously observed (see Sect. 3.3), it is the modes whose geometry features localized bumps, such as coma of trefoil, that first limit the range of aberration that the APF-WFS can account for. The APF-WFS can nevertheless operate on images whose core is saturated, over a 100 nm wavefront RMS range that is roughly one half of what it can achieve in the non-saturated operating regime: the general APF-WFS approach is more robust than at first expected and can be used despite the less than ideal conditions.
Conclusion
Following on from the conceptual study proposed by Martinache (2013), this paper described the implementation of the asymmetric pupil Fourier wavefront sensor as one of the wavefront control loops of the SCExAO instrument. This approach has proven capable of repeatedly accounting for the non-common path error that affects the instrument after a new telescope pointing and provides an updated zero-point for the upstream pyramid wavefront sensor currently implemented inside SCExAO.
A surprisingly simple asymmetric hard stop mask introduced in the pupil of a diffraction-limited imaging instrument is thus proving to be a powerful diagnostic tool for the control of the non-common path aberrations. The reported capture range of the technique is currently limited to a fraction of a wave (RMS ~λ/ 8). A combination of filters of decreasing wavelengths would provide a direct way to tolerate a cruder starting point. We are currently exploring the potential of an updated algorithm that simultaneously exploits the information sampled at multiple wavelengths to extend the capture range even more,
this time within the coherence length. We note that other approaches using combinations of non-redundant aperture masks (Cheetham et al. 2012, 2014) also rely on this idea to extend their capture range.
The asymmetry results in slight cosmetic degradations of the PSF. While this does impact a coronagraphic instrument, it can be tolerated in a general purpose AO-corrected imaging instrument. A very interesting feature of this image-based wavefront sensing approach is that, if multiple sources are available in a given field, the APF-WFS algorithm can be used on all sources simultaneously. Depending on the complexity of the field, the same asymmetric mask, combined with the analysis of multiple sources in one image, can be used for multi-reference wavefront sensing, opening the way to a full 3D reconstruction of the wavefront from the analysis of a single focal plane image. This very property can also be put to use on artificially introduced incoherent replicas of an on-axis PSF of tunable intensity, as described by Jovanovic et al. (2015a), thus making the use of the technique compatible with that of a coronograph that otherwise destroys the interferometric reference required for a sensible Fourier-analysis of the image, as described in this work.
The use of this wavefront control technique extends well beyond the control of low-order modes on SCExAO: this paper provides experimental evidence that the technique is actually effective where the theory predicts it should be. In an exposure that simultaneously features an unsaturated PSF core and the diffraction features at large separation with sufficient SNR, APF-WFS can be used to control an arbitrary number of modes, as was shown in the concept paper. The APF-WFS can, in fact, be easily applied in a wide variety of wavefront sensing contexts, for ground- as well space-borne telescopes, and with a pupil that can be continuous, segmented, or even sparse. APF-WFS is powerful because it measures the wavefront where it really matters, at the level of the science detector. Given its low impact on the instrument hardware, it is an option that should be given some consideration as part of any high contrast imaging instrument with wavefront control capability.
References
· Blain, C. 2013, Ph.D. Thesis, University of Victoria (Canada) (In the text)
· Bordé, P. J., & Traub, W. A. 2006, ApJ, 638, 488 [NASA ADS] [CrossRef] (In the text)
· Cady, E., Baranec, C., Beichman, C., et al. 2013, in Techniques and Instrumentation for Detection of Exoplanets VI, Proc. SPIE, 8864, 88640 [CrossRef] (In the text)
· Cheetham, A., Cvetojevic, N., Norris, B., Sivaramakrishnan, A., & Tuthill, P. 2014, Optics Express, 22, 12924 [NASA ADS] [CrossRef](In the text)
· Cheetham, A. C., Tuthill, P. G., Sivaramakrishnan, A., & Lloyd, J. P. 2012, Optics Express, 20, 29457 [NASA ADS] [CrossRef] (In the text)
· Give’On, A. 2009, in Techniques and Instrumentation for Detection of Exoplanets IV, Proc. SPIE, 7440, 74400 [NASA ADS] [CrossRef](In the text)
· Jennison, R. C. 1958, MNRAS, 118, 276 [NASA ADS] [CrossRef] (In the text)
· Jovanovic, N., Guyon, O., Martinache, F., et al. 2015a, ApJ, 813, L24 [NASA ADS] [CrossRef] (In the text)
· Jovanovic, N., Martinache, F., Guyon, O., et al. 2015b, PASP, 127, 890 [NASA ADS] [CrossRef] (In the text)
· Kraus, A. L., & Ireland, M. J. 2012, ApJ, 745, 5 [NASA ADS] [CrossRef] (In the text)
· Mahajan, V. N. 1981, J. Opt. Soc. Am. (1917–1983), 71, 75 [NASA ADS] [CrossRef] (In the text)
· Martinache, F. 2010, ApJ, 724, 464 [NASA ADS] [CrossRef] (In the text)
· Martinache, F. 2013, PASP, 125, 422 [NASA ADS] [CrossRef] (In the text)
· Martinache, F., Guyon, O., Jovanovic, N., et al. 2014, PASP, 126, 565 [NASA ADS] [CrossRef] (In the text)
· Minowa, Y., Hayano, Y., Oya, S., et al. 2010, in SPIE Conf. Ser., 7736 (In the text)
· Pope, B., Cvetojevic, N., Cheetham, A., et al. 2014, MNRAS, 440, 125 [NASA ADS] [CrossRef] (In the text)
· Sallum, S., Follette, K. B., Eisner, J. A., et al. 2015, Nature, 527, 342 [NASA ADS] [CrossRef] (In the text)
· Tuthill, P. G., Monnier, J. D., Danchi, W. C., Wishnow, E. H., & Haniff, C. A. 2000, PASP, 112, 555 [NASA ADS] [CrossRef] (In the text)
· Zernike, v. F. 1934, Physica, 1, 689 [NASA ADS] [CrossRef] (In the text)
All Tables