Chapter 4

Chapter 4, The Point Design

Section High Dynamic Range Imaging and the GSMT


The ability to study a faint source is strongly compromised when it is in close angular proximity to a much brighter source. A number of very exciting science programs fall into this category. Foremost among these is the study of preplanetary disks and related phenomena around young stars, planets, and other low-luminosity stellar companions, the inner regions of active galactic nuclei, and the host galaxies of quasi-stellar objects (QSOs). In each of these examples, as well as in many others, it is necessary to study faint sources within a few arcseconds of a much brighter source.

In order to put the following discussion in a pictorial context, Figures 1a and 1b show the parts of the adaptively corrected point spread function (PSF), discussed here and below. The inner region (the diffraction-limited part) is determined by the overall pupil shape, with larger, usually lower intensity structure due to filling factor, segmentation geometry, secondary obstructions, etc. Adaptive optics (AO) optimally corrects the image out to a radius ThetaAO=Nactlambda/2D, where Nact is the number of actuators across the telescope diameter, and lambda/D is the classical telescope resolution limit for wavelength lambda and telescope diameter D. Inside of this radius (that is, within the first few Airy rings), residual uncorrected light appears as speckles that interact with the diffraction features. Outside ThetaAO, there is an extended speckle halo determined by the power spectrum of the residual wavefront aberrations. This halo includes the usual "seeing halo" of the uncorrected wavefront, with an additional distribution of flux due to the imperfect fitting of the wavefront by the adaptive system.

Figure 1a A radial cut in synthesized PSFs for the GSMT point design. The broader profile corresponds to H-band and the narrower to the N-band. In each case, the residual wavefront error is 100 nm. In the H-band, this gives a Strehl of 0.76, and in the N-band, a Strehl of 0.99. The sampling is four pixels per resolution element in both cases. There is a peak at radial distance of 150 pixels, corresponding to the first Airy ring of the single segment. The halo becomes dominant at radial distance of about 300 pixels, which corresponds to the distance . These are long-exposure images, and hence time averaging smoothes the halo. Some diffraction structure is becoming apparent in the halo region. The hexagonal segments and the segment gaps produce symmetric structure out to high frequencies.
The subjects of coronagraphy, apodization, and nulling, and their impact on the PSF, are discussed in detail in Appendix 4.7.6.A. In this overview, certain general results and broad conclusions are described.

Figure 1b An image of the H-band PSF whose cross section is shown in 1a. Additional structure, which did not show up in a single cut, includes four peaks near a radial distance of 300 pixels. These correspond to the Shack-Hartman waffle mode, which is due to indeterminacy in the wavefront reconstruction. THE ADVANTAGES OF ADAPTIVE OPTICS AND GSMT FOR HIGH DYNAMIC RANGE IMAGING

AO support high dynamic range imaging by improving the concentration of flux for an unresolved faint source (proportional to S, the Strehl ratio), and by reducing the amplitude of the noncoherent seeing halo (proportional to (1-S)). In high dynamic range imaging (HDRI) applications, employing coronagraphy or nulling to suppress the coherent diffraction core results in the detection of the faintest sources usually being limited by speckle structure in the image, rather than by the photon noise. Therefore, AO, possibly enhanced with coronagraphy, should directly offer a gain for HDRI sensitivity proportional to S/(1-S).

For telescopes of differing diameter with similar AO performance (in the sense of equal Strehl ratio), the higher angular resolution of the larger will yield benefits of flux concentration and light gathering power. The combination of these factors will give a peak pixel brightness ratio gain (faint source to bright source halo) proportional to D3.

High dynamic range imagery of bright sources will often be limited by speckle structure in the uncorrected halo of the bright source rather than by its photon noise, particularly if coronagraphy or nulling is employed to reduce the amplitude of the diffracted component. Thus, for high dynamic range observations of a faint point source close to a bright one, at constant separation, a 30-m filled-aperture GSMT would have an advantage over an 8-m telescope of 53 in signal-to-noise ratio. Compared to a 10-m aperture, the advantage would be 27. These gains will enable observations of currently inaccessible types of sources. WHAT ISSUES MUST BE ADDRESSED

In evaluating GSMT concepts, it is necessary to examine the interplay between design parameters and the PSF. This includes the raw PSF, the AO-corrected PSF, and the PSF with any post-correction modifications. Not surprisingly, this is a complex and challenging study.

The adaptive correction can be predicted with some confidence by employing performance characteristics of proven components, with reasonable extrapolation of formats. Figures 2a and 2b show PSFs for the GSMT point design for two examples. In each case, multiple radial profile cuts are shown overplotted, giving rise to the vertical thickness of the plot. In the central region (first few Airy rings), the PSFs are symmetric, and the radial cuts follow a common curve. Further out, the radial cuts differ because of asymmetries in the pupil shape (hexagonal edges and segment boundaries, spiders, etc).

Part of the speckle distribution is related to the diffraction pattern, and effectively modulates it. Speckles tend to fall where the Airy rings are expected. This effect has been called speckle pinning,1 and intentional adjustment of the phase can, in principle, be employed to adjust the location of the diffraction peaks and hence the positional dependence of the speckle noise amplitude (speckle sweeping). Dark hole/dark speckle are other techniques proposed to exploit speckle structure to improve dynamic range.

The wavefront correction quality shown in Figures 1 and 2 is based on an adaptive system with an actuator spacing on the pupil of 20 cm. This number is similar to high performance AO systems in operation today. The implied total number of actuators (about 17,000) is a significant advance over current technology and will only be possible with developments in adaptive mirror and computing technology.

Figure 2a Radial plot of a simulated PSF for GSMT point design AO, H-band, 100 nm residual wavefront error, Strehl 0.76. The pixel size is 0.0028 arcseconds, and the full radial range shown is 0.41 arcseconds. THE GSMT POINT DESIGN CONFIGURATION

The point design features a compact, nearly circular pupil composed of hexagonal segments 1.152 m across flats. The nearly circular, nearly filled pupil provides a nearly symmetric and almost maximally compact PSF, with a small full width half-maximum (FWHM)-all features that are appropriate for HDRI. The near 100% filling factor is well-suited to the implementation of both classic and innovative coronagraphic techniques.

As may be seen in detail in Appendix 4.7.6.A, the interplay between pupil configuration and PSF is complicated in detail, but it has some simple features. Foremost, there is an obvious relation between the segment size and the PSF. If the pupil to segment diameter ratio is D/s, then the segments produce Airy rings on a scale D/s larger than the rings of the full pupil. Specifically, the first segment-enhanced peak of the PSF appears at a radial angle of 1.64(D/s)(lambda/D). The point design pupil to segment ratio of 26 provides a radial distance to the first segment diffraction ring at H, M, and N of 0.42, 1.3, and 2.7 arcseconds, which could impact the performance of extreme AO outside this angle. (An even smaller segment size would throw the segment diffraction to larger angles.)

Figure 2b Radial plot of a simulated PSF for GSMT point design AO, N-band, 50 nm residual wavefront error, Strehl 0.99+. The pixel size is 0.017 arcseconds, and the full radial range shown is 2.55 arcseconds.
Ideally, the significance of segment diffraction drops rapidly with reduced segment spacing. For the point design optical gap of 5 mm (including bevels), the segment diffraction is nearly negligible. However, if segment edges are associated with enhanced mirror surface figure errors, or if segment edges are the site of wavefront discontinuities, then the segment diffraction pattern may re-emerge as a limiting factor. These are critical issues for HDRI, particularly for the small segment size of the point design. CENTRAL SOURCE PSF SUPPRESSION: CORONAGRAPHY AND OTHER TECHNIQUES

Coronagraphy has a long history of demonstration, components are well understood, and accurate modeling of performance can be expected. A design concept for a GSMT coronagraph is presented in Section Apodization is sufficiently simple that modeling should give correct results. Nulling is well understood in theory, although new concepts are appearing at a dizzying pace. They depend in part on the characteristics of optical components for which there may be limited experience with respect to manufacturability and achievable performance (in many cases no demonstration on a telescope, and sometimes not even in the laboratory).

At present, combined modeling of adaptive correction with coronagraphic and nulling techniques is in its infancy. This area needs further work in evaluating GSMT designs for HDRI.

Appendix 4.7.6.A sets out in detail the basic formalism needed for design and modeling of various techniques, and gives extensive references to the literature. PROMISE OF GSMT

An idea of the GSMT potential for HDRI can be obtained from Figures 1a and 1b. In the near-infrared, illustrated with the H-band PSF, it may be expected that at angular separations greater than 0.1 arcsecond, close companions or surface brightnesses 4 to 5 orders of magnitude down will stand out above the core PSF. In the N-band, this performance will be achieved beyond about 0.4 arcseconds separation. These performance levels are extremely conservative, as they do not make assumptions about the potential for differential measurements. Four to five orders of magnitude correspond to 10 to 12.5 stellar magnitudes, which is already an outstanding achievement when combined with the angular resolution of a GSMT.

A differential measurement can be carried out by a number of techniques. For example, an observation of a binary star can be recorded and deconvolved with an observation of a single star. If the PSF is not time-varying, this method would be limited only by the photon noise, which will be set by the bright source.

However, for high dynamic range measurements, it is likely that the detection of faint sources will be limited by the speckle noise in the images. Speckle due to residual atmospheric wavefront error changes on a rapid timescale, and will average out in long integrations (as discussed in detail below).

In fact, the dominant residual phase errors in contemporary AO systems are not constant, but quasi-stable. They arise from sources (differential temperature variations, flexure, electronic drift) which are not fully controlled, many of which are intrinsically slowly varying during observations. In such a situation, the rotating field of view of an Alt-Az telescope can be exploited to obtain residual suppression of fixed speckle structure. This is illustrated in Figure 3.

The ability to detect sources down to the photon noise limit in HDRI requires stability of instrument and AO correction, or randomness with no systematic PSF changes. Correct PSF calibration will be most readily achieved with relatively short exposures and internally monitored PSF. The example above, employing a series of short exposures during telescope rotation, is one of many possible approaches. This concern becomes increasingly important with the use of long integrations to bring up sources which are much below bright star residuals. In this case also, a differential measurement with internal criteria for monitoring and confirming stability at the required level will have the greatest promise for extracting a clear result.

In practice, it should be expected that a variety of calibration and detection techniques will be required in order to defeat speckle arising from various causes on a variety of timescales. Some types of speckle will be removed by time averaging, and some kinds by PSF calibration and subtraction. At best, these techniques may ultimately bring observations to the photon noise limit as set by the diffracted or scattered light from the bright source. Then, in order to reach even greater contrast ratios, it will be necessary to employ high contrast specific methods such as coronagraphy or nulling.

Figure 3 These adaptively corrected images were obtained at Gemini North with the Hokupa'a AO system (C. Roddier, personal communication, 2000). The sequence of images above shows, left and middle, a bright star imaged twice. Circles highlight bright points in the image. Comparison between the two images shows that most of the bright points are fixed with respect to the telescope, hence they are pinned speckles. One spot, at 7 o'clock, has moved with the sky rotation, showing that it is part of the observed source. In the right image, a rotational sequence has been processed to determine the quasi-static speckle structure. In the sequence below, the left image is the uncompensated result. The middle image is compensated, showing the fixed speckles described above. Each image was deconvolved with the proper PSF, including pinned speckles; the images were rotated and combined to form the result on the right. The clean PSF and high confidence of detection are evident. (The bar in the right image has a length of 1 arcsecond.)
Coronagraphy and nulling intrinsically function to reject the light in the diffraction-limited image of an unresolved source. The choice of technique will depend on a number of factors, including the range of angular separations under study. Nulling has the advantage that it can allow observation of very close companion sources, even inside the first Airy dark ring. Partially resolved bright sources, on the other hand, will partially leak through a nuller, but not through a coronagraph, which employs a mask that is substantially oversize with respect to the source. As an illustration of the type of performance that may be expected with nulling, plans for study of the exo-zodiacal light at Keck will require star leakage of less the 10-3. It is expected to achieve this performance, near 10 microns wavelength, with currently operational AO technology. MODELING PERFORMANCE OF GSMT WITH ADAPTIVE OPTICS AND CORONAGRAPHY

The PSFs discussed above are based on detailed atmospheric and AO system models and the GSMT point design. In order to extrapolate the simulated PSF performance to long integration HDRI, we adopt the following derivation. Beginning with, for example, the PSF in Figure 1a, we expect that coronagraphy or nulling will reduce the amplitude of the coherent diffraction core by a factor of up to 10x, with a maximum reduction to the amplitude of the halo at ThetaAO. This should be a relatively conservative assumption on both counts. The speckle is assumed to have an amplitude contrast of 100% (as for narrowband imagery-broad-band imagery will produce lower speckle contrast). Long integration is assumed to reduce the speckle amplitude by (T/DeltaT)0.5.

A major uncertainty in the performance of HDRI is the speckle lifetime, DeltaT. Expressions for the speckle lifetime, suggested by various authors 2,3 and evaluated for the case of a 30-m GSMT and a wind speed of 10 m/sec, would range from a few to a few hundred milliseconds. (This enormous range is clearly a key topic for observational study.) Noting the advantages of a short speckle lifetime, Angel4 proposed that a small wavefront control sampling time (much less than the speckle time constant) would have the advantage of randomizing the speckle rapidly and ensuring that the factor (T/DeltaT)0.5 would have a large value. Limited tests with on-sky AO tests 5,6 are probably not representative of a high-Strehl system operating at an exceptional site, but they do indicate a strong interaction between wavefront measurement, AO loop speed, and observed speckle time constant. Stahl and Sandler show techniques for suppressing correlations greater than the phase measurement time.7 The method is based on a particular model for the origin of the correlations, and has been demonstrated only in numerical simulations. Based on this evidence, which is suggestive but not definitive, we make the assumption that AO speckle lifetimes will be determined by the phase measurement time. For DeltaT, a value of 0.6 milliseconds will be adopted. (For a detailed discussion of the AO parameters for coronagraphy, and for further discussion of other wavelengths, see Section In the event that speckle cannot be fully suppressed, a variety of techniques are available to calibrate or compensate - for example, differential wavelength and polarization, dark speckle, and others.

Applying this calculation,[1] we would estimate at 1.6 microns a single exposure dynamic range (S/N = 1) of 1 x 105, and a dynamic range after 1 hour of 2.5 x 108, achievable for radial separation greater than 0.1."

As a check, we can derive an independent estimate based on a high level schematic model for error in extreme AO.4 For detection limits inside ThetaAO, the fitting error should be suppressed. (Fitting error power is mostly in uncorrected higher spatial frequencies, and scatters light outside ThetaAO.) This calculation, with the same parameters, leads to a dynamic range approximately five times larger than that derived from the PSF. This is because the GSMT PSF simulation included a substantial added wavefront error component (based on the stipulated point design requirements), which adds to the classic AO errors.

Figure 4 This shows the estimated magnitude limits for high dynamic range imaging as a function of spectral resolution. Each curve is labeled with the wavelength band (H, M, N) and the corresponding dynamic range. The magnitude limits correspond to S/N = 1 in one hour, so with extended integrations, useful detections should be possible at these levels. The assumed AO system is discussed in detail in the text and in Section 4.7.6. The sensitivity scales by 2.5 magnitudes for each factor of 10 change in dynamic range. In the non-thermal regime, however, the dynamic range saturates to a limit. For the H-band, this limit is 2.5 x 10^8.
As long as speckle noise dominates over photon noise, the expected dynamic range will be independent of source brightness. When halo photon noise is dominant, the sensitivity will vary with the square root of the source brightness and inversely with the spectral resolution and the dynamic range.

The AO capability assumed here will produce very high Strehl performance in the thermal infrared. In fact, outside a few diffraction widths, the halo from the PSF will be negligible compared to the thermal background noise, and the sensitivity can be calculated simply from the source and background fluxes.

Scattering due to scintillation is assumed negligible in the region of the PSF under consideration. In the approximation that the atmospheric turbulent layers are at high altitude (typical of the best sites), the scintillation halo will be the same size as the natural seeing. The total scattered flux at 1.6 microns will be on the order of a few percent, and it is easy to show that this will be negligible for Strehls less than about 0.92. In our example (Figure 1a), the 1.6 micron Strehl is 0.76. GSMT AND ALTERNATIVE CONCEPTS: NEXT STEP STUDIES FOR HIGH DYNAMIC RANGE SCIENCE

In making comparisons, it is necessary to drop the GSMT acronym, because not all large telescope concepts are well described as "segmented." In the following, the term GT will be employed. All direct imaging GT concepts are likely to offer significant gains in high dynamic range performance. GSMT-like Concepts

For designs similar to the point design, issues of significant interest are the segment sizes, figure, gaps, the secondary, spider(s) (if any), and AO performance. Although large segments would introduce diffraction structure into the Airy core, it is difficult to generalize about any disadvantage of this, because the result will increase the level of diffracted light in some regions and decrease it in others. A complete analysis including instrument-specific particularities is required. Small segments would appear to be generally favorable, because any edge-correlated structure will tend to be diffracted out away from the central image core, according to the rule noted above.

Without question, smaller secondaries and spiders are preferred, with immediate benefits for high contrast imaging due to reduced diffraction intensity and less potential for asymmetry in the diffraction pattern.

The exact shape of the outer periphery of a compact-pupil GT is probably not a significant factor, because it will likely be masked in a Lyot stop in any event, but for some configurations this could result in enhanced light loss at the stop.

The most interesting and difficult comparison of GT concepts will be between the compact aperture and distributed aperture concepts. As far as we are aware, there is not yet a general study of aperture format optimization for optical astronomy, although there are a number of discussions within restricted approximations. There are two distributed aperture concepts currently under study, representing dramatically different configurations which illustrate some of the possibilities. Multi-Mirror Telescopes

The Large Aperture High Dynamic Range (LAHDR) concept8 is a multi-mirror style, hexagonal off-axis telescope9 consisting of six subapertures arranged in a ring on a common mount. This is in the style of the original (Multiple Mirror Telescope) MMT-the major difference is that the LAHDR telescope is intended to be fully phased.

The specific concept has "light collecting area equivalent to a 15.9 m unobstructed aperture," but a larger number of unit telescopes on a larger mount could certainly increase the equivalent aperture to 30 m. The ratio of largest chord across the pupil to the equivalent aperture is 22/15.9 = 1.38. This is a significant enhancement in the available resolution of this configuration, and is by no means a limit for an MMT approach. The LAHDR telescope adopts a number of features that enhance the high dynamic range capability, but are not necessarily unique to the configuration, such as unobscured subapertures achieved with off-axis unit telescopes.

The LAHDR PSF is much more complex than would be obtained with a more nearly filled aperture. However, the tradeoffs between filled and unfilled apertures are not obvious, because distributing a given total collecting area over a larger surface will provide successively higher resolution (and a narrower PSF core) at the cost of more structure in the PSF (and lower Strehl!). A first-order comparison between the GSMT point design and various MMT concepts is possible with only a description of array configurations.9 This would be a goal for further study. MMT concepts with on-axis unit telescopes could only be studied with considerable additional information about the secondary obstruction, beam transfer, and combination scheme.

It is worth noting that some nulling techniques are unsuitable for telescopes that deviate from circular symmetry. Direct-Imaging Arrays

If multiple telescopes are implemented on separate mounts (as opposed to a common mount), they begin to look like a configuration that is normally designated an interferometric array. However, there is still a critical distinction between concepts that form a real image, here called direct imaging, and those that do not. A real image permits optimum discrimination against sky background (as determined by the configuration and filling factor) and potentially offers a fainter limiting sensitivity. Direct imaging with independently mounted telescopes is significantly more difficult than interferometric combination, and in fact has not yet been implemented.

Direct imaging is sometimes called Fizeau interferometry, although it is no more interferometric than regular imaging.

The 20-20 concept4 deploys a total collecting area equivalent to a 30-m filled aperture in two 21-m aperture telescopes on separate mounts, with beam combination for direct imaging. The concept satisfies the direct imaging requirements of optical path difference (OPD) and pupil matching by employing mounts that move on a circular track in coordination, thereby providing a virtual common mount. The spacing between the two telescopes can be varied up to 100 m.

Each 21-m aperture can be employed for HDRI, as described for the point design. The larger segments of 20-20 impact the PSF, and a comparison with the point design depends strongly on details (in each case) of the segment boundaries, which are not yet available.

The availability of independent and movable telescopes opens up significant additional parameter space for HDRI. The achievable higher resolution gives access to smaller source separations. The two apertures can be combined with complementary phase to null a bright, on-axis point source. In direct imaging, the telescopes will form an image of the sky with dark fringes due to the null. Images in multiple position angles and with multiple separations can be used to extract a complete image with tomographic techniques and/or interferometry-based coherence measurements. Distributed direct imaging concepts open for exploration rich possibilities in HDRI which should be further developed for comparison with other GT options. Interferometric Arrays

Telescope arrays can also be employed interferometrically. By this we mean that beam combination techniques are exploited to sample the source coherence function without forming a real image. The coherence function information can be used to constrain the models of the image or to digitally reconstruct a consistent image. This technique is sometimes called Michelson interferometry, and it is the method that is employed by the generation of optical interferometers currently in operation or under construction. At the present time, phase measurement and control between pairs of telescopes is well developed and widely utilized. Phase control of arrays of a few telescopes is under development, but has not yet been attempted for arrays of many telescopes.

The Decadal Survey recommendations for a large telescope include a focus on dark sky science. Interferometry (in the Michelson sense) is probably not a strong competitor in this area due to the poorer discrimination against sky background compared to direct imaging. However, a distributed direct imaging array could be operated in interferometric mode. For HDRI, interferometry is an interesting contender. For one thing, because interferometry operates by measuring coherence, and because scattered light loses its coherence, interferometry strongly discriminates against scattered light, which may remain to contribute photon noise but contributes no coherent signal. The coherent signal can be used to study source structure at the baseline diffraction limit. Nulling can be employed to remove the unresolved bright source flux, thus reducing photon noise and leaving the companion or circumsource constituents for detailed study. There are techniques for interferometric combination of any number of telescopes, although the methods for two-telescope combination are best developed at present. Extensive effort has been invested in understanding nulling interferometry on the ground and in space, with the Keck and Large Binocular Telescope (LBT) interferometry programs offering a benchmark and a basis for further study of GT nulling interferometry. PROPOSED LONGER TERM STUDIES OF HIGH CONTRAST IMAGING WITH GIANT TELESCOPE CONCEPTS

Exploration of a range of HDRI techniques, pursuit of new ideas, and elaboration of selected GT designs offer the most critical evaluation of expected performance. We have mentioned single versus multiple aperture GTs, and optimum configurations and operating modes of each.

The point design has already been developed sufficiently to verify that it will have excellent characteristics for HDRI. Work proposed for the next study phase will further define the telescope requirements and the interplay between telescope and HDRI instrument design.

Optical surface quality, atmospheric effects, and the related performance of AO are foremost concerns. Ongoing work at Gemini and other observatories on multi-conjugate and high performance AO will undoubtedly continue to raise our sights for AO with giant telescopes.

High dynamic range imaging pushes telescope optics control harder than any other application, and yet our understanding of HDRI has much room for improvement. It should be possible to extend the understanding of HDRI imaging to derive guidelines for hardware control and stability for a required residual speckle and coronagraph/nulling performance down to the photon noise level with high Strehl adaptive optics operation, achieving and eventually exceeding the performance projections described here. REFERENCES:

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[1] Summary of Assumptions: The AO/coronagraph system described in 4.7.6 is the baseline concept. With 16,900 degrees of freedom and a servo loop update rate of 1250 Hz, the required K-band Strehl is 0.9. The telescope-instrument throughput is 0.74, and the emissivity is 0.18. A coronagraph or nulling arrangement reduces the diffraction-limited core by 10x, or to the residual halo level, whichever is greater. Atmospheric ro is 14 cm, and atmospheric speckle is assumed to change with every wavefront measurement, and to average out with the square root of the integration time. Slowly varying speckle due to telescope or instrument is to be removed by internal and external calibration of the effective PSF. The scintillation halo is negligible.

March 2002