Study of Instrument Effects inthe Large Synoptic Survey Telescope with an Atmospheric

Turbulence SimulatorPaul O'ConnorJustine Haupt

Brookhaven National Laboratory

A new initiative in the BNL Physics Department is the experimental study of dark energy and dark matter via astronomical surveys on ground-based telescopes. These include the ongoing Baryon Oscillation Spectroscopic Survey (BOSS), the Dark Energy Survey (DES) now under construction, and the Large Synoptic Survey Telescope (LSST) planned for construction starting in 2014. In all of these experiments BNL physicists have leading roles.

The scientific success of such surveys is highly dependent on the degree to which systematic errors introduced by the observational instrument can be corrected. The goal of this effort should be to construct a hardware simulator which will allow the most important instrumental effects to be studied in the laboratory, and to compare these to results to Monte-Carlo simulations. The approach requireselectro-optical testing of LSST prototype CCDs using an optical train that emulates the first-order optical characteristics of the telescope in conjunction with an atmospheric turbulence simulator.

The proposed telescope and atmosphere simulator will:- generate controlled image datasets in the laboratory with a level of

realism close to actual observatory data;- provide a testbed for validating Monte Carlo image simulations and

image processing pipeline software;- investigate low-level systematic effects in the new-generation CCDs

proposed for upcoming surveys;

The most important result of these studies will be an improved quantitative understanding of how instrument characteristics constrain the systematic errors in cosmological analysis, particularly weak lensing investigations of dark energy and dark matter. The discovery of dark energy in 1998, and the difficulty of reconciling it with standard theoretical models, has been recognized as one of the most compelling of all outstanding problems in physical science. A wide range of experimental programs have been proposed for further study of dark energy through a variety of observational techniques. The majority of these are based on wide-field surveys in the optical and infrared. The most ambitious of these surveys, the Large Synoptic Survey Telescope (LSST), is designed to provide a deep six-band (0.3 - 1.1um) imaging survey of over 18,000 square degrees. One of the

primary science missions of LSST is the study of dark energy and dark matter via weak gravitational lensing. In gravitational lensing, the observed shapes of distant galaxies are distorted as the light reaching our instruments is bent by the gravitational field of dark matter distributed along the line of sight. The evolution of structure in the dark matter as a function of redshift is a powerful tool for elucidating dark energy properties.

In weak lensing (WL) the induced shape distortions are subtle (~ 1%) and can only be detected statistically. Moreover, the WL shear signal is masked by spurious ellipticity correlations induced by the optics, atmosphere, and detector. Therefore, the first step in weak lensing analysis is to deconvolve the effects of point spread function (PSF) anisotropy, which can be estimated using the images of stars (point sources) in the field of view. Optical aberrations are of particular concern in LSST, whose fast f/1.2 optical system makes it sensitive to small flatness deviations in the mosaic focal plane. Jee and Tyson (2011) have modeled the effect of focal plane nonflatness on the LSST PSF and find that the induced ellipticities can be in excess of 10% and that their spatial variation is composed of smooth, long range changes from the optics aberrations and sharp discontinuities at chip boundaries (Fig. 1). They note that these PSF discontinuities present unprecedented challenges in PSF deconvolution for LSST's weak lensing studies.

Figure 1.Impact of focal plane CCD height variation on PSF ellipticity. Left: simulated height variation due to CCD nonflatness and focal plane assembly tolerances (10mm overall range). Right: resulting PSF ellipticity simulated by optical raytrace (no atmosphere). (J. Jee, J.A. Tyson, Publ. Astron. Soc. of the Pacific, Volume 123, issue 903, pp.596-614)

Turbulence in the atmosphere and charge diffusion in the detector increase the PSF size, diluting the weak lensing signal remaining after PSF anisotropy correction. The magnitude of these effects must be estimated accurately for proper shear calibration. In LSST, atmosphere and diffusion together increase the PSF size by about a factor of 4 compared to an ideal optical system (Figure 2). DES and LSST are both using thick fully-depleted CCDs (FDCCDs) for their enhanced IR sensitivity. FDCCDs have large charge diffusion contributions to PSF, and in fast optical systems beam divergence also increases PSF size at long wavelengths. Additionally, the electric field near the periphery of these chips is not normal to the imaging surface, causing shape distortions

which must be corrected in order to include the full chip area for WL analysis.

Figure 2. Simulated contributions to LSST PSF: optics, detector, and atmosphere effects. (J.G. Jernigan et al., “Simulating the LSST”, Bull. Amer. Astron. Soc., Vol. 41, p.371)

To predict the impact of instrumental effects on PSF, the DES and LSST collaborations have generated extensive sets of mock data using simulations based on source, atmosphere, and instrument models. To

check the accuracy of these models, they should be validated by testing prototype cameras on telescopes with similar optical systems under representative atmospheric conditions. However, opportunities for obtaining telescope time at major observatories are limited and costly. Therefore, we constructed an optical simulator to provide a laboratory facility for characterizing the chief systematic effects relevant to weak lensing. Laboratory measurements will be compared with the output of the LSST image simulator for similar experimental conditions. We will determine whether the observed features of the realistic PSF are handled adequately by the instrument signature removal stages of the weak lensing pipeline. If residual anisotropies are found, the degree to which they degrade the accuracy of the shear measurements will be assessed.

The system is illustrated below:

POINT SOURCE

WFS

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LLIMA

TOR

TURBULENCE SOURCE(PHASE SCREENS)

IRIS

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F/1.2 POINT PROJECTOR

BE

AM

SP

LITTER

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LLIMA

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NA

CO

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EN

SA

TOR

WIN

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Figure 3.Optical layout of proposed atmosphere and telescope simulator.

The arrangement is loosely based on similar systems at other laboratories (e.g. J. Moreno Raso, Proc. SPIE 7736, 7736-4B, 2010). Forthe most usual case in which adaptive optics systems require testing in the lab, the systempasses collimated light through a series of statistically accurate spatially-random phase screens representing turbulent layers at several distances (altitudes) from the telescope's entrance pupil. The telescope's simulated pupil is re-imaged as needed for the AO system and the wavefront is sampled at some strategic point. A final real image is generally formed where the resultant field-dependant PSF from a simulated star field can by analyzed.

There are noteworthy distinctions between the conventional atmosphere simulator described above and the setup depicted in fig. 3, which feeds not an AO system but a single-point LSST beam simulator. This setup is described below, beginning with consideration of the LSST-specific turbulence profile which drives the optical design of the simulator.

TURBULENCE SOURCE

The Fried-parameter (r0) at the LSST site in Chile is known to be~21cm. Three phase-screens were ordered from UC Santa Cruz with a Kolmogorov-like phase distribution in frequency space and r0 scaled forthe largest pupil that can be used on their 100mm diameter substrates in a rotating-disk arrangement.A 40mm pupil size was chosen, and with an aperture to Fried-parameter ratio (D/r0) of 40 for LSST, the desired r0length scale (on a 40mm pupil) is 1mm, and the as-measured r0 is .63mm. It is noted that for telescopes approaching or surpassing the aperture scale of LSST, the fine scale of the turbulence structure relative to aperture may become prohibitively small for the common phase-screen creation methods.

The power spectrum of the phase screens we obtained were measured at UCSC and are provided in figure 4 below.

Figure 4.Power spectrum and structure function of UCSC phase screens.

Such screens are created using an enamel-spray process on a 100mm diameter plastic disk, which is large enough for our pupil size with allowance for a spindle and dead space along the edge. This process is of course stochastic and the power

spectrum must be checked after production to confirm consistency with known turbulence models (namely that of Kolmogorov).

While the real atmosphere morphs form moment to moment, phase screen-based turbulence sources are of course static. The frozen-field approximation of atmospheric density variation asserts that a given frame of turbulence will be static over the time scale of the air's movement across the telescope's pupil; this makes a spinning disk an acceptable surrogate for true fluid turbulence.

We are also exploring alternative fluid-based methods of generating turbulence and have written several phase-screen generation programs to inform these efforts. Figure 5 provides example output of one such program, which uses a non-Fourier based method for generating the turbulence.

Figure 5. Simulated turbulence field (phase screen segment) from a non-Fourier monte-carlo based generation program

OPTICAL DESIGN

This apparatus can be divided into two modules: The atmosphere simulator and the telescope simulator.

Light from a single point source is collimated for phase-screen insertion and subsequently refocused using two identical off-the-shelf air-spaced acrhomats. This arrangement was selected for cost reasons. In its simplest form the second (decollimating) achromat would form an intermediate image to feed the telescope simulator, which is itself a point-projector requiring a point-source for input. In reality the telescope simulator (which we call the LSST Accurate Star Simulator Optic, or LASSO) must be fed by an input beam of faster numerical aperture than the output decollimator. An ideal design would incorporate a decollimator which would match the required input NA of LASP. Instead, we insert an additional off-the-shelf positive lens before the intermediate focus to compensate for the NA mismatch. This is effectively a focal reducer for the atmosphere simulator module. The free space in the vicinity of the intermediate focus is used to insert a beam splitter, where the unwanted wavefront degradation caused by introducing new surfaces is minimized.

A Thorlabs Shack-Hartmann wavefront sensor is used for real-time wavefront analysis. An additional collimator is placed before the wavefront sensor to minimize the need to remove the defocus term (sphere removal) in

the analysis software, as wavefront measurement accuracy is reduced for very divergent light with this sensor. A Canon photography lens is used here as the collimator.

The telescope simulator (LASSO, mentioned above) is meant to emulate the LSST beam for a single star to first order. That is, it creates an f/1.23 beam with a 65% obstruction. It has a flange focal distance of 53mm and can be tuned to compensate nearly completely for the spherical aberration induced by flat (vacuum) windows from 10 - 30mm in thickness. Being diffraction limited, we emulate the larger PSF expected in LSST by detuning and other means. While not fully explored, we believe it's possible to match the on-axis LSST PSF quite well.

Figure 6.Left to right: LASP optical design, mechanical design, and photograph.

The design is based on the Schwarzschild Objective, a well known form for microscope objectives. The traditional system consists of two spherical mirrors located concentrically whereby the convex surface is the primary mirror (M1) and the larger concave surface is the secondary mirror (M2). Introducing a vacuum window necessitated a variation on the design, and it was found that a positive lens could be used to negate the spherical aberration caused by the window nearly completely, at the expense of longitudinal chromatic aberration which is fairly severe but acceptable given the intended use of the optic. A nice characteristic of the design is that the source-M1 spacing can be used as a compensator for dewar window thickness so that dewar compatibility is assured. Design refinements led to a simpler configuration where M1 and the lens are merged.

As-measured and simulated PSF diagrams are given below, as well as a direct image of the projected spot (reimaged/magnified with a microscope objective) and a predicted vs. measured encircled energy diagram.

Figure 7.Top left: Simulated PSF, top right: measured PSFbottom left: magnified spot, bottom right: predicted and measured EE

We've recently combined the atmosphere and telescope modules to begin creating turbulence-aberrated star images. At present, only one phase screen is in use and is being driven directly with a gear motor. Proof-of-concept shot-exposure (<.1s) images have been obtained using a webcam-style CMOS video camera in place of an LSST CCD. Wavefront data and the corresponding Zernike decomposition (both in units of waves) has been obtained and are shown with images of the synthetic star in figure 8. Pixel pitch on this detector is 5μm.

Figure 8. Five stars (as imaged by LASSO) and their corresponding wavefronts and Zernike coefficients. Note scale changes.

Figure 9. Five stars reimaged/magnified by means of a microscope objective after passing through LASSO. The magnification is approximately 20X.