Post-Coronagraph Wavefront Sensor for Gemini Planet Imager

J. Kent Wallace*, John Angione, Randall Bartos, Paul Best, Rick Burruss,

Felipe Fregoso, B. Martin Levine, Bijan Nemati, Michael Shao, Chris Shelton

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109

ABSTRACT

The Gemini Planet Imager (GPI)1 will employ an apodized-pupil coronagraph to make direct detections of faint companions of nearby stars to a contrast level of the 10-7 within a few λ/D of the parent star. Such high contrasts from the ground require exquisite wavefront sensing and control both for the AO system as well as for the coronagraph. Un-sensed non-common path phase and amplitude errors after the wavefront sensor dichroic but before the coronagraph lead to speckles which limit the contrast2. The calibration wavefront system for GPI will measure the complex wavefront at the system pupil before the apodizer and provide slow phase corrections to the AO system to mitigate errors that would cause a loss in contrast.

Here we describe the low-order and high-order wavefront sensors that compose the calibration wavefront sensor, how they operate, and how their information is combined to form the wavefront estimate before the coronagraph. Detailed simulations that show the expected performance for this wavefront sensor will be described for typical observing scenarios. Finally, we will show preliminary lab results from our calibration testbed that demonstrate the operation of the key hardware.

Keywords: interferometry, wavefront sensing, planet detection, coronagraphy

1. INTRODUCTION Non-common path wave front errors, it not sensed and corrected, will set the limit for achievable contrast for a ground based AO system. These errors are particularly vexing due to their temporal evolution. If they were perfectly static, they could be measured once and subsequently removed in post processing. If they were perfectly random, they would average out to a smooth floor over long integrations. Non-common path errors that limit contrast tend to evolve over times scales of a few minutes to 10’s of minutes and therefore must be sensed and corrected during a science observation. The main goal of the calibration system for GPI is to sense these wave front errors and provide a measurement to the AO system so that they may be corrected. The most crucial wave front errors are those at spatial frequencies corresponding to the “dark hole” region of the PSF and outside the coronagraph’s inner working distance – 4-22 cycles per pupil. The calibration subsystem that will measure these mid-spatial frequency errors is called the high-order wave front sensor, HOWFS.

Many coronagraphs, including the apodized pupil Lyot coronagraph (APLC3) employed by GPI, are very sensitive to the location of the star on the focal plane mask – centering errors of as little as 3 miliarcseconds can begin to degrade contrast. As a separate task the calibration system will employ a low-order wave front sensor to establish the boresite of the instrument and ensure the centering is sufficient for achieving and maintaining high-contrast. This boresite will also be accurate and stable for precision astrometry. This calibration element is known as the low-order wave front sensor, or LOWFS, and will also measure the low-spatial-frequency wave front errors (e.g. focus) that the HOWFS is blind to.

*James.K.Wallace@jpl.nasa.gov; phone 1 818 393-7066; fax 1 818 393-3290; jpl.nasa.com

Adaptive Optics Systems, edited by Norbert Hubin, Claire E. Max, Peter L. Wizinowich,Proc. of SPIE Vol. 7015, 70156N, (2008)

0277-786X/08/$18 · doi: 10.1117/12.787258

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A description of the calibration subsystem is most easily accomplished by following the starlight path when encountering it. The system level drawing (Figure 1) will aide in this discussion. The light after leaving the apodized pupil converges to the focal plane to form an image at the focal plane mask. The light falling within the hard-edged focal plane mask will compose the reference arm, the light reflected will form the science arm, and the light that goes down both arms will meet again at the re-combination beamsplitter and be sensed at the HOWFS. The following discussion will then be in the same order: reference arm, science arm and HOWFS arm.

Fig. 1. Optical layout of the GPI calibration system. Light from the adaptive optics system enters from the top left,

passes through the apodized pupil to the focal plane that is located in the top-center of the drawing. The majority of the starlight passes through the focal plane mask and into the reference arm in the upper right of the diagram. Light that reflects off the focal plane mask heads to the science path in the lower left of the diagram. Both beams meet a the science re-combination beamsplitter and are sensed on the high-order wavefront sensor in the lower right portion of the image.

1.1 Cal System Optical Design

The calibration subsystem consists of two primary sub-elements: the high-order wave front sensor (HOWFS), the low order wave front sensor (LOWFS). This section will offer a description of the relevant parts of each sub-element, a description of the driving optical concerns and a ray trace of the sub-element. After a discussion of the optical design, we will review the simulation and predicted performance of the system.

1.2 Reference Arm

The starting point for the reference arm is the focal plane mask, or more specifically, the hole in the center of the focal plane mask. Several different focal plane masks are available in the focal plane mask occultor mechanism. The masks will be provided by our collaborators at AMNH while the mechanism is the responsibility of JPL. After the focal plane mask, the next optic is the reference arm recollimation OAP. This optic creates a five millimeter diameter beam. Next, the beam strikes the Tip/Tilt/Piston PZT mirror. This mirror plays several roles: 1) phase shifting for the high-order wave front sensor and 2) pointing correction for the pinhole spatial filter. The phase shifting is done in a collimated beam and all points in the pupil are shifted in phase equally

After the phase shifting mirror, the beam either passes through the beamsplitter to the LOWFS or reflects to the pinhole spatial filter. The LOWFS will be described below, so lets follow the path to the spatial filter assembly. This is the assembly that serves to remove residual wavefront errors on the beam such that the phase and amplitude of the

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reference beam electric field at recombination is largely uniform. The first OAP of the assembly forms a focus at the pinhole (currently sized to 1.4 λ/D, diameter, at 1.635 µm). The spatially filtered light passing through this pinhole is re-collimated by the second OAP in the assembly to roughly ten millimeters in diameter. Centering of the light on the pinhole is crucial for consistent, repeatable performance for the HOWFS. However, sensing where this beam is when it is even a little off from the pinhole is a challenge. To expedite the acquisition we have implemented what we call the pinhole camera which allows us to directly measure the starlight relative to the pinhole and thus expedite the co-alignment. Finally, we have a shutter in the reference arm that allows us to block the light. This option is necessary for allowing us to measure the transmission function of the input pupil apodizer and establishing detector darks without affecting the operation of the rest of the instrument.

1.3 Science Arm

For the science beam, the starlight suppression has just occurred at the focal plane mask, and the science re-collimation OAP creates a beam that is ten millimeters in diameter and parallel to the beam incoming to the focal plane mask (offset by 128 millimeters). A small portion of this light (roughly 20%, broadband) will pass through a spectrally-neutral, broadband beam splitter. This light will then pass through the science arm shutter (if it is open) and on to the recombination beamsplitter. The light that gets reflected from the science pick-off beam splitter heads to the pointing-and-centering mirror pair that feed the Integral Field Spectrograph (IFS). This mirror pair ensures proper image-plane and pupil-plane alignment between the calibration sub-system and the IFS.

1.4 High-order wavefront sensing arm

As mentioned previously, the optical layout of the HOWFS sub-element will begin at the location of the re-imaged pupil which occurs after the beams have been re-combined. This pupil is formed very near to vertex of the merge prism. Now, there are some optical matters that need to be addressed before the re-combination beamsplitter, and this is because the calibration HOWFS is a broad-band, white-light, phase-shifting interferometer. For the interferometer to perform properly, its internal optical paths, as a function of wavelength, from the point of separation at the focal-plane mask to the point of recombination must match to within a small fraction of a micron. This puts a constraint on the allowable dispersion (differential glass thickness) and DC phasing between the two arms of the interferometer. An interferometer is also sensitive to internal optical pathlength disturbances. In our case, these pathlength vibrations are only problematic when they are near the demodulation frequency. If they are at a higher frequency, they will average out during the integration time of a single measurement, while if they are slower, they will be frozen out. We have designed the optical beam height (and mechanical mounts) from the mounting surface to be small so as to increase any mount-related resonant frequency.

Since we’re working on a broadband astronomical instrument, atmospheric refraction is of necessity a concern. Left uncorrected, the residual atmospheric refraction will produce a chromatic smearing in the image plane and chromatic shear in the pupil plane. Both of these would have detrimental effects on the performance of both the LOWFS and HOWFS. An Atmospheric Despersion Corrector has been added to mitigate against these effects. All of these optical aspects have been addressed before the HOWFS relay.

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Fig. 2. Layout of high-order wavefront sensing arm of the calibration system. Two pupils, one each from the front and back of the re-combination beamsplitter are imaged at the plane in the upper-right of the drawing. The big lens images these pupils to infinity while forming an image in the focal plane. A re-collimation lens forms demagnified pupil images at its focus. A one-to-one lens relays this image to the final image plane.

The layout of the HOWFS optical relay is shown above in Figure 2. The pupil is traced from the upper right. The pupil size is ten millimeters in diameter and the separation is designed such that upon demagnification, the two pupil images are on separate readout quadrants of the InGaAs array. The HOWFS fold mirror redirects the light to the HOWFS pupil lens. This lens is designed such that the input pupil is located at the back focal length so it is imaged to infinity. At the front focus of this lens is located the anti-aliasing spatial filter. The HOWFS pupil lens is a triplet designed to give good, broadband imaging from 0.9 µm – 2.4 µm. The lens materials are common for the visible/near-infrared and the lens surface shapes are plano-spherical.

The next optical element is the pupil re-imaging lens. It is also a triplet based upon the design of the HOWFS pupil lens. In the space before this lens, the pupil is at infinity, so after this lens it is re-imaged to the back focal length and de-magnified to the size and separation that will occur on the final image plane. This pupil image is formed near the location of the warm chromatic filter this is advantageous as it makes the final image location of the focal plane array insensitive to the wedges in the warm chromatic filter.

1.5 Low-order wavefront sensor arm

In the reference arm of the calibration system, a real pupil image is formed approximately 75 millimeters after the LOWFS pick-off beamsplitter. The optical layout for the LOWFS, a traditional Shack-Hartman, is shown in Figure 3 below:

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Fig. 3. Optical layout of the low-order wavefront sensor or LOWFS. This image shows the light leaving the center of

the focal plane mask on the left. This light is re-collimated, reflects off the phase-shifting mirror, through a beamsplitter where the pupil is re-imaged. This pupil is relayed to form a real image on the lenslets. The lenslet array is just before the InGaAs array.

The two lenses are off-the-shelf and serve to compress the beam to the appropriate size for the lenslet array. The lenslet is also off-the-shelf and samples the pupil with an array of 7x7 subapertuers. These spots are then imaged directly onto the final Shack-Hartmann sensor. A geometrical optics analysis of this wave front sensor is only useful to get pupil locations and sizes correct. The sensor works by measuring tilts in diffraction PSF’s and has been modelled extensively and this work is described in the performance simulation section.

2. CALIBRATION SIMULATIONS AND SYSTEM PERFORMANCE The calibrator (CAL) system simulator, which is written in MATLAB, evaluates the field at phase screens corresponding to each element. The model is a wave-optics simulation, utilizing Fast Fourier Transforms (FFT’s) to provide Fraunhofer propagation. No near-field (Fresnel) propagation is performed in the current version of the simulation. The electric field at each plane is represented as a complex matrix and is calculated at each of the relevant inputs and outputs of the elements. The input field is taken to be a simple top-hat function with amplitude consistent with the magnitude of the star being simulated. A post-AO atmosphere simulated using the ARROYO4 adaptive optics package is then applied. Alternatively a test field at any given desired wavelength can be propagated starting from certain points of interest. Broadband phenomena are simulated by breaking up the input into multiple wavelengths and propagating each all the way to the detectors.

The two sensors of interest for the CAL system are the LOWFS and HOWFS.The (LOWFS) sees the light from low spatial frequency errors (<3 cycles/pupil) that goes through the focal-plane mask (FPM), and the HOWFS measures the mid-spatial frequency wavefront errors (4-22 cycles/pupil) from light reflected by the FPM. The quantity of interest is usually the electric field at the apodizer, which is at a pupil. Since this field is imaged at the focal plane and separated cleanly by the FPM, it is advantageous to estimate the field at the focal plane by each sensor, and stitch together the low spatial frequency aberrations estimated by the LOWFS with the mid-spatial frequency errors estimated by the HOWFS.

This section focuses on the simulation of the two primary sensors in the integrated model: the LOWFS and the HOWFS. After a brief description of each of these the performance results obtained so far are presented.

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2.1 HOWFS Simulation and Predicted Performance

In the CAL simulation phase and amplitude offsets are measured and (after combination with the complementary LOWFS measurements) the total phase offset is then applied to the GPI deformable mirror (DM); each HOWFS subaperture corresponds directly to a single element of the DM.

The HOWFS is tightly integrated into the wave-optics simulation of the Cal system. After the complex fields are split by the Focal Plane Mask and recombined at the final Cal beamsplitter, the HOWFS spatial filter is simulated using a hard-edged stop in Fourier space. The filtered images are then brought back into pupil space and imaged on the HOWFS detector. The simulated detector includes the effects of photon noise, read noise, and detector losses. Intensity is “lost” at the detector both from (1) a detector quantum efficiency (assumed at 0.75) and (2) the finite time required to reset and read the focal plane array – approximately 5 msec per read and 10 msec per reset. An example of a set of HOWFS ABCD measurements is shown below.

Fig. 4. Images of the four phase-shifted intensities as measured by the high-order wavefront sensor or HOWFS. These

intensity measurements form the heart of the HOWFS measurement. Pairs of images are differenced, scaled and normalized to given the resultant phase and intensity estimates.

Fig. 5. Expected performance for the HOWFS detector. These plots predict performance based upon photon noise, read

noise and dark noise for an InGaAs camera working at 60 Hz. Results for a 5th magnitude star are shown on the left while results from an 8th magnitude star are shown on the right. The largest noise source is dark-current.

2.2 LOWFS Simulation and Predicted Performance

The LOWFS is a Shack-Hartmann sensor with a 7x7 array of square lenselets and a COTS InGaAs CCD detector. The purpose of the LOWFS is to measure the low-order wavefront errors in the field at the apodizer. Of the various modes the most important are tip, tilt and focus. However, the focal plane hole is sufficiently wide as to allow Fourier modes up to about 2.5 λ/D through, depending on the band selected. Thus, a significant aspect of the LOWFS simulation effort is geared towards getting the most out of the LOWFS in terms of information about the low-order field.

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The geometry of the LOWFS detector active area assigned to each lenselet is shown in two alternative forms in the figure below: a 2x2 pixel area used as a quad cell or a 5x5 pixel area used in normal camera mode.

Fig. 6. Sensing geometry for the LOWFS. The transmission function of the apodized pupil results in non-uniform

illumination of the quad cells. We have explored sensing geometries of 2x2, 4x4 and 5x5 pixel configurations. The default is 5x5 given it has the largest linear range.

In quad cell mode, for each spot, four measurements (labeled A though D in the figure) give the electron count over each subaperture. The signals collected are the X and Y moments and the total detected signal from each subaperture:

Fig. 7. Tip/Tilt performance of the LOWFS on sky. These plots show the distribution of tip/tilt error on the LOWFS for

single-frame estimates and a range of representative input wavefronts. This simulations include photon, read and dark noise. The plot on the left is for a 5th magnitude star while that on the right is for an 8th magnitude star.

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Fig. 9. Predicted performance of the LOWFS for modes other than tip/tilt for an 8th magnitude star. The requirement is

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3. CALIBRATION TESTBED RESULTS In order to test the principles of calibration wave front sensing, we have constructed a testbed. This testbed has source optics which have a pupil and image plane conjugates that map directly to those that will be on the GPI instrument. The testbed system itself is a fully functional duplicate of the final GPI calibration system with both a HOWFS and a LOWFS. We will use this testbed to demonstrate algorithms and performance for wave front control at levels consistent with those for the final GPI calibration system. We will also be able to explore sensitivity, accuracy and systematic effects that set the limit on measurement accuracy.

A schematic of the testbed is shown below in Figures 10 and 11. The coronagraph of choice for this setup was the apodized-pupil Lyot coronagraph asit will be used for the starlight suppression system for the Gemini Planet Imager Project. The source optics are shown in the upper-center and left side of the drawing. The testbed instrument itself is shown in the lower right. The testbed is now fully assembled and aligned, and we are getting some preliminary measurements from the coronagraph, the HOWFS and the LOWFS.

Fig. 10. Layout of the calibration testbed. The source optics are shown in the upper-center and left side of the drawing.

The cal instrument itself is shown in the lower right. The cal testbed instrument is a duplicate of the optical system that will be used on Gemini.

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3.1 Cal LOWFS Testbed Results

The current status of the LOWFS wavefront sensor is shown below. The hardware is fully assembled and aligned. Indeed, this hardware will be used on the final GPI instrument. We have a functioning reconstructor and have demonstrated sensing of low order aberrations in the lab. The next steps involve refinement of the reconstruction algorithm by improvements to the flat-field and dark correction.

Fig. 12. Preliminary low-order wave front sensor results. The Shack-Hartman camera is shown on the left while the

image on the right shows the response of the LOWFS pixels. The transmission function of the apodized pupil is clearly evident in the illumination of the 2x2 spots.

3.2 Cal HOWFS Testbed Results

We have phased up the calibration interferometer and we’re taking measurements with the HOWFS camera. The interferometer is working fully broadband, with no optical bandpass filter. In nominal operation, there is no light in the science beam path, therefore, there is no signal. In order to phase up the interferometer, we had to misalign the instrument such that some light went down each arm. After this was established, we were able to get sufficient contrast and phase up. A pathlength scan of the fringes is shown below in Figure 13 (on the left) and a pupil image showing the whitelight tilt fringes is shown in Figure 13 on the right.

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Fig. 13. These images illustrate the white light fringe in the high-order wavefront sensor. The image on the left is the

response of a single pixel as a function of optical delay in the reference arm. The image on the right shows the white light fringes as taken on the HOWFS. Each arm was nearly equally illuminated by placing the point-spread function just at the edge of the focal plane mask. Images are taken completely broadband with a thermal source and no filter save the response of the InGaAs array.

In nominal operation of the cal system, the light on the HOWFS is completely dominated by the bright light in the reference arm. There is, in fact, very little contrast in the signal. The is illustrated in the images below that show the image on the HOWFS with the apodized pupil in place. The image on the right is with the dominant light from the reference arm removed. The residual fringe pattern is due to a combination of residual phase and amplitude errors. The demodulation of these fringes with the path length modulation will allow us to solve for each of these separately.

Fig. 14. Preliminary results from the GPI Cal HOWFS. The image at the left shows the raw interference image, while

the image on the right is the same image with the DC off-set of the reference arm removed.

4. CONCLUSION A method to suppress image plane speckles for planned and future planet-finding instruments has been described. This method is implemented as a calibration wavefront sensor that is composed of both a low-order, Shack-Hartman sensor and a high-order interferometric sensor. This calibration wavefront sensor has been designed for use with the Gemini Planet Imager (GPI) instrument. A laboratory experiment that is nearly identical to the GPI Calibration wavefront sensor has been build to demonstrate this method. The testbed, as described above, is assembled and providing early results of both key wavefront sensing elements. This testbed work forms the heart of the calibration system for the Gemini Planet Imager: GPI.

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5. ACKNOWLEDGEMENTS This work was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This work has been supported in part or full by the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz under cooperative agreement No. AST-9876783.

REFERENCES

[1] Bruce Macintosh, et. al., “The Gemini Planet Imager: from science to design to construction”, Proc SPIE, Astronomical Telescopes and Instrumentation, these proceedings. [2] S. Shaklan and J.J. Green, “Low-order Aberration Sensitivity of eighth-order coronagraphic masks”, ApJ, 628, 474-477 (2005). [3] R. Soummer, C. Aime, and P.E. Falloon, , ”Stellar coronagraph with prolate apodization”, A&A 397, 1161-1171 (2003). [4] Matthew C. Britton, “Arroyo”, Proc. SPIE, Integrated Modeling of Extremely Large Telescopes, Vol. 5497, 290 (2004)

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