Abstract

Sodium laser guide stars (LGSs) allow, in theory, Adaptive Optics (AO) systems to reach a full sky coverage, but they have their own limitations. The artificial star is elongated due to the sodium layer thickness, and the temporal and spatial variability of the sodium atom density induces changing errors on wavefront measurements, especially with Extremely Large Telescopes (ELTs) for which the LGS elongation is larger. In the framework of the Thirty–Meter–Telescope project (TMT), the AO-Lab of the University of Victoria (UVic) has built an LGS–simulator test bed in order to assess the performance of new centroiding algorithms for LGS Shack-Hartmann wavefront sensors (SH–WFS). The design of the LGS–bench is presented, as well as laboratory SH–WFS images featuring 29×29 radially elongated spots, simulated for a 30–m pupil. The errors induced by the LGS variations, such as focus and spherical aberrations, are characterized and discussed. This bench is not limited to SH–WFS and can serve as an LGS–simulator test bed to any other LGS–AO projects for which sodium layer fluctuations are an issue.

©2008 Optical Society of America

1. Introduction

Laser guide star (LGS) adaptive optics (AO) systems allow, in theory, full sky coverage opening new investigation fields in astronomy, but have their own limitations. The atmospherical tilt cannot be determined from a LGS [1] and the AO correction is incomplete because of the finite distance of the LGS. This issue, referred to as cone effect [2], can be overcome by using an asterism of several LGSs.

Other difficulties appear when using a sodium LGS for two main reasons. Firstly, the artificial star is not a point-like source but an extended source along the laser beam axis due to the sodium layer thickness. The angular source size is proportional to the distance from the laser beam axis and can reach several arcseconds for Extremely Large Telescopes (ELTs) (Eq. (1)). Secondly, the sodium layer is not static but ever-changing. The mean altitude fluctuates, as well as the thickness and the atom density vertical profile, with a time-scale of about one minute or less [3]. This temporal variability induces changing errors in wavefront measurements, especially with ELTs, for which the source elongation is larger [4].

Fluctuations of sodium layer mean altitude induce a focus error which can be almost cancelled by closed-loop focus tracking using a Natural Guide Star (NGS) wavefront sensor (WFS), zoom optics and electronic offsets. A zoom optics focus loop is already implemented on the Keck LGS-AO system [5], and optical focussing plus electronic slope offsets are planned for NFIRAOS, the LGS-AO facility of the Thirty-Meter-Telescope (TMT) [6]. Despite that correction, a residual focus and higher mode error, referred to as LGS aberrations [7], remains and affects the final performance of the AO system.

The image of a sodium LGS provided by a Shack-Hartmann (SH) WFS features an array of radially elongated spots whose size and intensity profile fluctuate. As these fluctuations affect the position of the centroid of each spot, the classical Center of Gravity (GoG) centroiding algorithm is no longer suited for sodium LGSs. New centroiding algorithms are under study to mitigate LGS aberrations with SH-WFSs, such as the matched filter [8] or the correlation [9, 10]. Radial CCD arrays are also under development [11] to reduce the number of required pixels and improve the read-out speed and the signal-to-noise ratio (SNR).

In the framework of the TMT project, the AO-Laboratory of the University of Victoria, BC, Canada, has built an LGS-simulator bench in order to assess the performance of wavefront sensing algorithms when using sodium LGS SH-WFS, in particular the matched filter centroiding algorithm planned for NFIRAOS.

This paper presents the requirements and the general principle of the LGS-bench simulator in sections 2 and 3 respectively. Section 4 describes the design of the bench built in our laboratory. Section 5 presents the first results obtained with the LGS-bench. Lastly, section 6 discusses the sources of LGS aberrations measured on the bench.

 

Fig. 1. (Color online) (a) SH-WFS spots geometry for the TMT pupil pointing an LGS at zenith. (b) The radial elongation of the spots can be reproduced in the laboratory with a DM generating an alternating defocus during the integration time. The source intensity is modulated synchronously with the DM to also reproduce sodium profile variations.

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2. Requirements for the LGS-bench

The main goal of the LGS-bench is to reproduce, in the laboratory, a LGS-like source as seen by the TMT LGS SH-WFS. Since the laser beam will be launched from behind the secondary mirror of the TMT, the spots of the LGS SH-WFS image will be radially and symmetrically elongated from the pupil centre (Fig. 1(a)). The angular elongation θ can be approximated as:

θrσNah02cos(z),

with r the distance of the SH subaperture from the pupil centre, h 0≈90 km and σNa≈10 km the typical sodium layer mean altitude and thickness, and lastly z the zenith angle. As 60×60 subapertures are planned for the NFIRAOS LGS SH-WFS, r=14.75 m for the subapertures located on the pupil edge. Consequently, the radial size of most elongated spots is θ=3.76″ at zenith.

The azimuthal size of spots is the full width at half maximum (FWHM) of a non-elongated spot (i.e. seen from the pupil centre) which is defined only by the upward turbulence, i.e. 1″ typically. This size can vary but it is totally independent of the sodium layer properties and will not affect much the LGS aberrations seen by the WFS. Only the typical size is considered for the bench design. Thus, the angular size of most elongated SH spots is about 1″×4″, i.e. 2×8 pixels with the image sampling planned for the NFIRAOS LGS SH-WFS camera.

The mean focus error induced by the variation of the mean altitude of the sodium layer will be measured with a NGS tip/tilt/focus WFS, and corrected thanks to zoom optics. This focus tracking loop has to be implemented on the LGS-bench too, in order to be, as much as possible, in the same conditions as the NFIRAOS SH-WFS.

Lastly, to distinguish the wavefront errors induced by the sodium layer fluctuations from those induced by the atmospherical turbulence, the matched filtering requires a sub-pixel periodic tip-tilt dithering signal that the bench has to reproduce too.

In summary, the bench has to reproduce in laboratory the following features:

  • the spot radial elongation due to the sodium layer thickness, with 2×8 pixels for the most elongated spots,
  • the spatial and temporal variability of the sodium layer (mean altitude, thickness and vertical profile),
  • the focus tracking loop planned in the NFIRAOS design to follow the sodium layer mean altitude variation,
  • the dithering tip-tilt signal required by the matched filter algorithm,
  • the residual atmospheric turbulence.

Although the NFIRAOS SH-WFS will provide 60×60 subapertures, we choose to start with only 29×29 subapertures on the bench (a larger camera is required to reproduce 60×60 spots), but the spot elongation is the same as for a 30 m-diameter pupil. Moreover 29×29 spots are enough to characterize high-order LGS aberrations induced by sodium layer fluctuations, as well as to compare performance of centroiding algorithms.

3. Principle of the bench

3.1. Reproduction of the LGS elongation

To mimic a LGS, the bench does not need to create a real distant extended source. It is sufficient to reproduce only the final effects of LGS elongation on the SH-WFS image plane. The camera of the bench must simply see 2×8 pixel elongated spots to be in a NFIRAOS-like case.

On the bench, the angular extent of spots is given either by the source size, or by λ/d, with λ the wavelength and d the SH-WFS lenslet diameter, depending if the source is resolved or not. In both cases, the spot blurring function is not a speckled pattern as for the real LGS, but the geometrical shape of the source or an Airy pattern, respectively. We assume that the blurring function profile has negligible effects on centroiding performance compared to those induced by the spot elongation and the sodium layer fluctuations. For convenience, we chose to work with a non-resolved source.

The basic idea of the bench is to reproduce the spot radial elongation of an LGS SH-WFS image by defocusing and refocusing a collimated beam during the integration time of the camera (Fig. 1(b) and Fig. 2); the source intensity is modulated during this time to reproduce a given sodium atom density profile. To understand this trick, let us review SH-WFS basics. A SH-WFS consists of a lenslet array, located in a pupil plane, followed by a detector in an image plane. Each lenslet forms, on the camera, a spot whose the position is related to the local slope (i.e. the derivative) of the wavefront. If a focus aberration is introduced, the wavefront becomes paraboloidal, and then, the position of a spot becomes proportional to the distance from the pupil centre to that spot. For this reason, a variable focus aberration stretches the spot along the radial direction, and the spot elongation is proportional to the radius.

3.2. Required focus stroke

The wavefront slope ξ, induced by defocus and seen by a lenslet on the pupil edge, should be equal to the half angular radial size of the spot (the elongated spot is assumed to be centred on the lenslet axis). That implies for a non-resolved source:

ξ=±E2λd,

with E the dimensionless elongation ratio of spots (i.e. the radial size divided by the azimuthal size).

The phase induced on the lenslet array plane by a focus aberration is:

ϕ(ρ)=Aptv(ρρ0)2,

with ρ the distance, of a lenslet, from the pupil centre, ρ 0 the radius of the pupil, and Aptv the peak-to-valley (ptv) amplitude of the focus. Then the wavefront slope seen by a lenslet on the edge of the pupil is:

dϕdρρ=ρ0=2Aptvρ0.

At last, the required focus stroke for the LGS-bench is found by equating Eq. (2) and Eq. (4):

Aptv=±Eλ8Nspot,

with Nspot=2ρ 0/d the number of lenslets across the pupil diameter.

Typically E≈4 for the TMT and for a 10 km-thick sodium layer (Eq. (1)), but thicker layers are possible. So, it is more prudent to consider the largest possible spot elongation, which is given by the WFS field of view (FOV). Actually, the NFIRAOS SH-WFS FOV will be limited by a field-stop to 8″, which matches the 16 pixel subaperture size, in order to avoid spot overlaps. This FOV corresponds to a 20 km altitude range for sodium layers, and implies E=8. Then, from Eq. (5) the recommended focus range for the bench is Aptv=±18.4µm with λ=0.635µm and Nspot=29.

Such a focus amplitude could be generated by a variable curvature mirror. But we prefer to use an high-stroke deformable mirror (DM), which can also generate the dithering tip-tilt signal required by the matched filter algorithm, as well as some residual turbulence.

3.3. Sodium profile generation

Figure 2 shows a possible control sequence for generating elongated spots whose the intensity profile matches a given sodium density profile. TheDMis calibrated in order to generate a focus staircase from +18.4 to -18.4µm ptv in 41 discrete steps (Sec. 4.3). Then, an elongated spot is made from the sum of 41 elementary spots (diffraction-limited) spread over 16 pixels (i.e. 2.56 spots per pixel, which meets the Shannon sampling theorem). As the focus stroke corresponds to a 20 km-thick sodium layer, the average altitude resolution for reproducing sodium profiles is 20/(41-1)=0.5 km per focus step. The central focus position (flat DM) corresponds to the central altitude of the sodium layer (h 0≈90 km), while the first (resp. last) focus position (i.e. +18.4µm, resp. -18.4µm) corresponds to the bottom (resp. top) of the sodium layer. Due to a projection effect, the relationship linking altitudes with the elementary spot positions (i.e. focus positions) is not exactly linear but scales as a tangent law. After some straightforward trigonometric calculations, the altitude h(p) corresponding to the pth elementary spot can be approximated as:

h(p)h01r2h03pΔe1+1h0pΔe,

with p an integer varying from -20 to +20, Δe=0.5km the average altitude step, h 0=90 km the mean sodium layer altitude, and r=14.5m the distance from the TMT pupil centre to a SH-WFS subaperture on the pupil edge (for the 29×29 subaperture case).

 

Fig. 2. (Color online) Control sequence of the DM, the source and the camera generating elongated spots for a given sodium profile. The DM generates a focus staircase from +18.4 to -18.4µm ptv with 41 discrete steps. The camera exposure begins with the first focus position. The source intensity is updated for each focus position to reproduce the sodium profile. The source is turned off between two steps to prevent the DM transient response from blurring the spot (Sec. 5.2). The camera exposure ends with the last focus position, and the DM goes back to the first focus position during the image acquisition in order to be ready for the next image.

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4. LGS-bench design

4.1. Optical layout of the bench

Figure 3 presents the optical layout with some key-parameters (image and pupil size, etc.) used for the current version of the LGS-bench. A picture of the bench is also shown in Fig. 4. The main components of the bench are a laser diode, a 52 actuator DM, a lenslet array and a CCD camera.

The source is the output of a 5µm core optical fibre lighted by a 635 nm wavelength laser diode. The beam is collimated onto a 15 mm diameter DM. This DM, manufactured by ALPAO, consists of 52 voice-coil actuators aligned on a 8×8 square grid, with a 100µm stroke on the wavefront. This stroke is large enough for generating the required alternating focus.

After the DM, a pair of lenses (referred to as beam reducer on Fig. 3) forms a pupil plane on the lenslet array and shrinks the beam to match the detector size. A 188µm pitch and 8 mm focal length lenslet array (from Adaptive Optics Associates) forms the 29×29 spot image which is relayed by a lens to the detector plane at a reduced scale in order to meet the sampling requirement (FWHM=2 pixels).

The detector is a Firewire Point-Grey-Research Dragonfly Express CCD camera with 640×480 pixels, each 7.4µm square. The camera response is linear when the gain is manually controlled.

 

Fig. 3. (Color online) Optical design of the LGS SH-WFS simulator bench, and key-parameters (pupil size and image sampling) used for generating 29×29 elongated spot SH-WFS images (Fig. 8).

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Fig. 4. (Color online) Picture of the LGS-bench.

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Fig. 5. (Color online) Control architecture of the LGS-bench. The bench control system can be subdivided into 4 tasks: (i) Source intensity modulation: A 16 bit analog output PCI DAQ-card (UEI PowerDAQ PD2-AO-8-16) drives the current of the source. (ii) DM control: A second PCI DAQ-card (Adlink PCI-7200) drives the DM actuators via the ALPAO-DE64 controller. (iii) Camera control: The camera must begin and end integration at varying time intervals, depending on the DM state, therefore it has been configured to be triggered externally. The UEI PowerDAQ PD2-AO-8-16 is also used for sending the trigger signal toward the camera, which sends back a strobe signal to confirm that the trigger has been successfully received. (iv) Image acquisition: The image readout is performed via a 9 pin Firewire cable and a fast PCI frame grabber (IEEE-1394b OHCI PCI Host Adapter 3-port 800Mb/s card).

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4.2. Bench control system

The key point of the LGS-bench is the control system. Actually, the control of the DM, the source and the camera should be perfectly synchronized in order to properly reproduce a given sodium profile (Sec. 3.3).

The bench hardware is fully controlled from one PC (Windows OS) with Matlab. To run faster, the drivers for the DM and the camera are two specific C-mex functions called from Matlab. Wavefront analysis is also performed within Matlab using the UVic AO library routines. Figure 5 sketches and details the whole control system of the LGS-bench.

4.3. Calibration of the DM

The DM was calibrated in closed-loop with the SH-WFS of the bench for the 41 required focus steps (Sec. 3.3). These 41 calibrations were automatically launched with a Matlab script. For each calibration, the reference for centroids is directly the position of the corresponding elementary spot. Then the calculation of the phase is not necessary for calibrating the DM in focus.

These closed-loop calibrations provide 41 actuator voltage arrays which are stored in a file. This sequence of voltage arrays will be played back later in open-loop for generating elongated spots. As the DM is very repeatable, the calibrated voltages remain valid for 2–3 weeks. For the 8 outer focus steps (4 on each side), the spots reach the image boundaries, and then the closed-loop calibration fails. To overcome this issue, the voltage arrays of outer focus steps are extrapolated from others.

 

Fig. 6. (Color online) Peak-to-valley residual wavefront errors (in tip-tilt, residual focus, astigmatism, coma and spherical) of closed-loop calibrations of the DM for 41 discrete focus amplitudes.

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Figure 6 shows the residual errors of the calibrations. Extrapolated focus positions could be ignored since they produce higher wavefront errors, and do not contribute much to the final elongated spot image (the sodium layer usually emits few flux at these altitudes). But, we choose to keep the extreme focus positions to be able to reproduce a 20 km-thick sodium profile and to mitigate as much as possible any truncation effect (Sec. 6).

At last, the DM was also calibrated in 4 discrete tip-tilt positions (±0.1 pixel in x and y) for generating the dither signal required by the matched filter algorithm. Smaller tip-tilt amplitudes can be generated by interpolation.

4.4. Focus tracking loop

A focus tracking loop is planned for NFIRAOS to cancel out the focus error induced by the variation of the zenithal angle and by the fluctuation of the sodium layer mean altitude (Sec. 1). No hardware is required for implementing this focus loop on the bench. Actually, it is sufficient to measure the focus error from the SH-WFS, then, convert this focus error into altitude difference, and shift (numerically by software) the sodium intensity profile for the next image.

4.5. Tip-tilt correction

A closed-loop tip-tilt correction is also implemented on the bench in order to automatically recentre the spots on the SH-WFS camera before recording a new image. This tip-tilt correction tracks the slow thermal drift of the bench (mainly due to the camera box expansion).

 

Fig. 7. (Color online) Sequence of 88 real sodium profiles used for generating LGS-like SH-WFS images on the bench. Time resolution is 70 s, altitude resolution is 25 m (file TMT.AOS.TEC.07.005_Nap).

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5. Bench results and performance

5.1. First images

The data containing the sodium profiles come from a time series of 88 real profiles measured by the Colorado State University LIDAR and used within the TMT consortium as a benchmark (Fig. 7). A sample of SH-WFS image obtained with the bench for one sodium profile is displayed in Fig. 8. The intensity profile of most elongated spots are in good agreement with the projected sodium profile. The global brightness of the spots decreases from pupil centre to the edge because of the elongation. It is also the case for a real LGS, but this brightness decreasing is slightly exaggerated on the bench because of the gaussian profile of the incoming beam (there are about 30% more flux on the centre than on the edge of pupil).

5.2. Profile generation speed

The generation and the acquisition of one elongated-spot SH-WFS image lasts 0.11 s for 10 km-thick sodium profiles, and 0.17 s for 20 km-thick profiles. A wavefront analysis (centroid and Zernike computation) lasts 0.15 s with Matlab. Thus the bench can generate and analyze four LGS SH-WFS images per second. This speed was fast enough for characterizing the LGS aberrations in the laboratory, but a higher speed will be required to generate also some residual atmospherical turbulence. Wavefront analysis could be written in C to run faster. But the speed is also limited by the transient response of the DM, which blur the spots if the DM is driven faster. Actually, the DM is controlled in open-loop and receives a sharp step-shaped command in focus, containing high frequency harmonics which can stimulate the DM eigenmode. To avoid this issue and to be able to run the DM much faster, the DM manufacturer recommends to smooth the command or, ideally, to invert the transfer function of the actuators. This upgrade, which affects only the software, is planned for the next phase of the bench development.

 

Fig. 8. (Color online) 29×29 elongated spot SH-WFS image obtained in laboratory. Spot sampling is 2×8 pixels on the edge of the pupil (for a 10 km-thick sodium profile) as for NFIRAOS (see enlarged spots). The sodium profile used for this image is the 87th profile of the LIDAR sequence (Fig. 7). The solid curve shows the intensity profile sent to the source (i.e. the projected sodium profile sampled over 41 altitude bins). The dashed curve shows the theoretical profile for a spot located on the edge of the pupil (i.e. the source intensity profile convolved by the PSF and resampled over 16 pixels). The measured spot profile (filled circles) perfectly matches the theoretical spot profile, except for the pixel 16 where the spot overlaps with another.

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Fig. 9. (Color online) Wavefront analysis made with the 29×29 spot SH-WFS of the bench, using the CoG centroiding algorithm for 4 different configurations: (I) with non-elongated spot images to assess the bench stability, (II) with static uniform 10 km-thick sodium profile to check the DM repeatability, (III) with variable sodium profiles without focus tracking to highlight the focus error induced by sodium layer variation, (IV) and with focus tracking to characterize the higher-order LGS aberrations. The temporal mean values and standard deviations of centroids and Zernike modes (ptv amplitude) were computed from a time sequence of 700 SH-WFS images for cases I/II, and from a sequence of 88 real sodium profiles for cases III/IV. The phase reference is a flat wavefront for cases I/II and a uniform 10 km-thick sodium profile SH-WFS image for cases III/IV.

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5.3. Bench stability and static errors

5.3.1. Wavefront analysis procedure

Before performing wavefront analysis with changing sodium profiles (Sec. 5.4), the intrinsic performance of the bench has to be known. For this purpose, SH wavefront analyses were made using the classical CoG centroiding algorithm for 2 different “static” configurations:

  • (I) with non-elongated spot images (NGS case) to assess the bench stability and residual jitter,
  • (II) with a uniform 10 km-thick sodium profile to check the bench repeatability and its ability to generate elongated spots.

For both cases, the tip-tilt correction is turned on, and the phase reference is a flat wavefront (centroid references are all zeros). Temporal mean values and standard deviations of centroid measurements are calculated from a sequence of 700 images. The same processing is also done for the reconstructed phase, in term of Zernike coefficients [12] estimated from centroids by a least-squares fitting. The phase amplitude of each Zernike mode is calculated in peak-to-valley (ptv) to make easier the comparison of different modes. Then, a temporal standard deviation of a sequence of ptv amplitudes will be expressed in this paper as nm ptv rms, by convention.

The maps of centroiding noise are displayed in Fig. 9. σx and σy denote the noise along the x and y directions respectively, while the quantity (σ 2 x+σ 2 y)1/2 highlights the dependency of the noise with the distance from the pupil centre. The 28 first Zernike modes are also plotted. Mean values correspond to static aberrations, while error bars provide the temporal fluctuation (±σ) of each mode. Table 1 summarizes the results and give the fluctuations for tip-tilt, focus and higher order modes.

5.3.2. Results with static non-elongated spots

With non-elongated spot images, the mean centroiding accuracy is 0.009 pixel rms and varies from 0.007 pixel rms, for the pupil centre, up to 0.011 pixel rms for the edge. This slight radial variation of the error is due to the intensity profile of the incoming beam. The beam features a gaussian profile and then the SNR is greater for the central spots. An average centroid error around 0.01 pixel rms is consistent with the theoretical value σc≈FWHM/SNR given for gaussian spots and photon-noise limited images [13]. Actually, FWHM=2 pixels and SNR≈150 on the bench. For the reconstructed phase, the total static errors reaches 110 nm ptv, mainly due to astigmatism (Z5) and trefoil (Z10), with a total fluctuations around 12 nm ptv rms.

5.3.3. Results with a static uniform sodium profile

When a static uniform 10 km-thick sodium profile is generated, the centroiding error is still 0.007 pixel rms on the centre but reaches 0.028 pixel rms on the edge, with a mean value of 0.016 pixel rms. This strong loss of accuracy from the centre to the edge of the pupil can be explained by the previous expression of σc (even if the elongated spots are not gaussian). Actually, the radial elongation spreads the flux over 8 pixels (i.e. increases the radial FWHM) and, consequently, decreases the SNR of each spot. This radial centroiding error induces on wavefront measurements a significant error in focus (26 nm ptv rms), while the accuracy for the higher order modes remains below 3.5 nm ptv rms (Table 1). It’s important to note that a static sodium profile already induces a focus error 10 times greater than non-elongated spots.

Lastly, the total static errors reach now 195 nm ptv on the reconstructed wavefront (mainly due to astigmatism, trefoil and spherical).

Tables Icon

Table 1. Typical temporal RMS fluctuations of the phase measured on the bench for the 4 configurations described in Fig. 9. σϕ is the ptv amplitude noise of the wavefront for all modes. σTT, σ Z4 and σHO are respectively the ptv amplitude noise for tip-tilt, focus and higher order modes. All values are in nm ptv rms.

 

Fig. 10. (Color online) Global tip versus global tilt for a time series of 352 (88×4) SH images with a 1/100th pixel dither signal (4 discrete positions) for non-elongated spots and for elongated spots (i.e. for sodium profiles). A similar dispersion pattern (inside each discrete position) is also obtained without dither signal.

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5.3.4. Result analysis

Achieving the theoretical centroiding accuracy with non-elongated spots over a long time means that the tip-tilt correction loop successfully tracks the bench thermal drifts. But such a stability is necessary to be able to generate and measure the sub-pixel tip-tilt dither signal required for the matched filtering algorithm. This algorithm will likely require a 10 milliarcsecond dither signal, i.e. 0.02 pixel. Figure 10 shows a dither signal sequence featuring half this amplitude, i.e. 0.01 pixel, which is the most stringent case since the accuracy of the bench is 0.01 pixel too. For elongated spots, the tip-tilt dispersion appears wider along one direction only. Such a non-symmetrical tip-tilt dispersion likely means that this tip-tilt noise come from the DM motions, rather than from the WFS photon noise which is radially symmetrical. Actually, the transient motions of the DM or the vibrations induced on the mirror holder can generate such a blurring. A smoother control of the DM, as proposed by the manufacturer (Sec. 5.2) should reduce the noise coming from the DM motions. Anyway, this noise remains comparable to the ultimate bench accuracy, since the centroid error for central lenslets is 0.007 pixel rms both for elongated and non-elongated spots.

The presence of absolute static errors in both cases means that the bench state has changed since the last calibrations of the DM. Moreover, these static errors are slightly greater for non-elongated spots (the total error is 195 nm ptv instead of 110 nm ptv), meaning that the spot elongation or the DM motions generate small systematic static errors, such as astigmatism (Z6) and spherical (Z11) aberrations. As the spot elongation is radially symmetrical, Z6 is likely due to the DM, while Z11 is certainly inherent to spot elongation and is a LGS aberration (Sec. 6). Anyway, residual static or quasi-static aberrations are not really an issue for LGS-AO systems since they can be measured with the NGS WFS, and then corrected by adjusting the centroid references. For this reason, the rest of the paper deals only with differential errors induced by sodium layer temporal variation. Therefore, the phase reference used on the bench for the wavefront analysis with variable sodium profile is now a 10 km-thick uniform profile image.

 

Fig. 11. (Color online) (a) Correlation between the mean altitude of 88 sodium profiles and the focus error measured on the bench for each profile, without focus tracking (config. III). (b) Correlation between the sodium profile asymmetry (Eq. (7)) and the spherical aberration (Z11) measured on the bench, with or without focus tracking (config. III or IV).

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5.4. Results with variable sodium profiles

This section presents SH wavefront analysis done for two “dynamic” configurations:

  • (III) with variable sodium profiles and the focus tracking turned off in order to measure the whole phase errors induced by the sodium layer fluctuations,
  • (IV) with variable sodium profiles and the focus tracking turned on to be in the NFIRAOS-case and to characterize the higher order LGS aberrations.

Sodium profiles come from a time series of 88 real profiles (Fig. 7). Figure 9 and Table 1 present also the results for these two last configurations.

Without focus tracking, the centroiding error spreads from 0.01 pixel rms for central (non-elongated) spots to 0.27 pixels rms for most elongated spots with a mean value of 0.18 pixels rms. This radial noise is mainly due to the variation of the mean altitude of the sodium layer, which induces a huge focus error (σ Z4=498 nm ptv rms). The correlation between the mean altitude of each profile and the induced defocus is clearly visible on Fig. 11(a).

This fluctuating focus error can be reduced to 45 nm ptv rms thanks to the focus tracking loop. A low gain (0.15) and 20 to 30 iterations (on the same sodium profile) were required to achieve this accuracy. Such a closed-loop behaviour is likely due to a profile truncation effect which adds some noise. Actually, only 20 km of the sodium layer are seen by the SH-WFS. Consequently, when elongated spots are recentred after a focus correction, a part of the unseen lower or upper tail of the sodium profile appears in the SH-WFS camera and will induce a new focus error on the next frame.

The higher order modes are largely dominated by the spherical aberration (Z11). Sodium profile variations induce a fluctuation of about 40 nm ptv rms for Z11, with or without focus tracking (Fig. 9), 12.5 nm for Z21 (pentafoil), 11 nm for Z14 (tetrafoil), 9 nm for Z17 (5th order coma), Z20 (pentafoil) and 6.7 nm for Z22 (5th order spherical). All other mode fluctuations remain below 5 nm ptv rms, close to the ultimate bench accuracy for higher modes.

6. Characterization of LGS aberrations

6.1. Origins of LGS aberrations

According to a model from [7], when the laser is projected from the pupil centre, the LGS aberrations are centro-symmetric, as Z11 and Z22, and square symmetric, as Z14 and Z26. The most probable origins for centro-symmetric aberrations are:

  • the asymmetry of the spot elongation, due to a projection effect (Eq. (6)) or to an asymmetry of the sodium profile itself,
  • the truncation of the LGS spots by a circular field-stop,
  • the telescope and AO system (as the LGS is not at infinity, some aberrations arise when LGS light pass through the whole optical train),

while square symmetric aberrations are likely due to:

  • LGS spot truncation by a square field-stop or by pixel boundaries (horizontally and vertically elongated spots are more truncated than diagonally elongated spots),
  • spot overlap (for square grid lenslet arrays, horizontally and vertically elongated spots are more prone to overlapping),
  • quad-cell or sampling effects on centroiding (pixels are square).

The spot overlap was not listed by [7], but we think it should be considered, according to our laboratory images (Fig. 8). Radial CDD arrays should mitigate square symmetric aberrations.

6.2. LGS aberrations measured on the bench

The wavefront analysis made on the bench with variable profiles actually features significant variations for Z11 and Z14, a weak fluctuation for Z22, and no detectable fluctuation for Z26. The presence of Z17, Z20 and Z21 cannot be explained by the previous model. These non-symmetric modes are likely due to the imperfections of the bench, such as DM transient motions, calibration errors (Sec. 4.3) or quilting errors generated by the extreme focus positions. Further work is planned to identify this problem and to improve the bench accuracy for high order modes.

As Z11 is the dominant LGS aberration, we attempted to detect a dependancy with the profile asymmetry, which is certainly the main source of Z11 on the bench for two reasons:

  • The DM focus stroke acts like a circular field-stop for LGS spots, but the circular truncation is likely not dominant since its FOV is twice the typical sodium layer thickness.
  • There are no aberrations from the optical train: the calibrations of the DM made for different focus steps use the same optical path than the LGS aberration measurements. Therefore, any aberrations induced by a focus change are compensated by the DM.

For each sodium profile, we defined an empirical “profile asymmetry” criterion as:

Asym=(h2hG)(hGh1)h2h1P(h)dh,

where P(h) is the sodium atom density profile, h 1, h 2 and hG respectively denote the altitude of the bottom, of the top and of the centre of gravity of the sodium layer. The bottom and top altitudes are the fist zeros of the profile after subtraction by a threshold (≈10% of the profile maximum).

A correlation between the measured Z11 and the profile asymmetry is actually quite visible on Fig. 11(b). Consequently, the Z11 due to the LGS fluctuations could be estimated from the spot intensity profile (Z11a Asym+b, with a=0.342 nm/ADU/km and b=100 nm for the bench), and then subtracted with the DM of the AO system. Such an open loop correction implemented on the bench, decreases the residual Z11 error to 26 nm ptv rms (instead of 40 nm without correction). This new laboratory result confirms the model and the assumptions made by [7]. Further modelling would be necessary to improve this empirical result, but such an exercise is beyond the scope of this paper.

7. Conclusion

The UVic AO-Laboratory has built an LGS-simulator bench for the TMT project in order to assess the performance of wavefront sensing when using sodium LGSs. Wavefront analysis have been done with a 29×29 spot SH-WFS and the conventional CoG centroiding algorithm. The temporal stability of the bench is about 0.01 pixel rms for centroiding, which corresponds to a total error of 12 nm ptv rms for the wavefront. The wavefront sensing accuracy for high order modes (beyond focus) reaches 3.5 nm ptv rms.

This accuracy allows us to detect and characterize in laboratory some of the wavefront errors induced by the sodium layer variations, such as focus, spherical and tetrafoil aberrations. Even with a focus tracking loop, as planned for TMT, a residual focus error of about 45 nm ptv rms arise due to the truncation of the LGS spots. A spherical aberration of about 40 nm ptv rms arise too, mainly due to the LGS spot profile asymmetry.

The implementation of the matched filter algorithm on the bench is under process. The experimental performance of this centroiding algorithm using a dithering signal will be described in a future paper. Some residual turbulence will be added too. Although the initial goal of the bench is focused on the matched filter, such a bench could serve as a LGS-source simulator for the whole NFIRAOS AO system during the integration phase and for calibrations on the telescope. Radial CCD arrays could be tested on our bench too, when they will be available.

Moreover, the UVic LGS-bench is not limited to SH-WFS and to the TMT framework. We are open to collaborations for testing any other WFS and any other future LGS-AO instruments for which LGS elongation and sodium layer variation are an issue.

Lastly, such a bench is certainly a useful research tool to understand the origins of LGS aberrations, and to validate experimentally the models elaborated by other authors [7, 14]. Actually, the bench can reproduce the LGS aberrations for any sodium layer time series, any telescope diameter, any field-stop sizes and shapes, any laser launch telescope positions. If a reliable model of the LGS aberrations exists, we should be able, in principle, to predict (and compensate) these aberrations only from the sodium layer profile (fast monitored by a part of the pupil, or by another telescope) and not from a dedicated NGS WFS. This approach could be an interesting alternative to improve the sky coverage of LGS-AO systems.

Acknowledgments

We are grateful to TMT consortium. The TMT Project gratefully acknowledges the support of the TMT partner institutions. They are the Association of Canadian Universities for Research in Astronomy (ACURA), the California Institute of Technology and the University of California. This work was supported as well by the Gordon and Betty Moore Foundation, the Canada Foundation for Innovation, the Ontario Ministry of Research and Innovation, the National Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the British Columbia Knowledge Development Fund, the Association of Universities for Research in Astronomy (AURA) and the U.S. National Science Foundation.

References and links

1. F. Rigaut and E. Gendron, “Laser guide star in adaptive optics : The tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

2. M. Talon and R. Foy, “Adaptive telescope with laser probe : Isoplanatism and cone effect,” Astron. Astrophys. , 235, 549–557 (1990).

3. D. S. Davis, P. Hickson, G. Herriot, and C-Y She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006). [CrossRef]   [PubMed]  

4. G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006). [CrossRef]  

5. M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006). [CrossRef]  

6. G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006). [CrossRef]  

7. R. M. Clare, M. A. van Dam, and A. H. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007). [CrossRef]   [PubMed]  

8. L. Gilles and B. Ellerbroek, “Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006). [CrossRef]   [PubMed]  

9. L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807–5815 (2003). [CrossRef]   [PubMed]  

10. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006). [CrossRef]  

11. J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005). [CrossRef]  

12. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]  

13. G. Rousset, “Wave-front sensors,” in Adaptive optics in astronomy, F. Roddier, eds. (Cambridge University Press, 1999), p.91.

14. L. Gilles, B. Ellerbroek, and J.-P. Véran, “Laser guide star multi-conjugate adaptive optics performance of the Thirty Meter Telescope with elongated beacons and matched filtering,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006). [CrossRef]  

References

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  1. F. Rigaut and E. Gendron, “Laser guide star in adaptive optics : The tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).
  2. M. Talon and R. Foy, “Adaptive telescope with laser probe : Isoplanatism and cone effect,” Astron. Astrophys.,  235, 549–557 (1990).
  3. D. S. Davis, P. Hickson, G. Herriot, and C-Y She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
    [Crossref] [PubMed]
  4. G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
    [Crossref]
  5. M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
    [Crossref]
  6. G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
    [Crossref]
  7. R. M. Clare, M. A. van Dam, and A. H. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007).
    [Crossref] [PubMed]
  8. L. Gilles and B. Ellerbroek, “Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
    [Crossref] [PubMed]
  9. L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807–5815 (2003).
    [Crossref] [PubMed]
  10. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
    [Crossref]
  11. J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
    [Crossref]
  12. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [Crossref]
  13. G. Rousset, “Wave-front sensors,” in Adaptive optics in astronomy, F. Roddier, eds. (Cambridge University Press, 1999), p.91.
  14. L. Gilles, B. Ellerbroek, and J.-P. Véran, “Laser guide star multi-conjugate adaptive optics performance of the Thirty Meter Telescope with elongated beacons and matched filtering,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
    [Crossref]

2007 (1)

2006 (7)

L. Gilles and B. Ellerbroek, “Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
[Crossref] [PubMed]

D. S. Davis, P. Hickson, G. Herriot, and C-Y She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
[Crossref] [PubMed]

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

L. Gilles, B. Ellerbroek, and J.-P. Véran, “Laser guide star multi-conjugate adaptive optics performance of the Thirty Meter Telescope with elongated beacons and matched filtering,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

2005 (1)

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

2003 (1)

1992 (1)

F. Rigaut and E. Gendron, “Laser guide star in adaptive optics : The tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

1990 (1)

M. Talon and R. Foy, “Adaptive telescope with laser probe : Isoplanatism and cone effect,” Astron. Astrophys.,  235, 549–557 (1990).

1976 (1)

Adkins, S.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Andersen, D. A.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Beletic, J. W.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Bleau, Ch.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Bouchez, A. H.

R. M. Clare, M. A. van Dam, and A. H. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007).
[Crossref] [PubMed]

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Boyer, C.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Burke, B.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Campbell, R. D.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Chin, J. C.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Clare, R.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Clare, R. M.

Davidge, T.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Davis, D. S.

Duvarney, R.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Ellerboek, B. L.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Ellerbroek, B.

L. Gilles and B. Ellerbroek, “Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
[Crossref] [PubMed]

L. Gilles, B. Ellerbroek, and J.-P. Véran, “Laser guide star multi-conjugate adaptive optics performance of the Thirty Meter Telescope with elongated beacons and matched filtering,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Erickson, D. A.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Foy, R.

M. Talon and R. Foy, “Adaptive telescope with laser probe : Isoplanatism and cone effect,” Astron. Astrophys.,  235, 549–557 (1990).

Fusco, T.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

Gendron, E.

F. Rigaut and E. Gendron, “Laser guide star in adaptive optics : The tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

Gilles, L.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

L. Gilles and B. Ellerbroek, “Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
[Crossref] [PubMed]

L. Gilles, B. Ellerbroek, and J.-P. Véran, “Laser guide star multi-conjugate adaptive optics performance of the Thirty Meter Telescope with elongated beacons and matched filtering,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Hartman, S. K.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Herriot, G.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

D. S. Davis, P. Hickson, G. Herriot, and C-Y She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
[Crossref] [PubMed]

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Hickson, P.

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

D. S. Davis, P. Hickson, G. Herriot, and C-Y She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
[Crossref] [PubMed]

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Johansson, E. M.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Jr. Stomski, P.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Kosicki, B.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Lafon, R. E.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Le Mignant, D.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Looze, D.

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Michau, V.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

Nelson, J.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Nicolle, M.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

Noll, R. J.

Powell, I. P.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Poyneer, L. A.

Reich, R.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Rigaut, F.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

F. Rigaut and E. Gendron, “Laser guide star in adaptive optics : The tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

Rousset, G.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

G. Rousset, “Wave-front sensors,” in Adaptive optics in astronomy, F. Roddier, eds. (Cambridge University Press, 1999), p.91.

Saddlemyer, L.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

She, C-Y

Smith, M.

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Stover, R.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Summers, D. M.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Suntharalingham, V.

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

Talon, M.

M. Talon and R. Foy, “Adaptive telescope with laser probe : Isoplanatism and cone effect,” Astron. Astrophys.,  235, 549–557 (1990).

Thomas, S.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

Tokovinin, A.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

van Dam, M. A.

R. M. Clare, M. A. van Dam, and A. H. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007).
[Crossref] [PubMed]

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Véran, J.-P.

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

L. Gilles, B. Ellerbroek, and J.-P. Véran, “Laser guide star multi-conjugate adaptive optics performance of the Thirty Meter Telescope with elongated beacons and matched filtering,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Wizinowich, P. L.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Ye, C. S.

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Appl. Opt. (2)

Astron. Astrophys. (2)

F. Rigaut and E. Gendron, “Laser guide star in adaptive optics : The tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

M. Talon and R. Foy, “Adaptive telescope with laser probe : Isoplanatism and cone effect,” Astron. Astrophys.,  235, 549–557 (1990).

Experimental Astronomy (1)

J. W. Beletic, S. Adkins, B. Burke, R. Reich, B. Kosicki, V. Suntharalingham, Ch. Bleau, R. Duvarney, R. Stover, J. Nelson, and F. Rigaut, “The Ultimate CCD for Laser Guide Star Wavefront Sensing on Extremely Large Telescopes,” Experimental Astronomy 19, 103–109 (2005).
[Crossref]

J. Opt. Soc. Am. (1)

Mon. Not. R. Astron. Soc. (1)

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a ShackHartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (3)

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C. S. Ye, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the thirty meter telescope,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

G. Herriot, P. Hickson, B. L. Ellerboek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Véran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

L. Gilles, B. Ellerbroek, and J.-P. Véran, “Laser guide star multi-conjugate adaptive optics performance of the Thirty Meter Telescope with elongated beacons and matched filtering,” in Advances in Adaptive Optics II, B. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, (2006).
[Crossref]

Publi. of the Astron. Soc. of the Pacific (1)

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Chin, S. K. Hartman, R. E. Lafon, P. Jr. Stomski, and D. M. Summers, “TheW. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization,” Publi. of the Astron. Soc. of the Pacific 118, 310–318 (2006).
[Crossref]

Other (1)

G. Rousset, “Wave-front sensors,” in Adaptive optics in astronomy, F. Roddier, eds. (Cambridge University Press, 1999), p.91.

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Figures (11)

Fig. 1.
Fig. 1. (Color online) (a) SH-WFS spots geometry for the TMT pupil pointing an LGS at zenith. (b) The radial elongation of the spots can be reproduced in the laboratory with a DM generating an alternating defocus during the integration time. The source intensity is modulated synchronously with the DM to also reproduce sodium profile variations.
Fig. 2.
Fig. 2. (Color online) Control sequence of the DM, the source and the camera generating elongated spots for a given sodium profile. The DM generates a focus staircase from +18.4 to -18.4µm ptv with 41 discrete steps. The camera exposure begins with the first focus position. The source intensity is updated for each focus position to reproduce the sodium profile. The source is turned off between two steps to prevent the DM transient response from blurring the spot (Sec. 5.2). The camera exposure ends with the last focus position, and the DM goes back to the first focus position during the image acquisition in order to be ready for the next image.
Fig. 3.
Fig. 3. (Color online) Optical design of the LGS SH-WFS simulator bench, and key-parameters (pupil size and image sampling) used for generating 29×29 elongated spot SH-WFS images (Fig. 8).
Fig. 4.
Fig. 4. (Color online) Picture of the LGS-bench.
Fig. 5.
Fig. 5. (Color online) Control architecture of the LGS-bench. The bench control system can be subdivided into 4 tasks: (i) Source intensity modulation: A 16 bit analog output PCI DAQ-card (UEI PowerDAQ PD2-AO-8-16) drives the current of the source. (ii) DM control: A second PCI DAQ-card (Adlink PCI-7200) drives the DM actuators via the ALPAO-DE64 controller. (iii) Camera control: The camera must begin and end integration at varying time intervals, depending on the DM state, therefore it has been configured to be triggered externally. The UEI PowerDAQ PD2-AO-8-16 is also used for sending the trigger signal toward the camera, which sends back a strobe signal to confirm that the trigger has been successfully received. (iv) Image acquisition: The image readout is performed via a 9 pin Firewire cable and a fast PCI frame grabber (IEEE-1394b OHCI PCI Host Adapter 3-port 800Mb/s card).
Fig. 6.
Fig. 6. (Color online) Peak-to-valley residual wavefront errors (in tip-tilt, residual focus, astigmatism, coma and spherical) of closed-loop calibrations of the DM for 41 discrete focus amplitudes.
Fig. 7.
Fig. 7. (Color online) Sequence of 88 real sodium profiles used for generating LGS-like SH-WFS images on the bench. Time resolution is 70 s, altitude resolution is 25 m (file TMT.AOS.TEC.07.005_Nap).
Fig. 8.
Fig. 8. (Color online) 29×29 elongated spot SH-WFS image obtained in laboratory. Spot sampling is 2×8 pixels on the edge of the pupil (for a 10 km-thick sodium profile) as for NFIRAOS (see enlarged spots). The sodium profile used for this image is the 87 th profile of the LIDAR sequence (Fig. 7). The solid curve shows the intensity profile sent to the source (i.e. the projected sodium profile sampled over 41 altitude bins). The dashed curve shows the theoretical profile for a spot located on the edge of the pupil (i.e. the source intensity profile convolved by the PSF and resampled over 16 pixels). The measured spot profile (filled circles) perfectly matches the theoretical spot profile, except for the pixel 16 where the spot overlaps with another.
Fig. 9.
Fig. 9. (Color online) Wavefront analysis made with the 29×29 spot SH-WFS of the bench, using the CoG centroiding algorithm for 4 different configurations: (I) with non-elongated spot images to assess the bench stability, (II) with static uniform 10 km-thick sodium profile to check the DM repeatability, (III) with variable sodium profiles without focus tracking to highlight the focus error induced by sodium layer variation, (IV) and with focus tracking to characterize the higher-order LGS aberrations. The temporal mean values and standard deviations of centroids and Zernike modes (ptv amplitude) were computed from a time sequence of 700 SH-WFS images for cases I/II, and from a sequence of 88 real sodium profiles for cases III/IV. The phase reference is a flat wavefront for cases I/II and a uniform 10 km-thick sodium profile SH-WFS image for cases III/IV.
Fig. 10.
Fig. 10. (Color online) Global tip versus global tilt for a time series of 352 (88×4) SH images with a 1/100 th pixel dither signal (4 discrete positions) for non-elongated spots and for elongated spots (i.e. for sodium profiles). A similar dispersion pattern (inside each discrete position) is also obtained without dither signal.
Fig. 11.
Fig. 11. (Color online) (a) Correlation between the mean altitude of 88 sodium profiles and the focus error measured on the bench for each profile, without focus tracking (config. III). (b) Correlation between the sodium profile asymmetry (Eq. (7)) and the spherical aberration (Z11) measured on the bench, with or without focus tracking (config. III or IV).

Tables (1)

Tables Icon

Table 1. Typical temporal RMS fluctuations of the phase measured on the bench for the 4 configurations described in Fig. 9. σϕ is the ptv amplitude noise of the wavefront for all modes. σTT , σ Z4 and σHO are respectively the ptv amplitude noise for tip-tilt, focus and higher order modes. All values are in nm ptv rms.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

θ r σ Na h 0 2 cos ( z ) ,
ξ = ± E 2 λ d ,
ϕ ( ρ ) = A pt v ( ρ ρ 0 ) 2 ,
d ϕ d ρ ρ = ρ 0 = 2 A pt v ρ 0 .
A pt v = ± E λ 8 N spot ,
h ( p ) h 0 1 r 2 h 0 3 p Δ e 1 + 1 h 0 p Δ e ,
Asym = ( h 2 h G ) ( h G h 1 ) h 2 h 1 P ( h ) dh ,

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