3.1.

Laser Guide Star

To measure the bench’s as-built parameters, we fix one parameter and derive all others. We chose the LGS asterism size as the fixed parameter since the LGSs are mounted in solid holes on a metallic plate, which are sturdy and least likely to change over time.

NFIRAOS will project its six LGSs within a radius of 35 arcsec on sky (one at the center and five on the circle), whose stretched correspondence on HeNOS is 6.4 arcsec. For simplicity, we designed the HeNOS bench with four fixed LGSs with a square asterism. For a square asterism, the corresponding side length is 4.5 arcsec. In order to preserve the LGS cone angle through the turbulence (and therefore keep a realistic focal anisoplanatism), we also multiply the nominal range of the LGS by the stretch factor ($90\mathrm{km}\times 11=990\mathrm{km}$). This value provides a reasonable overlap even at the highest turbulence layer, now at $16\mathrm{km}\times 11=176\mathrm{km}$. The LGS footprint at this layer is $8\mathrm{m}\times (990-176)/990=6.6\mathrm{m}$, and the footprint of two LGSs, 4.5 arcsec apart, are separated by 3.8 m, leaving 1.8 m or about 30% overlap.

All four LGSs are made with single-mode fiber laser diodes from Thorlabs (LPS-675-FC), whose optical output power is 2.5 mW. The laser diodes are controlled by a combination of an ADLINK data acquisition card (DAQe-2502) and a custom printed circuit board manufactured by Alberta Printed Circuit (Fig. 2). Using the DAQ card, the LGS timing and intensity can be controlled using computer commands.

Fig. 2

A photo of the LGS board. It provides an interface for the four LGSs, NGS, and SHWFS camera trigger.

3.2.

Natural Guide Star

To evaluate the AO performance across the entire science field, many PSFs on the science camera are needed. We originally created a grid of NGSs using a laser diode (same one as LGSs) and a microlens array (MA). The use of an MA was an easy way to produce many PSFs at the focus, but it creates a grid intensity pattern on the pupil [Fig. 3(a)]. This grid pattern is likely created by the concentrated light from the gaps between microlenses on top of the pupil.

Fig. 3

(a) Image of a grid pattern pupil from the old NGS light source with an MA. The grid pattern is likely created by the concentrated light from the gaps between microlenses on top of the pupil. (b) New NGS light source test setup on the bench. The new design uses a pinhole mask instead of an MA.

We are currently working on a new NGS design without an MA. The new design consists of a powerful LED, a collimating lens, a diffuser, and a pinhole mask in a lens tube. Figure 3(b) shows the test setup. To produce a PSF, the size of the pinhole has to be smaller than the diffraction limit of the bench, which is $\sim 10\mu \mathrm{m}$ at the NGS position in Fig. 1. The HeNOS bench uses many beamsplitters, including two beamsplitter cubes in front of the DMs, which waste a large fraction of photons, and the tiny pinhole blocks even more photons unlike the MA. We are adjusting the position of the collimating lens and pinhole mask to maximize photon count at the pinhole mask and adjusting the beamsplitters using different reflection-transmission ratios to give more weight to the NGS path.

For a temporary solution, we are using the laser diode itself, without MA nor pinhole mask, as a single NGS. The size of the laser diode is small enough to create a diffraction-limited PSF. Because it is only one PSF, we cannot evaluate AO performance over a whole FOV on the science camera, but it is used for a PTWFS experiment (see Secs. 3.9 and 4 for more about PTWFS). For performance evaluation, we place the science camera at the LGS focus and use LGSs as PSFs (see Sec. 3.6).

We are also looking into a design where the pinhole mask can be easily replaced by a single pinhole of a large radius. Using a bigger pinhole, we can experiment a wavefront sensing on an extended object using PWFS. This experiment is not a direct simulation of NFIRAOS; however, it is useful to advance observations. See Ref. 5 for PWFS simulations with extended guide objects and their science applications. Using a larger pinhole, the NGS is no longer diffraction-limited, and thus we cannot evaluate the performance directly from PSF. But since we have a separate LGS-SHWFS, we can check its performance using SHWFS measurements.

3.3.

Deformable Mirror

We use two magnetic DMs from ALPAO, whose specifications are listed in Table 4. Since both DMs have the same actuator pitch, they are located in the same collimated space, with DM1 conjugated to the high altitude and DM0 to the ground (see Fig. 1 for their locations). Beamsplitter cubes are placed in front of both DMs so that the incident beam hits the DM surfaces normally. These cubes simplify the bench design but waste a significant fraction of photons (see Sec. 3.2 for their drawback).

Table 4

DM specifications.

We determine the actuator spacing and the altitude conjugation of the mirrors by looking at the poke matrix taken with an SHWFS (see Sec. 3.5 for SHWFS details). From the poke matrix, we measure the actuator positions in the WFS geometry and fit a uniform grid to them using a least square fit. The center of the fit is used to better align the SHWFS to avoid vignetting of the pupil. The actuator spacing derived from the scaling of the fit to DM0 is 0.914 m, and the conjugation altitude of DM1 estimated from the shear of the metapupils, knowing the LGS separation is 4.5 arcsec, is 121 km with the stretch factor, $f_s$, applied (12 km without).

3.4.

Phase Screen

A key requirement of the HeNOS bench is the ability to generate realistic turbulence. To achieve this, we adopt well-calibrated turbulence screens: two screens from Lexitek⁶ and one from UCSC.⁷ Lexitek screens use an index matching technique, where the turbulence profile can be flexibly designed with any $r_0$ but is expensive. The UCSC screen uses the acrylic paint spraying technique, where the cost is less, but only small $r_0$ is available.

The two Lexitek phase screens (PS2 and PS3 in Fig. 1) are placed in the same collimated space as the two DMs. PS3 just before DM1 has the bigger $r_0$ and simulates the highest turbulence layer, and PS2 in between the two DMs simulates the middle layer turbulence. Because the UCSC screen (PS1) is conjugated to the ground, which is occupied by DM0, a separate pupil position is created (see PS1 position in Fig. 1). At this position, the designed beam size is 10 mm.

Two Lexitek PSs are mounted on Lexitek motorized rotary stages (LS-100), and the UCSC PS is controlled by a Galil motion controller. To measure wind speed, we measure the distance between the optical axis and the rotation center. The relationship between the physical dimensions and the simulated ones is given by the simulated telescope size and the physical pupil size in the collimated space (see Sec. 3.7 for the simulated telescope size). From this relationship, the circumferences of three PSs are 295 (PS1), 97 (PS2), and 92 m (PS3). Note that due to the rotational movement, the speed is never uniform across the metapupil.

The altitudes of the PSs are calculated from the physical positions of the optical surfaces. Knowing the physical position (actual physical distance between DM0 and DM1 on the bench measured by a ruler) and the simulated altitude (Sec. 3.3) of DM1, the scaling factor relating the bench and the altitude of the atmosphere in the collimated space, where DM0, DM1, PS2, and PS3 are placed, is $28.22\mathrm{mm}/\mathrm{km}$. The scaling factor is proportional to the square of the aperture size ratio, and thus the PS1 altitude is $28.22*{(10/13.5)}^2=15.8\mathrm{mm}/\mathrm{km}$, where aperture sizes are 10 m at PS1 and 13.35 mm at the DM0’s position.

For turbulence power measurements, we derive the Fried parameter using two independent methods: (1) the full-width-half-maximum of PSFs on the SC, assuming Kolomogorov statistics ($r_{0,\mathrm{SC}}$ on Table 5), and (2) the standard deviation of the wavefront reconstructed from WFS slopes using a CuReD⁸ reconstructor ($r_{0,\mathrm{WFS}}$ on Table 5). For method one, we use the NGS light source with an MA to create many stars for better statistics and take long exposure PSF images on the SC. For method two, we take the slope measurements on the SHWFS. In both cases, we use one PS and take data on 100 different positions across the PS at a time. Data without PSs are also taken for reference. The resultant Fried parameters are listed in Table 5 along with the nominal value used by the manufacturer $(r_0)$. Note that the measurements of the high altitude PS need to be corrected for the cone effect. All PS measurements are well within 10% of the nominal value, but $r_{0,\mathrm{WFS}}$ is larger than $r_{0,\mathrm{SC}}$. This is because the WFS is blind to the highest spatial frequencies of the turbulence, and thus we believe $r_{0,\mathrm{SC}}$ is more accurate. The relative powers of the PSs in terms of ${\sigma }^2\propto r_0^{-5/3}$ are 74.3%, 17.4%, and 8.2%.

Table 5

Fried parameter.

3.5.

Shack–Hartmann Wavefront Sensor

Our WFS is a custom-made SHWFS with a square MA ($300\mu \mathrm{m}$ pitch) and a PointGrey Grasshopper CCD ($2448\times 2048$ array with $3.45\mu \mathrm{m}\times 3.45\mu \mathrm{m}\text{pixel}$). The FOV of the lenslets is large enough to separately see all four LGSs, and thus a single detector is used to sense all four LGSs simultaneously. Depending on the experiment, individual LGS can be used as well if separate measurements are required. Our SHWFS has many subapertures (30 across the pupil) to sample the elongation finely at each distance away from the center.

We identify the spots created by the MA, and the average separation of the LGSs is $20.58\pm 0.51\text{pixel}$, which translates to the WFS pixel size being 0.22 arcsec. We fit a uniform grid to the SHWFS spots and define subapertures, including the ones outside of the illuminated zone. We then determine the pupil size by matching the measured illumination pattern and a modeled illumination pattern. The modeled illumination is the percentage coverage map of subapertures when a perfect circle is projected on a square subapertures. Applying this method to four LGSs separately, we find the radius of the pupil on the SHWFS to be 15.226 subapertures.

Assuming a small aberration approximation, we estimate a WFS fitting error using SR (SR) of NGS. First, we measure ${\mathrm{SR}}_1$ using flat mirrors instead of DMs and no phase screens. Then, we measure ${\mathrm{SR}}_2$ using DM0 and a ground layer PS after closing loop. The error is estimated as

More thorough derivation of the error budget can be found in Ref. 9.

3.6.

Science Camera

We originally used a PointGrey Grasshopper ($2448\times 2048$, $3.45\mu \mathrm{m}\text{pixel}$), the same model as the one used in the SHWFS, for the science camera; however, we realized that the Grasshopper has two readout channels that create background offset between the two sides of the detector. When a PSF falls near this divided region, it adds spatially different noise properties and complicates the modeling. We also noticed that the offset varies from time to time. We thus replaced the camera with an Andor sCMOS Zyla ($2048\times 2048$, $6.5\mu \mathrm{m}\text{pixel}$), which has a low noise and almost uniform background. The Andor sCMOS has a similar number of pixels but with larger pixels, and we realigned the lenses in front of it to have the same plate scale as when a Grasshopper was used.

Due to the NGS light source problem (Sec. 3.2), currently we do not have a proper NGS light source on the bench. While we work on new solutions, for a temporary fix, we locate the science camera at the focus of the LGSs and use them as science targets. At this location, their plate scale is 5.6 milli-arcsec.

3.7.

Telescope Size

The simulated on-sky telescope diameter was measured in the earlier stages of bench development using the PSF Airy rings. The bench had flat mirrors instead of DMs, an NGS light source with an MA, no PSs, and an iris at PS1’s position. We used a 3-mm iris to have the first ring distant enough from the core while keeping a sufficiently bright aperture to measure its size.

We took an image on the science camera and identified PSFs on the image. To obtain a high SNR, we stack all PSFs by aligning the brightest pixels [Fig. 4(a), the core masked out]. To measure the diameter of the ring, we linearized the PSF image by transforming it from polar to Cartesian coordinates [Fig. 4(b)]. The radius of the ring is the median position of the central line and is $1.64\lambda /D$, which corresponds to an aperture of 2.44 m on sky. Scaling it to the 10-mm aperture at the first pupil’s position (PS1’s position), the HeNOS telescope size is 8.13 m.

Fig. 4

To measure the simulated telescope size, many PSFs on the SC created by NGS source with an MA are stacked. (a) The core-masked stacked PSF. (b) The stacked PSF is then linearized by transforming from polar to Cartesian coordinate, and the radius of the ring is the median position of the central line.

3.8.

SHWFS Spot Elongation and Truth Wavefront Sensor

When a sodium (Na) laser is used as an LGS, the spots on an SHWFS are radially elongated due to the finite thickness of the Na layer. When the Na layer profile (i.e., height, thickness, and density distribution) changes, the photon distributions in the elongated spots also change. This introduces an additional centroid shift when centroding is applied.¹⁰ This spot elongation problem is more severe as the diameter of a telescope increases. Figure 5 explains how the thickness of the Na layer produces more elongated spots with larger telescopes, and why the fluctuation in Na profile causes aberrations. See for example Ref. 11 for more detail about SHWFS elongation and imperfection in centroiding.

Fig. 5

Schematic of LGS SHWFS spot elongation. The example spots shown here are for a center-launched LGS. The subapertures further away from the center see the Na layer with an angle compared to those near the center, resulting in more radially elongated spots. This offset from the center increases with telescope size, and is particularly severe for ELTs. The layer shown as orange in the sodium layer represents high Na density, and its location in SHWFS spots are also shown as orange. Because of the high Na density, the orange part of the spots has higher flux return, which would be confused as a radial spot shift.

To simulate the SHWFS elongation created by the Na layer, we apply a set of defocus commands to DM0 and change the LGS intensity according to the empirically obtained Na profile while the LGS-WFS camera shutter is open (or take individual WFS image and combine all). An example of the empirical Na profiles taken by the University of British Colombia group is shown in Fig. 6, and its reproduced SHWFS elongation at $t=0\mathrm{s}$ is shown in Fig. 7.

Fig. 6

(a) Empirically obtained Na profiles as functions of time over 1800 s. Darker color for higher density. (b) one-dimensional plot of Na profile at $t=0\mathrm{s}$.

Fig. 7

Simulated elongated SHWFS spots when Na profile at $t=0$ [Fig. 6(b)] is applied. (a) Full frame SHWFS camera image and (b) one zoomed spot in a magenta box.

3.9.

Pyramid Truth Wavefront Sensor

The one major update to HeNOS is the implementation of a TWFS made with a PWFS. This is to follow up on the NFIRAOS’ new decision to use a PWFS instead of an SHWFS for its TWFS (Ref. 12). The description of general TWFS functions and the HeNOS TWFS design are reported in Ref. 11, and our optical design is shown in Fig. 1 in green. In short, on HeNOS, the grid of NGSs hitting a star selection mirror (SSM) at the pupil is sent to a pinhole where only one NGS goes through. The single NGS beam is then modulated by a fast steering mirror (FSM) at the pupil, and the focused beam makes a circle around the vertex of the pyramid. The light is distributed in four directions and a relay lens behind the pyramid forms four separate pupil images on a detector. The incoming wavefront can be measured by comparing their intensity patterns.

Our SSM and FSM use a Zaber Motorized Gimbal Mount and a Newport FSM-300, respectively. While the Zaber controller is run by USB, the FSM-300 controller requires analog inputs, and thus we installed the same ADLINK data acquisition card (DAQe-2502) as the laser diodes in the HeNOS computer. The interface between the DAQ card and the FSM controller is an off-the-shelf ADLINK terminal board. The PWFS camera is a PointGrey Flea ($648\times 488$ array with $5.6\mu \mathrm{m}\text{pixel}$). To evaluate the PSF at the tip of the pyramid, we have inserted one more beamsplitter between the focusing lens and the pyramid and added one more camera (pyramid science camera, PSC, orange path in Fig. 1). The PSC is a PointGrey Grasshopper ($2448\times 2048$, $3.45\mu \mathrm{m}\text{pixel}$). Both the PWFS camera and the PSC are also connected to the ADLINK terminal board so that the PWFS camera, PSC, and FSM are all synchronized.

Our pyramid component is a double pyramid borrowed from the Arcetri group. A double pyramid consists of two pyramid-shaped prisms glued back to back. The two prisms are made with different materials (i.e., different index of refraction) to compensate for chromatic aberrations. Alternative pyramid components, such as double roof prisms, can be used (see, e.g., Ref. 11 for performance comparisons between different pyramid components).

3.10.

Bench Summary

All calibration results described in this section are summarized in Table 6. For simplicity, the values here are not including the stretch factor, $f_s$, described in Sec. 2. Table 7 summarizes how the as-built bench matches the design objective from Sec. 2. In general, the parameters of the HeNOS bench are in reasonable agreement with the desired parameters. In any case, the most important is to know the as-built parameters so that the models can be parameterized correctly. Knowing the HeNOS parameter well, we are ready to demonstrate and test the techniques that will be used on NFIRAOS and other instruments/AO systems. Please refer additional HeNOS tests in Refs. 9 and 13 for an SLODAR experiment and NCPA calibration using the focal plane sharpening method.

Table 6

As-built HeNOS parameters.

Table 7

Desired versus obtained objective.

4.1.

LGSAO with SHWFS

The steps to simulate the classical SCAO with LGS and SHWFS are shown in Fig. 8. The numbers in the flowchart indicate the order of process called in the loop. Currently, it takes about 3 s to take one frame on the bench, which leads to several hours of run-time for any experiment. We noticed that, over this time, the SR of the long exposure image drops while the instantaneous Strehl stays stable. This is indicative of a TT error at the WFS. The cause of this TT error is probably produced by the flexure in the paths. In the WFS and science paths on HeNOS after DM0, optical components, including WFS camera, are mounted in between four rods (called cage system) that are keener to thermal expansion. To correct this, we neglect the TT from the LGSWFS and use the TT from the SC (steps 9 and 10 in Fig. 8). This method prevents TT errors at the SC: the long exposure SR no longer drops and remains comparable to the average short exposure SR.

This mode is the most developed and most used mode on the HeNOS bench. Using this mode, we collaborate with TMT Observatory Corporation and Laboratoire d’Astrophysique de Marseille to demonstrate PSF reconstruction techniques by comparing the empirical data with analytic models (Refs. 14 and 15).

4.2.

NGSAO with PWFS

With the implementation of the PWFS, the bench now can be closed with the NGS and the PWFS. The steps of this mode are shown in Fig. 9.

Fig. 9

Flowchart describing how the HeNOS bench closes the loop with NGS and PWFS. The numbers indicate the order of process called in the loop.

As an example, (A) PSF, (B) raw PWFS image, (C) $x$- and (F) $y$-slope signal, (D) DM0 shape, and (E) reconstructed wavefront before [Fig. 10(a), zero commands on DM0] and after [Fig. 10(b)] the loop is closed are shown. In this example, there are no PSs in the path. The initial PSF is big and fuzzy, and after closing the loop, the diffraction rings are visible.

Fig. 10

(A) PSF on PSC, (B) raw pupil image, (C) $x$- and (F) $y$-slope signal, (D) DM0 shape, and (E) reconstructed wavefront. (a) Starting from zero command, (b) the loop is closed after 50 iterations with loop gain = 0.2, and diffraction rings are seen in the PSF (panel A).

Because the main purpose of the PWFS is a TWFS, this NGSAO with PWFS mode is currently quite basic. Once the new NGS source with a larger pinhole is added (Sec. 3.2), we will experiment wavefront sensing on an extended object with PWFS. Extended wavefront sensing in general is useful to increase the sky coverage, but also its application includes the use of LGS on a PWFS. As PWFS becomes a more popular choice for many future upgrades (e.g., GPI, Subaru, and Keck), the PWFS mode on the HeNOS bench is an interesting capability for future experiments.

4.3.

LGSAO with Elongated SHWFS and NGS PTWFS

The last mode available on the HeNOS bench is the loop with the LGS-SHWFS using the elongated SHWFS spots and the NGS-TWFS correction. The flowchart in Fig. 11 shows the steps.

Fig. 11

Flowchart describing how the elongated SHWFS is integrated into the SCAO loop and how measurements from the PTWFS are fed to the loop as SHWFS offsets. The numbers indicate the order of process called in the loop.

Because of the alignment imperfection in the PWFS path, as the amount of defocus applied on DM0 changes, the position of the beam at the tip of the pyramid drifts. To fix this problem, we update the zero-position of FSM each time (PWFS centering at the step 13). The new zero-position is measured by comparing the vertical and horizontal pupil intensities. As we apply the evolving Na profile (Fig. 6), the mean height of Na layer (thus focus term) needs to be measured. In the TMT+NFIRAOS case, the TWFS does not measure the defocus term and only measures higher order radial modes, but on the HeNOS bench, we measure the defocus term using the TWFS as well because we do not have a separate focus WFS.

Figure 12 shows one example of closing loop with the elongated SHWFS. Starting with the best DM flat from the previous day, the loop is closed using the elongated SHWFS spots. For this experiment, we apply the same Na profile shown in Fig. 6(b) for all iterations (i.e., Na profile does not evolve). We use a higher loop gain of 0.5 for this test to speed up the simulation. Before the TWFS feedback is applied [Fig. 12(a)], DM changes its shape to compensate the aberrations created in the elongated SHWFS spots by the Na profile, as described in Sec. 3.8, and thus the reconstructed phase by the elongated SHWFS (panel D) sees flat phase. However, the true wavefront on the science targets is not affected by the Na profile (the actual phase shown on panel E includes a big defocus and radial aberrations), and it actually adds “wrong” aberration onto the science targets. As a result, four LGS SRs (panel F) become low, and the final PSFs on panel C are big and fuzzy. After the loop is closed on the elongated SHWFS with Na profile, we then close the loop again but now with TWFS feedback [Fig. 12(b)]. The TWFS feedback is applied as a reference slope to the elongated SHWFS. After 20 iterations, the four LGS SRs (panel F) are improved ($>50\%$), and all three WFSs, PWFS (panels A and B), elongated SHWFS (panel D), and normal SHWFS (panel E) see small aberrations.

Fig. 12

(A) PWFS slope signal in $x$, (B) PWFS slope signal in $y$, (C) four LGSs on the science camera, (D) reconstructed phase using elongated SHWFS, (E) reconstructed phase using normal SHWFS, and (F) evolution of four LGS SRs while closing loop. (a) After closing loop on the elongated SHWFS spots with the Na profile shown in Fig. 6(b) without TWFS feedback. (b) After closing loop with TWFS feedback.