2.1.

Comparing Atmospheric Conditions in a Very Crowded Field: The Galactic Center

We expand upon the initial on-sky GC testing of Ref. 7 by including “good quality,” “average quality,” and “poor quality” datasets (hereafter GQ, AQ, and PQ, respectively) for further AIROPA validations on the GC. The GC case was used as the main science driver for the original development of AIROPA. This case is ideal since there already exists a rich high-resolution dataset spanning several decades, dozens of reference stars for PSF modeling, and a very bright, uniform tip/tilt (TT) star that is $\sim 13\mathrm{arcsec}$ arcsec off-axis. The longest-running high-resolution study of the stellar population immediately surrounding ${\mathrm{SgrA}}^{*}$ is being conducted by the Galactic Center Orbit Initiative.¹¹ This work has led to a deep and well-understood knowledge^9,10,12–14 of the environment immediately surrounding the central supermassive black hole.

We rank the three GC datasets, GQ, AQ, and PQ based on the historical quality of all GC epochs taken with NIRC2 since 2004.¹⁵ Note that our definition of “good,” “average,” and “poor” involves more than just the atmospheric conditions during those datasets. The overall image quality can be affected by multiple contributing factors related to atmospheric conditions, stability and performance of the AO system on a given night, brightness and variation of TT/guide stars, or the Strehl/FWHM reference star selection.

The GQ data were taken on August 11, 2017, the AQ data were taken $\sim 2$ weeks after the GQ data, on August 23, 2017, and the PQ data were taken on March 05, 2016. For all GC datasets, each frame was composed of 10 coadded exposures at 2.8 s per coadd for a total exposure time of 28 s per frame. One note about the PQ dataset – there does not exist phase-diversity calibration data from 2016, therefore the 2017 instrumental phase maps were used to substitute for the 2016 phase maps. This is not an issue, as Ref. 5 shows that the phase maps can remain stable across multiple years, and any potential difference between 2016 and 2017 phase-diversity is likely small enough for an analysis of the kind presented in this work. Figure 2 shows one frame from each of the three epochs, with the spatial scale given as the separation (in arcseconds) from the on-axis position (i.e., location of the LGS). We note that there are two other axes of importance; the direction of the TT star (given by the solid line in Figs. 3Fig. 4–5), and the position of the image sharpening (typically offset from the center of the image). Figure 3 shows the grid of FWHM values measured by AIROPA variable-PSF mode for each frame, plotted over the field of view to give a visualization of the field-dependent PSF. The FWHM grid values are calculated for every PSF generated by AIROPA in a PSF grid file. The AIROPA grid files for the fields analyzed in this work use a partition size (i.e., step width of the PSF grid) of 102.

Fig. 2

(a) Good-quality Galactic Center frame. (b) Average-quality Galactic Center frame. (c) Poor-quality Galactic Center frame. All images have the same color scale, the axes represent on-sky separation (in arcsecond) from the LGS position. North is up and East is left in all frames.

Fig. 3

Grid of FWHM values from AIROPA variable-PSF mode on (a) the GQ, (b) AQ, and (c) PQ datasets. Colored circle data points correspond to locations and K-band magnitudes of primary PSF reference stars. A solid line connects the on-axis LGS position to the off-axis TT guide star position.

Fig. 4

(a) NIRC2 frame of the OB150029 field taken on July 14, 2016, with the $\mathrm{K}p$ filter. (b) FWHM grid from AIROPA variable-PSF mode with selected PSF reference stars colored by magnitude and solid line connecting the on-axis position to the TT guide star.

Fig. 5

(a) M53 NIRC2 frame taken at PA = 0 deg, with accompanying FWHM grid generated by AIROPA. (b) Same as left, but for PA = 90 deg. The solid line connects the on-axis LGS position to the TT guide star. The color scale is identical for both images in the top row.

2.2.

Less Crowded Field: OGLE-2015-BLG-0029

The optical gravitational lensing experiment (OGLE) survey¹⁶ conducts wide-field visible and near-IR imaging of nearly the entire Galactic Bulge region at high cadence and detects over 1000 microlensing events every season. Most ground-based imaging data from current microlensing surveys are focused on the regions $3\mathrm{deg}>l>357\mathrm{deg}$ and $-2.5\mathrm{deg}<b<2.5\mathrm{deg}$. The first non-GC data analyzed in this work is OGLE-2015-BLG-0029 (hereafter OB150029), located at RA = 17:59:46.60, dec = –28:38:41.80 and Galactic coordinates ($l,b=(1.828\mathrm{deg},-2.523\mathrm{deg})$) in J2000 epoch. This target has been regularly monitored with NIRC2 since 2015 as part of a project to study isolated stellar-mass black hole candidates.¹⁷

The OB150029 observations were taken on July 14, 2016 in LGSAO mode with the Kp filter. Each of the frames consist of six coadded images, each with five second integration time, for a total integration time of 30 s per frame. The airmass during the six-frame observing window was $\sim 1.65$, and the median SR, FWHM, and RMS WFE values for the six frames are given in Table 1, as well as the DIMM/MASS data given in Fig. 1(b). This is the second-best dataset (behind GQ) in terms of quality metrics like the median SR and FWHM and their variances across all six frames. Similar to the PQ dataset, there are no 2016 phase maps available for NIRC2, therefore, the 2017 maps were substituted. Again, phase-diversity measurements have shown these maps to be stable within $\sim 59$ nm RMS across several years.⁵ Figure 4 shows a NIRC2 image of the field, which is clearly less crowded than the GC, particularly in the bright star regime.

There are a total of 10 PSF reference stars in this field that were used for AIROPA, compared to a total of 25 PSF reference stars used for the GC analysis described in Sec. 2.1. The total number and spatial location of selected PSF reference stars is important for constructing accurate PSF models, and the 10 stars chosen for the OB150029 field include the microlensing target itself (i.e., brightest star in the field), as well as stars within 1.5 mag of the target, and separations of $\pm 4$ arcsec from the target. The TT guide star used for the observations has an R mag $\sim 15.1$ and separation of $\sim 13.8\mathrm{arcsec}$ to the south-west of the target, as indicated by the solid line in Fig. 4(b).

2.3.

Comparing Different Position Angles: Globular Cluster M53

The globular cluster M53 (NGC 5024) located at RA = 13:12:54.51, dec = 18:10:13.95 (J2000) was observed with the NIRC2 narrow camera $\mathrm{K}p$ filter on May 04, 2015, as part of a project to characterize the NIRC2 geometric distortion.⁸ This was accomplished by comparing the NIRC2 stellar positions to precise astrometry from Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) observations.¹⁸ The NIRC2 camera and AO system were realigned in April 2015, and observations of M53 before and after this realignment show an increase in the average geometric distortion from ~0.5 mas prerealignment to $\sim 1.1\mathrm{mas}$ postrealignment.

Importantly for the current study, the M53 NIRC2 observations were taken at two different PAs; 0 deg and 90 deg. These observations present a unique dataset for us to compare the astrometric accuracy between single-PSF and variable-PSF modes in AIROPA as a function of PA. The previous study of Ref. 8 assumed a static PSF to derive the geometric distortion solution, which implies that using a variable-PSF on NIRC2 datasets will likely show residual distortion that was not modeled out by the static PSF used to derive the solution. Depending on the significance of this effect, some fraction of the difference in astrometric, photometric, or FVU results between the PSF modes may be attributed to this (Figs. 6, 10, 11, and 14). Due to the gradient in the NIRC2 distortion solution, the local pixel scale changes across the detector. This change, however small, is not detected in any PSF modeling because the aberration maps that are used are tip-tilt removed. This is very likely only a minor effect. As our intention in this paper is not to fully derive a new geometric distortion solution (with single and/or variable-PSF), we select only a subset of M53 NIRC2 images to remain consistent with the number of GC and microlensing frames used in previous sections. While it may prove beneficial to fully derive a new independent variable-PSF distortion solution for NIRC2, this is beyond the scope of the current paper. As shown in Ref. 7 and Fig. 6, the astrometric differences between single-PSF mode and variable-PSF mode become more severe at larger radii from the central on-axis position. This is predominantly caused by the difference in PSF shape between the spatially varying model and the static model, particularly closer to the sides and edges of the NIRC2 frame.

Fig. 6

(a) 2D positional difference in single versus variable PSF modes. Quiver plot shows positional differences as a function of field location. (b) 1D positional differences with errors derived from the RMS deviation of six positional measurements.

The M53 dataset includes six frames taken at a PA of 0 deg (north up, east left), and six frames taken at a PA of 90 deg (east up, south left). The $\mathrm{PA}=0\mathrm{deg}$ dataset consists of four frames taken at the central pointing, and two frames were taken after a dither of ${\mathrm{\Delta }}_x=-{0.14}^{\prime \prime },{\mathrm{\Delta }}_y={0.16}^{\prime \prime }$. The PA $=90\mathrm{deg}$ dataset consists of four frames taken at the central pointing, and two frames were taken after a dither of ${\mathrm{\Delta }}_x=+{0.14}^{\prime \prime },{\mathrm{\Delta }}_y=-{0.19}^{\prime \prime }$. The total exposure time is 50 s per frame for both PAs. Figure 5 shows one frame taken at PA 0 deg and the accompanying grid of FWHM values from AIROPA variable-PSF mode, as well as a PA 90 deg frame and FWHM grid. The same 10 PSF reference stars were used for each PA, as well as the same TT guide star, which has magnitude $R\sim 13.5$ located 24 arcsec to the south-west (solid line in the lower panels of Fig. 5).

3.1.

Galactic Center

For the very crowded GC datasets, identical reductions and analyses were performed across each of the six-frame sets. The same 25 PSF reference stars were used in each analysis and the astrometric, photometric, and FVU results are given in the following three subsections. Note that for each of the three datasets, we impose a requirement that in order for a star to be included in the analysis, it must be detected in at least five of the six cleaned frames.

3.2.

OB150029

The microlensing target OB150029 is located in the least-crowded stellar field analyzed in this work, with a total of 63 stars cross-matched in at least five out of six frames. For this data, 10 reference stars were used for the initial PSF model. Coincidentally, this is the same amount of reference stars as the M53 dataset and is 60% fewer reference stars than the GC datasets. We note this dataset has the second-highest measured SR, and smallest FWHM of all datasets analyzed (Table 1). Additionally, as can be seen in Fig. 4(b), this dataset has the smallest variance in FWHM as measured across the field ($\sim 6$ mas).

For the microlensing target itself, the AIROPA analysis shows a modest improvement of $\sim 13\%$ in the astrometric precision in variable-PSF mode (${\sigma }_r=0.223$ mas) over single-PSF mode (${\sigma }_r=0.252$ mas). Figure 9(a) shows the ratio of astrometric residuals for all stars detected in both PSF modes (binned by magnitude), OB150029 is shown by the red data point. The photometric uncertainty and FVU evaluated on the target for both PSF modes are very similar, within 5% for single-PSF and variable-PSF modes. It should not be surprising that the PSF fitting errors and metrics are quite similar between single-PSF and variable-PSF for the target star in this case since the location of the target on the detector is nearly on-axis [Fig. 8(a)] and the PSF shapes are not significantly different for the static PSF and the central PSF from the variable-PSF mode. The residual images show effectively identical over-subtracted and under-subtracted features for both PSF modes [Figs. 8(b) and 8(c)]. We note there is an unrelated neighbor star $\sim 0.36\mathrm{arcsec}$ to the SW of the target, with a flux ratio of $f/f_{\mathrm{OB}150029} \sim 0.1$. While the stellar profile of this fainter neighbor may have a small absolute effect on the SW wing of the OB150029 PSF, the magnitude of this effect will be the same for each case. Additionally, inspection of the residuals at the location of the nearby neighbor shows no statistically significant signal above or below the background noise in both cases.

Figure 9(a) shows the relationship (i.e., ratio) between the fitting metrics as a function of magnitude, and Table 3 reports the results for each metric and PSF mode. Generally, the same trend appears in the microlensing dataset as the GC datasets; a marginal improvement in the precision and fitting residuals in variable-PSF mode compared to single-PSF mode. The largest improvement is seen in both astrometric precision and FVU for variable-PSF mode, $\sim 10\%$ smaller than the single-PSF mode results.

As a final test for this microlensing dataset, we performed an identical AIROPA analysis while omitting the target itself as a PSF reference star. Ideally, the results of such a test will reveal the influence (if any) that the target (i.e., brightest star in the field) has on the PSF modeling and extraction as well as the fitting parameters and residuals measured by the single-PSF and variable-PSF algorithms. The results of this reanalysis show indistinguishable results for the astrometric and photometric precision for the microlensing target (${\sigma }_r=0.223$ mas, ${\sigma }_m=0.025$ mag), as well as an FVU value that is consistent (within $1\sigma$) of the value measured while including the target as a PSF reference star.

3.3.

M53

As described in Sec. 2.3, the two M53 datasets have significantly different data qualities. In particular, the PA 0 deg dataset has the largest variance in SR, FWHM, and RMS WFE of all data in this study. One cause of this is the observing window for the PA 0 deg data spans a time frame where the DIMM and MASS monitors recorded a particularly high seeing measurement [Fig. 1(b), green-colored data]. This is likely due to high cirrus cloud cover or other turbulent layers in the high-altitude atmosphere during two of the PA 0 deg exposures. A relatively small total number of PA 0 deg images were taken on the night (see Table 1 of Ref. 8), and the frames that correspond to the DIMM/MASS spike seen in Fig. 1 happen to be the images that have the most observed sources in common with the PA 90 deg images that were taken $\sim 1\mathrm{h}$ later in the same night. Because we want to maintain consistency amongst all datasets and to maximize the total number of cross-referenced stars in both PAs, we chose to keep all of the PA 0 deg frames for this particular dither position. This mostly affects the fainter stars in the field, as can be seen by comparing the limiting magnitudes in the PA 0 deg and PA 90 deg panels in Fig. 9. We note that AIROPA (and the Arroyo software) associates two PA 0 deg images with the large DIMM and MASS measurement.

3.3.2.

M53 PA 90

The higher quality PA 90-deg data has a total of 160 stars cross-matched in the images, with the same 10 stars used as PSF reference stars (lower-right panel of Fig. 5). Like the previous data sets, there is little to no improvement in the variable-PSF fitting metrics compared to the single-PSF results. The difference in stellar positions and magnitudes also follow similar trends seen in the previous data (Table 2). The average photometric error for all stars is $\sim 15\%$ larger in the variable mode compared to single mode. The average astrometric error is nearly identical in both modes, at a $\sim 1\%$ difference. The FVU values in both modes are within $1\sigma$ of each other (bottom row of Table 3).

Finally, we investigated the difference between astrometric residuals in both PSF modes after matching and transforming the PA 0-deg star list to the PA 90-deg list (and vice versa). We perform a first-order transformation using both stacked star lists from each PA as the master reference list and star list to be transformed in both cases. If the variable-PSF mode performs better, then we would expect astrometric residuals from this transformation process to be smaller for the spatially varying PSF mode, particularly for larger off-axis stars in the frames. Figure 10 shows the resulting astrometric quiver plots in the top panels, and the distribution and correlation between the astrometric residuals in both PSF modes in the bottom panels. The two distributions are very similar, and correlations largely follow the line of unity with a dispersion of ∼a few mas (bottom right panel of Fig. 10), which show that the astrometric residuals from the variable-PSF mode are not measurably smaller than the single-PSF residuals.

Fig. 10

(a) Quiver plot showing single-PSF astrometric residuals from the PA=0 → PA=90 transformation. (b) Same as (a), but for variable-PSF mode. (c) Distribution of astrometric residuals from both PSF mode transformations. (d) Correlation between astrometric residuals for both PSF modes, colored by Kp magnitude.

3.3.3.

HST cross reference

Both PA’s star lists were independently transformed to an HST reference frame described in Sec. 2.3, with the same intention of examining the difference in astrometric residuals between single and variable modes. Figure 11 shows the PA 90-deg astrometric residual quiver plots in the upper panels, and corresponding distribution of astrometric residuals as well as the correlation between single-PSF and variable-PSF residuals in the lower panels. The distribution of astrometric residuals peaks at 1.52 mas in both PSF modes, this is consistent with the residual distortion on the NIRC2 detector that was found in Ref. 8 (denoted by the vertical black line in the bottom left panel of Fig. 11). The weighted mean and central 68% of both PSF mode distributions are given in Table 4. This table includes all variations of star list transformations that were performed on the M53 data sets (i.e., NIRC2, HST, and Gaia, described below).

Fig. 11

Same as Fig. 10 but for stars transformed to HST. The color bar is given in F814W (Vega) magnitude. The vertical black line on the lower left panel shows the residual distortion calculated by Ref. 8.

Table 4

M53 astrometric residuals from NIRC2, HST, and Gaia.

Ref. Frame	Nmatched	⟨σrs⟩ [mas]	⟨σrv⟩ [mas]
PA 0
PA 90	94	${2.53}_{-0.47}^{+1.59}$	${2.82}_{-0.51}^{+1.67}$
HST	90	${1.93}_{-0.44}^{+1.39}$	${2.04}_{-0.45}^{+1.43}$
Gaia	24	${7.61}_{-1.19}^{+2.76}$	${7.35}_{-1.12}^{+2.71}$
PA 90
PA 0	94	${2.43}_{-0.49}^{+1.56}$	${2.89}_{-0.68}^{+1.70}$
HST	157	${1.85}_{-0.43}^{+1.36}$	${1.99}_{-0.45}^{+1.42}$
Gaia	24	${7.39}_{-1.20}^{+2.72}$	${7.80}_{-1.25}^{+2.79}$

Further, we used the HST photometric measurements as an absolute standard to compare the NIRC2 single-PSF and variable-PSF photometry against. We do this by generating a color-magnitude diagram (CMD) for each PSF mode and PA, where we compare the HST I – Keck K color against the Keck K magnitudes for all cross-matched stars in each catalog. The NIRC2 data were photometrically calibrated to 2MASS Ks band magnitudes for this process. We cross-identify two bright stars in common between the NIRC2 data and 2MASS (2MASS J13125435 + 1810172 and 2MASS J13125408 + 1810194). From this cross-identification we calculate a zero-point offset of 3.70 and apply this to all stars in each catalog, including a calibration error of 0.06 magnitudes.

We then used the open-source package SPISEA¹⁹ to generate a synthetic population for the cluster. We used parameters for the cluster age, metallicity, and mass fraction from Refs. 20 and 21. We also adopted the extinction law of Ref. 22 when generating the population. The top panels of Fig. 12 show the single-PSF and variable-PSF CMDs. The data are colored by off-axis radial distance in the NIRC2 frames, and the best-fit isochrone from SPISEA is overlaid (black curve). Characteristic errors in color and magnitude for the CMDs are given by the vertical columns. There is a clear trend seen in the comparison between the CMD stars and the isochrone model in the single-PSF CMD. The difference in color between the stars and isochrone model shows a relatively strong dependence on radial distance in the NIRC2 frames. This same dependence is not seen in the comparison of the variable-PSF CMD and best-fit isochrone model. The lower panels of Fig. 12 show the color difference measurements (and errors) as a function of off-axis distance. A linear fit is made to each distribution, and the resulting slopes are $0.041\pm 0.008{\mathrm{mag}\mathrm{arcsec}}^{-1}$ for single-PSF mode and $-0.002\pm 0.009{\mathrm{mag}\mathrm{arcsec}}^{-1}$ for variable-PSF mode. These results suggest roughly an order of magnitude improvement in the photometric performance of the variable-PSF mode compared to single-PSF mode. This marks the first definitive example of a significant improvement shown by variable-PSF mode over the single-PSF mode for on-sky science data.

Fig. 12

(a) The M53 HST I–Keck $K$ versus Keck $K$ CMDs for both single-PSF and variable-PSF star lists. The solid black curve gives the best-fit SPISEA isochrone, with age, metallicity, mass fraction, and extinction from Refs. 20–22. (b) The measured color index difference (i.e., empirical – isochrone) in single-PSF and variable-PSF modes as a function of off-axis radial distance. The solid red line shows the linear best-fit to each distribution, with the shaded gray region showing the $1\sigma$ spread around the best-fit. The distribution of color differences for single-PSF mode has a clear trend in radial distance, while the distribution is largely constant for variable-PSF mode.

3.3.4.

Gaia cross reference

We continue our comparison of the single-PSF and variable-PSF catalogs by transforming both lists to the Gaia EDR3 catalog.²³ While Gaia has delivered exquisite astrometric data for over one billion sources now, there is a sizable fraction of spurious values reported by the instrument that are not so reliable. Recently, it has been shown that numerous astrometric solutions reported by Gaia suffer quite significantly for low signal-to-noise sources as well as for sources in crowded fields.²⁴ Given that the central region of M53 is crowded, we perform a careful investigation of Gaia astrometric quality flags for the stars cross-matched between NIRC2 and Gaia. A consideration that we make when matching the two PA’s to Gaia is the astrometric fitting errors as described in Refs. 23 and 25. In particular, the “astrometric excess noise ($ϵ$)” parameter is described as the excess uncertainty that must be added in quadrature to obtain a statistically acceptable astrometric solution. Further, the excess term $ϵ$ is introduced in order to effectively reduce the statistical weight of observations that may be affected by things like instrument and attitude modeling errors. Another error term we consider is the “astrometric excess noise significance,” which is described as a dimensionless measure of the significance of the calculated $\epsilon$. A value of $>2$ indicates that the reported $ϵ$ is “probably significant.”²⁶ Further details on these astrometric error terms can be found in Ref. 26.

Figure 13 shows the values reported by Gaia for the two astrometric error terms described above. The star symbols in the figure represent 32 NIRC2 stars that were cross-identified in Gaia. All other Gaia stars within a 30 arcsec radius of the center of the NIRC2 frame are plotted as well, and both distributions are colored by Gaia G magnitude. Given the higher astrometric precision in both the Keck and HST data, we choose to make a cut on the Gaia stars at $ϵ<5$ mas and significance $<2$ (shaded regions in Fig. 13), which leaves 24 remaining Gaia stars (unshaded region) that are used for the final transformation. As a note, we tested more strict and less strict cutting thresholds for this process (i.e., some stars rejected by their significance value) and found similar results for each scenario. The cut at $ϵ<5$ mas left a sufficient number of stars needed for a reliable first-order transformation, while rejecting likely astrometric outliers (which are mostly faint, low-SNR stars).

Fig. 13

Astrometric excess noise significance versus astrometric excess noise as a function of Gaia $G$ magnitude in the 30 arcsec field surrounding the center of the NIRC2 images. The reference stars used for the NIRC2 $\to$ Gaia transformation are marked as star symbols. Dotted vertical and horizontal lines denote the noise and noise significance thresholds used to cut reference stars.

The quiver plots in the top panels of Fig. 14 show the 2D astrometric residuals after transforming the PA 0 deg stars to the Gaia reference frame. The distribution of astrometric residuals for both PA’s peaks at ${\sigma }_r\sim 5$ mas, and the faintest stars have the largest residuals, as expected. Table 4 shows the weighted mean for each distribution, where the mean and errors are largest for Gaia. As described earlier, there are several reasons why the Gaia residuals are largest —generally, the Gaia astrometric precision is worse than HST (and NIRC2), especially for crowded field sources. The astrometric excess noise and other error terms contribute overall larger residuals when transforming NIRC2 into the Gaia reference frame. Finally, the calculation of the weighted mean and central 68% of the distribution is more significantly affected by the spread in residuals (and possible outliers) for the much smaller Gaia data set (24 stars).

Fig. 14

Same as Figs. 10 and 11 but for stars transformed to Gaia EDR3. The color bar is given in Gaia G magnitude.

3.4.

Expected Performance and Comparison to Simulations

The expected reduction in astrometric and photometric uncertainties for variable-PSF mode was not seen for the on-sky datasets considered in this work. As described in Ref. 7, for simulated data (e.g., fiber sources and the simulated GC scene), the photometric and astrometric residuals were significantly reduced (by 80% on average in variable-PSF mode). In contrast, our on-sky results show an improvement in variable-PSF mode of only 15% in the best case. Figures 11–17 of Ref. 7 show simulation results, including comparisons of photometric and astrometric residuals, as well as the FVU values for single-PSF versus variable-PSF modes.

In more detail, the simulated GC scene analyzed in Ref. 7 shows a positional accuracy improvement from $8.3\times {10}^{-1}$ mas (single) to $1.7\times {10}^{-1}$ mas (variable). The photometric accuracy improved from $3.7\times {10}^{-2}$ mag (single) to $0.6\times {10}^{-2}$ mag (variable). Our best-quality, on-sky GC (GC GQ) results show only a small reduction in astrometric and photometric accuracy of $8.15\times {10}^{-1}$ mas (single) to $8.06\times {10}^{-1}$ mas (variable) and $3.64\times {10}^{-2}$ mag (single) to $3.62\times {10}^{-2}$ mag (variable), respectively. In the GC simulations, the median FVU for variable-PSF mode is $6.2\times {10}^{-5}$, significantly better than the single-PSF value of $5.7\times {10}^{-4}$. Again, our best on-sky GC results show identical median FVU values between both PSF modes for all stars as well as only bright stars ($5.0\times {10}^{-3}$ for bright stars in both modes). Finally, since the study of Ref. 7 shows similar improvement (e.g., same order of magnitude) in residuals between a sparse field of fiber sources and the simulated GC scene, then similar improvements are to be expected in the case of OB150029 and M53.