KPNO WHIRC INFORMATION

Introduction

 

The WIYN High-Resolution Infrared Camera (WHIRC) is a near-infrared (0.9 – 2.5 μm) imager which installs on the WIYN Tip/tilt module (WTTM) port.  The 0.1 arcsec pixel scale and 3.3 arcmin field of view are designed to take advantage of the excellent native seeing at the WIYN site and the near diffraction-limited image quality (~ 0.2 arcsec) which WTTM is expected to deliver in the 2 micron band.  A selection of wide- and narrow-band filters allow WHIRC to achieve a broad range of scientific goals in stellar physics, star-forming regions, and the ISM in galactic and extragalactic sources.

 

As noted in the current observing information, WHIRC is being offered for the 2009A semester in shared-risk mode in direct imaging mode, since the instrument has not yet been officially accepted by WIYN.  In addition, shared-risk operation with WTTM tip/tilt correction will be supported on a limited basis, contingent on the availability of support personnel familiar with WTTM operation.  This will permit the community to gain experience with the instrument as the commissioning effort is completed.  WHIRC has had several engineering runs on WIYN during 2007 and early 2008, as well as shared-risk science blocks in April, May, July and September 2008.  Unfortunately, the weather has limited the on-sky time for completing the commissioning effort prior to the September run, although significant progress has been made in the integration of the observing platform software.  This webpage is intended to give prospective investigators information which is available as a guide for writing proposals and will be updated as information becomes available.

 

The replacement of the IR Acquisition Board in the MONSOON data acquisition system appears to have largely eliminated the electrical pickup from the instrument rotator motor, resulting in noise performance which now meets the acceptance specifications.  The new board has also changed the conversion gain from 3.7 to 4.0 e/ADU.

 

Useful Facts

 

 

Wavelength Coverage

900 – 2500 nm

Filters

J, H, Ks; 10 narrowband

Pixel Scale

0.098 arcsec

Field of View

200 × 200 arcsec

Detector

Raytheon Virgo HgCdTe, 2048 × 2048

Detector Gain

4.0 e/ADU (0.7v bias)

Read Noise

~ 9 ADU (35 e) Fowler 1

Full Well

~ 35000 ADU (140000 e)

 

Instrument Description

 

WHIRC is a straight-through all-refractive imager with no moving parts except for the two filter wheels.  This design was dictated in part by the stringent instrument envelope and weight requirements of the WTTM port.  The optical system consists of a five-element collimator and a five-element camera.  A fixed cold stop is located at the pupil image formed by the collimator.  The two filter wheels are located on either side of this stop, placing the filters very close to the pupil image.  A single LN2 reservoir provides cooling for the optics and the HgCdTe detector, whose temperature is regulated by a servo control loop.  The detector controller is the Monsoon system developed at NOAO.  Figures 1 and 2 show schematics of the instrument and a closeup of the optical assembly.

 

 

 

Figure 1:   Assembly drawing of WHIRC.  The shim is used to adjust the axial location of WHIRC so that the WTTM focal plane is imaged onto the detector.

 

Figure 2:  Close up of Figure 1, showing the optical elements in more detail.

 

 

Filters

 

The two 8-position filter wheels allow a total of 13 filters.  Each filter wheel must have one open position and one wheel has an opaque blocker for taking dark frames.  Table 1 lists the filter characteristics, as well as the observed signal in ADU/s corresponding to a mag=10.0 star determined from observations of the IR standard FS 28 at a bias of 0.7 v.  The sky background levels in ADU/s-pixel have been measured during the observing runs from March through September 2008, spanning the temperature range -4 C to 18 C.  The background in the K band filters is dominated by thermal emission and varies a factor of four over this temperature range.   In addition, the background in the other filters, except for the 1.06 and 1.082 μm narrowband filters, is dominated by OH airglow, which can vary a factor of two from the values listed in Table 3.1.  Links to tracings of the individual filters are given at the bottom of this web page.

 

The three broadband filters are standard J, H, and Ks filters.   The narrowband filters include those for He I (H II regions, PNe), Br γ and Pa β (ionized gas), [Fe II] (photodissociation regions and PNe), H2 S(1) (shocked molecular gas), and CO (cool stellar atmospheres).  In addition, Br γ, Pa β and [Fe II] filters redshifted by ~ 4500 km/s are used to provide continuum images for emission line imaging in those filters or for observing these emission lines in redshifted galaxies.  Finally a filter near 1.06 μm is located in a region nearly devoid of telluric OH line emission for very low-background deep imaging.

 

Note:  The actual WHIRC filters were scanned by the vendor only at ambient temperature.   Instead, standard size (25 mm) witness samples which were coated during the filter run were scanned at both ambient and cryogenic temperatures, and the difference between them was used to correct the ambient WHIRC filter parameters to their calculated cryogenic values.  Because broadband filters often have oscillatory behavior in their transmission curves and narrowband filters of 1% fractional bandwidth rarely have a truly flat region at their peak transmission and may have broad wings, the definition of “average” transmission can be a matter of judgment.  For the purpose of this table, we calculated the integrated transmission under the ambient filter curves and divided by the vendor-calculated cryogenic FWHM of the filter to derive the number listed as average transmission.  Since the product of these is actually used in throughput calculations this is a somewhat artificial definition, but the FWHM is an important parameter, particularly for the study of high-redshift emission line targets.

 

 

Table 1.  WHIRC Filter Characteristics

 

Filter

λ(μm)

Δλ (μm)

tavg

Signal 10.0 mag

Background

    March          Sept

J

1.250

0.162

0.913

183000

5

6.7

H

1.651

0.310

0.867

195000

25

40

Ks

2.168

0.343

0.877

109000

70

270

Low airglow

1.060

0.0132

0.638

15300

0.18

0.22

He I

1.082

0.0094

0.706

10000

0.25

0.33

Pa β

1.280

0.0158

0.872

15500

1.3

1.4

Pa β (4500 km/s)

1.303

0.0133

0.863

13500

0.8

1.0

[Fe II]

1.646

0.0164

0.791

10500

1.9

2.6

[Fe II] (4500 km/s)

1.668

0.0162

0.917

11300

2.5

4.1

H2 S(1)

2.117

0.0216

0.680

7150

2.4

8.3

Br γ

2.162

0.0215

0.849

7500

3.8

13

Br γ (4500 km/s)

2.188

0.0237

0.940

8400

5.0

18

CO

2.293

0.0228

0.797

5800

6.9

30

 

 

 

Imaging Performance

 

Commissioning and characterization have been limited by three issues encountered during the T&E efforts over the past year.  The most annoying has been the presence of electrical pickup which completely dominates the noise performance.  This not only results in a read noise well above the requirement, but the spatial coherence leads to additional systematic errors in an aperture photometry measurement.  The majority of the pickup noise was determined to come from the instrument rotator power supply.  Relocating the WHIRC power supply near the instrument and shielding the cables helped reduce this.  Replacement of the Monsoon IR Acquisition Board by another (supposedly identical) board has effectively eliminated the spurious pickup, and we are now seeing read noise levels which meet the requirements.  While the noise could probably be reduced further with some effort, it is now sufficiently low to permit background-limited observing even in the narrowband filters.  A second issue was intermittent operation of the filter wheel, which resulted in the January 2008 T&E run in excellent conditions being restricted to the J filter.  This was traced to a cold solder joint in the filter wheel cable, which has now been repaired; no further problems have been seen in filter operation.  The third issue was an unusual spatially dependent nonlinearity in the detector response which made it difficult to characterize the flatfielding and photometric quality possible with the instrument.  We have found that lowering the detector bias from 1.0 v to 0.7 or 0.8 v results in a much more “normal” linearity performance which appears to be the same within 1 – 2 % over the array.  We have since chosen 0.7 v as the operating bias, and the data presented in Table 1 were obtained with that value.

 

During the January 2008 T&E run in the J filter, images as good as 0.29 arcsec FWHM were obtained without WTTM correction on a night of excellent seeing.  Optical testing using a pinhole array at the input of WTTM yields images with FWHM ~ 0.17 arcsec.  This gives some confidence that WTTM/WHIRC is not likely to limit the image quality and that images in the 0.2 – 0.25 arcsec FWHM are a realistic goal once WTTM is operating.  The signal levels shown in Table 1 were obtained with 0.5 arcsec FWHM images and utilized a 2 arcsec diameter extraction aperture.

 

Operation

 

Progress in integrating the operation of WHIRC with the telescope has been limited in part because of the concentration on the noise and detector issues noted above.  In addition, full operation, including guided offsetting with WTTM, has proved to be a challenging task which lies somewhat outside of the original WTTM operations requirements, but we have made significant progress in this area and plan to establish working procedures by the beginning of 2009.  A number of “canned” scripts to carry out dithered offsets have been written for the Monsoon Observing Platform (MOP), which is the standard user interface.  In addition, one can utilize the WHIRC Observation Manager and Planner (WHOMP) to set up specific dither/offset scripts for particular targets in advance and execute them at the telescope.  WHOMP scripts may also be edited at the telescope to provide some flexibility without the need to generate new scripts.  It is possible to guide during the execution of these scripts using the IAS guider if the WTTM is not being used.  However, for both WTTM and IAS guiding, it is necessary for the observer to ensure that the telescope motions during the script execution do not carry the selected guide star out of the range of the guide probe.  One goal for a “next generation” upgrade to the WHOMP is to include guide star selection so that observers can ensure that the guide star will remain in range of the probe motion.

 

The WHIRC detector operation uses the double-correlated sampling (DCS) technique employed with virtually all infrared arrays.  This involves a reset (biasing) of the detector, followed by a non-destructive readout of the array and a second readout starting after a predetermined time interval (which is the integration time).  These two readouts are then subtracted to yield a bias-subtracted image.  The minimum integration time is therefore the detector readout time, which is approximately 4 s for WHIRC.  This mode, also referred to as “Fowler 1” is identified as “Fowler-1” on the MOP interface (all readout modes utilize the rolling reset with four digital averages, so these are not explicitly noted on the MOP).  A second user mode, “Fowler-4” reads the array out four times at the beginning and four times at the end of the integration.   This effectively reduces the read noise by a factor of two and is therefore a preferred mode for low-background, faint target observations, where one would be read noise limited.   For such programs, one would want to use long frame times, so the longer detector readout time (16 s) does not represent a significant duty cycle penalty.  Note:  Multiple-readout data are not renormalized, so values in Fowler-4 mode will be four times those given in Table 1.

 

Performance

 

The reduction of the read noise as of September 2008 to typical values ~ 35 e in Fowler 1 mode and ~ 20 e in Fowler 4 mode should make it possible to achieve background-limited performance in all filters except perhaps the Low Airglow and HeI.  The small pixel size results in a background signal, even in the broadband filters, which is about ten times smaller than that which users of typical wide-field imagers may be accustomed to.   The combination of these factors means that relatively long integration times will be required to achieve background-limited performance, and narrowband imaging will be operationally similar to optical CCD imaging, utilizing a relatively small number of long (600s or more) exposures.

Sensitivity

 

One may roughly estimate the performance using the signal and background values listed in Table 1, under the assumption that the only sources of noise are the read noise of the detector and photon statistics (shot noise) from the signal and background.  For an integration time ‘t’ and a gain (e/ADU) of ‘g’, the signal from a source of magnitude ‘m’ is:

 

            S = 10-0.4 (m -10) * Ns * t * g  (e),  where Ns is the signal from Table 1.

 

The noise is given by:

 

            N = [ S + Nb * t * g * Npix + rn2 * Npix ] 0.5  ,

 

where Nb is the background level from Table 1 and Npix = 78.5 * A2 is the number of pixels within the extraction aperture of diameter A arcsec.

 

To do sky subtraction, at least two images of a field are required, and the subtraction of two images will effectively increase the noise by 1.414, which is the same as the signal gain from the increased target time resulting from two observations.  For very faint targets, one will take multiple dithered images and generate a master sky frame which can be subtracted from each raw image.  For a large number of frames, the increase in noise resulting from the sky subtraction can be quite small, and one can approach the theoretical signal-to-noise given by the ratio of S to N above.  For multiple frames of a target, the S/N should increase as nf0.5, where nf is the number of frames (total integration time = t * nf).

 

Table 2 gives examples of this calculation for the J, H, and Ks filters, where the performance is given as the source brightness corresponding to a 10σ detection in a total of 1 hour of on-source time.   We assume the use of the Fowler-4 observing mode, for which the read noise is assumed to be 20 e, and an extraction aperture 1.6 arcsec diameter, which is reasonable for an image FWHM = 0.5 arcsec.  WTTM correction of the image in the future should yield further improvements in point-source limits, as would the use of psf-fitting photometry.  The use of the Fowler-4 mode will increase the signal and noise values in ADU by a factor of four.

 

Note that the backgrounds in the J and H filters are close to the “typical” Kitt Peak values determined with other near-IR imaging instruments.  The background in the Ks filter is higher for two reasons:  WIYN is not an IR-optimized telescope and the emission from the central obscuration is not blocked by the internal cold stop; the optical path contains far more (9 vs 2) warm elements than seen by an imager mounted at a Cassegrain focus.  The temperature was actually quite cold (-4 C) on the night the performance was evaluated, and on summer nights, the K band background can be a factor of four higher (Table 1), degrading the performance by a factor of two (0.7 mag).  The anticipated goal is that once WTTM is operating, the smaller detection aperture will compensate for the higher background surface brightness.

 

 

Table 2:  WHIRC Imaging Signal and Background Levels (ADU-s-1) and Estimated Performance

Nread = 20 e; aperture = 1.6 arcsec diameter

 

Filter

Signal

(10 mag)

Background

(pixel)

Background

(mag-arcsec-2)

Performance

(10 σ; 1 hr)

J

1.83 × 105

   5.0

16.4

22.0

H

1.95 × 105

 25.0

14.7

21.3

Ks

1.09 × 105

70.0

12.9

20.1

 

 

These performance estimates are quite good, but possibly optimistic.  The calculation assumes the signal from the source to be negligible in comparison to the sky background, which is reasonable for a limiting calculation.   However, reduction steps such as sky subtraction and flat fielding will invariably add some noise, as will any cosmetic defects or variations in sky background over the observation.  During the July 2008 run, a series of twelve 300s integrations in J were obtained under (probably) photometric conditions and reduced using a local sky frame and dome flats to yield a 10 σ limit of 21.4, close to that calculated for Table 2 (the measured sky background in July was actually closer to 8 ADU/pixel, which would reduce the predicted limit in Table 2 to J = 21.8).  

 

Linearity

 

All infrared arrays utilizing a unit cell architecture are inherently nonlinear, since the potential well created by the application of the bias voltage has a capacitance which increases as the collected charge fills up the well (one may think of the two capacitor plates moving closer together).  In parallel with the capacitance of the rest of the unit cell, this yields a gain which varies slowly as the well fills up.  Under the condition of constant signal flux, the plot of signal vs. time would begin at a slope near unity and slowly roll off until the array saturates.  Alternatively, one can define a “linearity” function, which is essentially the slope of the signal vs. time plot normalized to the value at small signal levels.  A plot of the WHIRC linearity for a bias of 0.7 v is shown in Fig. 3a.  Note that the linearity decreases smoothly by about 3% at a signal level of 36000 ADU, then decreases suddenly as the array saturates.  One can obtain a linearity correction function by plotting the well-behaved data (below 36000 ADU) and fitting a second-order polynomial to it (Fig. 3a).

 

 

Figure 3: (left panel):  Plot of linearity vs. signal level for a bias value of 0.7 v for seven subregions on the array.  Note that the linearity behavior in a region near the lower left corner is different than that over the rest of the array.  A second-order polynomial was fit to the well behaved data [excluding region B and the saturated data above 36000 ADU].  (right panel):  The original data corrected for nonlinearity using the IRAF task irlincor and the coefficients derived from the second-order polynomial fit.  Note that one can achieve correction to ~ 0.5% up to 38000 ADU.

 

 

The quadratic fit to the data in Fig. 3a is of the form y = A + Bx + Cx2, where

 

            A = 1.000

            B = -3.62 × 10-7

            C = -1.839 × 10-11

 

By inverting this function, one can derive a linearity correction function so that the corrected signal S’ is related to the raw signal S by

S’ = S * (A + B*S + C*S2), where

 

            A = 1.000

            B = 1.29 × 10-7

            C = 2.506 × 10-11       

 

The IRAF task irlincor is specifically designed to carry out this correction.  It is critical that linearity correction be performed on the raw data, prior to any sky or dark subtraction.  The corresponding irlincor coefficients are:

 

            A = 1.000

            B = 0.004227

            C = 0.02691

Saturation

 

Because of the small pixel scale of WHIRC, it is tempting to think that saturation on brighter stars is not as critical as for a wide-field imager with larger pixels, but the combination of a 3.5-m aperture, a 4 s minimum integration time, and good image quality does mean that one must consider this issue.   If WHIRC attains its goal performance in conjunction with WTTM, it will yield image cores with FWHM < 3 pixels, similar to what one obtains with FLAMINGOS on the 4-m under median seeing conditions.

 

The data presented in Table 1 were obtained under seeing conditions ~ 0.5 arcsec (5 pixels FWHM).  Empirically, the peak pixel flux was typically 0.03 of the integrated flux within the 1.6 arcsec diameter aperture.  For a H = 10.0 star in the minimum integration time of 4 s, this yields a peak pixel signal of ~ 23000 ADU, seemingly at a safe level of slightly over half full well.  However, seeing fluctuations over these short times could result in “good” images which push the peak pixel close to saturation.

 

Finally, note that we have settled on a bias value of 0.7 v for operation, since the lower bias appears to give fewer “maverick” pixels.  However, the saturation level is ~ 36000 ADU.

 

Flatfielding

 

The quantitative performance of image flatfielding is still under investigation, as this effort had to await the resolution of the above-mentioned work on higher priority issues such as the noise, proper bias voltage selection, and linearity.   The initial tests with WHIRC, carried out at a detector bias of 1.0 v, gave very strange linearity behavior, which resulted in poor flatfielding.  The current bias of 0.7 v gives predictable linearity, as demonstrated above, and stable flatfielding performance.  The primary unresolved issue is an analytical correction for the pupil ghost, which is discussed below.

 

Pupil Ghosting

 

One feature which has not yet been quantitatively investigated is a pupil ghost in the flatfield images.  This is a characteristic which is found in many refractive imaging instruments, due in part to reflections from the detector and the optical surfaces.  The effect can be seen at all wavelengths (Fig. 4), although it is exacerbated at thermal wavelengths (K band) in the case of WHIRC by the large number of ambient temperature mirrors (9) in the optical train.  The pupil ghost manifests as a broad peak centered on the array, with a peak value about 5% above average at J, but almost 25% at Ks.  This does NOT represent a real peak in the response, so the use of a flatfield constructed from raw sky or lamp flats will give artificially low flux values for targets near the center of the array.  We are working on establishing a low spatial frequency “pupil flat” which would be applied to observed flats to yield a corrected flat for use in the data reduction.

 

We recommend the use of dome flats generated by the “lights on – lights off” technique.  This effectively subtracts out any pupil artifacts common to both, such as thermal radiation from the telescope or warm WTTM optics.  Sky flats will exhibit a pupil ghost which is a combination of that from the sky and the telescope; these two contributions not only have different spatial characteristics, but will vary in relative strength with ambient temperature.

 

 

 

Figure 4:  Flatfields through the J (left panel) and Ks (right panel) filters at a bias of 0.7 v.  These were taken using the dome screen and the “lights on – lights off” subtraction technique, and normalized to 1.0.  The decreased response at the top and bottom of the arrays probably represents variations in the detector quantum efficiency or antireflection coating characteristics, but appears to calibrate out.  The pupil ghost, visible as a bright spot in the center of the array, is not a true peak in the response, and must be calibrated out of the flats.

 

Dimples

 

A typical flatfield image (Figure 4) shows numerous circular features which appear to be array defects.  The cause of these features is unknown.  However, it is important to realize that these are not dead pixels, but regions of depressed sensitivity which still respond linearly to radiation; as a result, they can be largely corrected by flatfielding (Figure 5).  The system sensitivity within these regions is, of course, reduced.

 

The measured flux from a star which falls on one of these regions will be significantly reduced in unflattened images, but relatively unaffected in the flattened images.  In the analysis results presented below in Table 3, this factor is probably the greatest contribution to the higher sigma in the unflattened images and explains why only some stars were affected.

 

 

Figure 5:  (top left):  128 × 128 subimage of an H-band dome flat, showing the normal “tree-ring” structure and the circular, apparently dead features.  A line plot through one of the spots (lower left) shows that the features are not dead pixels, but regions of reduced responsivity.   The ratio of two separate flatfields taken five months apart (top right) shows that the features are quite stable over long periods to within a few percent (lower right).

 

Flatfield Stability

 

Although we have limited data taken under photometric conditions to establish the photometric accuracy which one can expect, flatfields taken over the time span from April through September 2008 (once we had settled on a bias voltage of 0.7 v) have proved to be remarkably stable.    All of these dome flats were taken using the same “lights on – lights off” procedure and normalized in the same way to the signal level in two subregions well away from the pupil ghost.  Figure 6 shows ratios of flatfields taken in September to those taken in April for the Ks broadband and Paβ narrowband filters.  Even in the vicinity of the pupil ghost in the Ks flat, the deviations are no more than 1 %.

 

 

 

Figure 6:  Ratios of dome flats taken in September to those taken in April for the Paβ narrowband filter (left panel) and the Ks filter (right panel).  The spatial stability of the flats is generally better than 1% over this time span, even near the Ks pupil ghost.

 

Photometric Performance

 

We have carried out several experiments to evaluate the photometric performance possible with WHIRC.  A complete report on these is available for downloading.  One of these experiments, described briefly here, suggests that accuracy of 1 – 2% should be presently possible in regions of the array away from the pupil ghost.  The goal, of course, is to generate pupil ghost correction algorithms which will yield this precision over the entire field of view.

 

In one experiment, the open cluster NGC 7790 was observed using a 3 × 3 grid on 30 arcsec centers through six filters (J, H, Ks, Paβ, FeII, and Brγ) to verify the photometric precision/flatfielding in both broad- and narrowband filters.  This cluster (Figure 7) has six well-determined photometric standards from the list of Hunt et al. (1998, AJ, 115, 2594).  The six stars are spread out over almost 2 arcmin, so the grid gave good coverage over the array.  The observations were reduced in the standard fashion by first correcting for linearity, then generating a sky frame from the median of the observations and subtracting this from each of the raw frames to yield a sky-subtracted image.  This was then divided by the dome flat for the appropriate filter, but with no correction for the pupil ghost.  The stars were then measured using the IRAF task phot, with a 3 arcsec aperture with sky subtraction and the measured magnitudes were then subtracted from the published values.

 

 

Figure 7:  WHIRC J band image of the open cluster NGC 7790.  The six stars from Hunt et al. are noted.  The results from star 5 were rejected because the published magnitudes included the faint companion which is easily resolved in this image.

 

The residuals (measured – published) were then averaged over the nine sky positions and the standard deviation of the mean calculated, for each of the six stars in the six filters.  This was done for the images both prior to and after flatfielding, to evaluate the effect of the procedure.  Table 3 presents the averages of the results for the nine positions:  the mean of the flatfielded images, and the standard deviation of the mean for the unflattened and flattened images.  Note that this experiment require photometric conditions, but is not sensitive to the accuracy of the published standard star magnitudes.  The last two columns represent the average (and standard deviation) over the six stars; this does bring into consideration the uncertainty of the published Hunt et al. magnitudes, which are formally in the 0.8 – 1.8 % range. 

 

The apparent discrepancy in the results for star 5 compared to the others was resolved when it became clear that Hunt et al. had included the flux from a companion star about 3.2 mag fainter approximately 3.5 arcsec away; the two stars were of course easily resolved in the WHIRC images.  The final column presents the results excluding star 5.  Since the 3 × 3 grid would have placed a star within the pupil ghost for at most one of the nine positions, the practical effect of neglecting the ghost was small for this experiment.  The results summarized in Table 3 suggest that photometric accuracy on the order of 1 – 2% should be possible away from the center of the field, where the pupil ghost is significant.   Correction for the pupil ghost is an important short-term goal.

 

Table 3:  Results of Position-averaging Photometry in NGC 7790

 

 

 

star0

star1

star2

star3

star4

star5

all

stars 0-4

J

mean

1.977

1.986

1.997

2.013

2.006

2.057

2.006

1.996

sd noflat

0.026

0.026

0.092

0.025

0.013

0.038

0.039

0.035

sd flat

0.019

0.018

0.007

0.015

0.009

0.019

0.028

0.015

H

mean

1.892

1.900

1.929

1.916

1.926

1.980

1.929

1.913

sd noflat

0.030

0.029

0.087

0.050

0.041

0.039

0.040

0.036

sd flat

0.020

0.019

0.010

0.014

0.011

0.044

0.031

0.016

Ks

mean

2.503

2.505

2.518

2.521

2.518

2.527

2.515

2.513

sd noflat

0.019

0.037

0.086

0.048

0.019

0.041

0.029

0.030

sd flat

0.031

0.019

0.010

0.021

0.015

0.016

0.009

0.008

PaB

mean

4.499

4.489

4.494

4.533