Cat 5sig AB-lim                                                                ---- 27.5  27.2  27.0  28.46 28.36 28.27  ----
    Counts 80% compl                                                               ---- 26.9  26.4  26.2  27.9  27.5  27.4   ----
    DelABlim(80%-ETC)                                                              ---- -1.0  -1.1  -1.1  +0.8  +0.3  +0.1   ----

    -----------------------------------------------------------------------------------------------------------------------------

Notes: For each object, line 1 lists the J2000 (RA, Decl.) tangent point to
which the images were drizzled, the observing date, the APT visit number, the
area covered, the net exposure time per filter and the net total hours per
visit, as well as the visit’s spacecraft efficiency. Line 2 lists for each
filter the stellar PSF-FWHM in arcsec as measured from unsaturated stars in
the drizzled images. Line 3 lists the 5-sigma point source sensitivity in AB-
mag predicted by the pre-launch ETC for the net integration time on the first
line of each target. NIRCam ETC Parameters used were aperture radii
r=0$\buildrel\prime\prime\over{.}$08 for SW and
r=0$\buildrel\prime\prime\over{.}$16 for LW, and sky annuli
r=0$\buildrel\prime\prime\over{.}$3–0$\buildrel\prime\prime\over{.}$99 for SW
and r=0$\buildrel\prime\prime\over{.}$6–1$\buildrel\prime\prime\over{.}$98 for
LW. Line 4 lists the 5-sigma detection limit derived from the AB-level in
Figure 4–6 where the median SourceExtractor catalog flux error is 0.20 mag.
Line 5 indicates the AB-level in Figure 4–8 where the galaxy counts are
$\sim$80% complete compared to a power law extrapolation. Line 6 indicates the
difference between the 80% galaxy count and predicted ETC 5-sigma point source
completeness limits in AB-mag. All PEARLS NIRCam images would have a zeropoint
of 28.0865 to convert the flux (in MJy/sr) in each drizzled
0$\buildrel\prime\prime\over{.}$0300 pixel to AB-mag. However, the ZPs in
Table 4 of Rigby et al. (2022) have not been implemented into NIRCam pipeline
v. 1.5.2–1.6.2 products before July 29, 2022. Therefore, effective ZPs
corrections for our drizzled 0$\buildrel\prime\prime\over{.}$0300 pixels are
listed for the broad-band filters in the JWIDF and VV191 and the medium-band
filters in TNJ in Appendix B.1. These ZPs corrections must be applied to our
JWIDF, VV191 and TNJ images and mosaics, or the catalog AB-magnitudes, until
STScI releases official updates of the NIRCam pipeline.

    Table 2. PEARLS Targets, Area Covered, Exposure Times, and Depth per Image or Grism: NIRCam, NIRISS, NIRSpec data to be taken
    =============================================================================================================================
    Instr.+Filters  R.A.  (J2000)  Decl.      Obs. Date  Visit   Area   SCeff Net ------------- Net t_exp (sec) -----------------
    Target           h  m  s.sss   o  ’   "   YYYY-MM-DD  Nr    (’)x(’) (%)   Hrs ------- 5-sigma point-source AB-limit ---------
    -----------------------------------------------------------------------------------------------------------------------------
    NIRCam Broad-band:                                                            F090W F115W F150W F200W F277W F356W F410M F444W
    -----------------------------------------------------------------------------------------------------------------------------
    IRAC-Dark-ep2   17 40 08.535 +68 58 27.00 2023-01-05 121.2 2.15x4.30 53.9 1.76 ----  ----  2512  2512  ----  2512  ----  2512
                                                                                ----  ---- 28.75 28.93  ---- 28.64  ---- 28.23
    IRAC-Dark-ep3   17 40 08.535 +68 58 27.00 2023-07-01 121.3 2.15x4.30 53.9 1.76 ----  ----  2835  2835  ----  2835  ----  2835
                                                                                ----  ---- 28.87 29.04  ---- 28.74  ---- 28.34
    NEP-TDF-ep1     17 22 47.896 +65 49 21.54 2023-05-21 111.1 2.15x6.36 64.9 3.49 2920  2920  3350  3350  3350  3350  2920  2920
                                                                                28.61 28.77 28.91 29.09 28.81 28.82 28.07 28.35
    NEP-TDF-ep2     17 22 47.896 +65 49 21.54 2022-08-26 112.1 2.15x6.36 64.9 3.49 2920  2920  3350  3350  3350  3350  2920  2920
                                                                                28.64 28.80 28.94 29.11 28.84 28.84 28.09 28.37
    NEP-TDF-ep3     17 22 47.896 +65 49 21.54 2022-11-22 113.1 2.15x6.36 64.9 3.49 2920  2920  3350  3350  3350  3350  2920  2920
                                                                                28.62 28.78 28.92 29.10 28.82 28.82 28.05 28.31
    NEP-TDF-ep4     17 22 47.896 +65 49 21.54 2023-02-18 114.1 2.15x6.36 64.9 3.49 2920  2920  3350  3350  3350  3350  2920  2920
                                                                                28.60 28.76 28.91 29.09 28.81 28.81 28.04 28.30
    WFC3-ERS-Field  03 32 42.397 -27 42 07.93 2023-07-29 131.1 2.15x4.30 63.3 3.48 3779  3779  2491  2491  2491  2491  3779  3779
                                                                                28.63 28.81 28.74 28.92 28.58 28.57 28.07 28.29
    MACS0416-24-ep1 04 16 08.900 -24 04 28.70 2022-09-26 211.1 2.15x4.30 64.4 3.72 3779  3779  2920  2920  2920  2920  3779  3779
                                                                                28.70 28.87 28.91 29.10 28.74 28.77 28.24 28.50
    MACS0416-24-ep2 04 16 08.900 -24 04 28.70 2022-12-10 212.1 2.15x4.30 64.4 3.72 3779  3779  2920  2920  2920  2920  3779  3779
                                                                                28.72 28.89 28.93 29.13 28.78 28.82 28.29 28.57
    MACS0416-24-ep3 04 16 08.900 -24 04 28.70 2023-09-26 213.1 2.15x4.30 63.9 3.61 3779  3350  2920  2920  2920  2920  3350  3779
                                                                                28.70 28.80 28.91 29.10 28.74 28.77 28.17 28.50
    Abell2744       00 14 21.200 -30 23 50.10 2023-07-29 221.1 2.15x4.30 62.1 3.25 3350  3350  2491  2491  2491  2491  3350  3350
                                                                                28.53 28.71 28.72 28.92 28.60 28.66 28.17 28.45
    MACS1149+22     11 49 36.400 +22 23 59.00 2024-01-23 231.1 2.15x4.30 66.4 3.25 3350  3350  2491  2491  2491  2491  3350  3350
                                                                                28.47 28.66 28.68 28.88 28.56 28.62 28.13 28.40
    PLCK-G165.7+67  11 27 15.000 +42 28 31.00 2023-03-25 251.1 2.15x4.30 57.3 2.50 2491  2491  1890  2104  2104  1890  2491  2491
                                                                                28.38 28.56 28.57 28.85 28.55 28.54 28.03 28.34
    Clio            08 42 20.893 +01 38 32.66 2023-03-17 261.1 2.15x4.30 52.9 1.74 2491  ----  1890  1890  1890  1890  ----  2491
                                                                                28.30  ---- 28.48 28.67 28.36 28.43  ---- 28.27
    RXC-J1212+27    12 12 19.250 +27 33 08.70 2023-01-01 271.1 2.15x4.30 52.9 1.74 2491  ----  1890  1890  1890  1890  ----  2491
                                                                                28.32  ---- 28.51 28.70 28.41 28.43  ---- 28.14
    PLCK-G191.24+62 10 44 42.600 +33 50 53.40 2023-04-03 281.1 2.15x4.30 57.3 2.50 2491  2491  1890  2104  2104  1890  2491  2491
                                                                                28.32 28.50 28.51 28.79 28.49 28.49 27.99 28.29

    NIRISS Grism:                                                                  ---- G150C G150R F200W  ----  ----  ----  ----
    -----------------------------------------------------------------------------------------------------------------------------
    NEP-TDF-ep1     17 22 47.896 +65 49 21.54 2023-05-21 111.2 2.22x4.90 58.7 3.49 ----  2835  2835  6456  ----  ----  ----  ----
                                                                                ---- 25.86 25.86 29.53  ----  ----  ----  ----
    NEP-TDF-ep2     17 22 47.896 +65 49 21.54 2022-08-23 112.2 2.22x4.90 58.7 3.49 ----  2835  2835  6456  ----  ----  ----  ----
                                                                                ---- 25.86 25.86 29.53  ----  ----  ----  ----
    NEP-TDF-ep3     17 22 47.896 +65 49 21.54 2022-11-22 113.2 2.22x4.90 58.7 3.49 ----  2835  2835  6456  ----  ----  ----  ----
                                                                                ---- 25.86 25.86 29.53  ----  ----  ----  ----
    NEP-TDF-ep4     17 22 47.896 +65 49 21.54 2023-02-18 114.2 2.22x4.90 58.7 3.49 ----  2835  2835  6456  ----  ----  ----  ----
                                                                                ---- 25.86 25.86 29.53  ----  ----  ----  ----

    NIRSpec Prism:                                                                            PRISM
    -----------------------------------------------------------------------------------------------------------------------------
    NDWFS1425+3254  14 25 16.408 +32 54 09.58 2023-04-27 311.1 0.10x0.10 39.9 1.14             4202
                                                                                26.25
    SDSSJ0005-0006  00 05 52.340 -00 06 56.86 2023-07-10 321.1 0.10x0.10 39.9 1.14             4202
                                                                                26.05
    -----------------------------------------------------------------------------------------------------------------------------
    Total PEARLS                                            165.66 (’)^2 59.5 68.9
    -----------------------------------------------------------------------------------------------------------------------------

Notes: As for Table 1. Obs.Date is the earliest observation date in the Long
Range Plan (LRP) windows on the STSCI website. For the two NIRISS grisms G150C
and G150R we list the 1-sigma continuum sensitivity for unbinned spectral
pixels. For the IFU PRISM observations the NIRSpec ETC suggests a 5$\sigma$
sensitivity at 2 µm for unresolved emission lines with a line flux of
$\sim$1.2$\times$10-17 erg/cm2/s, and a 2$\sigma$ sensitivity at 2 µm for a
continuum source of (9–10)$\times$10-21 erg/cm2/s (or AB$\simeq$26.05–26.25
continuum mag at 1.5 µm). The totals on the bottom line indicate the total
area, spacecraft efficiency, and net observing hours for the entire PEARLS GTO
program 1176+2738.

    Table 3. Parameters of 0.9-4.5 micron galaxy counts and IGL including JWST PEARLS data
    =================================================================================================================
    lambda_c  AB_25%  AB_50%   AB_75%  IGL_FWHM AB_peak  IGL_peak      Tot_IGL_int   IGL_tot AB22slope Err    Filter
    micron    AB-mag   AB-mag   AB-mag  ABmag    ABmag  W/Hz/m2/d2/mag W/Hz/m2/deg2  nW/m/sr dex/mag   mag    VISTA
    # (1)      (2)      (3)      (4)     (5)       (6)      (7)            (8)          (9)     (10)    (11)   (12)
    -----------------------------------------------------------------------------------------------------------------
    0.883     18.01    20.24    22.47    4.46     20.27     5.845e-28     4.697e-27    10.47    0.206   0.06    z
            +/-0.03  +/-0.02  +/-0.01  +/-0.02  +/-0.01   +/-0.1%       +/-0.4%      +/-0.07 +/-0.001
    1.020     17.88    20.07    22.35    4.47     19.99     7.403e-28     5.854e-27    11.30    0.232   0.07    y
            +/-0.03  +/-0.02  +/-0.01  +/-0.02  +/-0.01   +/-0.1%       +/-0.5%      +/-0.06 +/-0.001
    1.250     17.75    19.94    22.24    4.48     19.78     8.896e-28     7.141e-27    11.25    0.224   0.07    j
            +/-0.03  +/-0.02  +/-0.02  +/-0.02  +/-0.01   +/-0.1%       +/-0.3%      +/-0.06 +/-0.001
    1.650     17.60    19.64    21.89    4.29     19.40     1.233e-27     9.250e-27    11.03    0.233   0.06    h
            +/-0.02  +/-0.01  +/-0.01  +/-0.01  +/-0.01   +/-0.1%       +/-0.4%      +/-0.07 +/-0.001
    2.150     17.74    19.55    21.62    3.88     19.22     1.591e-27     1.079e-26    9.878    0.249   0.05    k
            +/-0.01  +/-0.01  +/-0.01  +/-0.02  +/-0.01   +/-0.1%       +/-0.2%      +/-0.02 +/-0.002
    3.540     18.95    20.42    22.17    3.22     19.90     1.465e-27     8.278e-27    4.603    0.218   0.04    IRAC1
            +/-0.01  +/-0.01  +/-0.01  +/-0.01  +/-0.01   +/-0.1%       +/-0.2%      +/-0.02 +/-0.001
    4.490     19.30    20.78    22.42    3.12     20.18     1.200e-27     6.948e-27    3.046    0.198   0.04    IRAC2
            +/-0.01  +/-0.01  +/-0.01  +/-0.01  +/-0.01   +/-0.1%       +/-0.2%      +/-0.01 +/-0.003
    -----------------------------------------------------------------------------------------------------------------

Notes: See Section 4.5 for definition of these parameters. The formal fitting
errors are listed below each parameter value. Because of the vast statistics
and dynamic range in the combined galaxy counts from AB$\simeq$10–29 mag, the
fitting errors are much smaller than the NIRCam ZP- and AB-flux scale
transformation uncertainties of Appendix B.2, which are listed in column 11.
These combined errors are therefore used for the IGL parameters of Figure 11.

    Table 4a. PEARLS sky-SB: ETC Predictions, JWST Observations, DGL, eEBL, Kelsall 1998 Model, and Diffuse Light limits
    =====================================================================================================================
    Field/sky-SB  Obs.Date  F090W       F115W       F150W       F200W       F277W       F356W       F410M       F444W
    ---------------------------------------------------------------------------------------------------------------------
    lambda_c (micron):      0.8985      1.1434      1.4873      1.9680      2.7279      3.5287      4.0723      4.3504
    MJy/(nW/m^2):           3337        2622        2016        1523        1099        849.6       736.2       689.1
    ---------------------------------------------------------------------------------------------------------------------

    VV191-Backlit 2022-07-02
    ---------------------------------------------------------------------------------------------------------------------
    Rigby22-straylight      0.052496    0.080266    0.073986    0.062039    0.058635    0.038679    0.037862    0.035899
    ETC-straylight          0.045678    0.048888    0.043277    0.032939    0.026557    0.019997    0.025215    0.037771
    ETC-zodi                0.280842    0.232496    0.199449    0.156536    0.101723    0.094726    0.152429    0.311742
    ETC-thermal             0.000000    0.000000    0.000000    0.000000    0.000003    0.000234    0.001226    0.002695

    L2-Zodi-Pred            0.194767    0.164668    0.137195    0.105349    0.067278    0.067173    0.131417    0.215132
                           (0.008508)  (0.006757)  (0.005367)  (0.004174)  (0.003049)  (0.002592)  (0.004548)  (0.006025)
    0.8*Straylight(R22)     0.041997    0.064213    0.059188    0.049631    0.046908    0.030943    0.030290    0.028720
                           (0.010499)  (0.016053)  (0.014797)  (0.012408)  (0.011727)  (0.007736)  (0.007572)  (0.007180)
    DGL-Predict             0.000361    0.000661    0.000809    0.000809    0.001084    0.001509    0.001826    0.002008
                           (0.000181)  (0.000331)  (0.000404)  (0.000405)  (0.000542)  (0.000755)  (0.000913)  (0.001004)
    PEARLS-IGL              0.003084    0.004317    0.006065    0.007084    0.006192    0.005436    0.004878    0.004562
    PEARLS-IGL(>28.5)       0.000077    0.000108    0.000152    0.000177    0.000155    0.000136    0.000122    0.000114
    ---------------------------------------------------------------------------------------------------------------------
    Total-Predict-skySB     0.23720     0.22965     0.19734     0.15597     0.11543     0.09999     0.16488     0.24867
                           (0.01352)   (0.01742)   (0.01575)   (0.01310)   (0.01213)   (0.00819)   (0.00888)   (0.00943)
    ---------------------------------------------------------------------------------------------------------------------
    PEARLS_observ-skySB     0.1684      ----        0.2033      ----        ----        0.1015      ----        0.2757
                           (0.0244)     ----       (0.0218)     ----        ----       (0.0071)     ----       (0.0121)
    ---------------------------------------------------------------------------------------------------------------------
    Obs-Pred (MJy/sr)      <0           ----        0.0060      ----        ----        0.0015      ----        0.0270
    Obs-Pred (nW/m^2/sr)   <0           ----        12          ----        ----        1           ----        19
    DL-upper-limit (nW)    <93          ----       <54          ----        ----       <9           ----       <19
    =====================================================================================================================

Notes: The top two lines give the central wavelength of each NIRCam filter,
and the factors needed to convert units of MJy/sr to nW m-2 sr-1. Obs.Date is
the actual observing date of the PEARLS target. For each target, line 1 gives
the Rigby et al. (2022) straylight in MJy/sr for each filter. Lines 2–4 give
quantities predicted by the JWST-ETC: straylight; Zodiacal Light; and thermal
radiation from a telescope model. Line 5+6 give the Zodiacal foreground
predicted for L2 at the time of the observation from the Spitzer IPAC model
and its uncertainty. All (model) uncertainties are between parentheses, with
details on the error budgets in Appendix B–C. Line 7+8 give the adopted
straylight level and its multiplier, $f$, following Section 5.2. Line 9+10
give the Diffuse Galactic Light level Zodiacal foreground predicted by the
IPAC IRSA model. Line 11+12 give the IGL levels from Section 4.5 and Table 3,
as well as the eEBL, i.e., the IGL fraction that comes from beyond our typical
NIRCam detection limits (AB$\gtrsim$28.5 mag). Line 13+14 give the total
predicted NIRcam sky-SB in each, following Equation 5. Line 15+16 give the
observed NIRCam sky-SB in each JWST image measured between the detected
objects (Section 5.2 and Windhorst et al., 2022). Line 17+18 give the
difference between the Observed–Predicted sky-SB in MJy/sr and nW m-2 sr-1,
respectively. Line 18 gives our 1$\sigma$ upper limit to diffuse light in nW
m-2 sr-1 for each observed PEARLS filter, accounting for the full error
budgets in both the Observed and Predicted sky-SB values in Appendix B–C.

    Table 4b. PEARLS sky-SB: ETC Predictions, JWST Observations, DGL, eEBL, Kelsall 1998 Model, and Diffuse Light limits
    =====================================================================================================================
    Field/sky-SB  Obs.Date  F090W       F115W       F150W       F200W       F277W       F356W       F410M       F444W
    ---------------------------------------------------------------------------------------------------------------------
    lambda_c (micron):      0.8985      1.1434      1.4873      1.9680      2.7279      3.5287      4.0723      4.3504
    MJy/(nW/m^2):           3337        2622        2016        1523        1099        849.6       736.2       689.1
    ---------------------------------------------------------------------------------------------------------------------

    JWIDF-epoch1  2022-07-08
    ---------------------------------------------------------------------------------------------------------------------
    Rigby22-straylight      0.052496    0.080266    0.073986    0.062039    0.058635    0.038679    0.037862    0.035899
    ETC-straylight          0.045758    0.059683    0.055036    0.043173    0.038475    0.026917    0.030043    0.035379
    ETC-zodi                0.175812    0.146354    0.127120    0.102019    0.069139    0.069044    0.114380    0.231812
    ETC-thermal             0.000000    0.000000    0.000000    0.000000    0.000003    0.000234    0.001226    0.002695

    L2-Zodi-Pred            0.090777    0.077508    0.065341    0.050953    0.033456    0.041297    0.095256    0.159093
                           (0.008508)  (0.006757)  (0.005367)  (0.004174)  (0.003049)  (0.002592)  (0.004548)  (0.006025)
    0.9*Straylight(R22)     0.047247    0.072239    0.066587    0.055834    0.052772    0.034811    0.034076    0.032310
                           (0.010499)  (0.016053)  (0.014797)  (0.012408)  (0.011727)  (0.007736)  (0.007572)  (0.007180)
    DGL-Predict             0.001096    0.002004    0.002454    0.002454    0.003288    0.004577    0.005537    0.006090
                           (0.000548)  (0.001002)  (0.001227)  (0.001227)  (0.001644)  (0.002289)  (0.002769)  (0.003045)
    PEARLS-IGL              0.003084    0.004317    0.006065    0.007084    0.006192    0.005436    0.004878    0.004562
    PEARLS-IGL(>28.5)       0.000077    0.000108    0.000152    0.000177    0.000155    0.000136    0.000122    0.000114
    ---------------------------------------------------------------------------------------------------------------------
    Total-Predict-skySB     0.13920     0.15186     0.13453     0.10942     0.08967     0.08106     0.13622     0.20030
                           (0.01353)   (0.01745)   (0.01579)   (0.01315)   (0.01223)   (0.00847)   (0.00926)   (0.00986)
    ---------------------------------------------------------------------------------------------------------------------
    PEARLS_observ-skySB     ----        ----        0.1541      0.1310      ----        0.0781      ----        0.2125
                            ----        ----       (0.0131)    (0.0101)     ----       (0.0046)     ----       (0.0089)
    ---------------------------------------------------------------------------------------------------------------------
    Obs-Pred (MJy/sr)       ----        ----        0.0196      0.0216      ----       <0           ----       <0.0122
    Obs-Pred (nW/m^2/sr)    ----        ----        39          33          ----       <0           ----       <8
    DL-upper-limit (nW)     ----        ----       <41         <33          ----       <8           ----       <9

    El-Gordo:    2022-07-29
    ---------------------------------------------------------------------------------------------------------------------
    ETC-straylight          0.039684    0.043976    0.039169    0.029558    0.024191    0.017063    0.019863    0.026836
    ETC-zodi                0.233085    0.193308    0.164389    0.126978    0.081585    0.071304    0.106510    0.211112
    ETC-thermal             0.000000    0.000000    0.000000    0.000000    0.000003    0.000234    0.001226    0.002695

    L2-Zodi-Pred            0.159645    0.133880    0.110478    0.083767    0.052469    0.047257    0.084041    0.136080
                           (0.008508)  (0.006757)  (0.005367)  (0.004174)  (0.003049)  (0.002592)  (0.004548)  (0.006025)
    0.6*Straylight(R22)     0.031498    0.048159    0.044391    0.037223    0.035181    0.023208    0.022717    0.021540
                           (0.010499)  (0.016053)  (0.014797)  (0.012408)  (0.011727)  (0.007736)  (0.007572)  (0.007180)
    DGL-Predict             0.000248    0.000454    0.000556    0.000556    0.000745    0.001037    0.001255    0.001381
                           (0.000124)  (0.000227)  (0.000278)  (0.000278)  (0.000373)  (0.000519)  (0.000627)  (0.000691)
    PEARLS-IGL              0.003084    0.004317    0.006065    0.007084    0.006192    0.005436    0.004878    0.004562
    PEARLS-IGL(>28.5)       0.000077    0.000108    0.000152    0.000177    0.000155    0.000136    0.000122    0.000114
    ---------------------------------------------------------------------------------------------------------------------
    Total-Predict-skySB     0.19147     0.18260     0.15558     0.12172     0.08855     0.07187     0.10936     0.16181
                           (0.01351)   (0.01742)   (0.01574)   (0.01309)   (0.01212)   (0.00818)   (0.00886)   (0.00940)
    ---------------------------------------------------------------------------------------------------------------------
    PEARLS_observ-skySB     0.1791      0.1732      0.1653      0.1062      0.0732      0.0715      0.1135      0.1871
                           (0.0154)    (0.0137)    (0.0136)    (0.0102)    (0.0052)    (0.0054)    (0.0052)    (0.0084)
    ---------------------------------------------------------------------------------------------------------------------
    Obs-Pred (MJy/sr)      <0          <0           0.0097     <0          <0          <0           0.0041      0.0253
    Obs-Pred (nW/m^2/sr)   <0          <0           20         <0          <0          <0           3           17
    DL-upper-limit (nW)    <68         <58         <42         <25         <14         <8          <8          <17
    =====================================================================================================================

Notes: These are given below Table 4a.

    Table 5. PEARLS sky-SB: ETC Predictions, JWST Observations, DGL, eEBL, Kelsall 1998 Model, and Diffuse Light limits
    ======================================================================================================================
    Field/sky-SB  Obs.Date  F090W       F115W       F150W       F182M       F210M       F300M       F335M       F360M
    ----------------------------------------------------------------------------------------------------------------------
    lambda_c (micron):      0.8985      1.1434      1.4873      1.8389      2.0908      2.9818      3.3538      3.6148
    MJy/(nW/m^2)            3337        2622        2016        1630        1434        1005        893.9       829.3
    ----------------------------------------------------------------------------------------------------------------------

    TNJ1338-1942  2022-07-01
    ---------------------------------------------------------------------------------------------------------------------
    Rigby22-straylight      0.052496    0.080266    0.073986    0.063820    0.061010    0.041216    0.038203    0.038679
    ETC-straylight          0.067593    0.075166    0.067042    0.057724    0.052513    0.034902    0.031816    0.033530
    ETC-zodi                0.445802    0.369774    0.317401    0.270570    0.231493    0.142155    0.118576    0.144350
    ETC-thermal             0.000000    0.000000    0.000000    0.000000    0.000000    0.000012    0.000104    0.000321

    L2-Zodi-Pred            0.438665    0.369418    0.303688    0.247075    0.213238    0.122854    0.107191    0.105611
                           (0.008508)  (0.006757)  (0.005367)  (0.004447)  (0.003920)  (0.002863)  (0.002525)  (0.002847)
    0.3*Straylight(R22)     0.015749    0.024078    0.022196    0.019146    0.018303    0.012365    0.011461    0.011605
                           (0.010499)  (0.016053)  (0.014797)  (0.012764)  (0.012202)  (0.008243)  (0.007641)  (0.007736)
    DGL-Predict             0.002497    0.004569    0.005595    0.005595    0.005595    0.008201    0.010372    0.010770
                           (0.001249)  (0.002285)  (0.002798)  (0.002798)  (0.002798)  (0.004101)  (0.005186)  (0.005385)
    PEARLS-IGL              0.003084    0.004317    0.006065    0.006632    0.007086    0.006077    0.005675    0.005436
    PEARLS-IGL(>28.5)       0.000077    0.000108    0.000152    0.000166    0.000177    0.000152    0.000142    0.000136
    ---------------------------------------------------------------------------------------------------------------------
    Total-Predict-skySB     0.45699     0.39818     0.33163     0.27199     0.23729     0.14357     0.12925     0.12842
                           (0.01357)   (0.01757)   (0.01599)   (0.01380)   (0.01312)   (0.00964)   (0.00957)   (0.00980)
    ---------------------------------------------------------------------------------------------------------------------
    PEARLS_observ-skySB     ----        ----        0.2996      0.2161      0.1676      0.1122      0.1149      0.1160
                            ----        ----       (0.0246)    (0.0268)    (0.0244)    (0.0077)    (0.0091)    (0.0082)
    ---------------------------------------------------------------------------------------------------------------------
    Obs-Pred (MJy/sr)       -----       -----      <0          <0          <0          <0          <0          <0
    Obs-Pred (nW/m^2/sr)    <0          <0         <0          <0          <0          <0          <0          <0
    DL-upper-limit (nW)     -----       -----      <59         <49         <40         <12         <12         <11
    =====================================================================================================================

Notes: These are given below Table 4a.

Figure 1: Summary of the area and depth covered by JWST Cycle 1 surveys. Data
came from G. Brammer’s website https://erda.ku.dk/vgrid/Gabriel_Brammer/JWST-
Cycle1/full_timeline.html. Colors and line types identify seven GO and GTO
surveys as shown in the legend, and the order in the legend matches the
maximum survey area as shown along the left ordinate. The thick black line
shows the total area–depth of all public Cycle 1 surveys, and the thick grey
line shows the same including surveys with proprietary data. The thick green
line indicates PEARLS, which combines a smaller area of significant depth with
a much larger area of 16 shallower fields to significantly average over Cosmic
Variance (Section 2 & 4.4), and include 7 lensing clusters.

Figure 2: PEARLS NIRCam image of the IRAC Dark Field (JWIDF) Epoch-1 at the
north Ecliptic pole. Filter F150W is rendered as blue, F200W as green, and
F356W+F444W as red using a log scaling (e.g., Lupton et al., 2004; Coe, 2015).
This 2040$\times$3644 pixel section covers 61$\farcs$2$\times$109$\farcs$3,
and image orientation is shown by the labeled arrows. Areas with remaining
wisps and snowball imprints were masked before making object catalogs and
counts. (Please magnify all PDF images to see details).

Figure 3: PEARLS NIRCam image of the El Gordo module 3′ away from the cluster.
Filters F090W+F1115W are rendered as blue, F150W+F200W+F277W as green, and
F356W+F410M+F444W as red. This 5000$\times$5000 pixel section covers
150″$\times$150″, and image orientation is shown by the labeled arrows. Areas
with remaining detector border effects and bright-star diffraction spikes
(e.g., the blue spike from a bright star just outside the lower-left FOV) were
masked before making object catalogs and counts.

Figure 4: NIRCam image of the $z=4.1$ TNJ1338 protocluster. Filters
F150W+F182M are rendered as blue, F210M+F300M as green, and F335M+F360M as
red. This 1850$\times$1850 pixel section covers
55$\farcs$5$\times$55$\farcs$5, and the image orientation is shown by the
labeled arrows. The radio galaxy is the irregular orange object in the center.

Figure 5: PEARLS NIRCam image of the VV 191 system. Filter F150W is rendered
as blue, F200W as green, and F356W+F444W as red. The elliptical galaxy VV 191a
at the top backlights the spiral VV 191b at the bottom. Separation between the
nuclei is 20$\farcs$4, and the image orientation is shown by the labeled
arrows. The orange arclet south of VV 191a is gravitationally lensed by the
bright elliptical (for details, see Keel et al., 2022). Note the background
objects of similar angular size but different color. This 707$\times$994 pixel
section covers 21$\farcs$21$\times$29$\farcs$82\.

Figure 6: Object detection, classification, and counts in the El Gordo non-
cluster module in the F090W, F115W, F150W, and F200W filters. [Left]: (a)
SourceExtractor AB-magnitude error bars vs. MAG_AUTO AB-mag resulting from the
adopted SourceExtractor-parameters (Section 3.1). Horizontal dashed lines show
the adopted 5$\sigma$ point-source detection limits (Table 1). [Middle]: (b)
Star–galaxy classification diagram based on SourceExtractor MAG_AUTO AB-
magnitudes vs. image FWHM. Left solid vertical lines indicate the NIRCam
diffraction limit for each image with its current sampling. Blue points
represent galaxies. The box to the right of the vertical line identifies
objects classified as stars (red points). Objects with FWHM $<$ FWHM(PSF) have
been flagged and removed from this plot as spurious detections or border
imperfections. The green dashed lines indicate for each image the effective
point source (horizontal) and SB (slanted) detection limits. [Right]: (c)
Resulting star counts (red) and galaxy counts (blue).

Figure 7: Same as Figure 6 for the object detection, classification, and
counts in the El Gordo non-cluster module in the F277W, F356W, F410M, and
F444W filters. (Please magnify these PDF plots to see all data points.)

Figure 8: Same as Figure 6 for the object detection, classification, and
counts for all detectors covering the JWIDF in the F150W, F200W, F356W, and
F444W filters. (Please magnify these plots figures to see all data points.)

Figure 9: NIRCam galaxy counts in the JWIDF and the El Gordo non-cluster
module (orange and brown filled circles, respectively). Each row of three
panels shows one wavelength as indicated in the panels. Left panels show the
galaxy counts in 0.5-mag bins. Middle panels show the energy counts after
dividing the left panels by a 0.40 dex/mag slope. Units used are described in
Section 4 and Koushan et al. (2021). Right panels show the integral of the
middle panels normalized to 100% of the IGL energy received. Open diamonds
show a combination of previous ground-based, HST, and Spitzer/WISE counts
(Driver et al., 2016b; Koushan et al., 2021) with different surveys shown in
different colors as indicated in the legends. When broad-band filters in
different instruments are similar but not identical, small corrections for
central wavelength differences may be needed (Koushan et al., 2021; Robotham
et al., 2020, see Appendix B.2 here). Triangles without error bars indicate
bins having only a single object. The brightest bins of the PEARLS counts at
18$\lesssim$AB$\lesssim$20 mag in the middle panels show Cosmic Variance
(Section 2 & 4.4), but do not weigh into the IGL fits, which at these flux
levels are dominated by the faint end of the brighter surveys. PEARLS counts
beyond the respective 80% completeness limits (as derived in Table 1 from a
best-fit power-law extrapolation) are plotted as lightly shaded points, and
are not included in the spline extrapolations to estimate the total IGL.

Figure 10: Same as Figure 9 for the ground-based+HST 1.6 & 2.2 µm and Spitzer
3.5 & 4.5 µm counts with JWST NIRCam counts in F150W, F200W, F356W and F444W
as brown/olive filled circles in the JWIDF and El Gordo non-cluster module.

Figure 11: Parameters of the 0.9–4.5 µm galaxy counts and integrated galaxy
light (IGL) as derived from Figures 9–10. Top panel show the AB-magnitude
level at which the normalized differential counts peak (see middle panels in
Figure 9–10). This is where most of the discrete IGL is generated at each
wavelength. Second panel shows the peak SB-value of the IGL derived from the
middle panels of Figures 9–10. Third panel shows the width around the peak
magnitude or interquartile (i.e., 25%–75%) range where 50% of the discrete IGL
is generated. We refer to this range as the “IGL FWHM.” The bottom panel shows
the total IGL values (in units of nW m-2 sr-1) of the converging integrals in
the right panels of Figures 9–10. Error bars were determined by combining the
NIRCam ZP uncertainties of Table 6 in Appendix B.1 with the uncertainties in
transforming the NIRCam flux scale to the fiducial flux scale of the
VISTA/IRAC filters in Appendix B.2 (see Section 4.4–4.5).

Figure 12: Comparison of the JWST NIRCam sky-SB values observed in our four
PEARLS fields to models. Black triangles indicate the PEARLS sky-SB
measurements of Section 5. The smaller (inner) error bars reflect the
variation of the object-free sky-SB measurements within the NIRCam detectors,
while the larger error bars reflect the median value of all sky-rms values
across the images in each filter. These error bars include the ZP and other
sky-SB uncertainties of Appendix B.3. Models are plotted for: TNJ1338 (upper
left in purple), El Gordo (upper right in green), VV191 (lower left in red),
and the JWIDF (lower right in blue). Short-dashed lines indicate the Zodiacal
sky-SB from L2 as predicted by the Spitzer model (Appendix C). Zodiacal light
is the highest amplitude component for all targets. Dot-dashed lines indicate
the JWST straylight (SL) model from Figure 4 of Rigby et al. (2022); long-
dashed lines indicate the DGL levels predicted by the IRSA model (Appendix C);
black dotted lines indicate the JWST thermal contributions to the sky-SB
predicted by the ETC; solid colored lines are the sum of all four components.
The SL level in each field was scaled down by factors $f$$\simeq$0.3–0.9
compared to the Rigby et al. (2022) SL amplitude to obtain a best fit of the
sum of the four model components to our 3.5–4.5 µm observations, where the
sky-SB is lowest. Details are given in Section 5.

Figure 13: Summary of astrophysical foreground and background energy relevant
to PEARLS. Dark brown filled upward-pointing triangles with error bars
indicate the PEARLS NIRCam 0.9–4.5 µm IGL measurements of Section 4 (Discrete
Light), and are lower limits to the total EBL. Dark brown downward-pointing
triangles with the grey error wedge indicate our current JWIDF and El Gordo
non-cluster 0.9–4.5 µm upper limits to Diffuse Light, with all known
components subtracted (see error budget in Section 5 and Appendix C), and are
in line with previous limits to Diffuse Light. (Brown starred and tripod
symbols indicate the less accurate VV191 and TNJ limits). Green triangles show
our 0.9–4.5 µm PEARLS NIRCam sky-SB observations in the El Gordo non-cluster
module compared to the models of Section 5 and Figure 12 (green solid line).
The left scale indicates the total energy $\nu$.$I_{\nu}$ in nW m-2 sr-1, and
the right scale shows the corresponding sky-SB in AB-mag arcsec-2 at 2.00 µm
(which can be scaled to other wavelengths as indicated). Filled circles show
previous IGL counts of Driver et al. (2016b) (red) and Koushan et al. (2021)
(orange). Solid and dashed colored lines show the (component and total)
discrete EBL models from Andrews et al. (2018). The orange line and hashed
area show $\gamma$-ray Blazar EBL constraints from the MAGIC TeV experiments
(see e.g., Dwek & Krennrich, 2013, for a summary), and light grey triangles
indicate total EBL estimates that require accurate modeling of DGL and ZL and
still include the IGL (Direct Light). Purple triangles show the Matsuura et
al. (2017) and Sano et al. (2020) CIBER estimates of Diffuse Light in excess
of the Kelsall et al. (1998) model prediction. Dark blue upper limits are the
SKYSURF 1.25–1.6 µm Diffuse Light limits from 34,000 WFC3/IR images of of
Carleton et al. (2022) and Windhorst et al. (2022). Light blue circles with
error bars at 0.61 µm are the Lauer et al. (2021, 2022) Diffuse Light
estimates with New Horizons at 43–51 AU. All Diffuse Light estimates plotted
in color have the IGL (=iEBL+eEBL) already subtracted. See Carleton et al.
(2022) for a discussion of possible causes of any remaining Diffuse Light.

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##  Appendix A NIRCam Pipeline Processing Details: 1/f Corrections

To remove the NIRCam $1/f$ noise effects caused by readout artifacts a number
of schemes were investigate. Due to the precise characteristics of the readout
process and the visual discontinuities evident in the images, the optimal
approach proved to be the following:

  * •

All pixels with data quality flag DQ = 0 are masked.

  * •

The brightest 10% of pixels are masked to filter out the real objects. Any
number for masking between 10% and 30% works well in practice for a diversity
of images (including, e.g., large galaxies in the field of view and extremely
empty frames).

  * •

Each $2040\times 2040$ calibrated frame is divided into four $510\times 2040$
sections (i.e., shorter runs in the image $x$-dimension).

  * •

In scan blocks of $512\times 1$, the $q=0.4$ quintile value is calculated
ignoring all masked pixels above. This creates a vector of length 2040 for
each of the four sections analyzed.

  * •

For each scan block vector of length 2040 the running median is computed with
a window side of 101 pixels. This smooth distribution reflects any large scale
structure we wish to preserve, and is removed from the vectors. Window sizes
between 51 and 201 pixels work well for the full diversity of images
available.

  * •

Each vector is expanded along the $x$-dimension to create $510\times 2040$
sections. The four sections are then combined to create a single $2040\times
2040$ $1/f$ noise image (see example in Figure 14c).

  * •

The final $x$-direction noise map is removed from the original image.

A similar procedure is then carried out on the $y$-dimension, with as
difference that the entire $y$-column is now analyzed (see example in Figure
14d). This noise pattern is also removed, creating our final $1/f$ corrected
frame. For a particularly difficult frame, Figure 14a shows an image before
its 1/f removal, and Figure 14b after 1/f removal. The above process is all
run by the function profoundSkyScan that is part of the ProFound package
(Robotham et al., 2017, 2018).

Figure 14e shows a comparison of the Willott 1/f-removal algorithm compared to
the ProFound-based 1/f subtraction. The average effect of the $1/f$ correction
is typically well below the pixel rms value. The rms of this particular image
is 0.06 in units of MJy/sr. The scatter away from the $y=x$ line in Figure 14e
shows that the two algorithms leave a residual noise imprint on the resulting
sky-SB that differs at the level of $\sim$0.005 MJy/sr, so that systematics
resulting from the 1/f correction algorithms are $\lesssim$10% of the pixel
rms level. Since 1.0 MJy/sr typically corresponds to a compact $\sim$5$\sigma$
source of AB$\sim$28 mag (Equation 2 and Table 1), the 1/f removal algorithms
create $\lesssim$1% flux changes for the faintest sources in the field, and
substantially less for brighter sources. Also, the large scale structure of
sources is preserved, and no discontinuities are present between scan regions,
at least those not caused by the $1/f$ correction itself.

The one difference between the Willott and ProFound-based 1/f removal
algorithms is that the Willott algorithm does not remove large scale
gradients, while the ProFound-based algorithm has the option to remove such
gradients, although these are then preserved as a separate layer in the output
fits files. As discussed in Section 4 of Windhorst et al. (2022), such large
scale gradients can be due to the real astrophysical scene (e.g., cluster
ICL), and/or due to imperfections in the subtracted dark-frames or color-terms
in the applied flat-field corrections, and are usually not more than a few
percent of the sky-SB across the image. Such gradients are general not an
issue for our purpose of constructing reliable, complete object catalogs for
faint and small objects. We preserve the information on large scale gradients
when measuring the Lowest Estimated Sky-SB (LES) following the methods of
Windhorst et al. (2022) that we apply for our JWST sky-SB study of Section 5.

Figure 14: [(a) Top Left]: Part of the JWIDF image before 1/f removal; [(b)
Top Right]: Same part of the JWIDF image after 1/f removal with the ProFound-
based 1/f subtraction code. (Please magnify these PDF figures to see the
details); [(c) Middle Left]: Row-wise 1/f pattern subtracted in the
$x$-direction. The inset color bars show the relative level of the corrections
applied. The imprint of the four 5512$\times$2048 pixel sections read by the
ASIC is apparent; [(d) Middle Right]: Column-wise pattern subtracted in the
$y$-direction; [(e) Bottom]:: Comparison of the Willott 1/f-removal algorithm
compared to the ProFound-based 1/f subtraction. The two algorithms leave
similar noise imprints on the resulting sky-SB at the level of
$\lesssim$0.02–0.04 MJy/sr, where 1.0 MJy/sr typically corresponds to a
5$\sigma$ source of $\rm AB\sim 28$ mag.

##  Appendix B NIRCam Pipeline Processing Details: ZP corrections and Error
Budget

In Appendix B.1, we discuss ZP corrections that need to be applied to our
first data as calibrated with the early pipelines and calibration files. In
Appendix B.2, we discuss if further corrections are needed to the NIRCam AB-
magnitude scale in order to compare our PEARLS 0.9-4.5 µm galaxy counts to
work done over the last few decades at the fiducial wavelengths of the
VISTA+IRAC surveys. In Appendix B.3, we summarize the modeling of NIRCam sky-
SB components and their uncertainties.

###  B.1 ZP corrections Applied to Early Pipeline and Calibration Results

JWST photometric calibration (“zeropoint” or ZP) has to be established in
flight and will evolve during the mission. Because standard-star observations
were not available in time, the earliest JWST observations had to be
calibrated with pre-flight ZPs. The MAST pipeline for NIRCam began using in-
flight ZPs on 2022 July 27. At NIRCam wavelengths $\leq$2.0 µm, the on-orbit
throughput turns out to be near pre-launch expectations (Rigby et al., 2022),
but can be up to 10% lower for a few filters. At wavelengths $>$2.0 µm, the
on-orbit throughput is about 15–30% higher than the pre-launch expectations
(Rigby et al., 2022, their Figure 8). Rigby et al. (2022) also wrote that the
throughput stability is no worse than 4% and is likely much better.

In principle, ZPs can differ for each of the 10 NIRCam detectors. In practice,
differences are $\lesssim$4% within the SW and LW module detectors (Rigby et
al., 2022). Table 6 lists the ratios of pre-launch to on-orbit ZPs kindly
provided to us by M. Rieke. These were based on standard star calibrations in
the NIRCam detectors NIRCB1 and BLong. These ZPs will likely be further
refined as the NIRCam GTO team delivers subsequent standard star calibrations
to STScI to ingest into the NIRCam pipeline. Numbers below 1.00 in Table 6
reflect an on-orbit throughput higher than pre-launch expectation. Data (in
MJy/sr) reduced with the CALWEBB pipeline versions 1.5.2–1.6.2 and context
files jwst_0927.pmap_filters or earlier need to be multiplied by the ratios in
Table 6 to match the most recent ZPs, or the ZPs in the image headers need to
be adjusted correspondingly. For PEARLS, we implemented the latter by applying
the listed ZP correction to the AB-magnitudes at the catalog stage:

${\rm ZP(current)=ZP(old)+\Delta ZP\quad.}$ (B1)

The PEARLS NIRCam images for the TNJ, VV 191, and the JWIDF were taken in
early July and were reduced with pipeline version 1.6.1.dev2+g408c711, CRDS
version 11.13.1, and context file jwst_0916.pmap_filters, which still
contained the pre-launch ZPs. Our El Gordo images of 2022 July 29 were reduced
by pipeline version 1.6.2, CRDS version 11.13.1, and context file
jwst_0942.pmap_filters, which implement the Rigby et al. (2022) ZPs in all
filters.

    Table 6. Ratio of pre-launch to on-orbit Rigby (2022) ZPs for JWIDF, VV191, and TNJ1338
    ===========================================================================================
    JWIDF/VV191:  F070W    F090W    F115W    F150W    F200W    F277W    F356W    F410M    F444W
    -------------------------------------------------------------------------------------------
    Ratio         0.995    1.114    1.093    1.031    1.099    0.934    0.868    0.875    0.777
    Deltamag     +0.006   -0.117   -0.097   -0.033   -0.103   +0.074   +0.154   +0.145   +0.274
    -------------------------------------------------------------------------------------------
    TNJ1338       F070W    F090W    F115W    F150W    F182M    F210M    F300M    F335M    F360M
    -------------------------------------------------------------------------------------------
    Ratio         ----     ----     ----     1.031    1.026    0.984    0.834    0.870    0.926
    Deltamag      ----     ----     ----    -0.033   -0.028   +0.018   +0.197   +0.151   +0.084
    -------------------------------------------------------------------------------------------

Notes: Ratio reflects the change in NIRCam zero points from pre-launch to on-
orbit (following Rigby et al. (2022) and CRDS file jwst_0942.pmap_filters),
and is defined as the scaling factor by which the pre-launch fits data values
(processed with pipeline versions 1.5.2–1.6.2) need to be multiplied to obtain
the correct flux scale. Ratios below 1.00 reflect an on-orbit increase in
throughput compared to the pre-launch expectation. The Deltamag row indicates
the ZP correction that needs to be added to pre-launch pipeline 1.5.2–1.6.2
and CRDS file jwst_0942.pmap_filters and earlier to obtain the current on-
orbit calibration on the correct AB-magnitude scale as of July 29, 2022.

The JWIDF has deep IRAC observations that allow direct comparison in two
NIRCam filters. The IRAC observations were accumulated over 15 years, and so
are very deep (e.g., Yan et al., 2018). For unsaturated, isolated, and matched
objects in the magnitude range 18$\lesssim$AB$\lesssim$20 mag in both sets of
images, Source Extractor MAG_AUTO gives average differences of
$\rm[F356W]-[IRAC1]\simeq-0.014$ mag and $\rm[F444W]-[IRAC2]\simeq+0.172$ mag.
The significant difference in $\rm[F444W]-[IRAC2]$ can likely be ascribed to a
combination of filter differences, aperture corrections, and source confusion
due to the vastly different PSFs of the two telescopes. The NIRCam PSF has a
2.362$\simeq$5.56$\times$ larger area in F444W compared to F090W (Table 1 and
Figures 6–8). F444W also has a $\sim$140$\times$ smaller PSF-area than the
Spitzer IRAC2 filter. Hence, PSF differences may be a cause of remaining ZP
offsets in the calibrations. This F444W difference — if real — would imply
that the current F444W flux scale is too faint, and so would make all F444W
fluxes $\sim$17% brighter if applied. With our model fitting in Section 5 and
Figure 12, this would make all sky-SB fits considerably worse, and would leave
even less room for diffuse light. While model-dependent (Appendix C), our sky-
SB analysis does give a nearly PSF-independent check on the zeropoints, to the
extent that the sky-SB is estimated in areas largely devoid of bright-object
PSF-wings. So to be conservative, we leave this F444W issue for a later
resolution. A more detailed comparison is warranted once the JWST calibration
and data are understood at higher precision. At this stage, we adopt the
current on-orbit calibration for all filters for consistency, and to be able
to compare our results with other current work.

In conclusion, we adopt the Rigby et al. (2022) flux scale and 4% as the
uncertainty in our knowledge of the JWST NIRCam flux scale after correcting
pre-launch pipeline 1.5.2–1.6.2 products as shown in Table 6.

###  B.2 Comparison of NIRCam AB-mag Counts to VISTA/IRAC Counts

In order to compare our PEARLS NIRCam 0.9–4.5 µm object counts in Figure 9–10
to previous work from ground-based telescopes and Spitzer/IRAC, the NIRCam
flux densities may need to be transformed to the same flux scale as used for
the filters in those previous surveys. The NIRCam filter wavelengths are
similar, but not identical, to those used previously. The most extensive
survey and number counts for $\lambda<3$ µm is that of Koushan et al. (2021,
and references therein), who combined many data sets. For $\lambda>3$ µm, we
use the compilation of Driver et al. (2016a, b), who included number counts
for AB$\lesssim$18 mag from WISE (Jarrett et al., 2017) and for
18$\lesssim$AB$\lesssim$26 mag from IRAC (Ashby et al., 2009, 2015).

Table 7 lists the central wavelengths $\lambda_{c}$ of the relevant VISTA/IRAC
and WISE filters in which these previous counts were done, as displayed in
Figure 9–10. We therefore use the central wavelengths of the VISTA/IRAC
filters in Table 7 as fiducial to compare our NIRCam object counts to. The
flux scale of the WISE W1 and W2 filters was already transformed to the flux
scale of these fiducial VISTA/IRAC filters. We used the ICRAR filter transform
tool (Robotham et al., 2020) 272727http://transformcalc.icrar.org and
https://github.com/asgr/ProSpect to calculate the corrections needed to bring
the NIRCam AB-magnitude scale onto that of the VISTA/IRAC filters that are
closest in wavelength. The tool uses the filter and telescope transmission
curves folded with the detector QE curves for a large number of facilities to
perform numerical integration over a range of SEDs and redshifts, and produces
AB-flux scale offsets, $\Delta\rm AB$, and their uncertainties,
$\sigma_{\Delta\rm AB}$, which we represent as:

${\rm NIRCam\ \ ABmag=VISTA/IRAC\ ABmag\ +\ \Delta AB\ \pm\sigma_{\Delta AB}}$
(B2)

The transformation requires an assumption for the redshift distribution of the
galaxy population at $\rm AB\simeq 20$–28 mag, for which we used a median
redshift of $z_{\rm med}$$\simeq$1–2 (e.g., Skelton et al., 2014; Inami et
al., 2017). The resulting values for $\Delta\rm AB$ and $\sigma_{\Delta\rm
AB}$ are given in Table 7.282828The NIRCam F115W filter is compared to VISTA
$J$, because the F115W filter is closer to $J$-band than the $Y$-band or VISTA
1.022 µm, which would have $\Delta\rm AB=+0.091$ mag. For most filters, the
uncertainty in the transformation is 3–6%, i.e., similar to or larger than the
actual flux scale correction needed, which is –0.04 to +0.03 mag. This is
mainly because of the wide redshift range sampled. Therefore, no AB-mag scale
corrections were applied to our PEARLS NIRCam number counts to compare them to
the VISTA/IRAC counts. But we do add this uncertainty to our error budget.

Table 7 also lists the Cosmic Variance uncertainty for our two PEARLS fields
used in the deep NIRCam galaxy counts thus far (Section 2 & 4.4). Assuming
both ZP uncertainties and the CV uncertainty are independent, we show the
combined total error on the bottom line of Table 7. These are our IGL errors
used in Figures 12–13. These errors are likely conservative, since other deep
fields from HST, VLT and Spitzer fold into the galaxy counts of Figure 9–10
thereby reducing CV, except at the faint end of the counts at wavelengths
$\gtrsim$2.0µm, where we only have NIRCam.

In summary, the uncertainty in the JWST NIRCam zeropoints is at least 4%,
while the uncertainty of transforming the NIRCam AB-mag scale onto the
fiducial VISTA/IRAC filters that have been used for galaxy counts at brighter
levels is $\lesssim$3–6%. The combined uncertainty to compare counts that were
done with slightly different filters systems on different telescopes is thus
$\sim$3–7%. Magnitude offsets of that size are hardly noticeable over the very
wide magnitude range plotted in Figures 9–10. Future improvements in the
NIRCam ZPs through further standard star monitoring and more detailed
comparison to the fluxes in the fiducial VISTA/IRAC filters can provide a more
accurate comparison, and observing more JWST fields will decrease the
uncertainty in the counts from Cosmic Variance.

    Table 7. ZP & Transformation Uncertainties of JWST NIRCam to VISTA system for Galaxy Counts/IGL
    =================================================================================================
    NIRCam filter:           F090W    F115W    F150W    F200W    F277W    F356W    F410M    F444W
    lambda_c (mum)           0.8985   1.1434   1.4873   1.9680   2.7279   3.5287   4.0723   4.3504
    NIRCam ZP uncertainty    0.04     0.04     0.04     0.04    <0.04    <0.04    <0.04    <0.04
    -------------------------------------------------------------------------------------------------
    VISTA/IRAC filter:      VISTA-Z  VISTA-J  VISTA-H  VISTA-K   -----    IRAC-1   -----    IRAC-2
    lambda_c (mum)           0.883    1.254    1.648    2.154    -----    3.544    -----    4.487
    -------------------------------------------------------------------------------------------------
    Delta_AB                +0.026   -0.006   -0.044   -0.003    -----    0.001    -----   +0.018
    Transform uncertainty    0.05     0.06     0.04     0.03     -----    0.01     -----    0.003
    -------------------------------------------------------------------------------------------------
    Total ZP uncertainty     0.06     0.07     0.06     0.05    <0.04    <0.04    <0.04    <0.04
    -------------------------------------------------------------------------------------------------
    CV error                 0.09     0.09     0.09     0.09     0.09     0.09     0.09     0.09
    -------------------------------------------------------------------------------------------------
    Total IGL error          0.11     0.12     0.11     0.10    <0.10    <0.10    <0.10    <0.10
    -------------------------------------------------------------------------------------------------

Note: The first tier of this Table lists the NIRCam ZP uncertainties from
Section B.1 for each filter. The second tier lists the central wavelengths of
the VISTA/IRAC filters used as fiducial for the PEARLS NIRCam galaxy counts in
Section 4.4. The third tier lists the correction $\Delta\rm AB$ that would
need to be added to the calibrated JWST AB magnitudes to bring them onto the
same AB-scale as used for the VISTA (Koushan et al., 2021) and IRAC (Ashby et
al., 2009, 2015) galaxy counts using the ICRAR filter transformation tool,
together with its transformation error. The fourth tier lists the combined
NIRCam ZP uncertainties and the ICRAR transformation error. The fifth tier
lists the Cosmic Variance error expected for the 0.9–4.5 µm galaxy counts in
our two current PEARLS NIRCam fields (Section 4.4). The bottom tier lists the
combined fractional error, assuming all contributions are independent, and is
used to assess the errors in our IGL parameters (Section 4.5).

###  B.3 Uncertainties in the Observed NIRCam sky-SB Estimates

For the uncertainties in our observed JWST NIRCam sky-SB values we need to
consider other error sources than those that apply to the flux-scale errors in
our galaxy counts in Appendix B.2. We wish to make an estimate of the absolute
sky-SB in our 13 NIRCam filters, and so the main sources of error are
different. For details of an assessment of this kind, we refer to Section 4
and Table 5 of (Windhorst et al., 2022), where the sources of error in the
absolute sky-SB as measured by WFC3/IR were summarized for the F125W–F160W
filters. In short, their total errors in the estimated WFC3/IR sky-SB were
3–4% in these filters, and dominated by the flat-field ($\lesssim$2%) and ZP
errors ($\lesssim$1.5%). This was through careful tracking of the WFC3/IR
performance and its calibration over 12 years in orbit. At this stage, such
errors for JWST are surely less well known, so we estimate our error budget by
giving conservative limits to each main component that affects our estimated
sky-SB values:

(1) Algorithm to get Lowest Estimated Sky-SB (LES): With the LES algorithm of
Windhorst et al. (2022) and O’Brien et al. (2022, in preparation), we divided
the 2048$\times$2048 pixel image from each individual NIRCam detector into
32$\times$32 boxes of 64$\times$64 pixels and used these to determine the
lowest estimated sky (LES) values following the percentile clip method of
Windhorst et al. (2022) and O’Brien et al. (2022, in preparation). From Monte
Carlo simulations with realistic object densities and CR distributions, they
showed that the LES method gives reliable estimates of the object-free sky-SB,
to within 0.4% of the simulated sky-SB, even in the presence of 10% gradients
across the field. While the object density in the NIRCam images of Section 4.4
is $\sim$3$\times$ higher to $\rm AB\lesssim 28.5$ mag compared to the HST
WFC3/IR image density at its detection limit of $\rm AB\lesssim 26.5$ mag, the
NIRCam SW and LW pixel size is also $\sim$16–4$\times$ smaller in area
compared to WFC3/IR, respectively, so that at least similar amounts of empty
sky are available to the current depth in the NIRCam images to measure object-
free LES sky-SB values. Hence we will adopt an uncertainty of $\lesssim$0.4%
of the algorithm itself estimates the sky-SB in the object free areas. When
applying this algorithm, we find that it does ignore areas with residual wisps
and snowballs well (as it flags those as potential objects with positive flux
to be avoided in the sky-SB estimate).

(2) ZP Uncertainties: The 4% NIRCam ZP uncertainties of Table 7 also apply to
the observed sky-SB values of Figure 12. Since we plot all data points at
their actual central NIRCam wavelengths the Transform uncertainties of Table 7
do not apply. Most of the JWST sky-SB comes from the Zodiacal belt at
distances $\lesssim$3–5 AU (e.g., Windhorst et al., 2022), and the IGL is
$\sim$10–70$\times$ dimmer than than the ZL (Figure 13). Hence, a $\lesssim$9%
CV error in the IGL (Section 4.5) is very small compared to these other errors
in the total sky-SB estimates.

(3) Flat-Field and Residual 1/f and Pedestal Uncertainties: We verified that
the LES algorithm of Section 5 and Windhorst et al. (2022) finds the cleanest
regions to estimate the sky-SB in each detector after the 1/f corrections of
Appendix A. With the most recent reduction of context file
jwst_0952.pmap_filters, the flat field uncertainty has improved to $\sim$2%
compared to the 7–8% uncertainty in our earlier reductions with context file
jwst_0942.pmap_filters (B. Sunnquist; private communication). Since flat-field
uncertainties can be a dominant component in our error budget for absolute
sky-SB estimates, we check for this as following. We find that the LES sky-SB
estimates have a $\lesssim$2–6% variation between the LW detectors in our
2.7–4.5 µm filters, including our TNJ1338 medium-band LW filters. However,
these variations increase to $\lesssim$6–10% for between the SW detectors in
SW 0.9–2.0 µm filters. This is likely due to the larger number of detectors,
some of which still have residual offsets after the flat-fielding and pedestal
removal procedure of Section 3.1. Hence, we adopt at least a 10% uncertainty
in the flat-field induced sky-SB estimate for all SW filters, and a 6%
uncertainty for all LW filters.

(4) Bias and Dark-Current Frame Subtraction Uncertainties: In the 12 years on-
orbit data analyzed for the WFC3/IR detectors, these errors were $\lesssim$1%
following Section 4 and Table 5 of Windhorst et al. (2022). The NIRCam bias
and dark current levels and their uncertainties listed in Section 3.1 and its
websites are also very low, typically $\lesssim$1.4–2.1% of the sky-SB at
3.5–2.0 µmin Table 4, respectively 292929This estimate uses the detector gains
(Section 3.1) and $PHOTMJSR$ and $PIXAR\\_SR$ keywords in the FITS headers..
Hence, uncertainties in the NIRCam dark current removal are much smaller than
the ZP and the flat-field plus residual pedestal uncertainties above.

In summary, following the discussion of Windhorst et al. (2022), we will
assume that the above errors in estimating the sky-SB are independent. This is
justified because the standard stars from which the NIRCam ZP are derived are
measured over an area much smaller than the above dominant flat-field/residual
pedestal errors. The resulting uncertainty in our combined error on the
absolute NIRCam sky-SB is thus $\sim$7% of the observed sky-SB for the LW
filters and $\sim$11% for the SW filters. We propagate these errors for each
filter and PEARLS field into the NIRcam sky-SB estimates of Tables 4–5 and
Figure 13.

##  Appendix C Thermal, Straylight, Zodiacal, and DGL Models to Interpret the
JWST sky-SB

In this section, we summarize the main components in the error budget when
modeling the sky-SB values observed by JWST NIRCam from L2. The ETC output
file ‘‘backgrounds.fits’’ contains an array in its second header which
contains the predicted ETC-straylight, ETC-thermal, and in-field ETC-Zodiacal
components, as well as the combined ETC-total foreground, respectively. Where
relevant, the uncertainties that we derived for these components below are
listed in Table 4–5 between parentheses on the lines directly below the model
prediction for each component.

(1) Thermal Component: The JWST ETC provides predictions for the thermal
contribution from its own components at their various temperatures. JWST
component temperatures are monitored continuously. They are typically
$\sim$42–45K for the OTE and 6–39 K for JWST’s science instruments
303030https://webb.nasa.gov/content/webbLaunch/whereIsWebb.html, i.e.,
considerably colder and more constant than the varying ambient temperatures of
HST across its orbit (see, e.g., Appendix A of Carleton et al., 2022). As a
consequence, the Thermal values for JWST NIRCam in Tables 4–5 are predicted to
be much lower than those for HST. The JWST thermal radiation is in fact more
than 100$\times$ lower than the predicted total sky-SB even at 4.5 µm, as can
be seen in Figure 12. JWST thermal sensors on the website above report typical
NIRCam temperatures stable at 38.5 K to well within 1 K for many days after
its initial cool-down period. We will thus adopt the ETC thermal sky-SB
predictions for NIRcam, and assume that we may ignore its uncertainties in our
total error budget as it is the smallest of all components. Note that this
situation is quite different for HST, where some component temperatures remain
at room temperature and can vary with $\pm$a few K within an orbit, resulting
in non-negligible thermal dark signal in the WFC3/IR F160W filter (Carleton et
al., 2022). As a consequence, JWST can make more accurate sky-SB observations
that are less sensitive to thermal signal than HST and can do so at much
longer wavelengths.

(2) Stray Light Model Prediction and its Uncertainty: The JWST SL model is
created by ray-tracing the infrared sky from 2MASS and WISE onto JWST, and
estimates the fraction of light that can make it onto the detector (Lightsey,
2016). This depends on the dust deposition on JWST mirrors, which after launch
appeared to be much smaller than the requirements (Rigby et al., 2022). This
straylight is significantly out of focus, and to first order generates an
elevated sky-SB onto the NIRCam detectors with a predicted overall spectrum.
The uncertainty in the predicted SL amplitude is not well known from first
principles. During its development, the JWST Project designed the telescope
and sunshield with a requirement that the SL in general be $\lesssim$40% of
the Zodiacal sky-SB at 2.0 µm wavelength. Figure 5 of Rigby et al. (2022)
suggests that the JWST 1–5 µm SL may be substantially lower than this
requirement. Hence, in Figure 12 we adopt the lower of the two Rigby et al.
(2022) SL curves as our fiducial.

Because the uncertainty in the SL prediction is not well known, we will assume
that at 3.5 µm — where the total JWST sky-SB in Equation 4 is lowest — the
JWST sky-SB prediction JWST(Pred) should not exceed but match the observed
sky-SB value JWST(Obs). We found that it was not possible to do this by
assuming the full Rigby et al. (2022) SL as fiducial — in all panels of Figure
12 the predicted JWST sky-SB would be much higher than the observed NIRCam
sky-SB values, if we assumed 100% of the Rigby et al. (2022) SL. We therefore
allowed the fraction $f$ in Equation 4 to vary, while assuming
$f$$\lesssim$1.0. We then attempted to find the fraction $f$ by which we need
to multiply the lower Rigby et al. (2022) SL-value to get a best fit to our
observed 3.5–4.5 µm sky-SB values in Tables 4–5. That is, we set $f$ to
produce the best match to the difference in JWST(Obs)–JWST(Pred) in Equation 5
at 3.5–4.5 µm using the sum in Equation 4.

For the TNJ1338, El Gordo, VV191, and JWIDF fields we find that the 3.5–4.5 µm
JWST(Pred) values in Equation 4 best match the observed sky-SB JWST(Obs) in
Tables 4–5 when we use multipliers for the Rigby et al. (2022) SL of
$f$$\simeq$0.3, 0.6, 0.8 and 0.9, respectively. We estimate that the
$f$$\times$SL values used in Tables 4–5 are uncertain by at least
0.2$\times$the Rigby et al. (2022) SL itself. Based on this variation, we
adopt 0.2$\times$SL as the straylight error in our error budget in Tables 4–5.
The $f$$\times$SL values are generally a factor of 2–10$\times$ lower than the
total predicted JWST sky-SB in Figure 12. Hence, the assumption of a
straylight uncertainty of 20% of the total Rigby et al. (2022) SL value
results in the JWST SL being the dominant uncertainty in predicting the JWST
sky-SB, as shown in Tables 4–5.

(3) L2 Zodiacal Light Model Prediction and its Uncertainty: Zodiacal light
intensities for PEARLS’ JWST observations were calculated using the Spitzer
background model. That model was derived from the Kelsall et al. (1998)
model,313131https://lambda.gsfc.nasa.gov/product/cobe/dirbe_zodi_sw.html which
was designed for the COBE/DIRBE observations from low Earth orbit (LEO). The
Spitzer model updated the scattering component to increase the contrast
between Ecliptic plane and poles and generalized the model to a wider and
continuous range of wavelengths and to arbitrary locations in the Solar
system, as needed for the slowly changing Spitzer position around the Sun
compared to the Earth. This model includes the L2 location, which is
$\sim$1,500,000 km from Earth. Details of this model are given on the IRSA
website.323232https://irsa.ipac.caltech.edu/data/SPITZER/docs/dataanalysistools/tools/contributed/general/zodiacallight/
and
https://irsa.ipac.caltech.edu/data/SPITZER/docs/files/spitzer/background.pdf
The Spitzer model was run using the ephemeris of JWST’s L2 orbit from the ESA
website333333https://www.cosmos.esa.int/web/spice/operational-kernels-data
using the kernel jwst_horizons_20211225_20240221_v01.bsp. This JWST ephemeris
may need to be corrected from time to time due to JWST station-keeping burns
that happen every few weeks. and the actual times of our PEARLS observations
in Table 1. Figure 12 shows the resulting Zodiacal Light intensities as
predicted for JWST’s position in L2.

The Zodiacal-light brightness depends on not only on distance from the Sun but
also on the density and temperature profiles of the interplanetary dust (IPD)
cloud and on the specific line of sight through the cloud. Solar elongation
angle in particular is a significant factor. L2’s distance from the Sun is on
average $\sim$1% larger than the Earth’s, but the other details matter for
specific observations. Comparing the four PEARLS observations so far to what
would have been seen in LEO, the scattered sunlight component was $\sim$1%
fainter for El Gordo and TNJ1338 but $\sim$1–2% brighter for VV 191 and the
JWIDF. (A larger-than-average path length through the IPD cloud at JWST’s
south-of-ecliptic orbital position at that time probably explains the latter.)
The thermal Zodiacal component at 3 µm was 3–7% dimmer at L2 compared to LEO,
but around $\sim$1.5 and 30µm there was at most 2% difference. The larger
difference at the shorter wavelengths occurs because the lower temperatures at
the larger solar distance of L2 have a stronger impact on the Wien side of the
thermal spectrum. Overall, the differences between L2 and LEO are modest.

Kelsall et al. (1998, their Table 7) reported uncertainties in their ZL model
of 15 nW m-2 sr-1 at 1.25 µm, 6 nW m-2 sr-1 at 2.2 µm, 2.1 nW m-2 sr-1 at 3.5
µm, and 5.9 nW m-2 sr-1 at 4.9 µm, respectively. These come from their IPD-
cloud modeling uncertainties. These uncertainties are also present in the
Spitzer model predictions and correspond to Zodiacal model uncertainties at
our NIRCam wavelengths in Table 1 of $\sim$11 nW m-2 sr-1 at 1.49 µm, $\sim$7
nW m-2 sr-1 at 2.0 µm, $\sim$2.2 nW m-2 sr-1 at 3.53 µm, and $\sim$4.1 nW m-2
sr-1 at 4.35 µm, respectively. At the darkest Zodiacal sky-SB measured in the
JWIDF of $\sim$131 nW m-2 sr-1 at 1.49 µm, $\sim$76.7 nW m-2 sr-1 at 2.0 µm,
$\sim$34.3 nW m-2 sr-1 at 3.53 µm, and $\sim$107 nW m-2 sr-1 at 4.35 µm, these
L2 Zodiacal modeling uncertainties are $\sim$8%, $\sim$9%, $\sim$6%, and
$\sim$4% at these four wavelengths, respectively. Blueward of the bluest
COBE/DIRBE 1.25µm filter, the Zodiacal sky-SB values predicted for the NIRCam
F115W and F090W filters are less reliable and should be viewed with caution.
Our four PEARLS fields observed so far span a wide range of Ecliptic
latitudes, and therefore the Zodiacal sky-SB differs significantly among the
fields. These differences are much more than the adopted 4–9% uncertainties
here, as shown in Figure 12. We fold these L2 Zodiacal model uncertainties
into the total error budget to predict the NIRCam sky-SB in Section 5.

(5) Diffuse Galactic Light Model Prediction and its Uncertainty: The DGL
intensities for each PEARLS target came from the Spitzer IPAC IRSA model
prediction (where it is referred to as
“ISM”)343434https://irsa.ipac.caltech.edu/applications/BackgroundModel/, as
discussed by Carleton et al. (2022, and references therein). The work of Sano
et al. (2016), Sano & Matsuura (2017), and Onishi et al. (2018) has suggested
that the DGL as derived from the IRSA model of Brandt & Draine (2012) can be
uncertain by a factor of two. Hence, in our error budget will include an DGL
uncertainty of $\pm$0.3 dex in the predicted JWST(Pred) values used in
Equation 4 in Tables 4–5. The DGL is generally a factor of 20–100$\times$
lower than the total predicted JWST sky-SB in Figure 12, so that a factor of
two DGL uncertainty is not the dominant error in predicting the total JWST
sky-SB. The IRSA model predicted the highest DGL for TNJ1138 amongst all our
PEARLS targets, in fact so high that zero SL would be required for TNJ1138,
which seems unrealistic. Assuming that the IRSA DGL prediction is too high by
0.3 dex for this field alone, we adopt this lower DGL value, in which case
still only a $\sim$0.3$\times$SL level is required in Figure 12a. In any case,
the Zodiacal level in the TNJ1138 field is the brightest of all PEARLS fields,
about 10$\times$higher than the nominal SL and $\sim$10–100$\times$ higher
than the DGL prediction. This illustrates the limitations of our current
assessment. Better SL and DGL models are needed to more accurately predict
JWST NIRCam’s observed sky-SB levels in future work.

(6) Subtracted eEBL and its Uncertainty: The last component in Equation 5 is
the eEBL, i.e., the fraction of the IGL extrapolated in Section 4 that comes
from discrete objects that remain undetected in the NIRCam images for
AB$\gtrsim$28.5 mag. This fraction is only 2.5% of the total IGL, which itself
has an uncertainty of $\sim$10% (section B.3). Hence, the eEBL uncertainty is
a very small part of the total error budget, and is not listed in Tables 4–5.

(7) Resulting Error Budget for the NIRCam sky-SB Model: In conclusion, in our
error budget of the diffuse light, the uncertainty in the JWST SL model
prediction is the largest uncertainty. Under the assumption that the
uncertainties in modeling the L2 Zodiacal Light, the JWST Stray Light, and the
Diffuse Galactic Light are independent, we add them in quadrature in Tables
4–5. The combined uncertainties in the modeled NIRCam sky-SB values are listed
on the line below each component of the predicted JWST sky-SB (Total-Predict-
skySB), and are typically $\sim$10%.

With the summaries of Appendix B3 and C we have all the tools to make
estimates of the object-free NIRCam sky-SB and compare these to the currently
available models. This is discussed in Section 5, Tables 4–5, and Figure 13.