5–25 μm Galaxy Number Counts from Deep JWST Data

The data reduction for SMILES and the JADES MIRI parallel are broadly similar; a full description can be found in Alberts et al. (2024). Both data sets were reduced using v.1.12.5 of the JWST calibration pipeline (Bushouse et al. 2023) using JWST Calibration Reference System (CRDS) context jwst_1188.pmap.

We supplement the standard pipeline with custom, external routines to remove warm pixels missed by the pipeline, "super" background subtraction (Pérez-González et al. 2024), and apply astrometry corrections, matched to GAIA through the JADES NIRCam catalog (Rieke et al. 2023). The final astrometry is accurate to 01−02 (1σ, per axis) for F560W–F2100W and 04 for F2550W, as imaging in this filter is relatively shallow compared to the rest of the survey, with fewer detections suitable for deriving an astrometric correction (Alberts et al. 2024).

Blind MIRI photometric catalogs are created with a modified version of the JADES photometric pipeline (Rieke et al. 2023; S. Tacchella et al. 2024, in preparation). Object detection is done using a stacked F560W and F770W signal-to-noise ratio (SNR) image for SMILES and F770W only for the JADES parallel; these detection images are then used to create a robust segmentation map through an iterative process that starts at a low threshold for detection and then performs deblending, cleaning to remove spurious noise spikes, and faint source detection.

Circular aperture photometry (in apertures of diameter 05, 06, 07, and 10) is then measured from the final, clean segmentation map using photutils with the windowed centroiding algorithm from SExtractor. Kron photometry (2.5× scaled) is also measured using a stacked signal map to define source centroids. Kron apertures smaller than our smallest circular aperture (d = 05) are replaced with that circular aperture photometry. SMILES photometry in filters longer than F770W is measured using the apertures defined by the stacked F560W+F770W detection image. We assess whether this approach misses long-wavelength-only detections and/or changes the derived long-wavelength flux densities; we find that these effects are small and that our photometric catalog is robust (Alberts et al. 2024).

Aperture corrections are applied to both the circular aperture and Kron aperture fluxes using custom PSFs. We derive the aperture corrections for the latter by measuring the fraction of the PSF flux that falls outside each Kron aperture, to account for the size and shape of the PSF. For F1000W–F2550W, PSFs are created using WebbPSF (Perrin et al. 2014). For F560W and F770W, the PSF modeling is complicated by the cross-like imaging artifact known as the "cruciform" (Gáspár et al. 2021), and so empirical PSFs are constructed using high dynamic range imaging of stars obtained during JWST commissioning (A. Gáspár, private communication). Finally, photometric uncertainties are obtained using randomly placed apertures across the mosaics, accounting for local exposure time and correlated pixel noise (e.g., Whitaker et al. 2011; Rieke et al. 2023).

The final SMILES photometric catalog has 3591 sources with SNR > 4 in either the F560W or F770W filter. The JADES MIRI parallel catalog has 2860 sources with SNR > 4 in F770W.

We measure the completeness—the probability of measuring a source at a given flux density given the mosaic noise properties—in our images by inserting and measuring the recovery rate of artificial point sources constructed from our PSFs (Section 2.2). We derive the completeness using point sources because faint galaxies are predominantly intrinsically small and unresolved or marginally resolved by MIRI, while MIRI-resolved sources tend to be bright. Bright extended sources are in a flux regime where the completeness corrections are negligible (see Figure 1), and we do not expect faint, extended sources (for which our completeness will be overestimated) to be numerous enough to significantly affect our counts.

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For SMILES, artificial sources are inserted in 43 flux bins with a width of 0.1 dex ranging from 0.01 to 200 μJy. Within each bin, the flux of each artificial source is chosen at random. For each filter and flux bin, we generate 10 mosaics with 150 artificial sources (<5% of the real source catalog) inserted into random positions (with masking of the map edges), totaling 1500 artificial sources per filter per flux bin, a number that ensures robust Gaussian statistics while limiting computational time requirements. Photometric catalogs are then created for each altered mosaic following the procedure outlined in Section 2.2. Artificial sources are considered recovered if they are found within 02 of the inserted position and the measured flux density is detected at >2σ and within 50% of the input flux. The latter accounts for flux boosting of faint sources from brighter neighbors under the approximation that galaxies are randomly distributed. As galaxies are in reality clustered, this is an underestimation, but we do not expect this to have a significant impact on our measured number counts given the small MIRI beam (Viero et al. 2013).

This procedure is repeated for the JADES MIRI parallel, with 53 flux bins ranging from 0.001 to 200 μJy with 0.1 dex bin width. Given the smaller area of the parallel, we inject 50 artificial sources at a time into 30 mosaics, again producing 1500 artificial sources per flux bin. The resulting completeness curves for both surveys are shown in Figure 1, and the 80% completeness level is reported in Table 1. A completeness of 80% in each band is reached at approximately the 5σ detection limit. This high completeness at faint fluxes is attributable to our careful background subtraction (Section 2.1). For the rest of this work, only sources above the 80% completeness limit will be considered.

We expect some fraction of our detected sources to be spurious: not true astrophysical sources, but peaks in the noise. The contribution of these "false positives" to our number counts is certainly insignificant at the bright end of the distribution, but it may become important to the total counts at the faint end.

To quantify the fraction of spurious sources our counts contain, we perform a source extraction on negative images (see Papovich et al. 2004). By inverting the images, the flux of all real sources becomes negative, and the only positive sources remaining in the image are random Gaussian peaks from noise. As the noise is random, the number of sources in the negative image should also reflect the number of spurious sources that will be detected in the original images and removed from the counts.

We invert the mosaic in each filter and mask the noisy edges before performing source detection (using Photutils' find_peaks algorithm), extracting photometry with a 12-diameter aperture. We find that the vast majority of spurious sources have integrated fluxes well below our completeness limits, with only a few noise peaks bright enough to contribute to the faint end of the counts. Normalizing by the areas of SMILES and JADES, we find that we expect ∼0.05–0.25 counts arcmin⁻² from spurious sources at the 80% completeness limits of SMILES, and even fewer in the JADES parallel. Contributions from spurious sources at brighter fluxes are, as expected, completely negligible, and we therefore make no corrections accounting for their presence.

Differential and cumulative number counts are derived from the photometric catalogs described in Section 2.2. Precise individual areas are measured for each mosaic by counting unmasked pixels (Table 1). The exposure times are largely uniform across the mosaics: 70%–80% of pixels have exposure times within 5% of the median.

We consider counts in each filter down to the 80% completeness limits, which are comparable to the 5σ point-source sensitivities (Table 1). The number counts discussed in the following sections and reported in Table 2 are completeness corrected, and the error bars reflect purely statistical error.

Our deepest data are at 7.7 μm. At low redshift, F770W traces the mid-IR polycyclic aromatic hydrocarbon (PAH) features and probes the rest-frame peak of stellar emission at higher redshift, z ∼ 2 to − 5. At all redshifts, 7.7 μm—and other mid-IR—counts will additionally contain a population of dust-obscured active galactic nuclei (AGNs) and composite (star-forming + AGN) galaxies. When corrected for the contribution of AGNs, 7.7 μm counts can therefore test the distribution of stellar mass, particularly at high redshift, of galaxy formation models.

The similarity between the MIRI F770W and Spitzer/IRAC Channel 4 (8 μm) filters also allows us to connect our very deep counts with those from wide-field Spitzer surveys, probing both the bright and faint ends of the distribution. However, the two filters are not identical. While the MIRI F770W filter has slightly higher throughput, the IRAC-4 bandpass is wider on the red side, extending to ∼9.5 μm compared to F770W's ∼8.75 μm. The largest difference between an individual source's IRAC-4 and F770W fluxes will likely occur for sources at redshifts where a bright PAH feature is shifted out of the F770W bandpass but remains in the IRAC-4 bandpass, but this occurs in only two small redshift ranges (z ∼ 0.13–0.27 and 0.41–0.52 for the 7.7 and 6.2 μm PAH features, respectively). Early JWST results comparing MIRI to IRAC counts indicate that the effect of this difference is very small (see, e.g., Wu et al. 2023; Yang et al. 2023) in the flux regime where MIRI and IRAC counts overlap.

We present our differential and cumulative 7.7 μm counts from SMILES and JADES in Figure 2, alongside bright-end IRAC-4 data from the Spitzer Deep Wide-Field Survey (SDWFS; Ashby et al. 2009). Together, these deep MIRI data and wide Spitzer data provide the deepest 8 μm counts ever observed, spanning more than five orders of magnitude in flux from <0.1 to more than 10⁴ μJy.

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The MIRI F770W counts in the SMILES and JADES fields are slightly offset from each other. We have verified that this offset is not due to any differences in the data reduction process. Instead, this is likely due to cosmic variance: the Hubble Ultra Deep Field (which forms the center of the SMILES footprint) is known to be slightly underdense, while a number of overdensities have already been cataloged in the small JADES parallel field (Alberts et al. 2023). The difference between the SMILES and JADES counts likely encodes the typical variation that will be observed between surveys (see also the variation in counts for fluxes probed by Spitzer; Béthermin et al. 2010).

The differential counts (right panel of Figure 2), which have been normalized to a Euclidean universe (multiplied by ${S}_{\nu }^{2.5}$), display the characteristic power-law decline toward faint fluxes observed by other telescopes and flatten at the bright end when we remove the contribution from Galactic stars from the model of Fazio et al. (2004).

For comparison, we also plot in Figure 2 the 8 μm number count predictions from a number of simulations and semianalytical models of galaxy formation, namely the GALFORM semianalytical model and GRASIL radiative transfer code (F770W; Cowley et al. 2018), the SHARK semianalytical model (IRAC-4; Lagos et al. 2019), the SPRITZ simulations (F770W; Bisigello et al. 2021), and the IRAC-4 model of Rowan-Robinson (2009, 2024). We discuss these models in greater depth in Section 4.1.

We plot our SMILES cumulative and differential counts at both 21 and 25 μm in Figure 3, as the counts in both bands have very similar distributions. Our new JWST counts also align with counts from deep 24 μm Spitzer surveys (Papovich et al. 2004; Béthermin et al. 2010; plotted as gray squares and black plus signs, respectively), which we use to extend our distribution to the bright end. Together, these 21/24 μm counts extend over approximately four orders of magnitude, from less than 100 to more than 10⁵ μJy, and probe deeper than any ∼24 μm counts previously published. Additionally, due to the unprecedented spatial resolution of JWST, our MIRI ∼24 μm counts are not confusion limited, unlike the Spitzer counts also shown in Figure 3.

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The flux at ∼25 μm probes the mid-IR warm dust continuum until z ∼ 1.5, when the bright 7.7 μm PAH feature begins to shift into the band. We observe the characteristic bump at ∼100 μJy in the Euclidean-normalized differential counts. Despite the minimal overlap of the MIRI F2100W and F2550W bands, the counts display very similar distributions down to the limit of the F2550W data.

The MIPS 24 μm filter is much broader than the MIRI filters, encompassing most of the wavelength range covered by the MIRI F2100W and F2550W filters. This discrepancy, however, does not appear to severely affect the magnitude or shape of the source counts' distribution, as the MIPS 24 μm data from Papovich et al. (2004) and Béthermin et al. (2010) display fair agreement, within the uncertainties and scatter, with the MIRI data. No correction has been applied to either the MIRI or MIPS counts to account for the very different bandpasses and bring the counts into alignment.

In addition to the Spitzer counts, we can compare our results to the counts obtained in two MIRI pointings of the CEERS survey by Wu et al. (2023). While the Wu et al. (2023) counts agree well with ours down to ∼100 μJy, their differential counts flatten at the faintest end of their data, between ∼10 and 100 μJy, rather than continuing to decrease as a power law like our SMILES counts or model predictions. This may be an artifact of those data's lack of background subtraction, as we observe a similar effect to a lesser extent in other bands longward of 10 μm (discussed below in Section 3.4).

In general, when normalized near 10³ μJy, the models of Rowan-Robinson (2009, 2024) reasonably closely follow our observed counts down to the faint end and reproduce the shape of the differential number count distribution well (right panel of Figure 3). The GALFORM model, on the other hand, underpredicts the number of faint sources and does not exhibit the peak in the differential counts near 100 μJy seen in both JWST and Spitzer data. Further discussion of these comparisons can be found in Section 4.1.

We plot the cumulative number counts for all remaining MIRI bands (F560W, F1000W, F1280W, F1500W, and F1800W) in Figure 4. We include, when available, other data and models in the bands, including AKARI counts (Pearson et al. 2010, 2014), MIRI counts in the CEERS field (Kirkpatrick et al. 2023; Wu et al. 2023), and the GALFORM (Cowley et al. 2018), SPRITZ (Bisigello et al. 2021), and Rowan-Robinson (2009, 2024) models.

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Counts from the AKARI North Ecliptic Pole (NEP) surveys at 15 and 18 μm (Pearson et al. 2010, 2014) extend our MIRI counts to the bright end and are in very good agreement with our counts where they overlap. As a result, the counts at 15 and 18 μm extend over nearly four orders of magnitude in flux. These AKARI counts have been corrected for the contributions of stars, but not for the difference between the MIRI F1500W/F1800W and AKARI IRC L15/L18 bandpasses. The AKARI bandpasses are significantly broader than the corresponding MIRI bandpasses: for example, while the two filters have roughly the same central wavelength, L15's half-power width (6.8 μm) is more than twice that of F1500W (∼3.1 μm). Nonetheless, the excellent agreement of the AKARI counts with our MIRI data demonstrates that the different filter shapes do not strongly affect the counts.

At the fainter end, we can compare our counts to the slightly shallower counts measured in two of the MIRI pointings of the CEERS field by Wu et al. (2023). These counts, in F1000W, F1280W, F1500W, and F1800W, drop off quickly at ∼100 mJy, due to the smaller area of the survey, and do not go quite as deep. While they agree fairly well with our counts, some of the bands (particularly F1000W and F1800W) display steeper slopes between 1 and 100 μJy. This may be a background subtraction artifact, similar to that observed near the faint end at 21 μm (right panel of Figure 3). This hypothesis is reinforced by the 10 μm counts from Kirkpatrick et al. (2023): these data, also from the CEERS survey, agree well with our 10 μm counts.

The error bars in Figures 2–4 reflect only statistical errors. Potentially larger errors occur because of cosmic variance: the differences in source characteristics among different fields on the sky (e.g., Trenti & Stiavelli 2008). Cosmic variance is reduced significantly as the number of distinct fields surveyed increases, and also with the area of the field(s) surveyed. In addition, the effects of cosmic variance are more pronounced for the brighter sources than the fainter ones (e.g., Driver & Robotham 2010; Robertson 2010; Moster et al. 2011).

By combining counts from the large-area, moderate-depth surveys of Spitzer and AKARI with the (to date) small areas surveyed to great depth by JWST, the cosmic variance effects at play can be understood and mitigated. We discuss cosmic variance for each wavelength in turn.

5.6 μm: The top left panel of Figure 4 compares our 5.6 μm counts with those in IRAC-3 reported in ∼8 deg² in the Bootes field by Ashby et al. (2009). The Ashby et al. (2009) counts demonstrate excellent agreement with those in the 0.38 deg² survey in the Extended Groth Strip surveyed to ∼5 times deeper reported by Barmby et al. (2008) and with counts from the IRAC Shallow Survey (Fazio et al. 2004). The large areas surveyed and the agreement of counts from two widely separated fields indicate that cosmic variance does not have a strong effect on these counts. Their close agreement with our JWST-based counts in the region of overlap indicates, despite the small area surveyed, that the latter counts are also representative without a large bias due to cosmic variance.

7.7 μm: Figure 2 compares our counts at 7.7 μm to those from Ashby et al. (2009) at 7.8 μm. As at 5.6 μm, the Ashby et al. (2009) 7.8 μm counts agree well with counts measured in other fields with Spitzer (Fazio et al. 2004; Barmby et al. 2008) and agree with our MIRI F770W counts where they overlap. We therefore do not expect cosmic variance to seriously bias our 7.7 μm counts.

15 and 18 μm: The counts in Figure 4 at 15 and 18 μm use results from the AKARI NEP surveys. ⁴ These observations were designed to reduce cosmic variance to the 5%−10% level (Pearson et al. 2010). ⁵ They cover areas of ∼0.4–0.6 deg² and 5.8 deg² to depths of 117 (150) and 250 (300) μJy, respectively, at 15 (18) μm (Pearson et al. 2010, 2014). The excellent agreement with the counts in the SMILES field in the region of overlap again implies that the entire range shown in Figure 4 is unlikely to be compromised by cosmic variance. On the other hand, MIRI counts from Wu et al. (2023) fall low at the bright end, suggestive of an influence of variance on those results, due possibly to the significantly smaller field available (∼6 arcmin²).

21–25 μm: Figure 3 compares JWST/MIRI counts at 21 and 25.5 μm with Spitzer/MIPS counts at 24 μm. The counts from Papovich et al. (2004) are from five widely separated fields with ∼0.61 deg² surveyed to a depth of ∼80 μJy and >10 deg² to a depth of at least 270 μJy. Béthermin et al. (2010) report surveys of ∼0.64 deg² to ∼80 μJy and 53 deg² to at least ∼400 μJy in seven additional fields. These surveys agree very well with each other and with our counts down to their limits of 80 μJy (see Figure 3). Again, this indicates that the full range of counts presented here is not strongly affected by cosmic variance.

Figures 2–4 show the predictions of number count models between 5 and 25 μm, many of which diverge from observed counts. Many models, even those published recently, use spectral energy distribution (SED) templates created before Spitzer IRS data were available and/or use relatively abstract templates that do not match the results with full Spitzer data (e.g., as in Rieke et al. 2008; Magdis et al. 2012; Schreiber et al. 2018; Bernhard et al. 2021). This could be important because the aromatic bands dominate the IR output of star-forming galaxies from 6 through 12 μm and fall within the wavelength range of JWST and Spitzer number counts for z ∼ 0–3. For example, Cowley et al. (2018) utilize a combination of models from GRASIL (Silva et al. 1998) and GALFORM (Granato et al. 2000). However, in these models the PAH bands are represented very schematically, and in the latter one the region between 15 and 40 μm is not represented accurately and the silicate absorption features at 10 and 18 μm are not included. The modeled number counts by Rowan-Robinson (2024) are based on mid-IR SEDs from Rowan-Robinson et al. (2004, 2005). These are constrained by Spitzer photometry, but the PAH bands are from ISO spectroscopy of a very small number of galaxies (Rowan-Robinson 2001) and again are quite schematic. This relatively limited sample of PAH spectra can cause problems: for an example, compare the proposed spectra in Figure 6 in Rowan-Robinson et al. (2005) for "Arp 220 starbursts" with the actual spectrum of Arp 220 from Spoon et al. (2004).

Two sets of models, SHARK (Lagos et al. 2019) and SPRITZ (Bisigello et al. 2021), do include accurate spectra of the PAH bands making use of Spitzer IRS spectra. The SHARK models are based on a semianalytic model (SAM) of galaxy formation and evolution. These models are compared with counts in the IRAC bands, and their good matching of the 7.7 μm counts presented here to very faint levels is very encouraging in terms of such models. Obviously, using this approach to model counts at the longer wavelengths is very desirable, continuing with accurate template SEDs. The SPRITZ models are empirically based on a global analysis of galaxy properties. They provide good fits out to 8 μm, including to our very deep 7.7 μm counts. At the longer wavelengths, their results are subject to substantial errors that undermine a quantitative assessment of their accuracy. For both sets of models, the agreement with our 7.7 μm counts demonstrates that representing the PAH bands accurately is critical to interpreting the number counts presented in this paper.

The CIB is the fraction of the extragalactic background light (EBL) emitted in the IR and arises mainly from dust-obscured star formation (with contributions from dust-obscured AGNs) in galaxies across cosmic time (Hauser et al. 1998; Gispert et al. 2000; Lagache et al. 2005). With more sensitive telescopes, more and more of the CIB can be resolved into individual sources, e.g., the sources making up our galaxy number counts. Our discussion below follows on from the treatment in Driver et al. (2016).

To estimate the total 8 μm flux from sources detectable in our MIRI data, we combine and integrate 8 μm number counts from the SDWFS (Ashby et al. 2009) at the bright end, with stars removed, and our JADES MIRI parallel at the faint end. To combine the data sets, we exclude all JADES MIRI parallel counts at fluxes brighter than S_ν = 50 μJy, because the counts in this flux regime are affected by cosmic variance owing to the small area of the survey. The wider-area SDWFS has data in this flux range, which will be less affected by cosmic variance. Correspondingly, we exclude all counts at fluxes fainter than S_ν = 30 μJy from the SDWFS IRAC data: this flux corresponds to the 8 μm SDWFS 80% completeness limit. In the small remaining region of overlap, the MIRI and IRAC counts agree well (see Figure 2). We also do not include the two brightest SDWFS IRAC points (S_ν > 2 × 10⁴ μJy) in our integration, as they deviate sharply from the flat, Euclidean trend expected at very bright fluxes in the right panel of Figure 2 owing to cosmic variance. After integrating and propagating through the statistical errors on each bin, we obtain an 8 μm CIB flux of 3.02 ± 0.09 nW m⁻² sr⁻¹, slightly larger than estimates from 8 μm Spitzer surveys (2.6 nW m⁻² sr⁻¹; Fazio et al. 2004).

Driver et al. (2016) estimated the CIB at 8 μm using Spitzer/IRAC data from Barmby et al. (2008), who surveyed 0.38 deg² in the Extended Groth Strip. Their uncertainty from cosmic variance (±0.08 mag) translates to approximately ±0.035 mag for the 10 deg² area we have used to anchor our counts at bright levels (Ashby et al. 2009). They overstate the zero-point error; the absolute calibration of the IRAC data is accurate to ∼3%. The ultradeep JWST data basically remove uncertainties due to extrapolation to low fluxes. The net error in our value should therefore be ∼10%.

We calculate number counts at 21/24 μm in the same manner, by combining Spitzer/MIPS counts (Papovich et al. 2004) and our new MIRI SMILES counts. We remove the brightest MIRI 21 μm points (S_ν > 200 μJy), which are most affected by cosmic variance. The 80% completeness limit for the Papovich et al. (2004) MIPS data lies at S_ν ∼ 100 μJy, so we do not include any fainter MIPS counts in our integration. The SMILES/MIRI and MIPS points agree very well (see Figure 3) near this remaining small region of overlap. We integrate from the faintest MIRI point (3.25 μJy) to the brightest MIPS point (4.76 × 10⁴ μJy) and do not extrapolate; this integrated value is therefore a lower limit on the 21/24 μm CIB flux. Propagating through only the statistical errors on the counts, we obtain a flux of 2.85 ± 0.04 nW m⁻² sr⁻¹. Since we have taken our bright 24 μm counts from the same source as Driver et al. (2016), their estimate of a cosmic variance error of ±0.07 also applies to our result. Most other errors listed in Driver et al. (2016) should be reduced by use of the JWST data. As before, the zero-point error is significantly overstated; the absolute calibration of MIPS is accurate to ∼3% (Rieke et al. 2008). We conclude that the total error in our value is, as at 7.8 μm, ∼10%.

Béthermin et al. (2010) found a CIB flux of 2.29 ±0.09 nW m⁻² sr⁻¹ from Spitzer 24 μm counts probing fluxes >35 μJy. However, when the counts were extrapolated at the faint end, they calculated an integrated 24 μm CIB flux of ${2.86}_{-0.16}^{+0.19}$ nW m⁻² sr⁻¹, in excellent agreement with our value. Dole et al. (2006) also measured the 24 μm CIB by adding ;up the flux from all sources brighter than 60 μJy and using the counts of Papovich et al. (2004) to determine the contribution from fainter sources, finding an EBL value of 2.7 ±0.26 nW m⁻² sr⁻¹. Because Dole et al. (2006) do not quote any additional error from the extrapolation to very faint limits, this uncertainty is likely somewhat underestimated.

TeV gamma rays are attenuated as they traverse intergalactic space through pair production with the ambient ultraviolet, optical, and IR photons. SAMs of the history of galaxy formation and galaxy properties can be combined with TeV gamma-ray measurements to predict the spectrum of the EBL. Our values at both 7.8 and 24 μm are in mild tension with the fiducial EBL model based on TeV gamma-ray sources by Gilmore et al. (2012), which predicts values of 2.4 nW m⁻² sr⁻¹ at both wavelengths. As shown by Abeysekara et al. (2019), the highest weight values based on TeV gamma-ray observations tend to fall on or below the Gilmore fiducial, although the disagreement with our values is not huge. It should be kept in mind that the EBL estimates from source counts are strictly lower limits, since they exclude any diffuse emission and discriminate against extended sources. The discrepancy might therefore be larger than indicated here. These accurate determinations of the mid-IR EBL suggest that some tuning of the SAMs used to predict the EBL may be desirable.