<figure><img src="image_29.png" /><figcaption>**Fig. 27.** Comparison between synthetic and measured stellar locus slopes in the SNLS-SDSS color diagram for the 4 SDSS camcols covered in the observation program.</figcaption></figure>

<table><caption>**Table 21.** β values as defined by Eq. (29) between SDSS and SNLS surveys.</caption><thead><tr><th></th><th>SDSS36</th><th>SDSS326</th><th>Combined</th></tr></thead><tbody><tr><td>u</td><td>-0.432 ± 0.002</td><td>-0.447 ± 0.002</td><td>-0.438 ± 0.001 ± 0.014</td></tr><tr><td>g</td><td>-0.082 ± 0.002</td><td>-0.074 ± 0.001</td><td>-0.076 ± 0.001 ± 0.008</td></tr><tr><td>r</td><td>-0.017 ± 0.001</td><td>-0.016 ± 0.001</td><td>-0.017 ± 0.001 ± 0.001</td></tr><tr><td>i</td><td>-0.001 ± 0.001</td><td>-0.003 ± 0.001</td><td>-0.002 ± 0.000 ± 0.002</td></tr><tr><td>i2</td><td>0.010 ± 0.003</td><td>0.012 ± 0.002</td><td>0.012 ± 0.001 ± 0.003</td></tr><tr><td>z</td><td>0.030 ± 0.001</td><td>0.035 ± 0.002</td><td>0.031 ± 0.001 ± 0.005</td></tr></tbody></table>

**Notes.** All numbers are expressed in magnitudes. Those numbers should not be interpreted as calibration offsets, part of the difference is expected from the definition of the magnitude systems. A discussion about AB offsets can be found in Sect. 9.

## 8.5. Average offsets

We can now tie the SNLS and SDSS calibrations together. Ultimately, the quantity of interest is the flux interpretation of a calibrated measurement. As filters themselves have uncertainties, the error on this quantity depends on the SED of the object itself (to first order in its color). We discuss this question in the next section. We display in Table 21 the offset between the two surveys for a star of color $g-i = 0.8$ (defined as the β term in Eq. (29)).

The offset is computed separately on each field. The statistical uncertainty is estimated from the night-to-night dispersion of measurements divided by the square root of the number of observation nights. We then combine the two numbers and use the difference between the two fields as an estimate of the uncertainty on the mean related to the residual non-uniformity of the surveys.

## 9. Combined calibration

The calibration products for both surveys consist of:

- measured natural magnitudes for a set of tertiary standards $m^3$, in an arbitrary magnitude system;

- magnitudes of primary spectrophotometric standards $m^s$ in the same magnitude system, affected by some measurement and systematic errors $n_s$.

The primary spectrophotometric standards are to be used to set the actual flux scale (equivalently determining a magnitude offset to the AB system $\delta_{ab}$) of the first by equating the measured magnitude of the standard $m^s$, with its expected magnitude $\tilde{m}^s$ synthesized from the spectrophotometric reference measurement:

$$m^s = \tilde{m}^s + \delta_{ab} \quad (30)$$

with:

$$\tilde{m}^s = -2.5 \log_{10} \frac{\int_{\lambda} \lambda T(\lambda) S^s(\lambda) d\lambda}{\int_{\lambda} \lambda T(\lambda) S_{ab}(\lambda) d\lambda}.$$

The result is affected by uncertainties on the effective instrument passbands $T$ and on the SED $S^s$ of the reference, as well as the error on the measured magnitude $n_s$.

In our case we have at our disposal:

- 59 direct measurements of 3 solar-analogs (P330E, P177D and SNAP2) performed with MegaCam and calibrated to the SNLS system (see Sect. 5.2).

- Landolt & Uomoto (2007) measurements of the star BD +17 4708, color transformed to the SNLS system in 5 bands (see Sect. 5.1).

- PT measurements of 4 photometric standards (BD +17 4708, P330E, P177D, P041C) color-transformed to the 2.5 m system in the 5 photometric bands (see Sect. 7). We do not use the PT observations of bluer standards as they are outside the valid range of the PT→SDSS system color transformation.

In addition, the cross-calibration data described in Sect. 8 yields 6 constraints on the relation between the two surveys' tertiary catalog flux scales, and a straightforward constraint on the $i_M$ and $i2_M$ magnitudes is given by the comparison of tertiary star magnitudes in these two bands (see Sect. 5.3). Altogether, we have a total of 91 measurements (or pseudo-measurements) and associated uncertainty estimates with which to constrain the AB offsets of the tertiary catalogs in the 11 photometric bands considered.

Our purpose here is to optimally combine the entire set of calibration data, to check its consistency, and to derive a reliable estimate of the uncertainty on the resulting calibration. As we want to combine several standard stars measured in different photometric systems related by linear transformations, we start by discussing and parametrizing the uncertainty on the instrument passbands and primary standard SEDs.

### 9.1. Uncertainties on passbands

The uncertainty on the effective instrument passband comes from various sources and may take some arbitrarily complex form. For instance, the portion of passband uncertainty from optical elements whose transmissions can be measured should approximately reduce to the uncertainty of the wavelength calibration of the monochromator (i.e. a global wavelength shift). On the other hand, the portion of passband uncertainty due to other elements, like the CCD QE, can be harder to characterize. The determination of the average atmospheric transmission is also affected by uncertainties, which primarily impact the u band calibration. In what follows, we assume that we can parametrize
the error affecting the effective passband defining the photometric band *b* by a shift in the passband's mean wavelength $\delta\lambda_{\text{eff}}^b$. In other words, when performing first order computations in the next section, we will assume that passband uncertainties result from a global shift of the filter. We now attempt to derive an estimate of the amplitude of the uncertainty on the mean wavelength $\delta\lambda_{\text{eff}}$.

### 9.1.1. SDSS passbands

Measurement errors on the SDSS passbands are not completely characterized by Doi et al. (2010), but we will estimate the uncertainty from data in that paper. The accuracy of the monochromator calibration is given as $\pm 3$ Å, which we assume is a constant error for all wavelengths in a given filter band. The ability to reproduce an independent quantum efficiency measurement (Fig. 2 in Doi et al. 2010) suggests that the amplitude error is less than 2%. Assuming a $\pm 2\%$ error that is linear in wavelength across the band, we calculate an error in the mean filter wavelength that is 0.3% of the filter bandwidth. Using 1500 Å for the filter width and combining that uncertainty with the monochromator uncertainty, results in a 6 Å uncertainty in mean filter response. The 1500 Å width is slightly too large for *g*, *r*, and *i* bands and a factor of 3 too large for *u* and *z*. However, we don't decrease the error estimate for these bands because there are probably other (unquantified) uncertainties for these bands (e.g. the difficulty of determining the UV transmission and the red cutoff in *z*).

### 9.1.2. SNLS passbands

The lack of monitoring for the MegaCam passbands proved to be a weak point in the SNLS survey. It was only recently realized that two of the interference filters may have undergone significant alteration in their early days.

The REOSC filters were measured twice (in 2002 and 2006) and both measurements appear to be in rough agreement in all bands but $i_M$ and $r_M$. Two arguments support the hypothesis that the 2006 measurements yield a better representation of the survey passbands: first, the stability of the color locus of tertiary stars during the 5 years of the survey, presented in Sect. 3.4.1, excludes the hypothesis of a slow aging of the filters between 2003 and 2008. Second, recent lab measurements of pieces of the broken $i_M$ filter were found to be in agreement with the 2006 measurement while incompatible with the 2002 ones. Because the 2006 measurements only cover the outer edge of the filters (12–15 cm away from the center), it was not possible to use them directly. Instead, we opt for applying a correction to the 2002 $i_M$ and $r_M$ measurements (see Appendix B). The unaltered 2002 measurements are used as-is for the $u_M$, $g_M$, and $z_M$ filters. We now try to quantify the size of the uncertainty on the mean passbands resulting from these choices.

The mean wavelength shift between the 2002 and 2006 measurements provides an estimate of the error at a specific position (about 15 cm away from the center). The measured differences amount to 5, 3, -37, -31 and 6 Å in $u_M$, $g_M$, $r_M$, $i_M$ and $z_M$ bands respectively. The spatial consistency of the filter model is then ensured by the agreement of modeled and measured color terms between different positions (as illustrated on Fig. 7). A noticeable exception is the $r_M$ filter for which the measured and modeled color terms start to disagree at radii greater than 10 cm. Without proper measurements of the $r_M$ filter at radius smaller than 10 cm, it is thus not possible to trust the corrected filter

model more than the uncorrected model. Therefore, we assign an uncertainty of 37 Å to the $r_M$ filter passband. The situation appears a bit better for the $i_M$ filter, since the accuracy of the 2006 measurement has been checked (cf. Appendix B), and the agreement between predicted and measured color-terms is quite good. Nevertheless, it seems premature to assign an uncertainty smaller than 31 Å to the $i_M$ passband without better understanding the source of the filter change. For the $u_M$, $g_M$, and $z_M$ filters, we also use the quoted differences between the two available measurements, namely 5, 3 and 6 Å, as an estimate of the measurement uncertainty.

The $i2_M$ BARR filter was never completely measured. In particular its effective refraction index is unknown and assumed to be similar to that of the $i_M$ filter. We base our estimate of the $i2_M$ passband uncertainty on the stellar locus in the plane $i2_M - i$ vs. $g - i$ which has been well-constrained by observations of Stripe 82 stars and synthetic photometry predictions (see Sect. 8.3). The comparison between synthetic predictions and measurements suggests an $i2_M$ shift of -30 Å (Table 20).

The uncertainty on the average atmospheric extinction curve is estimated in Buton et al. (2012) to be smaller than 0.02 mag/airmass. This has a negligible impact on the definition of any of the passbands. A noteworthy exception is the $z_M$ filter, which covers a region of strong H$_2$O absorption (8916–9929 Å). Errors in the modeling of the average extinction could cause the mean wavelength of the effective filter to shift by a few angstroms. However, the error is unlikely to exceed the uncertainty quoted for this filter. Given their high throughput and the smoothness of their transmission, we do not expect significant contributions to a wavelength shift from any of the instrument elements besides the interference filters.

## 9.2. SED of the primary standard stars

Five spectrophotometric standard stars from the CALSPEC database are being considered in our final calibration data: the F sub-dwarf BD+174708 and the 4 G-type stars P041C, P177D, P330E and SNAP2. All these stars have STIS spectra calibrated by the model spectra of the white dwarfs G191B2B, GD153, and GD71. Any error in the spectral modeling of those three fundamental standard stars would equally affect our 5 standard stars.

The calibration reference is affected by both the white dwarf atmosphere model error and uncertainties in the determination of the primary standard surface gravity and effective temperature from observations of their Balmer line profiles. Following R09, we base our estimate on considerations from Bohlin & Hartig (2002) and adopt a 0.5% slope uncertainty ($1\sigma$) over the range 3000 Å–10000 Å. Relative to *g* band$^{25}$, the resulting (correlated) uncertainties are 0.7, 1.1, 2.2 and 3.2 mmag in *u*, *r*, *i* and *z* bands respectively.

In addition, some measurement error is expected to affect the individual measurements. Similarly to what was done in R09, our estimate of the covariance of broadband magnitudes synthesized from STIS spectra is based on the repeatability of the monitoring spectra of AGK+81266. The individually measured spectra were integrated in the MegaCam and SDSS passbands and an empirical covariance matrix of the measurements was built. We found a repeatability of 5, 4, 5, 6 and 11 mmag in broadband magnitudes *ugriz* for both instruments, with

<footnote n="25">25 We are not interested in the overall flux scale. Otherwise the uncertainty would be dominated by the determination of the Vega absolute flux, which does not play any role here.</footnote>
significant correlation between neighboring bands, and (as expected) nearly perfect correlation between overlapping bands. The full covariance matrix is delivered in Table E.10. Some of the standard spectra were established with several independent measurements. When determining the expected broadband noise of the star measurement the covariance matrix is divided by the number of observations.

### 9.3. Mixing calibration data

For each available measurement (or pseudo-measurement in the case of a color-transformed magnitude) of a photometric standard *s* in a photometric band *b*, denoted $m_b^s$, the corresponding expected standard AB magnitude $\tilde{m}_b^s$ can be calculated from its CALSPEC spectrum. The model for the calibration data is:

$$m_b^s - \tilde{m}_b^s = \delta_{ab}^b + e_{s,b}, \quad (31)$$

where *e* is the error term affecting the estimate of $m_b^s - \tilde{m}_b^s$. It is further decomposed as:

$$e_{s,b} = n_{s,b} + c_{s,b} + \frac{\partial \tilde{m}_b^s}{\partial \lambda_{\text{eff}}^b} \delta \lambda_{\text{eff}}^b, \quad (32)$$

where $n_{s,b}$ is the measurement error affecting $m_b^s$ (including systematic uncertainties on the measurement), $c_{s,b}$ is the uncertainty affecting the broadband CALSPEC magnitudes, and $\frac{\partial \tilde{m}_b^s}{\partial \lambda_{\text{eff}}^b} \delta \lambda_{\text{eff}}^b$ describe the first order impact of the filter uncertainty on $\tilde{m}_b^s$.

The cross-calibration data (between SNLS and SDSS as well as between bands $i_M$ and $i2_M$) adds further constraints. These take the generic form of approximate linear relations between very similar filters, applicable on average to the tertiary stars:

$$m_b^s - m_{b'}^s \approx \alpha c + \beta \quad (33)$$

with some uncertainty on $\alpha$ and $\beta^{26}$. As before, we translate these color relations into cross-calibration constraints by assuming that those relations also apply to a spectrophotometric standard lying in the color range of the transformation. The extra error coming from the dispersion around the color transformation has to be estimated from stellar libraries. We thus add to our model the following terms:

$$\beta_{bb'} - \alpha_{bb'} c^s - \tilde{m}_b^s + \tilde{m}_{b'}^s = \delta_{ab}^b - \delta_{ab}^{b'} + e_{bb'} \quad (34)$$

where $(b, b')$ ranges over $\{(u_M, u), (g_M, g), (r_M, r), (i_M, i), (i2_M, i), (z_M, z), (i2_M, i_M)\}$. Again the error term is compound:

$$e_{bb'} = c_{s,b} - c_{s,b'} + \frac{\partial m_b^s}{\partial \lambda_{\text{eff}}^b} \delta \lambda_{\text{eff}}^b - \frac{\partial \tilde{m}_{b'}^s}{\partial \lambda_{\text{eff}}^{b'}} \delta \lambda_{\text{eff}}^{b'} + e_{\alpha} c + e_{\beta} + d,$$

where *d* is an uncertainty term accounting for the dispersion of stars around the color relation. We obtain the expected rms of the *d* term by measuring the dispersion around the average transformation of magnitudes synthesized from a stellar spectrum library. We find 48, 6, 2, 4, 3 and 2 mmag of dispersion around the relations between the SNLS and corresponding SDSS band for $u_M, g_M, r_M, i_M, i2_M, z_M$ respectively.

To ease the handling of correlated uncertainties between all the measurements, we can gather the 91 calibration measurements into a single vector *y* and write the linear model for the calibration data in matrix form:

$$y = Ax + e. \quad (35)$$

We want to solve for the vector of calibration offsets $x = (\delta_{ab}^{u_M}, \dots, \delta_{ab}^{z_M}, \delta_{ab}^u, \dots, \delta_{ab}^z)$. The Jacobian matrix *A* relates each measurement to the corresponding offset (or a difference between two offsets in the case of cross-calibration constraints), and *e* is the vector of error terms.

### 9.4. Covariance matrix of calibration data

Most of the measurement systematic uncertainties coherently affect different measurements (even across different bands). Neglecting the correlations would significantly underestimate the true error. We thus formed the full covariance matrix $R = \text{cov}(e)$ of the calibration measurements accounting for all the error terms in the model above.

We already described the computation of the covariance of broadband CALSPEC magnitudes in Sect. 9.2. The computation of the resulting contribution to $R$ accounts for the STIS measurement error and the uncertainty on white dwarf primary calibration differently. The STIS measurement errors are assumed to be uncorrelated from one star to another and divided by the number of observations for each star. The calibration error is assumed to be a systematic error that produces the same error for all the measurements of all the stars.

The error affecting the determination of the filter effective wavelength is assumed unrelated from one filter to another. Its contribution $R^F$ to $R$ is obtained as:

$$R^F = H^\dagger \text{diag}(\delta \lambda_{\text{eff}}^b)^2 H$$

where *H* is the matrix holding the terms $\frac{\partial m_b^s}{\partial \lambda_{\text{eff}}^b}$ corresponding to each measurement.

Due to the large number of systematic uncertainties to be accounted for, the construction of the covariance matrix of the measurement error terms is less straightforward. In brief, we have assumed that all statistical uncertainties arising from measurement noise (photon noise or flat-field noise) are uncorrelated from one measurement to another, whereas part of the systematic uncertainties affect measurements coherently and are therefore taken to be fully correlated. Full details of the assumptions made in the covariance matrix computation are given in Appendix E.4.

### 9.5. Least-square estimate of the calibration

We derived the combined estimate of the calibration offsets through weighted least-square minimization. The resulting offsets are given in Table 23, along with the diagonal component of their covariance matrix. The corresponding correlation matrix is given in Table 22. The offsets are applied to the catalog of tertiary standard stars to provide our best estimate of their AB magnitudes.

The global $\chi^2$ of the fit is 79.8 for 80 degrees of freedom. Note that we are mainly manipulating actual systematic uncertainties rather than Gaussian-distributed random variables. A better assessment of the agreement between the different sets of primary standard measurements is provided by Fig. 29. We defer the discussion of these results to the next section of the paper.

<footnote n="26">26 A complete interpretation of these relations is not trivial as it requires some spectral model of the stellar population composing the tertiary standard stars. The estimation of resulting uncertainties would be somewhat complex. We prefer to rely on a star with available and reliable spectrophotometry and model how it deviates from the average stellar population.</footnote>
<table><caption>**Table 22.** Correlation matrix of the final calibration.</caption><thead><tr><th></th><th>1.0</th><th>0.1</th><th>0.0</th><th>-0.0</th><th>-0.0</th><th>-0.0</th><th>0.0</th><th>0.0</th><th>0.0</th><th>-0.0</th><th>-0.1</th><th>u<sub>M</sub></th></tr></thead><tbody><tr><th>1.0</th><td>0.1</td><td>0.1</td><td>0.1</td><td>-0.0</td><td>0.1</td><td>0.2</td><td>0.1</td><td>0.0</td><td>-0.1</td><td>0.2</td><td>g<sub>M</sub></td><td>R<sub>m</sub></td></tr><tr><th>1.0</th><td>0.3</td><td>0.3</td><td>0.2</td><td>0.0</td><td>0.0</td><td>0.6</td><td>0.3</td><td>0.2</td><td>0.4</td><td>0.8</td><td>0.6</td><td>i<sub>M</sub></td></tr><tr><th>1.0</th><td>0.9</td><td>0.5</td><td>-0.1</td><td>-0.0</td><td>0.4</td><td>0.8</td><td>0.6</td><td>0.3</td><td>0.5</td><td>0.8</td><td>z<sub>M</sub></td><td>i2<sub>M</sub></td></tr><tr><th>1.0</th><td>0.5</td><td>-0.1</td><td>-0.1</td><td>-0.0</td><td>0.4</td><td>0.8</td><td>0.6</td><td>0.3</td><td>0.5</td><td>0.8</td><td>u</td><td>g</td></tr><tr><th>1.0</th><td>0.1</td><td>0.1</td><td>0.1</td><td>-0.1</td><td>-0.1</td><td>0.0</td><td>-0.1</td><td>0.0</td><td>-0.0</td><td>-0.1</td><td>0.4</td><td>r</td></tr><tr><th>1.0</th><td>0.1</td><td>0.1</td><td>0.1</td><td>-0.1</td><td>-0.1</td><td>0.0</td><td>-0.0</td><td>0.0</td><td>-0.1</td><td>-0.1</td><td>0.4</td><td>i</td></tr><tr><th>1.0</th><td>0.1</td><td>0.1</td><td>0.1</td><td>-0.1</td><td>-0.1</td><td>0.0</td><td>-0.1</td><td>0.0</td><td>-0.1</td><td>-0.1</td><td>0.4</td><td>z</td></tr></tbody></table>

<figure><img src="image_30.png" /><figcaption>**Fig. 29.** Agreement between complementary determinations of the SNLS AB offsets. SNLS BD+17 and SNLS SA lines refer to the SNLS calibration on Landolt standards and direct solar analog measurements respectively (cf. Sect. 4). The SDSS SA and SDSS BD+17 lines refer to the calibration obtained by translating the PT measurements of the solar analogs and BD +17 4708 respectively, to the SNLS system via the relations obtained in Sect. 8. The data points correspond to the calibration offset relative to the combined calibration including all the measurements and are not independent. The shaded region illustrates the uncertainty on the combined calibration.</figcaption></figure>

# 10. Results

## 10.1. Calibration products

We deliver natural broadband AB magnitudes for a large set of selected stars (the tertiary standards) in the SNLS and SDSS science fields. These tertiary standards will be used to calibrate the science images of the surveys and may be useful for other, similar purposes.

The calibration of the catalogs to the AB system results from the combination of all the calibration data gathered in this work. The details of the combination are described in Sect. 9. Briefly, we combined calibration constraints coming from observations of 5 different spectrophotometric standard stars from the CALSPEC database. Those observations were conducted following 3 mostly independent paths presented in Sect. 2.4 and described respectively in Sects. 5.1, 5.2 and 7. In addition, the SNLS and SDSS tertiary catalogs are tied together by a cross-calibration measurement described in Sect. 8.

We emphasize that the magnitudes are delivered in the natural photometric systems of the corresponding instrument, as defined in Sect. 2.2.1. As a consequence, their correct interpretation is given by Eq. (3) using the effective filters corresponding to the average position of the star observation in the field of view. We deliver a model of MegaCam passbands along with this paper and refer the reader to the work from Doi et al. (2010) for the SDSS effective passbands.

Another consequence of the variation of the natural photometric system with the position in the field of view is that, for calibration purposes, the reference catalogs are best matched with exposures sharing a compatible pointing (same pointing for MegaCam or same declination for SDSS). In other cases, small color terms accounting for the slight differences in the effective filters may have to be considered to obtain accurate zero points.

One may also note that the catalogs have been established using IQ-scaled aperture photometry in the case of SNLS and the usual PSF photometry algorithm in the case of SDSS. While the result does not depend on the photometry method to first order, small spatial or chromatic effects may need to be accounted for when comparing to measurements obtained using different photometry methods (see e.g. Sect. 4.3.3).

For most comparison purposes, it is also convenient to report MegaCam measurements in a single photometric system, close to the natural system. In this paper, we follow the convention adopted in R09 and define the MegaCam uniform magnitudes as the natural magnitudes that would have been observed

for objects *at the center* of the focal plane<sup>27</sup>. We have derived color transformations between the natural and uniform system (see Sect. 3.2) and include in the catalog MegaCam uniform magnitudes for all stars that can be accurately transformed.

Finally, we determine measured color terms between the uniform MegaCam photometric system and the average SDSS system in Sect. 8.3. These facilitate comparison of other data specifically obtained in these photometric systems.

Catalogs can be found in Tables E.1 and E.2<sup>28</sup>. AB offsets given in Table 23 are already applied to the released catalogs. The covariance matrix associated with this calibration is given in Tables 23 and 22. Finally the Megacam effective transmission models to be used in Eq. (2) are given in Tables E.3–E.8<sup>29</sup>. What follows is a general discussion of these results.

## 10.2. Agreement between the available calibration paths

A key feature of this work is the redundancy between several calibration paths established independently and subject to different systematics. An illustration of the agreement between the different paths is provided by Fig. 29.

The agreement between the SNLS and SDSS calibration appears better than one percent in the *gri* and *z* bands. There is an apparent offset of about 4% in *u* which is still compatible with the low precision of the cross-calibration data in this band. Internally, there is a small tension between the Landolt and solar analog calibrations of the SNLS in *i*<sub>M</sub>*i*2<sub>M</sub> and *r*<sub>M</sub> (~1.9 and 1.3%). To a lesser extent, a similar trend is visible in the SDSS which suggests that at least a part of the tension may be explained by an actual calibration difference between the BD +17 4708 and the solar analog CALSPEC reference spectra.

<footnote n="27"><sup>27</sup> Note that this choice is not representative of the “average” MegaCam natural system. Passbands at the center are redder than the spatial average.</footnote>

<footnote n="28"><sup>28</sup> Full catalogs can be retrieved from the CDS or the dedicated webpage http://supernovae.in2p3.fr/snls_sdss/</footnote>

<footnote n="29"><sup>29</sup> Higher resolution versions can be found on the webpage.</footnote>
<table><caption>**Table 23.** SDSS and SNLS combined AB offsets.</caption><thead><tr><th>Band</th><th>u<sub>M</sub></th><th>g<sub>M</sub></th><th>R<sub>m</sub></th><th>i<sub>M</sub></th><th>i2<sub>M</sub></th><th>z<sub>M</sub></th><th>u</th><th>g</th><th>r</th><th>i</th><th>z</th></tr></thead><tbody><tr><td>δ<sub>ab</sub></td><td>0.011</td><td>-0.000</td><td>0.001</td><td>-0.006</td><td>-0.007</td><td>0.014</td><td>0.068</td><td>-0.020</td><td>-0.005</td><td>-0.018</td><td>-0.010</td></tr><tr><td>σ</td><td>0.0145</td><td>0.0035</td><td>0.0051</td><td>0.0042</td><td>0.0043</td><td>0.0069</td><td>0.0089</td><td>0.0050</td><td>0.0031</td><td>0.0039</td><td>0.0060</td></tr><tr><td>With perfect passbands<sup>a</sup></td><td>0.0122</td><td>0.0033</td><td>0.0033</td><td>0.0041</td><td>0.0041</td><td>0.0069</td><td>0.0059</td><td>0.0040</td><td>0.0030</td><td>0.0039</td><td>0.0060</td></tr><tr><td>With perfect reference<sup>b</sup></td><td>0.0144</td><td>0.0031</td><td>0.0046</td><td>0.0029</td><td>0.0030</td><td>0.0044</td><td>0.0086</td><td>0.0047</td><td>0.0022</td><td>0.0024</td><td>0.0029</td></tr></tbody></table>

**Notes.** Figures are given in magnitudes. <sup>(a)</sup> Remaining uncertainty on the AB calibration when assuming that the passband measurements are perfect. <sup>(b)</sup> Remaining uncertainty on the AB calibration when assuming that the STIS spectra are perfect.

Overall, we reckon that the whole data sample is compatible with the modeled uncertainties. Consequently we opted for combining the whole data sample to set the flux scale of the tertiary catalogs and we believe that the uncertainties resulting from the combination are reliable.

## 10.3. Uncertainties on the combined calibration

A few points pertaining to the calibration uncertainties ought to be discussed.

First, one can observe from the correlation matrix in Table 22 that the cross-calibration data brings significant correlations in the calibration of all the SNLS and the SDSS overlapping bands but *u* and *g*, where the accuracy of the cross-calibration is limited by the less-similar filters and the higher dispersion of the stellar population about the color-tranformations. Consequently, flux measurements in the two surveys can now be compared with low cross-calibration uncertainty.

It is also interesting to compare the relative importance of the various contributions to the global calibration uncertainty. The last row of Table 23 shows that the uncertainty on the primary standard spectra amounts for about half the uncertainty (in variance) for the redder bands (riz). The imperfect knowledge of filters impacts mostly the *u* and *u*<sub>M</sub> band calibration due to the large variation of the standard star spectra in this wavelength region and the *r*<sub>M</sub> band due to the larger uncertainty remaining on the transmission of this filter.

Evidence for potential evolution of the *r*<sub>M</sub> and *i*<sub>M</sub> filters has been found and the resulting uncertainty on the filter passbands is discussed in Sect. 9.1. We emphasize that the impact of filter passband uncertainty depends on the color of the object whose flux is being determined. Specifically, this error cancels for objects whose spectrum is close to the spectrum of our standard stars (main sequence stars of color *g* − *i* ~ 0.55). This is why the poor knowledge of MegaCam *i*<sub>M</sub> and *r*<sub>M</sub> passbands only minimally affects AB calibration accuracy: the primary standards we observe have SEDs close to the AB spectrum in those bands (stars with *g* − *i* ~ 0.55 have *r* − *i* ~ 0.1). This is not the case for type Ia supernovae; therefore, the impact of filter passband uncertainty on their flux measurements is bound to be much larger.

## 10.4. Comparison with SNLS3

For the four photometric bands already calibrated in R09, we compared uniformity and absolute calibrations between the new and prior tertiary catalogs. A sign mistake affecting the R09 catalog was discovered in this comparison. It contributes to a slight deterioration of the catalog uniformity and shifts the average flux scale of the catalog by 8, 5, 6, 3 mmag on average for band *g*<sub>M</sub>, *r*<sub>M</sub>, *i*<sub>M</sub> and *z*<sub>M</sub> respectively. Once the error sign is corrected, the remaining offsets are given in Table 24. The comparison of calibrated magnitude differences as a function of the distance to the center of the focal plane is given in Fig. 30.

<table><caption>**Table 24.** Calibration offset between R09 and the present release of the SNLS calibration.</caption><thead><tr><th></th><th>g<sub>M</sub></th><th>r<sub>M</sub></th><th>i<sub>M</sub></th><th>z<sub>M</sub></th></tr></thead><tbody><tr><td>Offset<sup>a</sup></td><td>-0.000</td><td>0.006</td><td>0.008</td><td>-0.013</td></tr><tr><td>rms<sup>b</sup></td><td>0.004</td><td>0.006</td><td>0.004</td><td>0.012</td></tr></tbody></table>

**Notes.** <sup>(a)</sup> The offset should be added to the previous release to match the present result, and comes in addition to a sign error correction in the previous release (see text). <sup>(b)</sup> Rms of the differences between the two catalogs for stars brighter than *r*<sub>M</sub> < 18.

<figure><img src="image_31.png" /><figcaption>**Fig. 30.** Difference between SNLS-calibrated tertiary star magnitudes and previous R09 release as a function of the distance to the focal plane center. The 4 deep fields are compared separately (D1: red plus, D2: green squares, D3: black circles, D4: blue crosses.)</figcaption></figure>

## 10.5. Comparison with the previous calibration of the SDSS SN survey

Following the discovery of a non-uniformity in the SDSS PT flat-field, this work introduces two changes to the SDSS tertiary catalogs. The first is a correction of the tertiary catalog flat-fielding based on the Data Release 8 SDSS catalog (Padmanabhan et al. 2008) flat-fielding solution. The second is the new determination of the corresponding AB offsets. The previous calibration of the SDSS SN survey was based on the uncorrected version of the coadd catalog scaled to the AB system by the application of AB offsets from Holtzman et al. (2008, Table 1). As supernovae are uniformly distributed in declination, the calibration offset to be expected from this release is readily given by the weighted average of magnitude differences between the two calibrated catalogs. This offset is given in Table 25.

The difference in the average photometry is fairly small compared to the size of the PT flat-field correction. This is a fortunate consequence of the fact that the effect is close to symmetric with respect to the center of the PT focal plane, where standard stars were observed. The row labeled rms in Table 25 gives an
<table><caption>**Table 25.** Calibration offsets between first and third year release of the SDSS-II SN survey.</caption><thead><tr><th></th><th>u</th><th>g</th><th>r</th><th>i</th><th>z</th></tr></thead><tbody><tr><td>rms<sup>b</sup></td><td>0.018</td><td>0.007</td><td>0.006</td><td>0.006</td><td>0.011</td></tr><tr><td>ptp<sup>c</sup></td><td>0.085</td><td>0.031</td><td>0.029</td><td>0.035</td><td>0.050</td></tr><tr><td>offset<sup>a</sup></td><td>-0.031</td><td>-0.004</td><td>-0.000</td><td>-0.000</td><td>-0.006</td></tr></tbody></table>

**Notes.** (a) Calibration offset in mag (average difference between the present work and Holtzman et al. 2008). (b) Standard deviation of the photometry difference between the two catalogs (in mag). (c) Peak to peak difference between the two catalogs (in mag).

estimate of the gain in photometric precision that is to be expected from the improved flat-fielding.

## 10.6. Comparison with other work

While we have achieved excellent agreement with the SNLS and SDSS supernova surveys we did not attempt to compare our photometry with any other survey. The SDSS SN photometry has been compared with CSP (Mosher et al. 2012), where good agreement was found. The Pan-STARRS survey (Hodapp et al. 2004) has recently reported a small discrepancy with the SDSS stellar photometry (Tonry et al. 2012), but larger than might be expected on the basis of this work. Their analysis used the publicly available SDSS catalogs which lack the corrections applied in this paper and they did not use the filter transmission measurements of Doi, et al. However, the discrepancy in photometry might very well persist even with our revised catalog.

## 11. Conclusion

We have delivered updates to the tertiary standard star catalogs that define the photometric calibration of the SNLS and the SDSS supernovae surveys. The catalogs provide standard star calibrated AB magnitudes, in the *natural* photometric system of both instruments. The products are fully described in Sect. 10.1.

The flux calibration is based on the observation of 5 different HST primary spectrophotometric standard stars from the CALSPEC database. In addition, the SNLS and SDSS tertiary standard stars are now tied together by specifically designed cross-calibration observations. Three independent routes, each subject to different observational systematics, were used to transfer the HST primary standard star calibration to the tertiary standard stars. Good agreement was found between these 3 routes, which were then combined to provide the final products. In particular, the offsets derived in Sect. 9 from simultaneously fitting all available information have been applied to the delivered catalogs. These offsets have been determined with CALSPEC version 3 spectra, and may be updated as new CALSPEC versions are released. See Appendix E for more details.

With respect to previous releases, the photometric calibration evolved by less than 1% in all photometric bands but *u*. Major improvements arise from better flat-fielding processes (that also improve the uniformity of the resulting catalogs), and the introduction of more data to constrain the calibration transfer.

The calibration transfer from HST standard stars to stars in supernovae fields is thought to be accurate to about 3 mmag in the *riz* photometric bands. This is comparable, or better than the error related to the calibration uncertainty of the primary standard stars themselves. The error in band *g* is about 4 mmag and remains dominated by the error in the calibration transfer. The uncertainty on the *u* band calibration amounts to about 1% in

the SDSS and 2% in the SNLS, dominated by the uncertainty on the instrument effective passbands.

The photometric calibration was complicated by the need to overcome several instrumental effects as well as weaknesses in instrument or survey designs. The most important complications are summarized here:

- Uniform illumination of wide-field instruments is not enough to achieve accurate flat-fielding; internal reflections in the optical path must be accounted for. At least two elements, CCDs and filters, are reflective enough to feed significant amounts of light back into the wide-field corrector optics. Reflected by convex lens surfaces, this light causes ghosting as well as diffuse and structured contamination in the flat-fields. For this reason, photometric uniformity of both the SDSS and SNLS instruments ultimately relies on the analysis of dithered stellar observations. The variation of atmospheric conditions during the observation sequences ultimately limits the flat-field solution accuracy.

- Similarly, small-angle scattering of light caused by dust or defects in the optics can affect the photometry of point sources while leaving the flat-field twilight images unchanged. A remarkable illustration of such a phenomenon occurred during the SNLS survey: the progressive deposit of metal dust from the filter jukebox on one corner of the top corrector lens caused a local 6% deterioration of the effective throughput of the photometry, and was only detected and measured through dithered stellar observations. Such effects can also be detected by monitoring apparent star brightness in often-visited fields.

- For SNLS, spatial variations of the instrument effective passbands had to be accounted for in order to accurately conduct the calibration transfer and deliver relevant flat-fielding solutions. An extensive survey of the filters' transmission would make the calibration more accurate.

- The characterization of the SNLS photometric system would have been simplified by the implementation of a well-planned filter passband monitoring program. Nonetheless, no significant chromatic differences have been observed in repeat stellar photometry over the course of the survey, providing direct evidence of the photometric system's long-term stability.

- Slight readout electronics instabilities cause percent-level noise in the MegaCam flat-fielding. For the SNLS, this effect is mitigated by repeated measurements over the long duration of the survey; for shorter surveys, this effect would have been difficult to overcome. Reproducible illumination provided by artificial light sources might provide more reliable monitoring of the instrument throughput.

- The SDSS calibration relied on a separate telescope (the PT), but neither the flat-field nor the filter throughput was well-characterized enough for the precision photometry goals of this paper. Instead we had to rely on empirical color-transformations and correct the flat-field from external data.

Most of these effects were overcome by introducing redundancy in the measurements, or by the analysis of specifically designed additional observations. While such strategies allowed us to reach an accuracy of 0.3%, it would be prohibitively time-consuming to reduce this accuracy further. Future photometric surveys such as SkyMapper (Keller et al. 2007), DES (Bernstein et al. 2012) and LSST (LSST Science Collaborations et al. 2009) might take advantage of current developments regarding instrumental calibration with artificial calibration sources. Information provided by the SNDICE illumination prototype
(Barrelet & Juramy 2008), Guyonnet et al. (in prep.) installed at the CFHT has already proved immensely valuable in understanding MegaPrime instrumental effects such as flat-field pollution with ghosts and readout electronics gain variations. Ongoing analysis of SNDEX data may also give us a final understanding of the MegaCam filter passbands. A comparable device (Stubbs et al. 2010) has aided in the calibration of the Pan-STARRS instrument; the Dark Energy Survey is taking a similar approach with DECal (Rheault et al. 2012).

Acknowledgements. The authors heartily acknowledge the fruitful collaboration of the Canada France Hawaii telescope team, in gathering part of the data required for the present effort. We warmly thank the SNDEX collaboration for their help in the measurement of the SNLS passbands as well as for enlightening discussions on instrumental effects. We thank C. Buton and the SNF Collaboration for providing us early versions of their atmospheric transmission curve prior to publication. We are grateful to D. Tucker for giving us details about the SDSS calibration. This work was supported in part by the US Department of Energy under contract number DE-AC0276SF00515. Part of the data reduction was carried out at the Centre de Calcul de l'IN2P3 (CCIN2P3, Lyon, France).

## Appendix A: Monitoring of the MegaCam flat-field variability from deep fields

Variations of the instrumental response are determined by the time distribution of the photometric coefficient $\delta Z_{t,ccd}$ (where $t$ indexes the exposures, and ccd indexes the 36 MegaCam chips. We recall that $\delta Z_{t,ccd}$ is computed for each deep field by building an average photometric catalog of non-variable stars as described in Sect. 4. We then compute for each available exposure a zero point relative to the average catalog. Once the exposure $t$ is scaled by this zero point, we recompute a zero point offset for each CCD ($\delta Z_{t,ccd}$) relative to the average catalog. Non-zero offsets indicate that the throughput of the instrument has varied non uniformly. This can be due either to clouds or to a variation of the instrument response that is not corrected by the twilight flat-fielding.

For each exposure $t$ we compute the rms of $\delta Z_{t,ccd}$ of the 36 CCDs. The statistical uncertainty on the determination of $\delta Z_{t,ccd}$ is typically 2 mmag, so that sets the minimum expected value. The rms values observed throughout the survey are displayed in Fig. A.1. The measured rms is typically about 5 mmag. The observed excess relative to the minimum value of 2 mmag is to be expected for at least 3 reasons: 1) structured variations of the atmospheric transparency, such as clouds, affect the observations, 2) the gains of some CCDs amplifiers vary on time scales shorter than a single run, and therefore can't be calibrated by a single twilight flat-field, and 3) telescope modifications can have an impact on the photometric response, while leaving the twilight observations virtually unchanged. The effects of 1) and 3) can be observed directly in Fig. A.1, while 2) is a noise that contributes to a global increase of the measured rms.

Clouds are occasionally responsible for a large increase in the measured rms. These non-photometric conditions are easily detected and excluded from the averaging of the tertiary catalogs. Exposures detected as non photometric are displayed as black dots on Fig. A.1.

We have displayed telescope modifications that had a noticeable impact on the uniformity of the photometry as red vertical lines. The beginning of the survey was marked by continuous adjustment of the optical setup. We retained only the main modification (that had the greatest impact on the image quality): the flip of the third lens in the wide field corrector. It is denoted as

<table><caption>Table A.1. Grid observations and associated telescope events.</caption><thead><tr><th>Run<sup>a</sup></th><th>Date</th><th>Bands<sup>b</sup></th><th>Field</th><th>Events</th></tr></thead><tbody><tr><td rowspan="2">03Bm02</td><td>2003-10-02</td><td>i</td><td>2</td><td rowspan="4"></td></tr><tr><td>2003-10-03</td><td>r</td><td>2</td></tr><tr><td rowspan="2">03Bm03</td><td>2003-10-22</td><td>g, u, z</td><td>2</td></tr><tr><td>2003-10-23</td><td>i, r</td><td>2</td></tr><tr><td>04Am02</td><td>2004-03-18</td><td>u, g, r, i, z</td><td>1</td><td rowspan="2">(A) L3 lens flipped upside down.</td></tr><tr><td>04Bm05</td><td>2004-12-02</td><td>g, r, i</td><td>1</td></tr><tr><td></td><td>2004-12-02</td><td></td><td></td><td></td></tr><tr><td></td><td>2004-12-10</td><td>g, u, z</td><td>1</td><td rowspan="2">(B) Growing metal dust deposit.</td></tr><tr><td>05Bm02</td><td>2005-10-09</td><td>u, g, r, i, z</td><td>2</td></tr><tr><td>06Am04</td><td>2006-05-19</td><td></td><td></td><td></td></tr><tr><td rowspan="5">06Bm02</td><td>2006-09-13</td><td>i</td><td>2</td><td rowspan="5"></td></tr><tr><td>2006-09-14</td><td>r</td><td>2</td></tr><tr><td>2006-09-15</td><td>z</td><td>2</td></tr><tr><td>2006-09-16</td><td>u</td><td>2</td></tr><tr><td>2006-09-19</td><td>g</td><td>2</td></tr><tr><td>06Bm05</td><td>2006-12-27</td><td></td><td></td><td>(C) Top lens cleaning.</td></tr><tr><td rowspan="4">07Am02</td><td>2007-03-21</td><td>r</td><td>1</td><td rowspan="4"></td></tr><tr><td>2007-03-22</td><td>g, u</td><td>1</td></tr><tr><td>2007-03-23</td><td>i</td><td>1</td></tr><tr><td>2007-03-24</td><td>z</td><td>1</td></tr><tr><td>07Am06</td><td>2007-07-20</td><td></td><td></td><td>(D) i<sub>M</sub> filter broken.</td></tr><tr><td>07Bm01</td><td>2007-08-24</td><td></td><td></td><td>(E) Recoating.</td></tr><tr><td>07Bm03</td><td>2007-10-18</td><td></td><td></td><td>(F) New i2<sub>M</sub> filter installed.</td></tr><tr><td rowspan="3">07Bm04</td><td>2007-11-08</td><td>i2</td><td>1</td><td rowspan="3"></td></tr><tr><td>2007-11-11</td><td>r</td><td>1</td></tr><tr><td>2007-11-12</td><td>g</td><td>1</td></tr><tr><td>07Bm05</td><td>2007-12-03</td><td>u, z</td><td>1</td><td rowspan="4"></td></tr><tr><td>08Bm02</td><td>2008-09-03</td><td>u, g, r, i2, z</td><td>2</td></tr><tr><td>09Am06</td><td>2009-07-20</td><td>g, z</td><td>2</td></tr><tr><td>2009-07-21</td><td>r, u, i2</td><td>2</td></tr><tr><td rowspan="4">10Am01</td><td>2010-02-06</td><td>u</td><td>1</td><td rowspan="4"></td></tr><tr><td>2010-02-18</td><td>r, z</td><td>1</td></tr><tr><td>2010-02-19</td><td>i2</td><td>1</td></tr><tr><td>2010-02-20</td><td>g</td><td>1</td></tr><tr><td rowspan="3">10Bm02</td><td>2010-10-05</td><td>r</td><td>1</td><td rowspan="3"></td></tr><tr><td>2010-10-09</td><td>g, i2</td><td>2</td></tr><tr><td>2010-10-13</td><td>r</td><td>2</td></tr><tr><td>10Bm03</td><td>2010-11-08</td><td>g, u</td><td>2</td><td rowspan="3"></td></tr><tr><td rowspan="2">11Am06</td><td>2011-07-30</td><td>z</td><td>2</td></tr><tr><td>2011-08-02</td><td>g, r, u, y</td><td>2</td></tr><tr><td rowspan="2">11Bm01</td><td>2011-08-28</td><td>g, r, z</td><td>2</td><td rowspan="2"></td></tr><tr><td>2011-08-29</td><td>g, u, y</td><td>2</td></tr></tbody></table>

Notes. (a) Run id in the elixir pipeline nomenclature. (b) Observations selected as valid are bold-faced in this column.

event A on the graph. The rms of exposures obtained prior to this event can be seen to be higher. The second and most significant phenomenon was the accumulation of metal dust on a corner of the wide field corrector optics. Its effect was the scattering at small angles of a growing part of the light, decreasing progressively the flux fraction contained in the core of the
<figure><img src="image_32.png" /><figcaption>**Fig. A.1.** Standard deviation of the relative CCD zero points for each exposure in the survey. Black dots denote exposures that were excluded from the average because of cuts on the stability of the observing conditions or on the uniformity of the effective instrument response. Exposures are ordered by increasing observation date. The vertical gray dotted lines indicate the separation between different MegaCam runs (roughly one run per lunation). The twilight flat-field is common to all observations in a run. The vertical red lines indicate significant changes to the telescope. The letters refer to the events described in Table A.1. In this figure, the same photometric flat-field correction, determined from observations on 2005-10-09 (black vertical line), is applied to all the observations.</figcaption></figure>

PSF (and hence the throughput of the photometry), while leaving the twilight images essentially unchanged. The effect is clearly visible in Fig. A.1 as a progressive increase of the rms during the year 2006. Its detection and cleaning occurred at the end of 2006 and is denoted as event C. The beginning of the accumulation is harder to determine. We approximately determined that the effect becomes sufficiently important at the middle of 2006 (event B). The last events are the destruction (D) and replacement (E) of the *i*<sub>M</sub> filter in 2007. Exposures in *g*<sub>M</sub> and *r*<sub>M</sub> were apparently also affected by the same event (D), but we do not understand why they changed.

The events are summarized in Table A.1. They define 5 periods for which independent photometric corrections can be determined. The application of our set of photometric corrections to the survey flat-fielding is illustrated in Fig. A.2. This figure is similar to Fig. A.1, but made after the application of photometric corrections. After correction, the measurements are consistent within an error σ<sub>ff</sub>, which is estimated as the average rms of δZ<sub>ccd</sub>. Values of σ<sub>ff</sub> were given in Table 2 in the main text.

**Appendix B: MegaCam filters measurements**

The transmission curves of the original Sagem/REOSC MegaCam filters were measured twice: the first time by the manufacturer before their installation in MegaCam in 2002, and the second time in 2006 by the CFHT operational team. The 2006 measurements are available only at positions close to the border of the filter due to limitations in the bench clearance, and their spectral resolution is coarser. Comparison between the two measurements at 15 cm from the center (after convolution of the REOSC measurements to match resolutions) is given in Fig. B.1. The position of the *r*<sub>M</sub> and *i*<sub>M</sub> filter cut-offs can be seen to be shifted ~8 nm redder in the 2006 measurements. The origin of these discrepancies and the reason why only two filters are affected are unclear.

A confirmation of the 2006 measurements was recently given by the measurement of the transmission of one of the broken pieces of the *i*<sub>M</sub> filter. The measurement was conducted on the calibration bench of the SNDICE illumination device
<figure><img src="image_33.png" /><figcaption>Fig. A.2. Same as Fig. A.1, but different photometric flat-field corrections were used for the different periods of the survey. The vertical black lines indicate the date of grid observations used to compute the photometric corrections. The changes of data point color indicate the different flat-field corrections applied. These corrections were used to produce the multi-epoch tertiary catalogs described in Sect. 4.</figcaption></figure>

<table><caption>Table A.2. Dithering pattern of the grid exposures.</caption><thead><tr><th>Exposure</th><th>α (deg)<sup>a</sup></th><th>δ (deg)<sup>a</sup></th></tr></thead><tbody><tr><td>1</td><td>0.000</td><td>0.000</td></tr><tr><td>2</td><td>0.028</td><td>0.000</td></tr><tr><td>3</td><td>0.056</td><td>0.000</td></tr><tr><td>4</td><td>0.112</td><td>0.000</td></tr><tr><td>5</td><td>0.225</td><td>0.000</td></tr><tr><td>6</td><td>0.451</td><td>0.000</td></tr><tr><td>7</td><td>0.902</td><td>0.000</td></tr><tr><td>8</td><td>0.000</td><td>0.027</td></tr><tr><td>9</td><td>0.000</td><td>0.055</td></tr><tr><td>10</td><td>0.000</td><td>0.111</td></tr><tr><td>11</td><td>0.000</td><td>0.222</td></tr><tr><td>12</td><td>0.000</td><td>0.444</td></tr><tr><td>13</td><td>0.000</td><td>0.888</td></tr><tr><td>14<sup>b</sup></td><td>0.000</td><td>0.000</td></tr></tbody></table>

Notes. (a) Pointing deviation relative to the reference pointing of the field. (b) A concluding 14th exposure, that comes back to the first pointing has been added to grid sequences since September 2008. This redundancy provides a way to monitor the stability of the observation conditions during the sequence.

(Barrelet & Juramy 2008), and display a perfect agreement with the 2006 transmission curves 12 cm away from the center (the appropriate curve for the broken piece).

The possibility of a continuous (slow) aging of the filters is excluded by the examination of color-terms between the beginning and the end of the survey (cf. Sect. 3.4.1). It is thus likely that the 2006 measurements are the most representative of the state of MegaCam filters during the survey. The lack for measurements at the center of the filters in the 2006 data requires additional data or assumptions. We opt for correcting the $i_M$ and $r_M$ REOSC measurements to make them match the 2006 transmission curves. The application of a linear stretch in wavelength of the form:

$$T^*(\lambda) = T \left( \lambda_1 + \frac{\lambda_3 - \lambda_1}{\lambda_2 - \lambda_1} (\lambda - \lambda_1) \right)$$

was found to reconcile both measurement sets. We used $(\lambda_1, \lambda_2, \lambda_3) = (5300 \AA, 6837 \AA, 6891 \AA)$ for $r_M$ and $(6600 \AA, 8464 \AA, 8539 \AA)$ for $i_M$. The resulting transmission model at 15 cm is shown as a dashed black line in Fig. B.1; similar agreement is obtained with the 12 cm data.
<figure><img src="image_34.png" /><figcaption>**Fig. B.1.** Comparison of available measurements of the REOSC filter transmission curves at a distance of 15cm from the center.</figcaption></figure>

## Appendix C: SDSS Photometric Telescope (PT) flat-field

There are some overlapping secondary patches in stripe 82 that can be used to check for deviations from a uniform response of the PT. This section provides an analysis of that data.

The data sample consists of the 13 secondary patches listed in Table C.1. The fields labeled A, B, C, and D are the standard locations in declination for secondary patches in stripe 82. The field of view is 40 arcmin (2/3 degree), so there is no overlap between the A, B, C, and D secondary patches. The fields labeled E, F, and G are special patches that were placed approximately half-way in declination between the standard locations, providing a 50% overlap with the standard patches. The camera pointings are all in the same relative orientation with East-West being in the CCD column direction.

The analysis involved matching stars in the overlapping pointings and computing the difference in magnitude. The data come from the SDSS data processing (mtPipe) (Tucker et al. 2006). The differences in magnitude measure the difference in response of the focal plane between a given column and another one that is displaced by 1/2 the size of the CCD. If the response is uniform all the differences would be zero. It is convenient to measure the distance along the focal plane in terms of degrees of declination. We determine this distance as the declination of a matched star minus the reported declination of the telescope pointing. The matching star is nominally at a declination lower by 20 arcmin.

The results are summarized in Table C.2. The table gives the total number of comparison stars that were found and a fit to the equation

$$ \Delta m = a\delta + b \quad (C.1) $$

where $\Delta m$ is the magnitude difference, $\delta$ is the position on the focal plane in units of degrees of declination, and $a$ and $b$ are fit parameters. A $\chi^2$ is given for each fit. The fit is made to 6 binned

<table><caption>**Table C.1.** The PT data with secondary patch overlaps in SDSS stripe 82.</caption><thead><tr><th>Field</th><th>Date (MJD)</th><th>RA (deg)</th><th>Dec (deg)</th><th>Frame</th></tr></thead><tbody><tr><td>82A12</td><td>52551</td><td>315.0</td><td>-1.00</td><td>161156</td></tr><tr><td>82A16</td><td>52551</td><td>25.0</td><td>-1.00</td><td>161196</td></tr><tr><td>82B12</td><td>52577</td><td>315.0</td><td>-0.33</td><td>165233</td></tr><tr><td>82B16</td><td>52551</td><td>25.0</td><td>-0.33</td><td>161246</td></tr><tr><td>82C16</td><td>52577</td><td>25.0</td><td>0.33</td><td>165263</td></tr><tr><td>82D12</td><td>52577</td><td>315.0</td><td>1.00</td><td>162033</td></tr><tr><td>82D16</td><td>52584</td><td>25.0</td><td>1.00</td><td>166668</td></tr><tr><td>82E12</td><td>52557</td><td>315.0</td><td>-0.66</td><td>162058</td></tr><tr><td>2E16</td><td>52553</td><td>25.0</td><td>-0.66</td><td>161813</td></tr><tr><td>82F12</td><td>52557</td><td>315.0</td><td>0.00</td><td>162068</td></tr><tr><td>82F16</td><td>52553</td><td>25.0</td><td>0.00</td><td>161823</td></tr><tr><td>82G12</td><td>52578</td><td>315.0</td><td>0.66</td><td>165524</td></tr><tr><td>82G16</td><td>52557</td><td>25.0</td><td>0.66</td><td>162098</td></tr></tbody></table>

<table><caption>**Table C.2.** The results of PT fits.</caption><thead><tr><th>Band</th><th>Stars</th><th>χ<sup>2</sup></th><th>a</th><th>σ<sub>a</sub></th><th>b</th><th>σ<sub>b</sub></th></tr></thead><tbody><tr><td>u</td><td>699</td><td>5.6</td><td>-0.129</td><td>0.022</td><td>0.041</td><td>0.004</td></tr><tr><td>g</td><td>2514</td><td>2.2</td><td>-0.039</td><td>0.009</td><td>0.027</td><td>0.002</td></tr><tr><td>r</td><td>2971</td><td>6.5</td><td>-0.037</td><td>0.008</td><td>0.022</td><td>0.001</td></tr><tr><td>i</td><td>2581</td><td>8.0</td><td>-0.019</td><td>0.009</td><td>0.023</td><td>0.002</td></tr><tr><td>z</td><td>1127</td><td>3.0</td><td>-0.053</td><td>0.016</td><td>0.038</td><td>0.003</td></tr><tr><td>gri</td><td>8066</td><td>39.5</td><td>-0.032</td><td>0.005</td><td>0.024</td><td>0.001</td></tr></tbody></table>

data points so there are 4 degrees of freedom for each fit, except for the combined fit to $g$, $r$, and $i$ (last line in Table C.2). This fit is performed on 18 binned data points from $g$, $r$, and $i$ so there are 16 degrees of freedom for that fit. The chi-squared's are generally good although they could probably be improved by the addition of a quadratic term. However, it was felt that a quadratic term was unnecessary and possibly sensitive to unknown systematic errors. Every filter shows a consistent trend of positive residuals and a negative slope with declination. However, the fits are quite precise and there are statistically significant differences between the filters.

The results above only give the difference in response between the two halves of the PT. Determining the actual response requires additional data or assumptions. There seem to be two obvious models that could explain some features of the data:

- The CCD readout uses different amplifiers for the two halves of the chip we are considering. It is possible that the gain difference between the two amplifiers has not been properly calibrated. Such a mis-calibration could occur, for example, if the light levels in the flat-field exposures resulted in a non-linear amplifier response that was different for the two amplifiers while normal exposure levels remained in the linear regime. This scenario could explain the offset between the two halves of the CCD but doesn't seem very plausible and would not explain the observed slopes.

- The illumination of the flat-field exposures may be non-uniform. This would lead to an error in the calibration of the CCD response. The non-uniformity is most likely to be a slowly varying function of position.

In any case the data are not compatible with a uniform photometric response in the PT flat-fielded exposures. The PT flat-field error has two consequences. First it is transferred to the 2.5 m as a
flat-fielding error. It should imprint a periodic pattern 0.6 degrees wide in declination on the photometry. Second, as primary standard stars are observed preferentially at the center of the focal plane, it can bias the calibration relative to the tertiary stars that are observed throughout the focal plane. It is thus necessary to provide a correction of the 2.5 m flat-field independent of the PT *and* to characterize the PT flat-field error to derive accurate calibration from its measurement.

## Appendix D: DR8 catalog retrieval

The Stripe 82 DR8 catalog has been retrieved from the DR8 database using the following query: `select psfmag_u, psfmag_g, psfmag_r, psfmag_i, psfmag_z, ra, dec, run, camcol, psfmagerr_u, psfmagerr_g, psfmagerr_r, psfmagerr_i, psfmagerr_z` into `mydb.MyTable` from phototag where `dec` between -1.3 and 1.3 and (`ra` between 300 and 360) or (`ra` between 0 and 60)) and `type = 6` and `mode = 1` and `psfmag r < 22.5`.

## Appendix E: SNLS and SDSS calibration products

Our main delivery are catalogs of natural magnitudes for a large set of tertiary standard stars calibrated to the AB flux scale. We also provide the material required for the interpretation of those magnitudes in term of physical fluxes (instrument transmission functions) as well as the material required to update the AB calibration as new CALSPEC spectra for our primary standards are released.

All the material described below is available from the SNLS and SDSS joint calibration webpage: http://supernovae.in2p3.fr/snls_sdss/

### E.1. Tertiary stars catalogs

We provide catalogs of natural AB magnitudes in each of the MegaCam filters for selected tertiary standard stars in the four CFHTLS deep fields in the natural MegaCam photometric system. This system is described in Sect. 3.1 and the corresponding transmission curves are given below (Sect. E.2). Note that the transmission depends on the location on the focal plane. A sample of the D1 catalog is given in Table E.2.

Similarly, we deliver natural SDSS AB magnitudes for selected tertiaries in the Stripe 82. The magnitudes are given for the average filter response as given by Doi et al. (2010), i.e., they should not be adjusted for the small differences in the filter responses of the different CCD columns. An excerpt from the catalog is given in Table E.1.

In both cases the released magnitudes are already placed on the AB system by the addition of the zero points given in Table 14. Full catalogs in electronic format can be retrieved from the CDS or from the SNLS and SDSS joint calibration webpage.

### E.2. MegaCam transmission functions

Low resolution version of the Megacam effective transmission curves are tabulated in Tables E.3–E.8. Higher resolution versions are available on the joint calibration webpage.

As described in Sect. 3.1, the transmission functions depend on the location in the MegaCam focal plane. Assuming that the transmission vary continuously with the radius from the focal plane center provides an effective description. We deliver tabulated measurements at regularly spaced radii. Those measurements can be linearly interpolated to other positions.

### E.3. HST standard measured magnitudes

The tertiary catalogs define a magnitude system. This system has been anchored to the AB flux scale according to a calibration reference. We choose to use, as our reference, 5 stars from the HST CALSPEC database for which direct or indirect magnitudes in the system defined by the tertiary catalogs were available. Therefore, our calibration reference is the current release (stinic_003) of the CALSPEC spectra for those 5 stars.

The natural magnitudes of the measured HST standards are given in Table E.9. Those measurements can be used to update the AB calibration of the catalogs, given revised synthetic magnitudes for these stars. Measurements in Table E.9 are delivered in the same photometric system than the published tertiary standards catalog, i.e. with the AB offsets derived in this work (Table 23) already applied. Therefore, any offset computed, according to Eq. (31), from the difference between a measurement given in Table E.9 and the synthetic AB magnitude for the corresponding star readily applies to the published catalog.

When computing synthetic AB magnitudes for a star in the MegaCam focal plane, the peculiar position of the star in the focal plane must be taken into account. Also, we describe in Sect. E.4 the constitution of the covariance matrix for measurements in Table E.9. This matrix can be used to combine all measurements similarly to what has been done in Sect. 9.

### E.4. Covariance matrices

The assumptions made to build the covariance matrix of systematic measurement errors in the calibration data follows.

In SNLS, we assume that the shutter bias affects identically all measurements of flux ratios between short and long exposures. The error resulting from aperture corrections is assumed to affect coherently the measurements of the solar analogs in a given band, and without correlation from one band to another. We account for the aperture correction residuals in the Landolt-based BD +17 4708 measurements independently as the observation strategy was different and the derivations of the corrections were independent. The survey non-uniformity affects coherently the measurement of solar analogs that are related to the survey through the SNLS D3 field. The Landolt non-uniformity is included to account for a potential departure of the BD +17 4708 measurements from the average Landolt system. The errors on the color transformation of BD +17 4708 are assumed to be independent from one band to another. This may not be fully justified, but this error matters only in band z and potential correlations with other bands are negligible.

In SDSS, the statistical uncertainty on the color transformation between the PT and 2.5 m system affects coherently all the measurements in a given band. Star-to-star dispersion around the color transformation is assumed independent from one star to another. The non uniformity of the Smith catalog coherently affects the measurement of solar analogs as they lie at approximately the same hour angle.

The resulting covariance matrix of measurements in Table E.9 (including measurement noise and systematics) is available from the SNLS/SDSS calibration webpage.

As described in Sect. 9, when combining the available measurements to provide the final calibration, we account for other contributions to the covariance of the AB offsets: the HST-STIS spectrum measurement error, the STIS calibration error, and the uncertainty on instrument filters. A corresponding covariance matrix for each of these contributions is also available from the SNLS/SDSS calibration webpage.
The estimation of the STIS measurement error is discussed in Sect. 9.2. The corresponding covariance matrix for a single epoch STIS measurement is displayed in Table E.10.

## References

Abell, P. A., Allison, & J. 2009, LSST Science Collaborations [arXiv:0912.0201]

Astier, P., Guy, J., Regnault, N., et al. 2006, A&A, 447, 31

Barrelet, E., & Juramy, C. 2008, Nucl. Instruments Meth. Phys. Res. A, 585, 93

Bernstein, J. P., Kessler, R., Kuhlmann, S., et al. 2012, ApJ, 753, 152

Bohlin, R. C., & Cohen, M. 2008, AJ, 136, 1171

Bohlin, R. C., & Gilliland, R. L. 2004, AJ, 127, 3508

Bohlin, R. C., & Hartig, G. 2002, HRC and WFC Flat Fields: Dispersors, Anomalies, and Photometric Stability, Tech. rep., ACS

Bohlin, R. C., Dickinson, M. E., & Calzetti, D. 2001, AJ, 122, 2118

Boulade, O., Charlot, X., Abbon, P., et al. 2003, in Instrument Design and Performance for Optical/Infrared Ground-based Telescopes, eds. M. Iye, & A. F. M. Moorwood, Proc. SPIE, 4841, 72

Buton, C., Copin, Y., Aldering, G., et al. 2013, A&A, 549, A8

Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245

Chen, Y., Davis, T. A., Hager, W. W., & Rajamanickam, S. 2008, ACM Trans. Math. Softw., 35, 22:1

Conley, A., Guy, J., Sullivan, M., et al. 2011, ApJS, 192, 1

Doi, M., Tanaka, M., Fukugita, M., et al. 2010, AJ, 139, 1628

Fukugita, M., Ichikawa, T., Gunn, J. E., et al. 1996, AJ, 111, 1748

Gunn, J. E., & Stryker, L. L. 1983, ApJS, 52, 121

Gunn, J. E., Carr, M., Rockosi, C., et al. 1998, AJ, 116, 3040

Gunn, J. E., Siegmund, W. A., Mannery, E. J., et al. 2006, AJ, 131, 2332

Guy, J., Sullivan, M., Conley, A., et al. 2010, A&A, 523, A7

Hodapp, K. W., Kaiser, N., Aussel, H., et al. 2004, Astron. Nachr., 325, 636

Holtzman, J. A., Marriner, J., Kessler, R., et al. 2008, AJ, 136, 2306

Ivezić, Ž., Lupton, R. H., Schlegel, D., et al. 2004, Astron. Nachr., 325, 583

Ivezić, Ž., Smith, J. A., Miknaitis, G., et al. 2007, AJ, 134, 973

Keller, S. C., Schmidt, B. P., Bessell, M. S., et al. 2007, PASA, 24, 1

Kessler, R., Becker, A. C., Cinabro, D., et al. 2009, ApJSS, 185, 32

Landolt, A. U. 1992, AJ, 104, 340

Landolt, A. U., & Uomoto, A. K. 2007, AJ, 133, 768

Lidman, C., Ruhlmann-Kleider, V., Sullivan, M., et al. 2013, PASA, 30, e001

Limboz, F., Karataş, Y., Kilic, M., Benoist, C., & Aliş, S. 2008, MNRAS, 383, 957

Magnier, E. A., & Cuillandre, J.-C. 2004, PASP, 116, 449

Manfroid, J. 1995, A&AS, 113, 587

Manfroid, J. 1996, A&AS, 118, 391

Moffat, A. F. J. 1969, A&A, 3, 455

Mosher, J., Sako, M., Corlies, L., et al. 2012, AJ, 144, 17

Padmanabhan, N., Schlegel, D. J., Finkbeiner, D. P., et al. 2008, ApJ, 674, 1217

Pickles, A. J. 1998, PASP, 110, 863

Regnault, N., Conley, A., Guy, J., et al. 2009, A&A, 506, 999

Rheault, J.-P., DePoy, D. L., Marshall, J. L., et al. 2012, in Am. Astron. Soc. Meet. Abstracts, 219, #248.02

Schlafly, E. F., Finkbeiner, D. P., Juric, M., et al. 2012, ApJ, 756, 158

Smith, J. A., Tucker, D. L., Kent, S., et al. 2002, AJ, 123, 2121

Stoughton, C., Lupton, R. H., Bernardi, M., et al. 2002, AJ, 123, 485

Stubbs, C. W., Doherty, P., Cramer, C., et al. 2010, ApJS, 191, 376

Sullivan, M., Guy, J., Conley, A., et al. 2011, ApJ, 737, 102

Tonry, J. L., Stubbs, C. W., Lykke, K. R., et al. 2012, ApJ, 750, 99

Tucker, D. L., Kent, S., Richmond, M. W., et al. 2006, Astron. Nachr., 327, 821
<table><caption>Table E.1. Catalog of natural AB SDSS magnitudes for selected tertiary standards in the Stripe 82.</caption><thead><tr><th>RA<br>(deg)</th><th>Dec<br>(deg)</th><th>u<br>(mag)</th><th>g<br>(mag)</th><th>r<br>(mag)</th><th>i<br>(mag)</th><th>z<br>(mag)</th></tr></thead><tbody><tr><td>-51.50000</td><td>-0.60412</td><td>-0.089 ± 0.000</td><td>20.386 ± 0.009</td><td>18.795 ± 0.005</td><td>17.927 ± 0.004</td><td>17.413 ± 0.007</td></tr><tr><td>-51.50000</td><td>1.21455</td><td>-0.066 ± 0.000</td><td>19.443 ± 0.005</td><td>17.980 ± 0.003</td><td>17.178 ± 0.003</td><td>16.735 ± 0.005</td></tr><tr><td>-51.49960</td><td>-0.59146</td><td>-0.092 ± 0.000</td><td>21.264 ± 0.016</td><td>20.219 ± 0.010</td><td>19.823 ± 0.009</td><td>-0.001 ± 0.000</td></tr><tr><td>-51.49960</td><td>0.25187</td><td>-0.075 ± 0.000</td><td>19.973 ± 0.007</td><td>19.395 ± 0.006</td><td>19.163 ± 0.006</td><td>0.001 ± 0.000</td></tr><tr><td>-51.49951</td><td>0.63092</td><td>-0.109 ± 0.000</td><td>20.665 ± 0.008</td><td>19.948 ± 0.006</td><td>19.690 ± 0.007</td><td>0.007 ± 0.000</td></tr><tr><td>-51.49951</td><td>0.70459</td><td>-0.057 ± 0.000</td><td>19.446 ± 0.005</td><td>18.796 ± 0.004</td><td>18.555 ± 0.005</td><td>18.406 ± 0.012</td></tr><tr><td>-51.49951</td><td>0.69510</td><td>19.719 ± 0.014</td><td>18.417 ± 0.004</td><td>17.859 ± 0.003</td><td>17.659 ± 0.003</td><td>17.568 ± 0.007</td></tr><tr><td>-51.49930</td><td>0.70751</td><td>-0.057 ± 0.000</td><td>21.059 ± 0.013</td><td>20.043 ± 0.008</td><td>19.668 ± 0.009</td><td>-0.006 ± 0.000</td></tr><tr><td>-51.49930</td><td>-0.43479</td><td>-0.114 ± 0.000</td><td>21.322 ± 0.016</td><td>19.707 ± 0.007</td><td>18.857 ± 0.005</td><td>18.353 ± 0.011</td></tr><tr><td>-51.49930</td><td>-0.11023</td><td>-0.055 ± 0.000</td><td>20.765 ± 0.011</td><td>19.228 ± 0.005</td><td>18.408 ± 0.004</td><td>17.935 ± 0.009</td></tr><tr><td>-51.49921</td><td>0.33849</td><td>-0.051 ± 0.000</td><td>20.151 ± 0.007</td><td>19.591 ± 0.006</td><td>19.409 ± 0.007</td><td>0.009 ± 0.000</td></tr><tr><td>-51.49890</td><td>0.77932</td><td>-0.077 ± 0.000</td><td>19.379 ± 0.005</td><td>18.159 ± 0.004</td><td>17.640 ± 0.003</td><td>17.352 ± 0.006</td></tr><tr><td>-51.49890</td><td>0.75056</td><td>-0.057 ± 0.000</td><td>20.494 ± 0.009</td><td>20.118 ± 0.009</td><td>19.971 ± 0.011</td><td>-0.012 ± 0.000</td></tr><tr><td>-51.49890</td><td>0.30273</td><td>-0.051 ± 0.000</td><td>20.948 ± 0.011</td><td>19.425 ± 0.006</td><td>18.553 ± 0.005</td><td>18.068 ± 0.010</td></tr><tr><td>-51.49869</td><td>-0.98086</td><td>-0.066 ± 0.000</td><td>19.407 ± 0.006</td><td>18.430 ± 0.004</td><td>18.080 ± 0.004</td><td>17.844 ± 0.008</td></tr><tr><td>-51.49860</td><td>-0.17120</td><td>-0.057 ± 0.000</td><td>21.328 ± 0.016</td><td>19.899 ± 0.007</td><td>19.319 ± 0.007</td><td>18.981 ± 0.019</td></tr><tr><td>-51.49860</td><td>-0.98718</td><td>-0.062 ± 0.000</td><td>20.157 ± 0.008</td><td>18.835 ± 0.004</td><td>18.319 ± 0.004</td><td>17.968 ± 0.009</td></tr><tr><td>-51.49851</td><td>1.19985</td><td>18.017 ± 0.008</td><td>16.588 ± 0.002</td><td>16.010 ± 0.002</td><td>15.813 ± 0.003</td><td>15.723 ± 0.005</td></tr><tr><td>-51.49838</td><td>1.08040</td><td>-0.091 ± 0.000</td><td>20.493 ± 0.009</td><td>19.620 ± 0.007</td><td>19.258 ± 0.008</td><td>0.005 ± 0.000</td></tr><tr><td>-51.49838</td><td>-0.10840</td><td>20.161 ± 0.021</td><td>18.967 ± 0.005</td><td>18.407 ± 0.004</td><td>18.230 ± 0.004</td><td>18.118 ± 0.009</td></tr><tr><td>-51.49829</td><td>0.22556</td><td>-0.068 ± 0.000</td><td>20.316 ± 0.008</td><td>19.720 ± 0.007</td><td>19.528 ± 0.008</td><td>-0.009 ± 0.000</td></tr><tr><td>-51.49829</td><td>1.04860</td><td>-0.076 ± 0.000</td><td>20.535 ± 0.007</td><td>19.268 ± 0.004</td><td>18.757 ± 0.004</td><td>18.449 ± 0.010</td></tr><tr><td>-51.49820</td><td>0.33468</td><td>-0.074 ± 0.000</td><td>18.492 ± 0.005</td><td>17.645 ± 0.007</td><td>17.362 ± 0.011</td><td>17.197 ± 0.011</td></tr><tr><td>-51.49820</td><td>0.70993</td><td>-0.058 ± 0.000</td><td>20.563 ± 0.009</td><td>19.099 ± 0.005</td><td>18.413 ± 0.004</td><td>18.029 ± 0.008</td></tr><tr><td>-51.49789</td><td>-0.57415</td><td>19.323 ± 0.014</td><td>18.103 ± 0.004</td><td>17.498 ± 0.004</td><td>17.261 ± 0.003</td><td>17.131 ± 0.007</td></tr><tr><td>-51.49768</td><td>1.19547</td><td>-0.060 ± 0.000</td><td>20.814 ± 0.011</td><td>20.401 ± 0.013</td><td>20.242 ± 0.017</td><td>0.000 ± 0.000</td></tr><tr><td>-51.49750</td><td>0.21928</td><td>-0.076 ± 0.000</td><td>21.277 ± 0.015</td><td>20.227 ± 0.009</td><td>19.838 ± 0.009</td><td>-0.003 ± 0.000</td></tr><tr><td>-51.49750</td><td>0.73620</td><td>-0.075 ± 0.000</td><td>20.000 ± 0.009</td><td>18.555 ± 0.005</td><td>17.961 ± 0.005</td><td>17.622 ± 0.009</td></tr><tr><td>-51.49735</td><td>1.10949</td><td>-0.044 ± 0.000</td><td>21.276 ± 0.015</td><td>19.847 ± 0.007</td><td>18.292 ± 0.004</td><td>17.452 ± 0.007</td></tr><tr><td>-51.49735</td><td>-0.89879</td><td>-0.062 ± 0.000</td><td>21.218 ± 0.019</td><td>19.712 ± 0.007</td><td>18.974 ± 0.006</td><td>18.518 ± 0.012</td></tr><tr><td>-51.49735</td><td>1.23392</td><td>19.262 ± 0.012</td><td>18.128 ± 0.003</td><td>17.643 ± 0.003</td><td>17.475 ± 0.003</td><td>17.407 ± 0.007</td></tr><tr><td>-51.49728</td><td>0.72424</td><td>-0.060 ± 0.000</td><td>20.440 ± 0.009</td><td>19.457 ± 0.006</td><td>19.127 ± 0.006</td><td>18.916 ± 0.015</td></tr><tr><td>-51.49719</td><td>-0.03586</td><td>-0.073 ± 0.000</td><td>21.276 ± 0.015</td><td>20.061 ± 0.008</td><td>19.649 ± 0.008</td><td>0.005 ± 0.000</td></tr><tr><td>-51.49719</td><td>-1.01131</td><td>-0.047 ± 0.000</td><td>20.443 ± 0.010</td><td>19.173 ± 0.005</td><td>18.649 ± 0.005</td><td>18.303 ± 0.011</td></tr><tr><td>-51.49719</td><td>0.74200</td><td>-0.075 ± 0.000</td><td>20.551 ± 0.009</td><td>19.213 ± 0.005</td><td>18.690 ± 0.005</td><td>18.406 ± 0.010</td></tr><tr><td>-51.49701</td><td>-0.93142</td><td>-0.075 ± 0.000</td><td>19.961 ± 0.008</td><td>19.298 ± 0.005</td><td>19.045 ± 0.006</td><td>18.895 ± 0.017</td></tr><tr><td>-51.49701</td><td>1.07940</td><td>19.788 ± 0.016</td><td>18.390 ± 0.003</td><td>17.788 ± 0.003</td><td>17.578 ± 0.003</td><td>17.463 ± 0.007</td></tr><tr><td>-51.49692</td><td>-0.54050</td><td>-0.079 ± 0.000</td><td>19.940 ± 0.007</td><td>18.949 ± 0.005</td><td>18.540 ± 0.005</td><td>18.270 ± 0.010</td></tr><tr><td>-51.49692</td><td>-0.61986</td><td>-0.098 ± 0.000</td><td>21.225 ± 0.015</td><td>20.040 ± 0.009</td><td>19.578 ± 0.008</td><td>0.002 ± 0.000</td></tr><tr><td>-51.49692</td><td>-0.14299</td><td>-0.031 ± 0.000</td><td>20.106 ± 0.007</td><td>19.590 ± 0.006</td><td>19.447 ± 0.007</td><td>0.006 ± 0.000</td></tr><tr><td>-51.49680</td><td>-0.00895</td><td>-0.061 ± 0.000</td><td>20.092 ± 0.007</td><td>19.409 ± 0.005</td><td>19.171 ± 0.006</td><td>19.021 ± 0.021</td></tr><tr><td>-51.49670</td><td>-0.95457</td><td>-0.052 ± 0.000</td><td>20.108 ± 0.008</td><td>19.480 ± 0.006</td><td>19.227 ± 0.007</td><td>19.056 ± 0.034</td></tr><tr><td>-51.49655</td><td>1.12279</td><td>17.199 ± 0.007</td><td>16.071 ± 0.002</td><td>15.631 ± 0.002</td><td>15.486 ± 0.003</td><td>15.435 ± 0.004</td></tr><tr><td>-51.49655</td><td>-0.50931</td><td>-0.091 ± 0.000</td><td>21.206 ± 0.017</td><td>20.087 ± 0.009</td><td>19.634 ± 0.008</td><td>0.009 ± 0.000</td></tr><tr><td>-51.49616</td><td>-0.83636</td><td>-0.071 ± 0.000</td><td>20.087 ± 0.006</td><td>19.479 ± 0.005</td><td>19.220 ± 0.005</td><td>19.034 ± 0.017</td></tr></tbody></table>
<table><caption>Table E.2. Catalog of natural AB MegaCam magnitudes for selected tertiary standards in the D1 field.</caption><thead><tr><th>RA<br>(deg)</th><th>Dec<br>(deg)</th><th>u<sub>M</sub><br>(mag)</th><th>g<sub>M</sub><br>(mag)</th><th>R<sub>M</sub><br>(mag)</th><th>i<sub>M</sub><br>(mag)</th><th>i<sub>2M</sub><br>(mag)</th><th>z<sub>M</sub><br>(mag)</th></tr></thead><tbody><tr><td>36.38510</td><td>-4.99688</td><td>21.273 ± 0.009</td><td>19.131 ± 0.001</td><td>17.887 ± 0.001</td><td>16.971 ± 0.001</td><td>17.044 ± 0.001</td><td>16.599 ± 0.001</td></tr><tr><td>36.53275</td><td>-4.99662</td><td>19.306 ± 0.002</td><td>18.510 ± 0.001</td><td>18.143 ± 0.001</td><td>17.988 ± 0.001</td><td>17.997 ± 0.001</td><td>17.952 ± 0.001</td></tr><tr><td>36.09325</td><td>-4.99260</td><td>19.705 ± 0.003</td><td>17.795 ± 0.000</td><td>16.834 ± 0.000</td><td>16.412 ± 0.001</td><td>16.436 ± 0.002</td><td>16.236 ± 0.001</td></tr><tr><td>36.47386</td><td>-4.99281</td><td>18.428 ± 0.002</td><td>17.413 ± 0.000</td><td>16.940 ± 0.000</td><td>16.763 ± 0.001</td><td>16.761 ± 0.001</td><td>16.691 ± 0.001</td></tr><tr><td>36.54650</td><td>-4.99460</td><td>23.000 ± 0.046</td><td>20.823 ± 0.002</td><td>19.560 ± 0.001</td><td>18.022 ± 0.001</td><td>18.131 ± 0.001</td><td>17.401 ± 0.001</td></tr><tr><td>36.58690</td><td>-4.99623</td><td>21.494 ± 0.015</td><td>20.979 ± 0.002</td><td>20.839 ± 0.002</td><td>20.843 ± 0.004</td><td>21.162 ± 0.009</td><td>20.833 ± 0.018</td></tr><tr><td>36.26135</td><td>-4.99125</td><td>21.188 ± 0.008</td><td>19.048 ± 0.001</td><td>17.794 ± 0.000</td><td>16.895 ± 0.001</td><td>16.960 ± 0.001</td><td>16.524 ± 0.001</td></tr><tr><td>36.30102</td><td>-4.99325</td><td>20.781 ± 0.006</td><td>19.402 ± 0.001</td><td>18.794 ± 0.001</td><td>18.558 ± 0.001</td><td>18.573 ± 0.001</td><td>18.481 ± 0.002</td></tr><tr><td>36.84051</td><td>-4.99460</td><td>21.328 ± 0.011</td><td>20.712 ± 0.002</td><td>20.464 ± 0.002</td><td>20.386 ± 0.003</td><td>20.381 ± 0.004</td><td>20.420 ± 0.012</td></tr><tr><td>36.59163</td><td>-4.99306</td><td>22.907 ± 0.061</td><td>20.994 ± 0.002</td><td>19.902 ± 0.001</td><td>19.303 ± 0.001</td><td>19.355 ± 0.002</td><td>19.051 ± 0.003</td></tr><tr><td>36.25865</td><td>-4.99148</td><td>23.322 ± 0.057</td><td>21.129 ± 0.002</td><td>19.846 ± 0.001</td><td>18.797 ± 0.001</td><td>18.890 ± 0.001</td><td>18.363 ± 0.002</td></tr><tr><td>36.04552</td><td>-4.99251</td><td>23.224 ± 0.056</td><td>21.252 ± 0.002</td><td>20.076 ± 0.001</td><td>19.351 ± 0.001</td><td>19.388 ± 0.002</td><td>19.026 ± 0.003</td></tr><tr><td>36.89012</td><td>-4.99279</td><td>21.641 ± 0.017</td><td>21.056 ± 0.002</td><td>20.830 ± 0.002</td><td>20.743 ± 0.003</td><td>20.737 ± 0.006</td><td>20.816 ± 0.017</td></tr><tr><td>36.65816</td><td>-4.99284</td><td>22.096 ± 0.019</td><td>21.496 ± 0.003</td><td>21.236 ± 0.003</td><td>21.155 ± 0.005</td><td>21.170 ± 0.010</td><td>21.192 ± 0.024</td></tr><tr><td>36.14973</td><td>-4.98829</td><td>19.426 ± 0.002</td><td>18.532 ± 0.001</td><td>18.156 ± 0.001</td><td>18.024 ± 0.000</td><td>18.030 ± 0.001</td><td>18.001 ± 0.001</td></tr><tr><td>36.25174</td><td>-4.98940</td><td>21.277 ± 0.009</td><td>19.248 ± 0.001</td><td>18.138 ± 0.000</td><td>17.563 ± 0.000</td><td>17.601 ± 0.001</td><td>17.321 ± 0.001</td></tr><tr><td>36.54013</td><td>-4.99079</td><td>21.751 ± 0.013</td><td>21.055 ± 0.002</td><td>20.795 ± 0.002</td><td>20.710 ± 0.003</td><td>20.720 ± 0.005</td><td>20.764 ± 0.014</td></tr><tr><td>36.95613</td><td>-4.99045</td><td>21.979 ± 0.020</td><td>21.798 ± 0.004</td><td>21.570 ± 0.004</td><td>21.592 ± 0.007</td><td>21.572 ± 0.012</td><td>21.403 ± 0.026</td></tr><tr><td>36.15851</td><td>-4.98740</td><td>19.821 ± 0.003</td><td>18.594 ± 0.000</td><td>18.046 ± 0.000</td><td>17.833 ± 0.000</td><td>17.843 ± 0.001</td><td>17.760 ± 0.001</td></tr><tr><td>36.16302</td><td>-4.98960</td><td>23.390 ± 0.064</td><td>22.019 ± 0.004</td><td>21.221 ± 0.003</td><td>20.833 ± 0.003</td><td>20.843 ± 0.006</td><td>20.702 ± 0.013</td></tr><tr><td>36.27337</td><td>-4.98826</td><td>23.671 ± 0.262</td><td>22.113 ± 0.007</td><td>20.755 ± 0.002</td><td>18.805 ± 0.001</td><td>18.914 ± 0.001</td><td>17.997 ± 0.001</td></tr><tr><td>36.26092</td><td>-4.98886</td><td>24.089 ± 0.103</td><td>21.933 ± 0.004</td><td>20.657 ± 0.002</td><td>19.645 ± 0.001</td><td>19.714 ± 0.002</td><td>19.203 ± 0.003</td></tr><tr><td>36.83998</td><td>-4.98953</td><td>23.237 ± 0.053</td><td>22.078 ± 0.005</td><td>21.438 ± 0.003</td><td>21.145 ± 0.005</td><td>21.144 ± 0.008</td><td>21.038 ± 0.018</td></tr><tr><td>36.37521</td><td>-4.98974</td><td>22.810 ± 0.036</td><td>22.120 ± 0.005</td><td>21.802 ± 0.005</td><td>21.621 ± 0.006</td><td>21.632 ± 0.011</td><td>21.555 ± 0.027</td></tr><tr><td>36.52906</td><td>-4.98853</td><td>23.932 ± 0.093</td><td>21.838 ± 0.003</td><td>20.629 ± 0.002</td><td>19.625 ± 0.001</td><td>19.710 ± 0.002</td><td>19.231 ± 0.003</td></tr><tr><td>36.60251</td><td>-4.98351</td><td>18.040 ± 0.002</td><td>17.153 ± 0.000</td><td>16.771 ± 0.000</td><td>16.621 ± 0.001</td><td>16.630 ± 0.001</td><td>16.590 ± 0.001</td></tr><tr><td>36.50657</td><td>-4.98856</td><td>21.359 ± 0.009</td><td>21.190 ± 0.002</td><td>21.141 ± 0.003</td><td>20.941 ± 0.004</td><td>21.029 ± 0.007</td><td>20.993 ± 0.016</td></tr><tr><td>36.98082</td><td>-4.98706</td><td>22.351 ± 0.025</td><td>21.096 ± 0.002</td><td>20.481 ± 0.001</td><td>20.189 ± 0.002</td><td>20.199 ± 0.004</td><td>20.086 ± 0.008</td></tr><tr><td>36.04928</td><td>-4.98642</td><td>23.804 ± 0.080</td><td>21.710 ± 0.003</td><td>20.438 ± 0.001</td><td>19.208 ± 0.001</td><td>19.268 ± 0.002</td><td>18.671 ± 0.002</td></tr><tr><td>36.31037</td><td>-4.98424</td><td>19.416 ± 0.002</td><td>18.453 ± 0.000</td><td>17.951 ± 0.000</td><td>17.718 ± 0.000</td><td>17.732 ± 0.001</td><td>17.638 ± 0.001</td></tr><tr><td>36.58115</td><td>-4.98026</td><td>18.937 ± 0.002</td><td>17.374 ± 0.000</td><td>16.640 ± 0.001</td><td>16.307 ± 0.001</td><td>16.336 ± 0.002</td><td>16.175 ± 0.001</td></tr><tr><td>36.98122</td><td>-4.98534</td><td>24.936 ± 0.418</td><td>22.913 ± 0.010</td><td>21.643 ± 0.004</td><td>20.711 ± 0.003</td><td>20.748 ± 0.006</td><td>20.296 ± 0.009</td></tr><tr><td>36.52662</td><td>-4.98517</td><td>21.308 ± 0.008</td><td>20.659 ± 0.001</td><td>20.400 ± 0.001</td><td>20.321 ± 0.002</td><td>20.316 ± 0.003</td><td>20.369 ± 0.008</td></tr><tr><td>36.87478</td><td>-4.98405</td><td>23.535 ± 0.073</td><td>21.339 ± 0.002</td><td>20.073 ± 0.001</td><td>19.352 ± 0.001</td><td>19.397 ± 0.002</td><td>19.040 ± 0.003</td></tr><tr><td>36.42190</td><td>-4.98455</td><td>22.233 ± 0.018</td><td>21.885 ± 0.003</td><td>21.975 ± 0.005</td><td>21.523 ± 0.006</td><td>21.295 ± 0.008</td><td>21.485 ± 0.023</td></tr><tr><td>36.31201</td><td>-4.97952</td><td>21.392 ± 0.008</td><td>19.281 ± 0.000</td><td>18.067 ± 0.000</td><td>16.687 ± 0.001</td><td>16.859 ± 0.001</td><td>16.127 ± 0.001</td></tr><tr><td>36.97860</td><td>-4.98196</td><td>24.141 ± 0.114</td><td>21.709 ± 0.003</td><td>20.400 ± 0.001</td><td>19.028 ± 0.001</td><td>19.096 ± 0.001</td><td>18.441 ± 0.002</td></tr><tr><td>36.48674</td><td>-4.98136</td><td>21.088 ± 0.007</td><td>20.911 ± 0.001</td><td>20.642 ± 0.001</td><td>20.675 ± 0.003</td><td>20.660 ± 0.004</td><td>20.572 ± 0.010</td></tr><tr><td>36.98416</td><td>-4.98185</td><td>20.459 ± 0.005</td><td>19.759 ± 0.001</td><td>19.443 ± 0.001</td><td>19.315 ± 0.001</td><td>19.314 ± 0.002</td><td>19.309 ± 0.004</td></tr><tr><td>36.15043</td><td>-4.98003</td><td>23.940 ± 0.088</td><td>21.840 ± 0.003</td><td>20.574 ± 0.001</td><td>19.050 ± 0.001</td><td>19.116 ± 0.001</td><td>18.419 ± 0.002</td></tr><tr><td>36.81017</td><td>-4.97627</td><td>18.645 ± 0.001</td><td>17.567 ± 0.000</td><td>17.101 ± 0.000</td><td>16.922 ± 0.000</td><td>16.935 ± 0.001</td><td>16.882 ± 0.001</td></tr><tr><td>36.85117</td><td>-4.98075</td><td>22.211 ± 0.017</td><td>21.595 ± 0.003</td><td>21.349 ± 0.003</td><td>21.223 ± 0.004</td><td>21.230 ± 0.007</td><td>21.269 ± 0.020</td></tr><tr><td>36.70455</td><td>-4.97555</td><td>18.696 ± 0.001</td><td>17.362 ± 0.000</td><td>16.800 ± 0.000</td><td>16.594 ± 0.001</td><td>16.607 ± 0.001</td><td>16.525 ± 0.001</td></tr><tr><td>36.45521</td><td>-4.97674</td><td>22.788 ± 0.029</td><td>20.812 ± 0.001</td><td>19.617 ± 0.001</td><td>18.076 ± 0.000</td><td>18.181 ± 0.001</td><td>17.452 ± 0.001</td></tr><tr><td>36.30635</td><td>-4.97895</td><td>21.902 ± 0.011</td><td>21.249 ± 0.002</td><td>20.936 ± 0.002</td><td>20.818 ± 0.003</td><td>20.811 ± 0.005</td><td>20.804 ± 0.012</td></tr></tbody></table>
<table><caption>Table E.3. $u_M$ transmission curve at an airmass of 1.25.</caption><thead><tr><th>λ<br>(Å)</th><th>T<sub>uM</sub>(λ; r)<br>r = 0 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 23 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 47 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 70 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 93 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 117 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 140 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 163 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 186 mm</th><th>T<sub>uM</sub>(λ; r)<br>r = 210 mm</th></tr></thead><tbody><tr><td>3200</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>3250</td><td>0.0001</td><td>0.0002</td><td>0.0003</td><td>0.0003</td><td>0.0002</td><td>0.0002</td><td>0.0001</td><td>0.0001</td><td>0.0002</td><td>0.0002</td></tr><tr><td>3300</td><td>0.0047</td><td>0.0065</td><td>0.0098</td><td>0.0090</td><td>0.0075</td><td>0.0062</td><td>0.0054</td><td>0.0054</td><td>0.0065</td><td>0.0068</td></tr><tr><td>3350</td><td>0.0427</td><td>0.0489</td><td>0.0576</td><td>0.0562</td><td>0.0526</td><td>0.0492</td><td>0.0464</td><td>0.0471</td><td>0.0511</td><td>0.0524</td></tr><tr><td>3400</td><td>0.1015</td><td>0.1059</td><td>0.1106</td><td>0.1117</td><td>0.1124</td><td>0.1128</td><td>0.1132</td><td>0.1163</td><td>0.1222</td><td>0.1242</td></tr><tr><td>3450</td><td>0.1357</td><td>0.1371</td><td>0.1381</td><td>0.1400</td><td>0.1429</td><td>0.1463</td><td>0.1501</td><td>0.1553</td><td>0.1613</td><td>0.1633</td></tr><tr><td>3500</td><td>0.1687</td><td>0.1689</td><td>0.1684</td><td>0.1688</td><td>0.1698</td><td>0.1717</td><td>0.1740</td><td>0.1775</td><td>0.1818</td><td>0.1831</td></tr><tr><td>3550</td><td>0.1860</td><td>0.1862</td><td>0.1862</td><td>0.1876</td><td>0.1890</td><td>0.1902</td><td>0.1912</td><td>0.1926</td><td>0.1946</td><td>0.1948</td></tr><tr><td>3600</td><td>0.1883</td><td>0.1893</td><td>0.1910</td><td>0.1938</td><td>0.1970</td><td>0.1995</td><td>0.2013</td><td>0.2023</td><td>0.2047</td><td>0.2074</td></tr><tr><td>3650</td><td>0.2055</td><td>0.2052</td><td>0.2050</td><td>0.2069</td><td>0.2093</td><td>0.2108</td><td>0.2111</td><td>0.2099</td><td>0.2074</td><td>0.2047</td></tr><tr><td>3700</td><td>0.1916</td><td>0.1899</td><td>0.1886</td><td>0.1913</td><td>0.1955</td><td>0.1996</td><td>0.2038</td><td>0.2085</td><td>0.2155</td><td>0.2160</td></tr><tr><td>3750</td><td>0.1888</td><td>0.1890</td><td>0.1907</td><td>0.1946</td><td>0.2006</td><td>0.2079</td><td>0.2179</td><td>0.2295</td><td>0.2438</td><td>0.2465</td></tr><tr><td>3800</td><td>0.2373</td><td>0.2393</td><td>0.2427</td><td>0.2462</td><td>0.2512</td><td>0.2574</td><td>0.2659</td><td>0.2742</td><td>0.2825</td><td>0.2840</td></tr><tr><td>3850</td><td>0.2934</td><td>0.2932</td><td>0.2922</td><td>0.2939</td><td>0.2962</td><td>0.2987</td><td>0.3014</td><td>0.3021</td><td>0.3020</td><td>0.3021</td></tr><tr><td>3900</td><td>0.2977</td><td>0.2952</td><td>0.2924</td><td>0.2930</td><td>0.2947</td><td>0.2961</td><td>0.2979</td><td>0.2981</td><td>0.2984</td><td>0.2983</td></tr><tr><td>3950</td><td>0.3074</td><td>0.3063</td><td>0.3054</td><td>0.3046</td><td>0.3036</td><td>0.3030</td><td>0.3034</td><td>0.3025</td><td>0.3019</td><td>0.3019</td></tr><tr><td>4000</td><td>0.3163</td><td>0.3168</td><td>0.3181</td><td>0.3187</td><td>0.3189</td><td>0.3185</td><td>0.3180</td><td>0.3167</td><td>0.3159</td><td>0.3155</td></tr><tr><td>4050</td><td>0.3135</td><td>0.3077</td><td>0.2952</td><td>0.2985</td><td>0.3049</td><td>0.3093</td><td>0.3120</td><td>0.3127</td><td>0.3115</td><td>0.3098</td></tr><tr><td>4100</td><td>0.2514</td><td>0.2298</td><td>0.1925</td><td>0.2000</td><td>0.2169</td><td>0.2317</td><td>0.2424</td><td>0.2426</td><td>0.2344</td><td>0.2312</td></tr><tr><td>4150</td><td>0.1133</td><td>0.0940</td><td>0.0669</td><td>0.0723</td><td>0.0854</td><td>0.0990</td><td>0.1111</td><td>0.1124</td><td>0.1049</td><td>0.1028</td></tr><tr><td>4200</td><td>0.0289</td><td>0.0228</td><td>0.0155</td><td>0.0170</td><td>0.0207</td><td>0.0251</td><td>0.0297</td><td>0.0309</td><td>0.0285</td><td>0.0277</td></tr><tr><td>4250</td><td>0.0071</td><td>0.0058</td><td>0.0041</td><td>0.0045</td><td>0.0053</td><td>0.0063</td><td>0.0073</td><td>0.0076</td><td>0.0070</td><td>0.0067</td></tr><tr><td>4300</td><td>0.0020</td><td>0.0015</td><td>0.0009</td><td>0.0011</td><td>0.0013</td><td>0.0015</td><td>0.0018</td><td>0.0020</td><td>0.0018</td><td>0.0017</td></tr><tr><td>4350</td><td>0.0003</td><td>0.0002</td><td>0.0000</td><td>0.0001</td><td>0.0001</td><td>0.0002</td><td>0.0002</td><td>0.0003</td><td>0.0002</td><td>0.0002</td></tr><tr><td>4400</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4450</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4500</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4550</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4600</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4650</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4700</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4750</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4800</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4850</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4900</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>4950</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>5000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>5050</td><td>0.0000</td><td>0.0002</td><td>0.0016</td><td>0.0019</td><td>0.0020</td><td>0.0020</td><td>0.0020</td><td>0.0021</td><td>0.0022</td><td>0.0022</td></tr><tr><td>5100</td><td>0.0000</td><td>0.0004</td><td>0.0015</td><td>0.0018</td><td>0.0021</td><td>0.0021</td><td>0.0020</td><td>0.0018</td><td>0.0012</td><td>0.0010</td></tr><tr><td>5150</td><td>0.0000</td><td>0.0001</td><td>0.0003</td><td>0.0004</td><td>0.0005</td><td>0.0005</td><td>0.0004</td><td>0.0003</td><td>0.0001</td><td>0.0000</td></tr><tr><td>5200</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>5250</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr><tr><td>5300</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr></tbody></table>
<table><caption>Table E.4. g<sub>M</sub> transmission curve at an airmass of 1.25.</caption><thead><tr><th>λ<br>(Å)</th><th>T<sub>gM</sub>(λ; r)<br>r = 0 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 23 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 47 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 70 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 93 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 117 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 140 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 163 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 186 mm</th><th>T<sub>gM</sub>(λ; r)<br>r = 210 mm</th></tr></thead><tbody><tr><td>4000</td><td>0.0006</td><td>0.0006</td><td>0.0017</td><td>0.0017</td><td>0.0017</td><td>0.0018</td><td>0.0020</td><td>0.0023</td><td>0.0043</td><td>0.0052</td></tr><tr><td>4050</td><td>0.0054</td><td>0.0073</td><td>0.0148</td><td>0.0151</td><td>0.0152</td><td>0.0160</td><td>0.0188</td><td>0.0127</td><td>0.0194</td><td>0.0263</td></tr><tr><td>4100</td><td>0.0376</td><td>0.0585</td><td>0.0890</td><td>0.0901</td><td>0.0908</td><td>0.0952</td><td>0.1082</td><td>0.1201</td><td>0.1789</td><td>0.1976</td></tr><tr><td>4150</td><td>0.1751</td><td>0.2334</td><td>0.2798</td><td>0.2810</td><td>0.2816</td><td>0.2872</td><td>0.3035</td><td>0.3167</td><td>0.3662</td><td>0.3784</td></tr><tr><td>4200</td><td>0.3377</td><td>0.3707</td><td>0.4067</td><td>0.4075</td><td>0.4089</td><td>0.4109</td><td>0.4147</td><td>0.4168</td><td>0.4215</td><td>0.4234</td></tr><tr><td>4250</td><td>0.3634</td><td>0.3796</td><td>0.4163</td><td>0.4168</td><td>0.4186</td><td>0.4205</td><td>0.4234</td><td>0.4252</td><td>0.4341</td><td>0.4386</td></tr><tr><td>4300</td><td>0.3839</td><td>0.4166</td><td>0.4395</td><td>0.4397</td><td>0.4415</td><td>0.4436</td><td>0.4468</td><td>0.4487</td><td>0.4551</td><td>0.4582</td></tr><tr><td>4350</td><td>0.4174</td><td>0.4348</td><td>0.4411</td><td>0.4423</td><td>0.4458</td><td>0.4493</td><td>0.4535</td><td>0.4554</td><td>0.4618</td><td>0.4648</td></tr><tr><td>4400</td><td>0.4271</td><td>0.4224</td><td>0.4489</td><td>0.4506</td><td>0.4544</td><td>0.4589</td><td>0.4648</td><td>0.4678</td><td>0.4753</td><td>0.4776</td></tr><tr><td>4450</td><td>0.4324</td><td>0.4428</td><td>0.4674</td><td>0.4682</td><td>0.4709</td><td>0.4736</td><td>0.4770</td><td>0.4785</td><td>0.4800</td><td>0.4812</td></tr><tr><td>4500</td><td>0.4505</td><td>0.4576</td><td>0.4700</td><td>0.4701</td><td>0.4719</td><td>0.4738</td><td>0.4764</td><td>0.4779</td><td>0.4838</td><td>0.4870</td></tr><tr><td>4550</td><td>0.4494</td><td>0.4504</td><td>0.4838</td><td>0.4845</td><td>0.4857</td><td>0.4878</td><td>0.4910</td><td>0.4927</td><td>0.4982</td><td>0.5001</td></tr><tr><td>4600</td><td>0.4524</td><td>0.4579</td><td>0.5034</td><td>0.5035</td><td>0.5037</td><td>0.5037</td><td>0.5034</td><td>0.5029</td><td>0.5001</td><td>0.5000</td></tr><tr><td>4650</td><td>0.4525</td><td>0.4633</td><td>0.5025</td><td>0.5024</td><td>0.5023</td><td>0.5011</td><td>0.4994</td><td>0.4984</td><td>0.4954</td><td>0.4963</td></tr><tr><td>4700</td><td>0.4455</td><td>0.4644</td><td>0.4965</td><td>0.4960</td><td>0.4956</td><td>0.4950</td><td>0.4950</td><td>0.4954</td><td>0.4996</td><td>0.5033</td></tr><tr><td>4750</td><td>0.4448</td><td>0.4793</td><td>0.5048</td><td>0.5038</td><td>0.5033</td><td>0.5036</td><td>0.5053</td><td>0.5065</td><td>0.5133</td><td>0.5168</td></tr><tr><td>4800</td><td>0.4680</td><td>0.4973</td><td>0.5184</td><td>0.5181</td><td>0.5183</td><td>0.5189</td><td>0.5199</td><td>0.5203</td><td>0.5230</td><td>0.5248</td></tr><tr><td>4850</td><td>0.4907</td><td>0.4973</td><td>0.5207</td><td>0.5212</td><td>0.5222</td><td>0.5228</td><td>0.5232</td><td>0.5229</td><td>0.5215</td><td>0.5220</td></tr><tr><td>4900</td><td>0.4811</td><td>0.4817</td><td>0.5232</td><td>0.5228</td><td>0.5226</td><td>0.5219</td><td>0.5209</td><td>0.5202</td><td>0.5168</td><td>0.5164</td></tr><tr><td>4950</td><td>0.4639</td><td>0.4805</td><td>0.5148</td><td>0.5142</td><td>0.5142</td><td>0.5128</td><td>0.5105</td><td>0.5090</td><td>0.5028</td><td>0.5030</td></tr><tr><td>5000</td><td>0.4331</td><td>0.4546</td><td>0.4849</td><td>0.4844</td><td>0.4857</td><td>0.4868</td><td>0.4885</td><td>0.4894</td><td>0.4953</td><td>0.4999</td></tr><tr><td>5050</td><td>0.4193</td><td>0.4639</td><td>0.4785</td><td>0.4770</td><td>0.4784</td><td>0.4810</td><td>0.4848</td><td>0.4872</td><td>0.4978</td><td>0.5032</td></tr><tr><td>5100</td><td>0.4535</td><td>0.4651</td><td>0.4671</td><td>0.4658</td><td>0.4686</td><td>0.4727</td><td>0.4787</td><td>0.4828</td><td>0.4976</td><td>0.5029</td></tr><tr><td>5150</td><td>0.4359</td><td>0.4503</td><td>0.4541</td><td>0.4541</td><td>0.4586</td><td>0.4643</td><td>0.4732</td><td>0.4793</td><td>0.4984</td><td>0.5042</td></tr><tr><td>5200</td><td>0.4444</td><td>0.4526</td><td>0.4579</td><td>0.4593</td><td>0.4643</td><td>0.4707</td><td>0.4812</td><td>0.4880</td><td>0.5070</td><td>0.5115</td></tr><tr><td>5250</td><td>0.4354</td><td>0.4481</td><td>0.4746</td><td>0.4765</td><td>0.4813</td><td>0.4864</td><td>0.4928</td><td>0.4956</td><td>0.4979</td><td>0.4988</td></tr><tr><td>5300</td><td>0.4268</td><td>0.4597</td><td>0.4590</td><td>0.4606</td><td>0.4652</td><td>0.4684</td><td>0.4717</td><td>0.4734</td><td>0.4803</td><td>0.4853</td></tr><tr><td>5350</td><td>0.4461</td><td>0.4425</td><td>0.4469</td><td>0.4499</td><td>0.4551</td><td>0.4608</td><td>0.4694</td><td>0.4744</td><td>0.4893</td><td>0.4930</td></tr><tr><td>5400</td><td>0.4284</td><td>0.4385</td><td>0.4569</td><td>0.4603</td><td>0.4656</td><td>0.4696</td><td>0.4732</td><td>0.4741</td><td>0.4641</td><td>0.4604</td></tr><tr><td>5450</td><td>0.4325</td><td>0.4275</td><td>0.4108</td><td>0.4142</td><td>0.4195</td><td>0.4206</td><td>0.4199</td><td>0.4191</td><td>0.4099</td><td>0.4091</td></tr><tr><td>5500</td><td>0.3879</td><td>0.3476</td><td>0.3516</td><td>0.3556</td><td>0.3620</td><td>0.3669</td><td>0.3725</td><td>0.3755</td><td>0.3747</td><td>0.3717</td></tr><tr><td>5550</td><td>0.3050</td><td>0.3017</td><td>0.3160</td><td>0.3211</td><td>0.3277</td><td>0.3303</td><td>0.3308</td><td>0.3308</td><td>0.3322</td><td>0.2880</td></tr><tr><td>5600</td><td>0.2608</td><td>0.2455</td><td>0.2252</td><td>0.2310</td><td>0.2376</td><td>0.2353</td><td>0.2272</td><td>0.2227</td><td>0.1705</td><td>0.1508</td></tr><tr><td>5650</td><td>0.1635</td><td>0.1283</td><td>0.1043</td><td>0.1085</td><td>0.1131</td><td>0.1102</td><td>0.1016</td><td>0.0965</td><td>0.0589</td><td>0.0480</td></tr><tr><td>5700</td><td>0.0596</td><td>0.0440</td><td>0.0343</td><td>0.0357</td><td>0.0370</td><td>0.0350</td><td>0.0305</td><td>0.0280</td><td>0.0146</td><td>0.0115</td></tr><tr><td>5750</td><td>0.0174</td><td>0.0129</td><td>0.0094</td><td>0.0096</td><td>0.0098</td><td>0.0089</td><td>0.0074</td><td>0.0067</td><td>0.0067</td><td>0.0027</td></tr><tr><td>5800</td><td>0.0042</td><td>0.0030</td><td>0.0019</td><td>0.0019</td><td>0.0021</td><td>0.0018</td><td>0.0015</td><td>0.0012</td><td>0.0003</td><td>0.0002</td></tr><tr><td>5850</td><td>0.0006</td><td>0.0003</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr></tbody></table>
<table><caption>Table E.5. $r_M$ transmission curve at an airmass of 1.25.</caption><thead><tr><th>λ<br>(Å)</th><th>T<sub>Rm</sub>(λ; r)<br>r = 0 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 23 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 47 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 70 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 93 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 117 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 140 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 163 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 186 mm</th><th>T<sub>Rm</sub>(λ; r)<br>r = 210 mm</th></tr></thead><tbody><tr><td>5300</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0001</td><td>0.0002</td><td>0.0003</td><td>0.0008</td><td>0.0013</td><td>0.0011</td><td>0.0007</td></tr><tr><td>5350</td><td>0.0003</td><td>0.0003</td><td>0.0007</td><td>0.0012</td><td>0.0017</td><td>0.0022</td><td>0.0034</td><td>0.0045</td><td>0.0043</td><td>0.0033</td></tr><tr><td>5400</td><td>0.0021</td><td>0.0022</td><td>0.0031</td><td>0.0041</td><td>0.0052</td><td>0.0062</td><td>0.0092</td><td>0.0119</td><td>0.0116</td><td>0.0090</td></tr><tr><td>5450</td><td>0.0059</td><td>0.0061</td><td>0.0080</td><td>0.0103</td><td>0.0130</td><td>0.0158</td><td>0.0240</td><td>0.0316</td><td>0.0313</td><td>0.0244</td></tr><tr><td>5500</td><td>0.0144</td><td>0.0149</td><td>0.0197</td><td>0.0258</td><td>0.0331</td><td>0.0404</td><td>0.0611</td><td>0.0800</td><td>0.0808</td><td>0.0649</td></tr><tr><td>5550</td><td>0.0354</td><td>0.0368</td><td>0.0483</td><td>0.0627</td><td>0.0795</td><td>0.0954</td><td>0.1360</td><td>0.1691</td><td>0.1728</td><td>0.1480</td></tr><tr><td>5600</td><td>0.0825</td><td>0.0857</td><td>0.1088</td><td>0.1356</td><td>0.1640</td><td>0.1888</td><td>0.2423</td><td>0.2783</td><td>0.2808</td><td>0.2566</td></tr><tr><td>5650</td><td>0.1677</td><td>0.1731</td><td>0.2068</td><td>0.2415</td><td>0.2735</td><td>0.2984</td><td>0.3431</td><td>0.3662</td><td>0.3620</td><td>0.3431</td></tr><tr><td>5700</td><td>0.2787</td><td>0.2845</td><td>0.3171</td><td>0.3452</td><td>0.3668</td><td>0.3822</td><td>0.4036</td><td>0.4107</td><td>0.4050</td><td>0.3933</td></tr><tr><td>5750</td><td>0.3705</td><td>0.3740</td><td>0.3925</td><td>0.4019</td><td>0.4077</td><td>0.4122</td><td>0.4117</td><td>0.4076</td><td>0.4071</td><td>0.4075</td></tr><tr><td>5800</td><td>0.4068</td><td>0.4071</td><td>0.4108</td><td>0.4051</td><td>0.4007</td><td>0.3984</td><td>0.3891</td><td>0.3810</td><td>0.3791</td><td>0.3851</td></tr><tr><td>5850</td><td>0.4030</td><td>0.4020</td><td>0.3997</td><td>0.3936</td><td>0.3880</td><td>0.3838</td><td>0.3792</td><td>0.3731</td><td>0.3622</td><td>0.3594</td></tr><tr><td>5900</td><td>0.3990</td><td>0.3983</td><td>0.3958</td><td>0.3941</td><td>0.3913</td><td>0.3884</td><td>0.3886</td><td>0.3850</td><td>0.3723</td><td>0.3626</td></tr><tr><td>5950</td><td>0.4021</td><td>0.4015</td><td>0.4002</td><td>0.3997</td><td>0.3993</td><td>0.3983</td><td>0.4003</td><td>0.3988</td><td>0.3891</td><td>0.3808</td></tr><tr><td>6000</td><td>0.4068</td><td>0.4066</td><td>0.4078</td><td>0.4105</td><td>0.4120</td><td>0.4121</td><td>0.4177</td><td>0.4198</td><td>0.4111</td><td>0.4012</td></tr><tr><td>6050</td><td>0.4211</td><td>0.4214</td><td>0.4246</td><td>0.4305</td><td>0.4332</td><td>0.4345</td><td>0.4433</td><td>0.4491</td><td>0.4432</td><td>0.4316</td></tr><tr><td>6100</td><td>0.4421</td><td>0.4425</td><td>0.4461</td><td>0.4514</td><td>0.4551</td><td>0.4578</td><td>0.4666</td><td>0.4732</td><td>0.4721</td><td>0.4645</td></tr><tr><td>6150</td><td>0.4591</td><td>0.4596</td><td>0.4623</td><td>0.4658</td><td>0.4700</td><td>0.4730</td><td>0.4793</td><td>0.4845</td><td>0.4863</td><td>0.4847</td></tr><tr><td>6200</td><td>0.4696</td><td>0.4701</td><td>0.4720</td><td>0.4756</td><td>0.4798</td><td>0.4820</td><td>0.4875</td><td>0.4914</td><td>0.4909</td><td>0.4907</td></tr><tr><td>6250</td><td>0.4767</td><td>0.4769</td><td>0.4782</td><td>0.4825</td><td>0.4866</td><td>0.4888</td><td>0.4938</td><td>0.4959</td><td>0.4922</td><td>0.4904</td></tr><tr><td>6300</td><td>0.4817</td><td>0.4818</td><td>0.4826</td><td>0.4864</td><td>0.4902</td><td>0.4923</td><td>0.4947</td><td>0.4938</td><td>0.4984</td><td>0.4879</td></tr><tr><td>6350</td><td>0.4893</td><td>0.4893</td><td>0.4900</td><td>0.4933</td><td>0.4950</td><td>0.4953</td><td>0.4926</td><td>0.4872</td><td>0.4832</td><td>0.4837</td></tr><tr><td>6400</td><td>0.4957</td><td>0.4953</td><td>0.4950</td><td>0.4948</td><td>0.4922</td><td>0.4894</td><td>0.4805</td><td>0.4707</td><td>0.4662</td><td>0.4686</td></tr><tr><td>6450</td><td>0.4958</td><td>0.4947</td><td>0.4930</td><td>0.4890</td><td>0.4832</td><td>0.4776</td><td>0.4659</td><td>0.4544</td><td>0.4469</td><td>0.4477</td></tr><tr><td>6500</td><td>0.4909</td><td>0.4892</td><td>0.4864</td><td>0.4794</td><td>0.4716</td><td>0.4652</td><td>0.4526</td><td>0.4410</td><td>0.4328</td><td>0.4317</td></tr><tr><td>6550</td><td>0.4799</td><td>0.4775</td><td>0.4729</td><td>0.4606</td><td>0.4514</td><td>0.4468</td><td>0.4348</td><td>0.4256</td><td>0.4194</td><td>0.4193</td></tr><tr><td>6600</td><td>0.4541</td><td>0.4515</td><td>0.4460</td><td>0.4310</td><td>0.4237</td><td>0.4226</td><td>0.4145</td><td>0.4110</td><td>0.4088</td><td>0.4096</td></tr><tr><td>6650</td><td>0.4172</td><td>0.4152</td><td>0.4113</td><td>0.3982</td><td>0.3940</td><td>0.3970</td><td>0.3946</td><td>0.3993</td><td>0.4046</td><td>0.4071</td></tr><tr><td>6700</td><td>0.3795</td><td>0.3786</td><td>0.3774</td><td>0.3697</td><td>0.3697</td><td>0.3763</td><td>0.3832</td><td>0.3976</td><td>0.4088</td><td>0.4112</td></tr><tr><td>6750</td><td>0.3525</td><td>0.3522</td><td>0.3535</td><td>0.3524</td><td>0.3594</td><td>0.3707</td><td>0.3920</td><td>0.4157</td><td>0.4258</td><td>0.4248</td></tr><tr><td>6800</td><td>0.3401</td><td>0.3407</td><td>0.3460</td><td>0.3599</td><td>0.3797</td><td>0.3942</td><td>0.4171</td><td>0.4184</td><td>0.4216</td><td>0.4305</td></tr><tr><td>6850</td><td>0.3490</td><td>0.3503</td><td>0.3579</td><td>0.3728</td><td>0.3717</td><td>0.3718</td><td>0.3258</td><td>0.2731</td><td>0.2811</td><td>0.3209</td></tr><tr><td>6900</td><td>0.3414</td><td>0.3370</td><td>0.3217</td><td>0.2594</td><td>0.2100</td><td>0.1965</td><td>0.1233</td><td>0.0839</td><td>0.0931</td><td>0.1264</td></tr><tr><td>6950</td><td>0.1990</td><td>0.1909</td><td>0.1670</td><td>0.0916</td><td>0.0598</td><td>0.0533</td><td>0.0275</td><td>0.0185</td><td>0.0216</td><td>0.0313</td></tr><tr><td>7000</td><td>0.0536</td><td>0.0507</td><td>0.0431</td><td>0.0208</td><td>0.0140</td><td>0.0127</td><td>0.0076</td><td>0.0057</td><td>0.0066</td><td>0.0089</td></tr><tr><td>7050</td><td>0.0123</td><td>0.0118</td><td>0.0103</td><td>0.0057</td><td>0.0042</td><td>0.0039</td><td>0.0024</td><td>0.0017</td><td>0.0022</td><td>0.0031</td></tr><tr><td>7100</td><td>0.0036</td><td>0.0034</td><td>0.0030</td><td>0.0015</td><td>0.0010</td><td>0.0009</td><td>0.0004</td><td>0.0002</td><td>0.0004</td><td>0.0007</td></tr><tr><td>7150</td><td>0.0007</td><td>0.0007</td><td>0.0005</td><td>0.0001</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td></tr></tbody></table>
<table><caption>Table E.6. $i_M$ transmission curve at an airmass of 1.25.</caption><thead><tr><th>λ<br>(Å)</th><th>T<sub>im</sub>(λ; r)<br>r = 0 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 23 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 47 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 70 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 93 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 117 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 140 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 163 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 186 mm</th><th>T<sub>im</sub>(λ; r)<br>r = 210 mm</th></tr></thead><tbody><tr><td>6650</td><td>0.0008</td><td>0.0008</td><td>0.0006</td><td>0.0013</td><td>0.0016</td><td>0.0016</td><td>0.0021</td><td>0.0030</td><td>0.0032</td><td>0.0030</td></tr><tr><td>6700</td><td>0.0027</td><td>0.0026</td><td>0.0023</td><td>0.0035</td><td>0.0044</td><td>0.0046</td><td>0.0062</td><td>0.0090</td><td>0.0096</td><td>0.0091</td></tr><tr><td>6750</td><td>0.0054</td><td>0.0053</td><td>0.0047</td><td>0.0070</td><td>0.0089</td><td>0.0094</td><td>0.0130</td><td>0.0194</td><td>0.0212</td><td>0.0201</td></tr><tr><td>6800</td><td>0.0105</td><td>0.0103</td><td>0.0093</td><td>0.0141</td><td>0.0182</td><td>0.0194</td><td>0.0276</td><td>0.0424</td><td>0.0473</td><td>0.0451</td></tr><tr><td>6850</td><td>0.0202</td><td>0.0198</td><td>0.0176</td><td>0.0275</td><td>0.0360</td><td>0.0387</td><td>0.0558</td><td>0.0863</td><td>0.0971</td><td>0.0935</td></tr><tr><td>6900</td><td>0.0429</td><td>0.0420</td><td>0.0374</td><td>0.0588</td><td>0.0769</td><td>0.0827</td><td>0.1173</td><td>0.1726</td><td>0.1922</td><td>0.1874</td></tr><tr><td>6950</td><td>0.0953</td><td>0.0935</td><td>0.0837</td><td>0.1279</td><td>0.1620</td><td>0.1730</td><td>0.2298</td><td>0.3043</td><td>0.3285</td><td>0.3239</td></tr><tr><td>7000</td><td>0.1872</td><td>0.1843</td><td>0.1683</td><td>0.2365</td><td>0.2813</td><td>0.2950</td><td>0.3552</td><td>0.4162</td><td>0.4334</td><td>0.4306</td></tr><tr><td>7050</td><td>0.3073</td><td>0.3043</td><td>0.2866</td><td>0.3564</td><td>0.3934</td><td>0.4043</td><td>0.4430</td><td>0.4721</td><td>0.4797</td><td>0.4788</td></tr><tr><td>7100</td><td>0.4093</td><td>0.4077</td><td>0.3959</td><td>0.4395</td><td>0.4575</td><td>0.4632</td><td>0.4780</td><td>0.4856</td><td>0.4883</td><td>0.4884</td></tr><tr><td>7150</td><td>0.4484</td><td>0.4482</td><td>0.4440</td><td>0.4593</td><td>0.4640</td><td>0.4660</td><td>0.4689</td><td>0.4687</td><td>0.4696</td><td>0.4701</td></tr><tr><td>7200</td><td>0.4445</td><td>0.4450</td><td>0.4445</td><td>0.4467</td><td>0.4465</td><td>0.4469</td><td>0.4464</td><td>0.4446</td><td>0.4442</td><td>0.4442</td></tr><tr><td>7250</td><td>0.4445</td><td>0.4449</td><td>0.4450</td><td>0.4445</td><td>0.4435</td><td>0.4430</td><td>0.4421</td><td>0.4403</td><td>0.4384</td><td>0.4374</td></tr><tr><td>7300</td><td>0.4507</td><td>0.4509</td><td>0.4508</td><td>0.4506</td><td>0.4495</td><td>0.4488</td><td>0.4480</td><td>0.4463</td><td>0.4432</td><td>0.4412</td></tr><tr><td>7350</td><td>0.4635</td><td>0.4637</td><td>0.4636</td><td>0.4636</td><td>0.4624</td><td>0.4618</td><td>0.4612</td><td>0.4596</td><td>0.4561</td><td>0.4535</td></tr><tr><td>7400</td><td>0.4671</td><td>0.4674</td><td>0.4677</td><td>0.4671</td><td>0.4659</td><td>0.4658</td><td>0.4656</td><td>0.4641</td><td>0.4612</td><td>0.4587</td></tr><tr><td>7450</td><td>0.4624</td><td>0.4629</td><td>0.4637</td><td>0.4623</td><td>0.4610</td><td>0.4617</td><td>0.4618</td><td>0.4607</td><td>0.4591</td><td>0.4573</td></tr><tr><td>7500</td><td>0.4532</td><td>0.4539</td><td>0.4550</td><td>0.4530</td><td>0.4520</td><td>0.4533</td><td>0.4537</td><td>0.4533</td><td>0.4531</td><td>0.4520</td></tr><tr><td>7550</td><td>0.4216</td><td>0.4222</td><td>0.4232</td><td>0.4216</td><td>0.4210</td><td>0.4223</td><td>0.4232</td><td>0.4235</td><td>0.4242</td><td>0.4237</td></tr><tr><td>7600</td><td>0.3147</td><td>0.3150</td><td>0.3153</td><td>0.3148</td><td>0.3148</td><td>0.3156</td><td>0.3167</td><td>0.3175</td><td>0.3182</td><td>0.3180</td></tr><tr><td>7650</td><td>0.3099</td><td>0.3099</td><td>0.3093</td><td>0.3104</td><td>0.3107</td><td>0.3111</td><td>0.3126</td><td>0.3141</td><td>0.3146</td><td>0.3140</td></tr><tr><td>7700</td><td>0.3997</td><td>0.3993</td><td>0.3978</td><td>0.4004</td><td>0.4009</td><td>0.4010</td><td>0.4032</td><td>0.4052</td><td>0.4052</td><td>0.4041</td></tr><tr><td>7750</td><td>0.4256</td><td>0.4250</td><td>0.4230</td><td>0.4263</td><td>0.4265</td><td>0.4263</td><td>0.4282</td><td>0.4294</td><td>0.4288</td><td>0.4274</td></tr><tr><td>7800</td><td>0.4248</td><td>0.4244</td><td>0.4226</td><td>0.4249</td><td>0.4244</td><td>0.4240</td><td>0.4247</td><td>0.4240</td><td>0.4228</td><td>0.4218</td></tr><tr><td>7850</td><td>0.4178</td><td>0.4177</td><td>0.4167</td><td>0.4171</td><td>0.4154</td><td>0.4149</td><td>0.4138</td><td>0.4106</td><td>0.4090</td><td>0.4085</td></tr><tr><td>7900</td><td>0.4057</td><td>0.4060</td><td>0.4058</td><td>0.4041</td><td>0.4015</td><td>0.4006</td><td>0.3975</td><td>0.3924</td><td>0.3901</td><td>0.3899</td></tr><tr><td>7950</td><td>0.3929</td><td>0.3933</td><td>0.3934</td><td>0.3906</td><td>0.3873</td><td>0.3857</td><td>0.3813</td><td>0.3753</td><td>0.3720</td><td>0.3716</td></tr><tr><td>8000</td><td>0.3812</td><td>0.3813</td><td>0.3811</td><td>0.3785</td><td>0.3750</td><td>0.3724</td><td>0.3677</td><td>0.3618</td><td>0.3575</td><td>0.3563</td></tr><tr><td>8050</td><td>0.3733</td><td>0.3732</td><td>0.3725</td><td>0.3705</td><td>0.3670</td><td>0.3639</td><td>0.3594</td><td>0.3540</td><td>0.3491</td><td>0.3471</td></tr><tr><td>8100</td><td>0.3600</td><td>0.3600</td><td>0.3596</td><td>0.3571</td><td>0.3534</td><td>0.3509</td><td>0.3467</td><td>0.3414</td><td>0.3372</td><td>0.3353</td></tr><tr><td>8150</td><td>0.3311</td><td>0.3316</td><td>0.3327</td><td>0.3280</td><td>0.3241</td><td>0.3231</td><td>0.3189</td><td>0.3131</td><td>0.3111</td><td>0.3104</td></tr><tr><td>8200</td><td>0.3062</td><td>0.3076</td><td>0.3110</td><td>0.3030</td><td>0.2986</td><td>0.2993</td><td>0.2945</td><td>0.2878</td><td>0.2884</td><td>0.2897</td></tr><tr><td>8250</td><td>0.2862</td><td>0.2882</td><td>0.2934</td><td>0.2829</td><td>0.2784</td><td>0.2799</td><td>0.2744</td><td>0.2673</td><td>0.2694</td><td>0.2723</td></tr><tr><td>8300</td><td>0.2648</td><td>0.2666</td><td>0.2715</td><td>0.2619</td><td>0.2579</td><td>0.2585</td><td>0.2530</td><td>0.2467</td><td>0.2486</td><td>0.2516</td></tr><tr><td>8350</td><td>0.2484</td><td>0.2496</td><td>0.2529</td><td>0.2459</td><td>0.2423</td><td>0.2418</td><td>0.2367</td><td>0.2314</td><td>0.2326</td><td>0.2347</td></tr><tr><td>8400</td><td>0.2311</td><td>0.2332</td><td>0.2375</td><td>0.2284</td><td>0.2235</td><td>0.2252</td><td>0.2197</td><td>0.2126</td><td>0.2165</td><td>0.2196</td></tr><tr><td>8450</td><td>0.1945</td><td>0.2000</td><td>0.2127</td><td>0.1907</td><td>0.1831</td><td>0.1916</td><td>0.1841</td><td>0.1719</td><td>0.1833</td><td>0.1915</td></tr><tr><td>8500</td><td>0.1316</td><td>0.1399</td><td>0.1619</td><td>0.1274</td><td>0.1190</td><td>0.1325</td><td>0.1239</td><td>0.1096</td><td>0.1253</td><td>0.1383</td></tr><tr><td>8550</td><td>0.0676</td><td>0.0744</td><td>0.0947</td><td>0.0647</td><td>0.0590</td><td>0.0697</td><td>0.0634</td><td>0.0533</td><td>0.0650</td><td>0.0762</td></tr><tr><td>8600</td><td>0.0282</td><td>0.0316</td><td>0.0428</td><td>0.0268</td><td>0.0243</td><td>0.0295</td><td>0.0264</td><td>0.0217</td><td>0.0273</td><td>0.0332</td></tr><tr><td>8650</td><td>0.0112</td><td>0.0125</td><td>0.0170</td><td>0.0106</td><td>0.0097</td><td>0.0117</td><td>0.0105</td><td>0.0087</td><td>0.0109</td><td>0.0132</td></tr><tr><td>8700</td><td>0.0048</td><td>0.0053</td><td>0.0070</td><td>0.0046</td><td>0.0043</td><td>0.0050</td><td>0.0045</td><td>0.0038</td><td>0.0047</td><td>0.0056</td></tr><tr><td>8750</td><td>0.0022</td><td>0.0024</td><td>0.0031</td><td>0.0022</td><td>0.0020</td><td>0.0023</td><td>0.0021</td><td>0.0018</td><td>0.0022</td><td>0.0026</td></tr><tr><td>8800</td><td>0.0008</td><td>0.0008</td><td>0.0011</td><td>0.0008</td><td>0.0007</td><td>0.0008</td><td>0.0007</td><td>0.0007</td><td>0.0008</td><td>0.0009</td></tr></tbody></table>
<table><caption>Table E.7. $I_{2M}$ transmission curve at an airmass of 1.25.</caption><thead><tr><th>λ<br>(Å)</th><th>T<sub>12M</sub>(λ; r)<br>r = 0 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 20 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 40 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 60 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 80 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 100 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 120 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 140 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 160 mm</th><th>T<sub>12M</sub>(λ; r)<br>r = 180 mm</th></tr></thead><tbody><tr><td>6600</td><td>0.0007</td><td>0.0007</td><td>0.0007</td><td>0.0009</td><td>0.0008</td><td>0.0010</td><td>0.0016</td><td>0.0015</td><td>0.0012</td><td>0.0014</td></tr><tr><td>6650</td><td>0.0028</td><td>0.0028</td><td>0.0028</td><td>0.0037</td><td>0.0035</td><td>0.0043</td><td>0.0078</td><td>0.0068</td><td>0.0053</td><td>0.0065</td></tr><tr><td>6700</td><td>0.0103</td><td>0.0100</td><td>0.0100</td><td>0.0135</td><td>0.0129</td><td>0.0160</td><td>0.0279</td><td>0.0249</td><td>0.0194</td><td>0.0237</td></tr><tr><td>6750</td><td>0.0356</td><td>0.0348</td><td>0.0346</td><td>0.0461</td><td>0.0440</td><td>0.0541</td><td>0.0922</td><td>0.0824</td><td>0.0648</td><td>0.0784</td></tr><tr><td>6800</td><td>0.1158</td><td>0.1133</td><td>0.1129</td><td>0.1448</td><td>0.1389</td><td>0.1643</td><td>0.2433</td><td>0.2253</td><td>0.1887</td><td>0.2174</td></tr><tr><td>6850</td><td>0.2602</td><td>0.2564</td><td>0.2561</td><td>0.2963</td><td>0.2899</td><td>0.3177</td><td>0.3818</td><td>0.3703</td><td>0.3422</td><td>0.3651</td></tr><tr><td>6900</td><td>0.3841</td><td>0.3819</td><td>0.3822</td><td>0.4002</td><td>0.3985</td><td>0.4093</td><td>0.4273</td><td>0.4253</td><td>0.4190</td><td>0.4247</td></tr><tr><td>6950</td><td>0.4510</td><td>0.4500</td><td>0.4506</td><td>0.4545</td><td>0.4545</td><td>0.4570</td><td>0.4609</td><td>0.4604</td><td>0.4598</td><td>0.4606</td></tr><tr><td>7000</td><td>0.4702</td><td>0.4695</td><td>0.4700</td><td>0.4714</td><td>0.4713</td><td>0.4723</td><td>0.4744</td><td>0.4736</td><td>0.4729</td><td>0.4731</td></tr><tr><td>7050</td><td>0.4756</td><td>0.4751</td><td>0.4756</td><td>0.4760</td><td>0.4760</td><td>0.4764</td><td>0.4769</td><td>0.4765</td><td>0.4763</td><td>0.4761</td></tr><tr><td>7100</td><td>0.4760</td><td>0.4755</td><td>0.4760</td><td>0.4759</td><td>0.4761</td><td>0.4762</td><td>0.4766</td><td>0.4762</td><td>0.4763</td><td>0.4759</td></tr><tr><td>7150</td><td>0.4617</td><td>0.4613</td><td>0.4617</td><td>0.4620</td><td>0.4621</td><td>0.4624</td><td>0.4628</td><td>0.4624</td><td>0.4623</td><td>0.4617</td></tr><tr><td>7200</td><td>0.4425</td><td>0.4422</td><td>0.4426</td><td>0.4424</td><td>0.4426</td><td>0.4424</td><td>0.4416</td><td>0.4414</td><td>0.4420</td><td>0.4408</td></tr><tr><td>7250</td><td>0.4382</td><td>0.4379</td><td>0.4383</td><td>0.4378</td><td>0.4380</td><td>0.4378</td><td>0.4375</td><td>0.4373</td><td>0.4377</td><td>0.4370</td></tr><tr><td>7300</td><td>0.4421</td><td>0.4418</td><td>0.4421</td><td>0.4422</td><td>0.4423</td><td>0.4426</td><td>0.4433</td><td>0.4429</td><td>0.4431</td><td>0.4429</td></tr><tr><td>7350</td><td>0.4541</td><td>0.4537</td><td>0.4541</td><td>0.4545</td><td>0.4545</td><td>0.4549</td><td>0.4558</td><td>0.4553</td><td>0.4554</td><td>0.4550</td></tr><tr><td>7400</td><td>0.4586</td><td>0.4583</td><td>0.4585</td><td>0.4589</td><td>0.4589</td><td>0.4592</td><td>0.4592</td><td>0.4589</td><td>0.4592</td><td>0.4581</td></tr><tr><td>7450</td><td>0.4553</td><td>0.4551</td><td>0.4553</td><td>0.4549</td><td>0.4552</td><td>0.4549</td><td>0.4533</td><td>0.4535</td><td>0.4547</td><td>0.4532</td></tr><tr><td>7500</td><td>0.4459</td><td>0.4458</td><td>0.4460</td><td>0.4452</td><td>0.4456</td><td>0.4452</td><td>0.4443</td><td>0.4443</td><td>0.4454</td><td>0.4445</td></tr><tr><td>7550</td><td>0.4155</td><td>0.4153</td><td>0.4154</td><td>0.4157</td><td>0.4157</td><td>0.4161</td><td>0.4177</td><td>0.4171</td><td>0.4167</td><td>0.4167</td></tr><tr><td>7600</td><td>0.3128</td><td>0.3126</td><td>0.3127</td><td>0.3134</td><td>0.3133</td><td>0.3139</td><td>0.3152</td><td>0.3146</td><td>0.3142</td><td>0.3140</td></tr><tr><td>7650</td><td>0.3096</td><td>0.3097</td><td>0.3096</td><td>0.3098</td><td>0.3099</td><td>0.3098</td><td>0.3095</td><td>0.3092</td><td>0.3096</td><td>0.3086</td></tr><tr><td>7700</td><td>0.3947</td><td>0.3949</td><td>0.3948</td><td>0.3942</td><td>0.3945</td><td>0.3940</td><td>0.3925</td><td>0.3927</td><td>0.3938</td><td>0.3926</td></tr><tr><td>7750</td><td>0.4106</td><td>0.4109</td><td>0.4107</td><td>0.4095</td><td>0.4101</td><td>0.4094</td><td>0.4078</td><td>0.4085</td><td>0.4103</td><td>0.4094</td></tr><tr><td>7800</td><td>0.3991</td><td>0.3995</td><td>0.3992</td><td>0.3985</td><td>0.3991</td><td>0.3989</td><td>0.3991</td><td>0.3992</td><td>0.4005</td><td>0.4001</td></tr><tr><td>7850</td><td>0.3880</td><td>0.3883</td><td>0.3879</td><td>0.3886</td><td>0.3886</td><td>0.3893</td><td>0.3914</td><td>0.3907</td><td>0.3905</td><td>0.3904</td></tr><tr><td>7900</td><td>0.3799</td><td>0.3802</td><td>0.3798</td><td>0.3810</td><td>0.3809</td><td>0.3815</td><td>0.3834</td><td>0.3826</td><td>0.3821</td><td>0.3818</td></tr><tr><td>7950</td><td>0.3727</td><td>0.3732</td><td>0.3727</td><td>0.3732</td><td>0.3733</td><td>0.3734</td><td>0.3738</td><td>0.3735</td><td>0.3738</td><td>0.3731</td></tr><tr><td>8000</td><td>0.3631</td><td>0.3637</td><td>0.3631</td><td>0.3631</td><td>0.3635</td><td>0.3633</td><td>0.3632</td><td>0.3633</td><td>0.3640</td><td>0.3635</td></tr><tr><td>8050</td><td>0.3543</td><td>0.3549</td><td>0.3543</td><td>0.3544</td><td>0.3548</td><td>0.3548</td><td>0.3547</td><td>0.3549</td><td>0.3558</td><td>0.3553</td></tr><tr><td>8100</td><td>0.3406</td><td>0.3413</td><td>0.3406</td><td>0.3407</td><td>0.3412</td><td>0.3412</td><td>0.3408</td><td>0.3410</td><td>0.3421</td><td>0.3413</td></tr><tr><td>8150</td><td>0.3152</td><td>0.3160</td><td>0.3153</td><td>0.3155</td><td>0.3159</td><td>0.3159</td><td>0.3155</td><td>0.3155</td><td>0.3162</td><td>0.3153</td></tr><tr><td>8200</td><td>0.3003</td><td>0.3010</td><td>0.3004</td><td>0.3006</td><td>0.3010</td><td>0.3008</td><td>0.3001</td><td>0.3003</td><td>0.3009</td><td>0.3003</td></tr><tr><td>8250</td><td>0.2946</td><td>0.2954</td><td>0.2947</td><td>0.2941</td><td>0.2948</td><td>0.2941</td><td>0.2919</td><td>0.2930</td><td>0.2949</td><td>0.2941</td></tr><tr><td>8300</td><td>0.2839</td><td>0.2847</td><td>0.2841</td><td>0.2828</td><td>0.2838</td><td>0.2831</td><td>0.2813</td><td>0.2825</td><td>0.2848</td><td>0.2840</td></tr><tr><td>8350</td><td>0.2717</td><td>0.2726</td><td>0.2722</td><td>0.2694</td><td>0.2721</td><td>0.2704</td><td>0.2574</td><td>0.2659</td><td>0.2740</td><td>0.2718</td></tr><tr><td>8400</td><td>0.2292</td><td>0.2319</td><td>0.2326</td><td>0.2147</td><td>0.2267</td><td>0.2167</td><td>0.1701</td><td>0.1948</td><td>0.2299</td><td>0.2169</td></tr><tr><td>8450</td><td>0.1245</td><td>0.1283</td><td>0.1299</td><td>0.1044</td><td>0.1200</td><td>0.1069</td><td>0.0638</td><td>0.0841</td><td>0.1243</td><td>0.1073</td></tr><tr><td>8500</td><td>0.0378</td><td>0.0397</td><td>0.0405</td><td>0.0291</td><td>0.0360</td><td>0.0306</td><td>0.0160</td><td>0.0225</td><td>0.0388</td><td>0.0314</td></tr><tr><td>8550</td><td>0.0090</td><td>0.0094</td><td>0.0096</td><td>0.0070</td><td>0.0087</td><td>0.0075</td><td>0.0042</td><td>0.0058</td><td>0.0097</td><td>0.0079</td></tr><tr><td>8600</td><td>0.0025</td><td>0.0026</td><td>0.0026</td><td>0.0020</td><td>0.0024</td><td>0.0021</td><td>0.0013</td><td>0.0017</td><td>0.0027</td><td>0.0023</td></tr><tr><td>8650</td><td>0.0008</td><td>0.0008</td><td>0.0008</td><td>0.0007</td><td>0.0008</td><td>0.0007</td><td>0.0004</td><td>0.0006</td><td>0.0009</td><td>0.0007</td></tr><tr><td>8700</td><td>0.0002</td><td>0.0002</td><td>0.0002</td><td>0.0002</td><td>0.0002</td><td>0.0002</td><td>0.0001</td><td>0.0002</td><td>0.0002</td><td>0.0002</td></tr></tbody></table>
<table><caption>Table E.8. z<sub>M</sub> transmission curve at an airmass of 1.25.</caption><thead><tr><th>λ<br>(Å)</th><th>T<sub>zM</sub>(λ; r)<br>r = 0 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 23 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 47 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 70 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 93 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 117 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 140 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 163 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 186 mm</th><th>T<sub>zM</sub>(λ; r)<br>r = 210 mm</th></tr></thead><tbody><tr><td>7850</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0001</td><td>0.0002</td><td>0.0006</td><td>0.0008</td><td>0.0003</td><td>0.0001</td></tr><tr><td>7900</td><td>0.0000</td><td>0.0000</td><td>0.0003</td><td>0.0006</td><td>0.0009</td><td>0.0013</td><td>0.0022</td><td>0.0025</td><td>0.0016</td><td>0.0009</td></tr><tr><td>7950</td><td>0.0008</td><td>0.0007</td><td>0.0016</td><td>0.0023</td><td>0.0028</td><td>0.0034</td><td>0.0053</td><td>0.0057</td><td>0.0039</td><td>0.0026</td></tr><tr><td>8000</td><td>0.0026</td><td>0.0024</td><td>0.0040</td><td>0.0052</td><td>0.0064</td><td>0.0078</td><td>0.0127</td><td>0.0140</td><td>0.0092</td><td>0.0058</td></tr><tr><td>8050</td><td>0.0054</td><td>0.0051</td><td>0.0085</td><td>0.0114</td><td>0.0142</td><td>0.0178</td><td>0.0303</td><td>0.0340</td><td>0.0219</td><td>0.0130</td></tr><tr><td>8100</td><td>0.0114</td><td>0.0107</td><td>0.0186</td><td>0.0257</td><td>0.0326</td><td>0.0411</td><td>0.0697</td><td>0.0782</td><td>0.0524</td><td>0.0305</td></tr><tr><td>8150</td><td>0.0251</td><td>0.0233</td><td>0.0415</td><td>0.0572</td><td>0.0718</td><td>0.0885</td><td>0.1371</td><td>0.1510</td><td>0.1127</td><td>0.0707</td></tr><tr><td>8200</td><td>0.0579</td><td>0.0540</td><td>0.0913</td><td>0.1192</td><td>0.1426</td><td>0.1660</td><td>0.2203</td><td>0.2340</td><td>0.1994</td><td>0.1462</td></tr><tr><td>8250</td><td>0.1214</td><td>0.1150</td><td>0.1694</td><td>0.2021</td><td>0.2257</td><td>0.2451</td><td>0.2787</td><td>0.2850</td><td>0.2693</td><td>0.2331</td></tr><tr><td>8300</td><td>0.2025</td><td>0.1959</td><td>0.2436</td><td>0.2649</td><td>0.2775</td><td>0.2853</td><td>0.2936</td><td>0.2934</td><td>0.2904</td><td>0.2810</td></tr><tr><td>8350</td><td>0.2625</td><td>0.2589</td><td>0.2806</td><td>0.2871</td><td>0.2897</td><td>0.2903</td><td>0.2895</td><td>0.2878</td><td>0.2854</td><td>0.2854</td></tr><tr><td>8400</td><td>0.2808</td><td>0.2799</td><td>0.2837</td><td>0.2843</td><td>0.2842</td><td>0.2840</td><td>0.2844</td><td>0.2837</td><td>0.2793</td><td>0.2764</td></tr><tr><td>8450</td><td>0.2757</td><td>0.2755</td><td>0.2762</td><td>0.2770</td><td>0.2775</td><td>0.2781</td><td>0.2801</td><td>0.2802</td><td>0.2763</td><td>0.2711</td></tr><tr><td>8500</td><td>0.2678</td><td>0.2675</td><td>0.2694</td><td>0.2708</td><td>0.2718</td><td>0.2726</td><td>0.2740</td><td>0.2742</td><td>0.2726</td><td>0.2687</td></tr><tr><td>8550</td><td>0.2615</td><td>0.2612</td><td>0.2631</td><td>0.2641</td><td>0.2646</td><td>0.2649</td><td>0.2647</td><td>0.2644</td><td>0.2650</td><td>0.2641</td></tr><tr><td>8600</td><td>0.2546</td><td>0.2546</td><td>0.2549</td><td>0.2549</td><td>0.2548</td><td>0.2546</td><td>0.2530</td><td>0.2523</td><td>0.2537</td><td>0.2552</td></tr><tr><td>8650</td><td>0.2447</td><td>0.2450</td><td>0.2438</td><td>0.2431</td><td>0.2427</td><td>0.2422</td><td>0.2403</td><td>0.2394</td><td>0.2404</td><td>0.2425</td></tr><tr><td>8700</td><td>0.2329</td><td>0.2333</td><td>0.2315</td><td>0.2307</td><td>0.2302</td><td>0.2298</td><td>0.2285</td><td>0.2277</td><td>0.2277</td><td>0.2290</td></tr><tr><td>8750</td><td>0.2207</td><td>0.2210</td><td>0.2195</td><td>0.2190</td><td>0.2188</td><td>0.2187</td><td>0.2181</td><td>0.2177</td><td>0.2168</td><td>0.2168</td></tr><tr><td>8800</td><td>0.2090</td><td>0.2091</td><td>0.2085</td><td>0.2084</td><td>0.2084</td><td>0.2085</td><td>0.2087</td><td>0.2086</td><td>0.2073</td><td>0.2062</td></tr><tr><td>8850</td><td>0.1985</td><td>0.1984</td><td>0.1986</td><td>0.1988</td><td>0.1990</td><td>0.1992</td><td>0.1997</td><td>0.1998</td><td>0.1987</td><td>0.1972</td></tr><tr><td>8900</td><td>0.1877</td><td>0.1875</td><td>0.1881</td><td>0.1884</td><td>0.1886</td><td>0.1888</td><td>0.1891</td><td>0.1893</td><td>0.1888</td><td>0.1875</td></tr><tr><td>8950</td><td>0.1698</td><td>0.1696</td><td>0.1702</td><td>0.1703</td><td>0.1703</td><td>0.1704</td><td>0.1703</td><td>0.1704</td><td>0.1706</td><td>0.1700</td></tr><tr><td>9000</td><td>0.1534</td><td>0.1531</td><td>0.1534</td><td>0.1533</td><td>0.1530</td><td>0.1528</td><td>0.1522</td><td>0.1522</td><td>0.1528</td><td>0.1530</td></tr><tr><td>9050</td><td>0.1469</td><td>0.1467</td><td>0.1466</td><td>0.1461</td><td>0.1456</td><td>0.1453</td><td>0.1442</td><td>0.1440</td><td>0.1447</td><td>0.1455</td></tr><tr><td>9100</td><td>0.1363</td><td>0.1362</td><td>0.1366</td><td>0.1349</td><td>0.1343</td><td>0.1338</td><td>0.1326</td><td>0.1321</td><td>0.1327</td><td>0.1337</td></tr><tr><td>9150</td><td>0.1281</td><td>0.1281</td><td>0.1272</td><td>0.1265</td><td>0.1258</td><td>0.1253</td><td>0.1241</td><td>0.1233</td><td>0.1235</td><td>0.1245</td></tr><tr><td>9200</td><td>0.1249</td><td>0.1249</td><td>0.1239</td><td>0.1232</td><td>0.1225</td><td>0.1221</td><td>0.1210</td><td>0.1201</td><td>0.1197</td><td>0.1203</td></tr><tr><td>9250</td><td>0.1151</td><td>0.1151</td><td>0.1143</td><td>0.1137</td><td>0.1131</td><td>0.1128</td><td>0.1119</td><td>0.1111</td><td>0.1102</td><td>0.1103</td></tr><tr><td>9300</td><td>0.0878</td><td>0.0877</td><td>0.0872</td><td>0.0869</td><td>0.0866</td><td>0.0864</td><td>0.0859</td><td>0.0852</td><td>0.0842</td><td>0.0839</td></tr><tr><td>9350</td><td>0.0639</td><td>0.0638</td><td>0.0637</td><td>0.0636</td><td>0.0634</td><td>0.0634</td><td>0.0632</td><td>0.0627</td><td>0.0617</td><td>0.0611</td></tr><tr><td>9400</td><td>0.0647</td><td>0.0646</td><td>0.0646</td><td>0.0646</td><td>0.0646</td><td>0.0646</td><td>0.0646</td><td>0.0642</td><td>0.0630</td><td>0.0620</td></tr><tr><td>9450</td><td>0.0626</td><td>0.0625</td><td>0.0628</td><td>0.0628</td><td>0.0628</td><td>0.0629</td><td>0.0630</td><td>0.0626</td><td>0.0614</td><td>0.0604</td></tr><tr><td>9500</td><td>0.0593</td><td>0.0592</td><td>0.0595</td><td>0.0596</td><td>0.0597</td><td>0.0597</td><td>0.0599</td><td>0.0596</td><td>0.0586</td><td>0.0575</td></tr><tr><td>9550</td><td>0.0580</td><td>0.0578</td><td>0.0582</td><td>0.0584</td><td>0.0584</td><td>0.0585</td><td>0.0586</td><td>0.0584</td><td>0.0576</td><td>0.0566</td></tr><tr><td>9600</td><td>0.0568</td><td>0.0567</td><td>0.0571</td><td>0.0572</td><td>0.0572</td><td>0.0572</td><td>0.0573</td><td>0.0572</td><td>0.0566</td><td>0.0558</td></tr><tr><td>9650</td><td>0.0574</td><td>0.0572</td><td>0.0575</td><td>0.0576</td><td>0.0576</td><td>0.0576</td><td>0.0575</td><td>0.0575</td><td>0.0571</td><td>0.0565</td></tr><tr><td>9700</td><td>0.0570</td><td>0.0569</td><td>0.0571</td><td>0.0571</td><td>0.0570</td><td>0.0569</td><td>0.0568</td><td>0.0568</td><td>0.0566</td><td>0.0562</td></tr><tr><td>9750</td><td>0.0536</td><td>0.0536</td><td>0.0535</td><td>0.0535</td><td>0.0534</td><td>0.0533</td><td>0.0531</td><td>0.0530</td><td>0.0530</td><td>0.0529</td></tr><tr><td>9800</td><td>0.0505</td><td>0.0505</td><td>0.0504</td><td>0.0503</td><td>0.0501</td><td>0.0500</td><td>0.0497</td><td>0.0496</td><td>0.0497</td><td>0.0497</td></tr><tr><td>9850</td><td>0.0463</td><td>0.0462</td><td>0.0461</td><td>0.0459</td><td>0.0458</td><td>0.0456</td><td>0.0453</td><td>0.0452</td><td>0.0453</td><td>0.0454</td></tr><tr><td>9900</td><td>0.0409</td><td>0.0409</td><td>0.0407</td><td>0.0405</td><td>0.0404</td><td>0.0402</td><td>0.0400</td><td>0.0399</td><td>0.0399</td><td>0.0400</td></tr><tr><td>9950</td><td>0.0349</td><td>0.0349</td><td>0.0347</td><td>0.0346</td><td>0.0344</td><td>0.0343</td><td>0.0341</td><td>0.0340</td><td>0.0339</td><td>0.0340</td></tr><tr><td>10000</td><td>0.0178</td><td>0.0178</td><td>0.0177</td><td>0.0176</td><td>0.0175</td><td>0.0174</td><td>0.0173</td><td>0.0173</td><td>0.0173</td><td>0.0173</td></tr></tbody></table>
<table><caption>**Table E.9.** Measured magnitudes for CALSPEC standards.</caption><thead><tr><th>Instrument</th><th>Band</th><th>Star</th><th>x<sub>fp</sub></th><th>y<sub>fp</sub></th><th>Mag</th></tr></thead><tbody><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>BD17</td><td>0.00</td><td>0.00</td><td>10.199</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>BD17</td><td>0.00</td><td>0.00</td><td>9.593</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>BD17</td><td>0.00</td><td>0.00</td><td>9.339</td></tr><tr><td>MegaCam</td><td>i<sub>M</sub></td><td>BD17</td><td>0.00</td><td>0.00</td><td>9.256</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>BD17</td><td>0.00</td><td>0.00</td><td>9.226</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.12</td><td>14.179</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.45</td><td>14.714</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.92</td><td>17.507</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.92</td><td>17.442</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.12</td><td>14.163</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.92</td><td>17.480</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.12</td><td>14.185</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.45</td><td>14.731</td></tr><tr><td>MegaCam</td><td>u<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.92</td><td>17.685</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.11</td><td>13.209</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P177D</td><td>-0.53</td><td>-3.45</td><td>13.693</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>SNAP2</td><td>-1.05</td><td>-2.91</td><td>16.458</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>SNAP2</td><td>-1.05</td><td>-2.91</td><td>16.443</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.11</td><td>13.206</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P177D</td><td>-0.55</td><td>-3.46</td><td>13.681</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>16.448</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>16.433</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P330E</td><td>0.66</td><td>-3.11</td><td>13.213</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.11</td><td>13.208</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P177D</td><td>-0.56</td><td>-3.46</td><td>13.693</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>16.443</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>16.466</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.11</td><td>13.226</td></tr><tr><td>MegaCam</td><td>g<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>16.445</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.808</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.44</td><td>13.271</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>16.035</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>16.018</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.805</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.45</td><td>13.267</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.989</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.999</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.815</td></tr><tr><td>MegaCam</td><td>r<sub>M</sub></td><td>P177D</td><td>-0.51</td><td>-3.45</td><td>13.279</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.688</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.45</td><td>13.160</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>15.874</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>15.890</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.686</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.45</td><td>13.153</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.889</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.846</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.703</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.45</td><td>13.161</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.895</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.903</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.11</td><td>12.699</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>P177D</td><td>-0.55</td><td>-3.46</td><td>13.169</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>15.899</td></tr><tr><td>MegaCam</td><td>i2<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>15.868</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.695</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>P177D</td><td>-0.51</td><td>-3.44</td><td>13.140</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.874</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>P330E</td><td>-0.78</td><td>-3.11</td><td>12.676</td></tr></tbody></table>

**Notes.** $x_{fp}$ and $y_{fp}$ are the coordinates of measurements in the MegaCam focalplane (in cm, with the origin taken at the center of the focalplane).

<table><caption>**Table E.9.** continued.</caption><thead><tr><th>Instrument</th><th>Band</th><th>Star</th><th>x<sub>fp</sub></th><th>y<sub>fp</sub></th><th>Mag</th></tr></thead><tbody><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.44</td><td>13.130</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>SNAP2</td><td>-1.03</td><td>-2.91</td><td>15.827</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>P330E</td><td>-0.79</td><td>-3.11</td><td>12.679</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>P177D</td><td>-0.52</td><td>-3.44</td><td>13.136</td></tr><tr><td>MegaCam</td><td>z<sub>M</sub></td><td>SNAP2</td><td>-1.04</td><td>-2.91</td><td>15.900</td></tr><tr><td>SDSS2.5</td><td>u</td><td>P041C</td><td>—</td><td>—</td><td>13.501</td></tr><tr><td>SDSS2.5</td><td>g</td><td>P041C</td><td>—</td><td>—</td><td>12.281</td></tr><tr><td>SDSS2.5</td><td>r</td><td>P041C</td><td>—</td><td>—</td><td>11.849</td></tr><tr><td>SDSS2.5</td><td>i</td><td>P041C</td><td>—</td><td>—</td><td>11.734</td></tr><tr><td>SDSS2.5</td><td>z</td><td>P041C</td><td>—</td><td>—</td><td>11.717</td></tr><tr><td>SDSS2.5</td><td>u</td><td>P330E</td><td>—</td><td>—</td><td>14.485</td></tr><tr><td>SDSS2.5</td><td>g</td><td>P330E</td><td>—</td><td>—</td><td>13.300</td></tr><tr><td>SDSS2.5</td><td>r</td><td>P330E</td><td>—</td><td>—</td><td>12.844</td></tr><tr><td>SDSS2.5</td><td>i</td><td>P330E</td><td>—</td><td>—</td><td>12.715</td></tr><tr><td>SDSS2.5</td><td>z</td><td>P330E</td><td>—</td><td>—</td><td>12.685</td></tr><tr><td>SDSS2.5</td><td>u</td><td>P177D</td><td>—</td><td>—</td><td>15.050</td></tr><tr><td>SDSS2.5</td><td>g</td><td>P177D</td><td>—</td><td>—</td><td>13.763</td></tr><tr><td>SDSS2.5</td><td>r</td><td>P177D</td><td>—</td><td>—</td><td>13.304</td></tr><tr><td>SDSS2.5</td><td>i</td><td>P177D</td><td>—</td><td>—</td><td>13.175</td></tr><tr><td>SDSS2.5</td><td>z</td><td>P177D</td><td>—</td><td>—</td><td>13.138</td></tr><tr><td>SDSS2.5</td><td>u</td><td>BD17</td><td>—</td><td>—</td><td>10.492</td></tr><tr><td>SDSS2.5</td><td>g</td><td>BD17</td><td>—</td><td>—</td><td>9.651</td></tr><tr><td>SDSS2.5</td><td>r</td><td>BD17</td><td>—</td><td>—</td><td>9.357</td></tr><tr><td>SDSS2.5</td><td>i</td><td>BD17</td><td>—</td><td>—</td><td>9.263</td></tr><tr><td>SDSS2.5</td><td>z</td><td>BD17</td><td>—</td><td>—</td><td>9.251</td></tr></tbody></table>
<table><caption>**Table E.10.** Covariance matrix of synthetic STIS magnitudes.</caption><thead><tr><th></th><th>25.8</th><th>17.2</th><th>9.8</th><th>-2.9</th><th>-2.1</th><th>-16.4</th><th>26.3</th><th>18.7</th><th>10.2</th><th>-1.4</th><th>-16.6</th><th>u<sub>M</sub></th></tr></thead><tbody><tr><th></th><th>15.5</th><th>3.9</th><th>-4.4</th><th>-3.7</th><th>-15.6</th><th>16.8</th><th>16.3</th><th>4.2</th><th>-3.2</th><th>-15.9</th><th>g<sub>M</sub></th></tr><tr><th></th><th></th><th>26.0</th><th>21.0</th><th>20.8</th><th>26.0</th><th>9.9</th><th>3.8</th><th>26.6</th><th>20.8</th><th>26.9</th><th>r<sub>m</sub></th></tr><tr><th></th><th></th><th></th><th>35.5</th><th>33.5</th><th>58.6</th><th>-3.6</th><th>-5.0</th><th>21.1</th><th>32.9</th><th>60.2</th><th>i<sub>M</sub></th></tr><tr><th></th><th></th><th></th><th></th><th>31.8</th><th>54.7</th><th>-2.7</th><th>-4.4</th><th>20.9</th><th>31.2</th><th>56.2</th><th>i2<sub>M</sub></th></tr><tr><th></th><th></th><th></th><th></th><th></th><th>119.1</th><th>-17.6</th><th>-17.2</th><th>26.1</th><th>52.6</th><th>122.5</th><th>z<sub>M</sub></th></tr><tr><th></th><th></th><th></th><th></th><th></th><th></th><th>27.5</th><th>18.3</th><th>10.3</th><th>-2.0</th><th>-17.9</th><th>u</th></tr><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th>17.3</th><th>4.0</th><th>-3.8</th><th>-17.5</th><th>g</th></tr><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th>27.3</th><th>20.9</th><th>26.9</th><th>r</th></tr><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th>30.7</th><th>54.1</th><th>i</th></tr><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th>125.9</th><th>z</th></tr></tbody></table>