The next interesting characteristics to establish for absolute photometric work is the flux of a zero magnitude star in the three DENIS bands. Many infrared systems and several ways to calibrate them exist. We have decided to use the calibration scheme described by Cohen et al. ([1992]): they start from a model of Vega from Kurucz ([1991]), taking into account its lower than solar metallicity, and normalize it to $F_{5556} = 3.44 \ 10^{-8}$ W m $^{-2} \mu{\rm m}^{-1}$ from Hayes ([1985]). Additionally, we adopt V = 0.03 mag, V-I = 0, so I = 0.03 mag, but JHKLM = 0.00 mag for this star. For a more detailed discussion of Vega magnitudes and colours, see Bessell et al. ([1998]).

We must now determine the isophotal wavelength of each filter, taking into account the filter response curve, the atmospheric transmission, the detector radiance response and the Vega spectrum. Isophotal wavelengths are preferred over effective wavelengths, because the latter vary with input source spectrum much more than do the former (see Golay [1974], for details and definitions). Results are given in Table 3.

Using the isophotal wavelengths of our bands, and the Vega spectrum, we can compute the flux densities for a zero magnitude star. Table 4 gives the results in wavelength and frequency units.

Table 5: Theoretical and observed zero-points. Derived overall transmission and its components ( $\tau$ , $\rho$ and QE correspond to transmission, reflection and quantum efficiency, respectively)
Parameter i J $K_{\rm s}$

Theoretical zero-point 25.10 23.29 20.43

Observed zero-point (7'') 23.4 21.1 19.1

Corrected zero-point 23.5 21.3 19.2

Measured overall transmission 0.24 0.16 0.32

$\tau_{\rm atmosphere}$ 0.955 0.912 0.912

$\tau_{\rm mirrors}$ 0.868² 0.964³ 0.978³

$\tau_{\rm blade,\ field\ lens}$ 0.938² 0.939² 0.940²

$\tau_{\rm dichroics}$ 0.784 $0.810 \times 0.870$

$\rho_{\rm dichroics}$ 0.993 0.970

$\tau_{\rm coated\ mirrors}$ 0.993² 0.970 0.97²

$\tau_{\rm objective}$ $0.979^3 \times 0.982^2$ $0.979^3 \times 0.985^2$ $0.70 \times 0.982$

$\tau_{\rm cryostat\ window}$ 0.94 0.985 0.982

$\tau_{\rm filter}$ 0.909 0.846 0.926

${QE}_{\rm detector}$ 0.65 0.8 0.8

Resulting overall transmission 0.31 0.32 0.25

**Table 5:** Theoretical and observed zero-points. Derived overall transmission and its components ( $\tau$ , $\rho$ and QE correspond to transmission, reflection and quantum efficiency, respectively)
Parameter	i	J	$K_{\rm s}$

Theoretical zero-point	25.10	23.29	20.43
Observed zero-point (7'')	23.4	21.1	19.1
Corrected zero-point	23.5	21.3	19.2
Measured overall transmission	0.24	0.16	0.32

$\tau_{\rm atmosphere}$	0.955	0.912	0.912
$\tau_{\rm mirrors}$	0.868²	0.964³	0.978³
$\tau_{\rm blade,\ field\ lens}$	0.938²	0.939²	0.940²
$\tau_{\rm dichroics}$		0.784	$0.810 \times 0.870$
$\rho_{\rm dichroics}$	0.993	0.970
$\tau_{\rm coated\ mirrors}$	0.993²	0.970	0.97²
$\tau_{\rm objective}$	$0.979^3 \times 0.982^2$	$0.979^3 \times 0.985^2$	$0.70 \times 0.982$
$\tau_{\rm cryostat\ window}$	0.94	0.985	0.982
$\tau_{\rm filter}$	0.909	0.846	0.926
${QE}_{\rm detector}$	0.65	0.8	0.8

Resulting overall transmission	0.31	0.32	0.25

From these flux densities, we can estimate how many ADUs would be measured if the atmosphere, telescope and instrument totally transmitted the photons from this zero magnitude star. Comparing to the actually observed zero-point will give the overall transmission of the system. We first integrate the product of the Vega spectrum (shifted by 0.03 mag in i) by the transmission of the full system (fad), over the wavelength domain of our filters ( $\lambda_0$ and $\lambda_1$ correspond to the first and last wavelengths where filter transmission reaches 0), to obtain the measured flux of a zero magnitude star:

Zero-points are measured during calibration nights, where only photometric standards are observed, and routinely during survey nights, to follow possible instrumental variations and make a rough estimate of the extinction coefficients. They are measured from aperture magnitudes inside a 7 arcsec diameter circle around the standard star. To make a valid comparison with the theoretical zero-points, a first correction is necessary to include flux falling outside this aperture. This has been estimated to amount to 0.1 mag in all three bands from a comparison of observations through a 15 arcsec diameter aperture.

A linear fit of the observed magnitudes vs. airmass (assuming that Bouguer's [1729], law is valid) gives the extinction coefficient as the slope and the zero-point as the intercept. However, it is well known that extrapolation to zero airmass leads to a systematic error in the near-infrared (the Forbes [1842], effect), which has been quantified for the J and K bands by Manduca & Bell ([1979]). For the La Silla typical water vapour contents (1 to 10 mm of precipitable water), the error is about 0.10 mag in J and 0.02 mag in K, and should be similar in $K_{\rm s}$ . Therefore, we also add this J correction to the observed zero-point, while we neglect the K correction, given the uncertainty in measured zero-points. The corrected zero-points (for infinite aperture and non-linear variation with airmass) are given in Table 5, and the derived overall transmissions follow.

To interpret the measured overall transmission, we have tried to estimate the contribution of each component of the system, namely atmosphere, aluminium reflections (telescope mirrors, and microscanning mirror for J and $K_{\rm s}$ ), thin blade protecting the field lens, field lens itself, dichroics, coated mirrors, objectives, cryostat entrance windows, filters, and detector quantum efficiency (converted to radiance response). For details about each value, see Galliano ([1999]). Table 5 gives all these estimates, and their final product. The agreement with the measured overall transmission is satisfying, and shows a good performance of the instrument, with overall throughput of 20 to 30% in all three bands.

4 Absolute calibration