**Table 3:** List of the XMM-Newton sources with mid-IR counterparts in the Lockman Hole region ordered with decreasing 0.5-2 keV flux. For each association we report: the XMM number with previous ROSAT name within brackets (1); the coordinates of the X-ray source (2, 3); the offset between associated sources in arcseconds and the probability of random association in 10^-3 units for X-ray vs. optical (4, 5), mid-IR vs. optical (6, 7) and X-ray vs. mid-IR (8, 9), respectively; the V, I, R and K' magnitudes based on CFHT and Calar Alto observations (10-13); the X-ray fluxes in the soft (0.5-2 keV) and hard (2-10 keV) X-ray bands in 10^-15 cgs units (14, 15); the hardness ratios (16-18); the 2-10 keV luminosity (19); the mid-IR fluxes at 6.75 $\mu$ m (20) and 15 $\mu$ m in mJy (21); the $\alpha _{\rm IX}$ index (22) described in the text; the measured redshift (23) and the AGN type (24). Zero probability of random association means less than $0.5 \times 10^{-3}$ . The hardness ratios, defined as (H-S)/(H+S) (where H and S represent hard and soft bands, respectively), compare 0.2-0.5 vs. 0.5-2 keV, 0.5-2 vs. 2-4.5 keV and 2-4.5 vs. 4.5-10 keV, respectively. In three cases a 15 $\mu$ m source has been marginally detected (*SNR* < 4) at 6.75 $\mu$ m. We report their 6.75 $\mu$ m fluxes inside brackets. Detections in the 5-10 keV X-ray bands are marked with an asterisk on the 2-10 keV flux. The 6.75 $\mu$ m flux of the source #95 has been derived by deblending two close sources. Redshifts are taken from Lehmann et al. (2000, 2001) except for #82 (Fadda et al. 2002). Photometric redshifts computed on the basis of V, I, R and K' magnitudes are reported inside brackets.
$\begin{table} \par\par\includegraphics[width=17.5cm,clip]{tab3.eps}\par\end{table}$

Table 4: List of the Chandra sources with mid-IR counterparts in the Hubble Deep Field and flanking fields ordered with decreasing 0.5-2 keV flux. For each association we report: the number of Brandt et al. (2001a) Chandra source and the name of the ISOCAM counterpart (Aussel et al. 1999) (1); the J2000 coordinates (2, 3) of the Chandra source; the offset between associated sources in arcseconds and the probability of random association in 10^-3 units for X-ray vs. optical (4, 5), mid-IR vs. optical (6, 7) and X-ray vs. mid-IR (8, 9), respectively; the V, I magnitudes (10, 11) from Barger et al. (1999), the R and Ks magnitudes (12, 13) from Hogg et al. (2000); the X-ray fluxes in the soft (0.5-2 keV) and hard (2-8 keV) X-ray bands in 10^-15 cgs units (14, 15); the 2-10 keV luminosity (16); the mid-IR fluxes at 6.75 $\mu$ m (17) and 15 $\mu$ m (18) in mJy (from Aussel et al. 1999, 2002); the $\alpha _{\rm IX}$ index described in the text (19); the measured redshift (20); the spectral classification (21) by Cohen (2000, 2001) and the AGN type (22). A dash in Col. (6) indicates that the source is not in the LW2 field. The source marked with the label "Var'' is a variable X-ray source detected by Brandt et al. (2001) and below the detection threshold in more recent observations (Brandt et al. 2001a). Sources detected in the ultra-hard band (4-8 keV) are marked with an asterisk on the hard-band flux. For the source #172 we recompute I and V magnitudes on the images of Barger et al. (1999) since the original catalogue lists one source instead of two close sources. We classified the spectra of #178, #190 and #Var according to Cohen (2000) by inspecting the reduced spectra of Barger et al. (1999). Redshifts sources are: (0) Hawaii group, (1) Cohen et al. (1996), (2) Lowental et al. (1997), (3) Hogg et al. (1997), (4) Waddington et al. (1999), (5) Cohen et al. (2000), (6) Dawson et al. (2001).
Names J2000 Coords X-Op IR-Op X-IR Optical X-ray mid-IR

$\alpha{-}12^{\rm h}$ $\delta{-}62^{\rm o}$ $\Delta \ \ P$ $\Delta \ \ P$ $\Delta \ \ P$ V V-I R R-Ks SX HX $L_{\rm X}$ LW2 LW3 $\alpha _{\rm IX}$ z C T

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22)

144 PM3_6 36:36.64 13:46.9 0.4 0 1.5 5 1.9 1 22.1 1.3 20.8 2.7 4.43 * 5.53 $\$ 44.02 - 0.35 ^+0.04_-0.07 $\$ 1.26 0.957⁰ $\mathcal{Q}$ 1

171 PM3_20 36:46.35 14:04.8 0.3 0 1.2 3 1.4 3 22.9 2.1 21.7 3.9 2.80 *20.10 $\$ 44.19 0.19 ^+0.04_-0.09 0.11 ^+0.09_-0.02 $\$ 1.03 0.961² - 1

163 PS3_10 36:42.22 15:45.8 0.2 0 1.1 3 1.2 0 23.3 2.4 21.6 4.3 0.84 * 2.48 $\$ 43.32 - 0.46 ^+0.05_-0.09 $\$ 1.35 0.857⁵ $\mathcal{I}$ -

198 PS3_24 36:55.46 13:11.4 0.4 1 0.9 4 0.6 1 24.5 2.8 22.9 4.7 0.40 * 0.89 $\$ 43.53 <0.4 0.02 ^+0.01_-0.01 $\$ 1.16 1.315³ $\mathcal{A}$ -

190 PM3_29 36:51.75 12:21.4 1.3 5 1.9 10 1.4 5 22.6 1.6 21.5 2.9 0.28 * 2.59 $\$ 42.27 <0.04 0.05 ^+0.03_-0.01 $\$ 1.14 0.401⁰ $\mathcal{E}$ -

142 PM3_5 36:35.60 14:24.4 0.5 2 0.3 1 0.5 0 23.9 1.2 23.5 4.5 0.28 * 2.82 $\$ 44.11 - 0.44 ^+0.04_-0.08 $\$ 1.33 2.011⁶ - 2

134 PM3_2 36:34.46 12:12.9 0.3 0 0.6 0 1.0 0 21.1 2.0 18.8 2.7 0.23 <0.27 <41.63 - 0.45 ^+0.07_-0.06 >1.56 0.456⁰ $\mathcal{I}$ -

176 PS2_3 36:48.05 13:09.1 0.3 0 0.9 1 0.9 2 22.5 2.5 20.4 3.2 0.18 * 0.63 $\$ 41.95 0.04 ^+0.06_-0.03 < 0.07 <1.30 0.475² $\mathcal{I}$ -

172 PM3_21 36:46.41 15:29.2 0.2 0 0.6 2 0.7 0 24.6 3.1 23.2 4.2 0.14 * 0.40 $\$ 42.07 - 0.42 ^+0.09_-0.09 $\$ 1.51 (0.6) - -

160 PM3_12 36:41.80 11:32.0 1.5 2 1.4 1 2.7 5 20.6 0.9 19.4 1.7 0.13 <0.26 <39.78 <0.07 0.24 ^+0.06_-0.06 >1.50 0.089¹ $\mathcal{EI}$ -

136 PM3_3 36:34.51 12:41.6 0.7 4 1.2 11 1.1 0 24.2 2.0 23.2 4.5 0.10 <0.27 <42.87 - 0.36 ^+0.08_-0.04 >1.53 1.219⁰ $\mathcal{E}$ -

161 PS3_6e 36:42.11 13:31.6 - - - - 1.3 6 - - >26 >4.6 0.10 <0.21 <44.66 <0.07 0.02 ^+0.01_-0.01 >1.29 4.424⁴ $\mathcal{E}$ 1

188 PM3_28 36:51.11 10:30.7 0.3 0 0.4 0 0.5 0 21.9 2.0 20.2 3.6 0.10 <0.26 <41.42 - 0.34 ^+0.04_-0.07 >1.53 0.410¹ $\mathcal{I}$ -

194 PM3_32 36:53.41 11:39.6 0.6 2 2.1 27 1.8 3 23.3 1.4 23.2 4.0 0.09 <0.15 <42.67 - 0.18 ^+0.06_-0.04 >1.52 1.275⁰ $\mathcal{EA}$ -

Var PM3_17 36:44.20 12:51.0 1.9 6 1.8 6 0.2 0 22.6 2.1 21.4 2.1 0.08 <0.29 <41.93 <0.05 0.28 ^+0.06_-0.06 >1.50 0.557⁰ $\mathcal{E}$ 2

155 PM3_11 36:40.00 12:50.2 0.8 2 1.1 4 0.9 1 23.2 2.2 21.5 3.6 0.07 0.27 $\$ 42.37 <0.06 0.30 ^+0.07_-0.06 $\$ 1.52 0.848⁰ $\mathcal{I}$ -

175 PS3_14 36:47.95 10:19.9 - - - - 2.3 8 - - - - 0.07 0.89 - - 0.10 ^+0.09_-0.02 1.30 - - -

185 PM3_27 36:49.76 13:13.0 2.0 11 0.4 0 2.0 6 23.0 2.0 21.5 3.4 0.07 <0.17 <41.41 0.14 ^+0.07_-0.06 0.16 ^+0.04_-0.04 >1.51 0.475¹ $\mathcal{I}$ -

178 PM3_24 36:48.38 14:26.2 0.7 0 1.4 1 1.1 1 19.5 1.0 18.7 2.0 0.06 <0.17 <40.04 0.25 ^+0.07_-0.07 0.31 ^+0.06_-0.07 >1.56 0.139⁰ $\mathcal{E}$ -

220 PM3_42 37:02.04 11:22.4 0.3 0 2.0 2 2.0 4 20.3 1.2 18.7 2.2 0.06 <0.18 <40.04 - 0.16 ^+0.08_-0.05 >1.50 0.136² $\mathcal{I}$ -

183 PM2_3 36:49.45 13:47.2 0.6 0 0.8 0 1.0 3 19.2 1.5 18.0 2.4 0.05 <0.18 <39.62 0.04 ^+0.07_-0.03 < 0.05 - 0.089¹ - -

148 PM3_7 36:37.01 11:34.9 1.3 1 1.4 1 1.2 1 19.6 1.0 17.7 1.8 0.04 <0.09 <39.19 <0.14 0.30 ^+0.06_-0.07 >1.62 0.078¹ $\mathcal{I}$ -

229 PS3_37 37:04.66 14:29.0 0.2 0 1.4 3 1.5 5 22.7 2.3 21.0 3.2 <0.05 0.29 $\$ 41.86 - 0.07 ^+0.06_-0.02 $\$ 1.38 0.561¹ $\mathcal{I}$ -

149 PS3_6b 36:38.50 13:39.5 0.7 2 1.0 5 1.2 4 23.6 2.0 22.3 3.3 <0.04 0.75 $\$ 41.57 - 0.05 ^+0.03_-0.01 $\$ 1.26 0.357⁵ $\mathcal{I}$ -

**Table 4:** List of the Chandra sources with mid-IR counterparts in the Hubble Deep Field and flanking fields ordered with decreasing 0.5-2 keV flux. For each association we report: the number of Brandt et al. (2001a) Chandra source and the name of the ISOCAM counterpart (Aussel et al. 1999) (1); the J2000 coordinates (2, 3) of the Chandra source; the offset between associated sources in arcseconds and the probability of random association in 10^-3 units for X-ray vs. optical (4, 5), mid-IR vs. optical (6, 7) and X-ray vs. mid-IR (8, 9), respectively; the V, I magnitudes (10, 11) from Barger et al. (1999), the R and Ks magnitudes (12, 13) from Hogg et al. (2000); the X-ray fluxes in the soft (0.5-2 keV) and hard (2-8 keV) X-ray bands in 10^-15 cgs units (14, 15); the 2-10 keV luminosity (16); the mid-IR fluxes at 6.75 $\mu$ m (17) and 15 $\mu$ m (18) in mJy (from Aussel et al. 1999, 2002); the $\alpha _{\rm IX}$ index described in the text (19); the measured redshift (20); the spectral classification (21) by Cohen (2000, 2001) and the AGN type (22). A dash in Col. (6) indicates that the source is not in the LW2 field. The source marked with the label "Var'' is a variable X-ray source detected by Brandt et al. (2001) and below the detection threshold in more recent observations (Brandt et al. 2001a). Sources detected in the ultra-hard band (4-8 keV) are marked with an asterisk on the hard-band flux. For the source #172 we recompute I and V magnitudes on the images of Barger et al. (1999) since the original catalogue lists one source instead of two close sources. We classified the spectra of #178, #190 and #Var according to Cohen (2000) by inspecting the reduced spectra of Barger et al. (1999). Redshifts sources are: (0) Hawaii group, (1) Cohen et al. (1996), (2) Lowental et al. (1997), (3) Hogg et al. (1997), (4) Waddington et al. (1999), (5) Cohen et al. (2000), (6) Dawson et al. (2001).
Names	J2000 Coords	X-Op	IR-Op	X-IR	Optical	X-ray	mid-IR
	$\alpha{-}12^{\rm h}$	$\delta{-}62^{\rm o}$	$\Delta \ \ P$	$\Delta \ \ P$	$\Delta \ \ P$	V	V-I	R	R-Ks	SX	HX	$L_{\rm X}$	LW2	LW3	$\alpha _{\rm IX}$	z	C	T
(1)	(2)	(3)	(4) (5)	(6) (7)	(8) (9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)	(21)	(22)
144 PM3_6	36:36.64	13:46.9	0.4	0	1.5	5	1.9	1	22.1	1.3	20.8	2.7	4.43	* 5.53	$\$ 44.02	-	0.35 ^+0.04_-0.07	$\$ 1.26	0.957⁰	$\mathcal{Q}$	1
171 PM3_20	36:46.35	14:04.8	0.3	0	1.2	3	1.4	3	22.9	2.1	21.7	3.9	2.80	*20.10	$\$ 44.19	0.19 ^+0.04_-0.09	0.11 ^+0.09_-0.02	$\$ 1.03	0.961²	-	1
163 PS3_10	36:42.22	15:45.8	0.2	0	1.1	3	1.2	0	23.3	2.4	21.6	4.3	0.84	* 2.48	$\$ 43.32	-	0.46 ^+0.05_-0.09	$\$ 1.35	0.857⁵	$\mathcal{I}$	-
198 PS3_24	36:55.46	13:11.4	0.4	1	0.9	4	0.6	1	24.5	2.8	22.9	4.7	0.40	* 0.89	$\$ 43.53	<0.4	0.02 ^+0.01_-0.01	$\$ 1.16	1.315³	$\mathcal{A}$	-
190 PM3_29	36:51.75	12:21.4	1.3	5	1.9	10	1.4	5	22.6	1.6	21.5	2.9	0.28	* 2.59	$\$ 42.27	<0.04	0.05 ^+0.03_-0.01	$\$ 1.14	0.401⁰	$\mathcal{E}$	-
142 PM3_5	36:35.60	14:24.4	0.5	2	0.3	1	0.5	0	23.9	1.2	23.5	4.5	0.28	* 2.82	$\$ 44.11	-	0.44 ^+0.04_-0.08	$\$ 1.33	2.011⁶	-	2
134 PM3_2	36:34.46	12:12.9	0.3	0	0.6	0	1.0	0	21.1	2.0	18.8	2.7	0.23	<0.27	<41.63	-	0.45 ^+0.07_-0.06	>1.56	0.456⁰	$\mathcal{I}$	-
176 PS2_3	36:48.05	13:09.1	0.3	0	0.9	1	0.9	2	22.5	2.5	20.4	3.2	0.18	* 0.63	$\$ 41.95	0.04 ^+0.06_-0.03	< 0.07	<1.30	0.475²	$\mathcal{I}$	-
172 PM3_21	36:46.41	15:29.2	0.2	0	0.6	2	0.7	0	24.6	3.1	23.2	4.2	0.14	* 0.40	$\$ 42.07	-	0.42 ^+0.09_-0.09	$\$ 1.51	(0.6)	-	-
160 PM3_12	36:41.80	11:32.0	1.5	2	1.4	1	2.7	5	20.6	0.9	19.4	1.7	0.13	<0.26	<39.78	<0.07	0.24 ^+0.06_-0.06	>1.50	0.089¹	$\mathcal{EI}$	-
136 PM3_3	36:34.51	12:41.6	0.7	4	1.2	11	1.1	0	24.2	2.0	23.2	4.5	0.10	<0.27	<42.87	-	0.36 ^+0.08_-0.04	>1.53	1.219⁰	$\mathcal{E}$	-
161 PS3_6e	36:42.11	13:31.6	-	-	-	-	1.3	6	-	-	>26	>4.6	0.10	<0.21	<44.66	<0.07	0.02 ^+0.01_-0.01	>1.29	4.424⁴	$\mathcal{E}$	1
188 PM3_28	36:51.11	10:30.7	0.3	0	0.4	0	0.5	0	21.9	2.0	20.2	3.6	0.10	<0.26	<41.42	-	0.34 ^+0.04_-0.07	>1.53	0.410¹	$\mathcal{I}$	-
194 PM3_32	36:53.41	11:39.6	0.6	2	2.1	27	1.8	3	23.3	1.4	23.2	4.0	0.09	<0.15	<42.67	-	0.18 ^+0.06_-0.04	>1.52	1.275⁰	$\mathcal{EA}$	-
Var PM3_17	36:44.20	12:51.0	1.9	6	1.8	6	0.2	0	22.6	2.1	21.4	2.1	0.08	<0.29	<41.93	<0.05	0.28 ^+0.06_-0.06	>1.50	0.557⁰	$\mathcal{E}$	2
155 PM3_11	36:40.00	12:50.2	0.8	2	1.1	4	0.9	1	23.2	2.2	21.5	3.6	0.07	0.27	$\$ 42.37	<0.06	0.30 ^+0.07_-0.06	$\$ 1.52	0.848⁰	$\mathcal{I}$	-
175 PS3_14	36:47.95	10:19.9	-	-	-	-	2.3	8	-	-	-	-	0.07	0.89	-	-	0.10 ^+0.09_-0.02	1.30	-	-	-
185 PM3_27	36:49.76	13:13.0	2.0	11	0.4	0	2.0	6	23.0	2.0	21.5	3.4	0.07	<0.17	<41.41	0.14 ^+0.07_-0.06	0.16 ^+0.04_-0.04	>1.51	0.475¹	$\mathcal{I}$	-
178 PM3_24	36:48.38	14:26.2	0.7	0	1.4	1	1.1	1	19.5	1.0	18.7	2.0	0.06	<0.17	<40.04	0.25 ^+0.07_-0.07	0.31 ^+0.06_-0.07	>1.56	0.139⁰	$\mathcal{E}$	-
220 PM3_42	37:02.04	11:22.4	0.3	0	2.0	2	2.0	4	20.3	1.2	18.7	2.2	0.06	<0.18	<40.04	-	0.16 ^+0.08_-0.05	>1.50	0.136²	$\mathcal{I}$	-
183 PM2_3	36:49.45	13:47.2	0.6	0	0.8	0	1.0	3	19.2	1.5	18.0	2.4	0.05	<0.18	<39.62	0.04 ^+0.07_-0.03	< 0.05	-	0.089¹	-	-
148 PM3_7	36:37.01	11:34.9	1.3	1	1.4	1	1.2	1	19.6	1.0	17.7	1.8	0.04	<0.09	<39.19	<0.14	0.30 ^+0.06_-0.07	>1.62	0.078¹	$\mathcal{I}$	-
229 PS3_37	37:04.66	14:29.0	0.2	0	1.4	3	1.5	5	22.7	2.3	21.0	3.2	<0.05	0.29	$\$ 41.86	-	0.07 ^+0.06_-0.02	$\$ 1.38	0.561¹	$\mathcal{I}$	-
149 PS3_6b	36:38.50	13:39.5	0.7	2	1.0	5	1.2	4	23.6	2.0	22.3	3.3	<0.04	0.75	$\$ 41.57	-	0.05 ^+0.03_-0.01	$\$ 1.26	0.357⁵	$\mathcal{I}$	-

3.1 Cross-correlation of X-ray and mid-IR catalogues

In the case of the Lockman Hole observations, XMM sources have position errors of 1-3'' (Hasinger et al. 2001), while 15 $\mu$ m and 6.75 $\mu$ m ISOCAM sources have position errors of 2-4'' (depending on the redundancy of mid-IR observation, see Fadda et al. 2002). In practice, we match X-ray and mid-IR sources within a circle of 4''. In total, we found 22 matches with 15 $\mu$ m sources detected at the 3 $\sigma$ level and 7 with 6.75 $\mu$ m sources at the 4 $\sigma$ level. For the sake of completeness, we list also upper limits of the LW2 and LW3 fluxes when a source is detected in only one of the two ISOCAM filters.

In the case of the Hubble Deep Field image, we have reprocessed the ISOCAM data to recompute more accurate positions of the LW3 sources. We have used the I-band image of Barger et al. (1999) available on the Web to which we added the astrometry according to the catalogue of Hogg et al. (2000). Position errors of the Chandra sources are estimated to be less than 1'' (Brandt et al. 2001a), while ISOCAM sources thanks to the microscan technique of observation have errors less than 2''. Therefore, we match X-ray and mid-IR sources within a circle of 2''.

For each source we have computed the probability of random association of the X-ray source with its mid-IR and optical counterparts, and of the mid-IR source with its optical counterpart. Assuming that the counterpart belongs to a Poissonian distributed population of sources,

Contours of the matched sources are also plotted on optical images in Figs. 2 and 3. In most of the cases there is a clear correspondence between X-ray and mid-IR sources. Only in a few cases (#149 in the Hubble Deep Field and #41, #79 in the Lockman Hole) optical counterparts are uncertain and the match relies only on the distance criterion. Three sources are optically faint (see Alexander et al. 2001a).

Results of these cross-correlations are reported in Tables 3 and 4 which contain positions of the X-ray sources, distances, and probability of random associations between sources and proposed counterparts, optical magnitudes in the V, I, R and K bands, X-ray and mid-IR fluxes, redshifts and AGN types when known, as well as other quantities described in the following.

For the sources without spectroscopic redshifts, we have estimated photometric redshifts using four optical magnitudes (V, I, R and K) under the assumption that the optical emission is dominated by the host galaxy. We used a library of synthetic SEDs generated with PEGASE2.0 (Fioc & Rocca-Volmerange 1997) to fit the distribution of optical magnitudes. The median error on photometric redshifts, derived from a study on the Hubble Deep Field South (Franceschini et al., in prep.), is 0.1.

3.2 Comparison of mid-IR and X-ray common surveys

Up to now, only two ISOCAM surveys have been studied in the X-ray bands: the Elais-S1 field (Alexander et al. 2001) and the HDF-N field (Hornschemeier et al. 2001). In this paper we extend the study of mid-IR-X-ray cross-correlation in the HDF-N field and flanking fields using the new observations of Brandt et al. (2001a) and justifying the associations between X-ray and mid-IR sources.

Figure 4 compares the mid-IR and X-ray fluxes of the sources detected in these surveys as well as the sensitivity limits of the X-ray observations and the 80% completeness limits of the 15 $\mu$ m surveys. The survey in the Lockman Hole region is intermediate between the Elais-S1 and HDF-N surveys. It covers an area of 218 square arcminutes that is $\sim$ 30 times smaller than the Elais-S1 survey ( $\sim$ 6000 square arcminutes) and $\sim$ 10 times larger than the HDF-N survey (24 square arcminutes). In terms of sensitivity it is approximately one order of magnitude shallower than the HDF-N in the soft and hard X-ray bands, but it is two orders of magnitudes deeper than the Beppo-SAX observations. Moreover, the XMM-Newton data allow us to explore with a good sensitivity the ultra-hard energy band (4.5-10 keV), which has been pioneered by Beppo-SAX and is not well covered by Chandra. As we have already seen, this band is very interesting because more than 60% of the ultra-hard sources in the Lockman Hole have mid-IR counterparts.

Taking into account the limits in sensitivity, the three surveys are compatible in terms of source density. Within the sensitivity limits of the Lockman Hole observations ( $F_{15\,\mu {\rm m}} \ge 0.4$ mJy and $F_{0.5-2~{\rm keV}} > 0.3\times10^{-15}$ erg cm^-2 s^-1, $F_{2-10~\rm keV} > 1.4\times10^{-15}$ erg cm^-2 s^-1) we find 13 and 11 sources in the soft and hard X-ray bands, respectively. Therefore, we expect to detect in the HDF-N within the same flux limits 1.4 ^+0.5_-0.4 and 1.2 ^+0.5_-0.4 sources in the soft and hard band, respectively, while we detect one and two sources. Moreover, in the hard X-ray band within the sensitivity limits of Elais-S1, we expect to detect $0.2 \pm 0.1$ sources in the Lockman Hole and $0.03 \pm 0.01$ sources in the HDF-N while no sources have been detected in these two surveys.

In conclusion, the survey in the Lockman Hole is intermediate between the surveys in the Elais-S1 and HDF-N fields. Due to its large sky coverage, the Elais-S1 survey picks up very powerful and rare hard-X ray sources. On the other hand, the deep X-ray survey in the HDF-N allows the detection of very faint X-ray sources, and therefore also normal and starburst galaxies, in a small region of sky. So far, only the survey in the Lockman Hole region has sufficient depth and sky coverage to study a representative population of AGNs detected in the ISOCAM mid-IR surveys.

3 Basic analysis

3.1 Cross-correlation of X-ray and mid-IR catalogues

3.2 Comparison of mid-IR and X-ray common surveys