We present a measurement of faint source confusion in deep , wide-field 4 \mu m images .
The 1.8 ^ { \circ } \times 1.8 ^ { \circ } images with 17 ^ { \prime \prime } resolution are centered about the nearby edge-on spiral galaxies NGC 4565 and NGC 5907 .
After removing statistical noise and gain fluctuations in the focal plane array , we measure spatial fluctuations in the sky brightness to be \delta \nu I _ { \nu } = 2.74 \pm 0.14 nW m ^ { -2 } sr ^ { -1 } , approximately 1 % of the diffuse background level observed in a single pixel .
The brightness fluctuations are confirmed to be associated with the sky by subtracting sequential images of the same region .
An auto-correlation analysis shows the fluctuations are well described by unresolved point sources .
We see no evidence for surface brightness fluctuations on larger angular scales ( 2 ^ { \prime } < \theta < 28 ^ { \prime } ) .
The statistical distribution of brightness fluctuations allows us to estimate the density of sources below the detection limit .
We present a Monte-Carlo analysis of the undetected sources , which appear to be dominated by galaxies .
Galaxies producing detected sky fluctuations contribute \nu I _ { \nu } ( > S ) = 1.04 ^ { +0.86 } _ { -0.34 } nW m ^ { -2 } sr ^ { -1 } to the cosmic infrared background , evaluated at S = 4.0 \times 10 ^ { -8 } nW m ^ { -2 } .
From the fluctuation data we can determine the integrated source counts N ( > S ) = 1.79 ^ { +0.26 } _ { -0.40 } \times 10 ^ { 7 } sr ^ { -1 } , evaluated at S = 4.0 \times 10 ^ { -8 } nW m ^ { -2 } .
The observed fluctuations are consistent with reddened K -band galaxy number counts .
The number counts of extracted point sources with flux \nu F _ { \nu } > 6.3 \times 10 ^ { -7 } nW m ^ { -2 } are dominated by stars and agree well with the Galactic stellar model of Wright & Reese ( 2000 ) .
Removing the stellar contribution from DIRBE maps with zodiacal subtraction results in a residual brightness of 14.0 \pm 2.6 ( 22.2 \pm 5.9 ) nW m ^ { -2 } sr ^ { -1 } at 3.5 ( 4.9 ) \mu m for the NGC 5907 field , and 24.0 \pm 2.7 ( 36.8 \pm 6.0 ) nW m ^ { -2 } sr ^ { -1 } at 3.5 ( 4.9 ) \mu m for the NGC 4565 field .
The NGC 5907 residuals are consistent with tentative detections of the infrared background reported by Dwek & Arendt ( 1998 ) , Wright & Reese ( 2000 ) , and Gorjian , Wright & Chary ( 2000 ) .