The K -band light-profiles from two statistically complete , diameter-limited samples of disk galaxies have been simultaneously modelled with a seeing-convolved Sérsic r ^ { 1 / n } bulge and a seeing-convolved exponential disk .
This has enabled an accurate separation of the bulge and disk light , and hence an estimate of the central disk surface brightness \mu _ { 0 ,K } and the disk scale-length h .
There exists a bright envelope of galaxy disks in the \mu _ { 0 ,K } – \log h diagram ; for the early-type ( \leq Sbc–Sc ) disk galaxies \mu _ { 0 ,K } is shown to increase with \log h , with a slope of \sim 2 and a correlation coefficient equal to 0.75 .
This relation exists over a range of disk scale-lengths from 0.5 to 10 kpc ( H _ { 0 } = 75 km s ^ { -1 } Mpc ^ { -1 } ) .
In general , galaxy types Scd or later are observed to deviate from this relation ; they have fainter surface brightnesses for a given scale-length .

With a sub-sample of 59 low-inclination ( i \leq 50 ^ { o } ) and 29 high-inclination ( i \geq 50 ^ { o } ) galaxies having morphological types ranging from S0 to Sc , the need for an inclination correction to the K -band disk surface brightness is demonstrated .
Certain selection criteria biases which have troubled previous surface brightness inclination tests ( for example , whether the galaxies are selected from a magnitude- or diameter-limited sample ) do not operate in the \mu _ { 0 ,K } – \log h diagram .
Measured central disk surface brightnesses are found to be significantly ( > 5 \sigma ) brighter for the high-inclination disk galaxies than for the low-inclination disk galaxies .
With no surface brightness inclination correction or allowance for the trend between \mu _ { 0 ,K } and \log h , the standard deviation to the distribution of \mu _ { 0 ,K } values is \sim 1 mag arcsec ^ { -2 } , while the standard deviation about the mean \mu _ { 0 ,K } – \log h relation decreases from 0.69 mag arcsec ^ { -2 } , when no inclination correction is applied , to 0.47 mag arcsec ^ { -2 } when the inclination correction is applied .
Possible changes to the disk scale-length with inclination , due to radial gradients in the disk opacity , have been explored .
The maximum possible size of such corrections are too small to provide a valid explanation for the difference between the low- and high-inclination disk galaxies in the \mu _ { 0 ,K } – \log h diagram .