## Mapping Grey Levels to Optical Density for the DBA Scanner

A step-wedge phantom film was scanned on the DBA scanner at the full 42 micron
per pixel spatial resolution, and scaled via bilinear interpolation to a spatial resolution of 210 microns per pixel. Here's a look at a cropped, rotated version of the phantom image.

On the film, the optical density of each of the 21 wedges was measured as well
as that of the film background. On the 210 micron image, the grey level mean
and standard deviation of an 80 by 30 pixel region (240 pixels) within each
wedge and the film background was computed. Here's the results of these
measurements:

Measured Grey Level Mean
Optical Density (Standard Deviation)
--------------- --------------------
0.04 55722 (350.3)
0.21 37201 (583.6)
0.34 26986 (318.4)
0.50 18445 (217.1)
0.69 12569 (148.0)
0.82 8296 ( 99.9)
0.96 5648 (106.5)
1.13 3797 ( 44.4)
1.28 2603 ( 32.7)
1.44 1772 ( 22.7)
1.59 1217 ( 18.2)
1.74 847 ( 13.4)
1.89 581 ( 9.0)
2.07 393 ( 6.1)
2.21 271 ( 4.3)
2.37 185 ( 3.2)
2.52 132 ( 2.7)
2.68 94 ( 2.5)
2.84 65 ( 2.1)
2.99 47 ( 1.8)
3.13 34 ( 1.6)
3.60 5 ( 1.1)

Here's a plot of mean grey level versus the measured optical density of
the step wedge phantom. The error bars indicate the standard deviation of
the grey levels within each wedge.

Since the scanner has a logrithmic response, it may be useful to plot the
logarithm of the mean grey levels versus the measured optical density. This
plot is pictured below.

Using simple regression to fit a line to the data, we get a slope of -1.07553, and a y-intercept of 4.80662. The equation for the line is:

y = -1.07553x + 4.80662
So, to convert a grey level (GL) value to optical density (OD), simply use the
following equation:

**Eq. 1** | OD = ( log(GL) - 4.80662 ) / -1.07553 |

Example: A grey level of 1217 maps to an optical density of 1.60045. Looking
at the table above, we see that a grey level of 1217 mapped to a *measured*
optical density of 1.59. The small discrepancy can be attributed to the noise in
the experimental measurement of the OD function, and the noise introduced by the
digitization process.