University of Illinois at Urbana-Champaign

16-Bit Analysis

The Leaf Scanner was characterized using a step tablet consisting of several sections of known optical density. The step tablet was placed in the scanner and scanned as a 4"x5" portrait B&W positive image, but this time the image was recorded in 16-bit format. The image produced was analyzed using NIH Image. This process was then repeated three more times, and the average pixel value obtained from the four scans was modeled as the function:

pv = 275 + ( 60000 / ( 10 ^ ( 1.3525 * OD ) ) )


where pv is the pixel value of the image and OD is the optical density of the step in the step tablet. Results are shown below.

Model for Leaf Scanner -- 16-Bit Data

The above data was then transformed to produce a linear graph of optical density as a function of pixel value. This conversion was accomplished with the following formula:

cpv = 0.7394 * log10( 60000 / ( pv - 275 ) )


where pv is the original pixel value and cpv is the converted pixel value. The transformed data was then fitted to a line. A plot of the optical density vs. converted pixel value and the corresponding line fit are shown below.

Transform to Linear for Leaf Scanner -- 16-Bit Data

As a check, this line fit was used to calculate the optical density from the pixel measurement data. Results are displayed in the table below. Values corresponding to optical densities greater than 1.65 were not included because they could not be seen on the screen for analysis in NIH Image.

Pixel Value Converted Pixel Value Calculated Optical Density Optical Density Deviation
53988.92 0.0355 0.04 0.04 -0.004
39777.25 0.1342 0.14 0.14 -0.005
29026.15 0.2362 0.24 0.24 -0.002
21050.88 0.3405 0.34 0.34 0.004
15321.55 0.4441 0.45 0.44 0.008
11453.41 0.5396 0.54 0.54 0.004
8532.39 0.6368 0.64 0.63 0.013
6165.75 0.7453 0.75 0.74 0.012
4654.62 0.8405 0.85 0.84 0.008
3466.13 0.9421 0.95 0.94 0.011
2626.01 1.0402 1.05 1.04 0.010
2011.48 1.1375 1.15 1.14 0.008
1535.98 1.2402 1.25 1.24 0.011
1190.91 1.3429 1.36 1.35 0.005
960.76 1.4358 1.45 1.44 0.009
775.97 1.5367 1.55 1.54 0.011
523.42 1.7619 1.78 1.65 0.128

As shown above, the model agrees with the actual data quite well.

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