Andrew Reed : Giss Directory
Each page linked by the directory on the left is composed of a group of 12 images. Each group was derived from two primary images shot with a tripod mounted Nikon digital camera fitted with a circular polarizing filter. The object was to graphically illustrate the degree of polarization defined by:

|A-B| ÷ A+B

Initially, exposure was checked using a Spectra P251 light meter with the circular polarizing filter fitted over its sensor. These readings (on axis & off axis) were compared to those provided by the built in light meter in the Nikon under identical conditions and were found to correlate perfectly.

The images were processed in Adobe's Photoshop CS4 v11 using built in layer blending options.

|A-B| is directly available ("difference".) This checked out empirically using quantified single color samples in two test layers and was found to calculate the difference in bit values between layers.

A+B is similarly available directly ("Linear Dodge".) This was evaluated by using two quantified single color layers just as was used for the previous operation. It simply adds together bit values. This posed a problem in that full range exposures clipped up to 50% of the summed data. This issue was addressed by applying 50% linear compression to both images prior to processing so even if original data contained bit values of 255 in both layers, the summed values would not exceed 255. All processing for images in the compressed groups used compressed data for all steps in the process. Similarly, all steps in the uncompressed groups, used uncompressed images for all steps in those processes. Clipping is almost always very obvious in the uncompressed summed images indicated by washed out highlights.

Photoshop does not have a division function so division was derived from "Inverse" followed by multiply.

The inverse function is straightforward. It simply creates an image similar to a photographic negative (without the orange color mask) ie all values of 255 become zero, 0 becomes 255. Inverse was applied to the summed (∑A,B) layer to create a new 1/∑A,B layer.

"Multiply" is a bit trickier. Multiply does multiply both layers together but then divides by a scaling factor of 255 which is used to bring the multiplied values back down to earth (to within the 0 to 255 scale.) The ∆B,A layer was positioned above the 1/∑A,B layer. Multiply was then applied to the ∆B,A top layer. To remove the scaling factor, a "Levels" adjustment layer was applied to the multiplied layers. The levels were then adjusted down to 20. Adjusting all the way to zero caused an excessive degree of posterization and while this result may be mathematically correct, the amount of detail lost and the aesthetic result provided some justification for artistic license. The uncompressed series were provided for reference.

The images on the pages linked on the left are arranged as per the chart below. The images derived from uncompressed images are posted in the left columns. The images derived from compressed images are shown in the right columns.

* "PS" = Adobe Photoshop CS4 v11


50% linear compression

A=polarizing filter aligned with lightsource ploararizationA compressed
B=polarizing filter set at 90° with respect to the axis of lightsource ploararizationB compressed
∆B,A=mathematical difference between A & B (PS "Difference")∆B,A compressed
∑ A,B=sum of A + B (PS "Linear Dodge")∑ A,B compressed
1÷∑ A,B=inverse of sum of A+B (PS "Inverse" applied to previous step.) 1÷∑ A,B compressed
∆B,A÷∑A,B=degree of polarization (PS "Multiply" applied to 2 previous steps with an offset of 235 applied over the product. The difference layer was always the top layer and was always the layer to have the multiply fuction applied.∆B,A÷∑A,B compressed