Links:
Further Examples of Camera Design ... Web Page
"Camera Design Using Locus of Unit Monochromats," paper for CIC 14 in pdf form
Jim Worthey Home Page
Foveon X3 Sensors, Without Prefilter
Foveon X3 sensors

Locus of Unit Monochromats for Foveon X3 Sensors Without Prefilter
Locus Derived by "Fit First" Method
Locus of Unit Monochromats for Foveon X3 Sensors Without Prefilter
Locus Derived by "Fit First" Method
Usage note: To see some preset views, click 'view' arrows below the 3D picture.

In the virtual reality picture above, the Locus of Unit Monochromats for the human 2° observer is drawn in the usual way, as the edge of the multicolored surface. The LUM of the camera is indicated by spheres. The short arrows indicate the transition from the camera's LUM itself to the best fit, so the arrow tips are the best fit curve. If the spheres lay right along the human LUM, that would mean that the camera fulfills Maxwell-Ives. In that case, the camera's LUM would be the best fit, and the arrows would have zero length.

The camera LUM is derived by the "fit first" steps:
  • Find a best fit to human LUM by a linear combination of the camera's sensor functions. The best fit functions will look more or less like achromatic, red-green, blue-yellow, but will not be an orthnormal set.
  • Preserving that sequence, orthonormalize the functions by the Gram-Schmidt method .
  • Combining those 3 functions into a 3-dimensional graph gives the camera LUM, indicated by spheres.
  • Yes, the best fit found as an intermediate step is the same best fit indicated by the tips of the short arrows.
The steps just specified all result in adding and subtracting of the camera sensor functions. We can then ask if the red-green function is really made by subtracting the camera's green function from its red function, and so forth. Such questions are answered by the transformation matrix relating the camera's orthonormal basis to the sensor functions. Let the camera sensors be the columns of array rgbSens, and CamOmega be the camera's orthonormal basis. Then
CamOmega = rgbSens*Y, where
Y = inv(CamOmega'*rgbSens)    .
The tiny apostrophe, ', denotes matrix transpose. The transform Y can be found for any camera, and indeed for the eye itself.
2° observer himself
Foveon X3, no filter
Prefiltered Foveon X3
Y = inv(OrthoBasis'*rgbbar) =

0.0725
0.267 0.0376
0.0447 -0.310 -0.0543
0
0
0.138

Y = inv(CamOmega'*rgbSens) =
 
0.962 5.56 1.919
2.41 -6.98 -5.72
-0.783 1.61 5.84

Y = inv(CamOmega'*rgbSens) =

-0.544 9.40 2.67
5.61 -13.1 -7.86
-1.72 3.56 7.99

Column amplitudes =
     0.0852      0.409      0.153
Column amplitudes =
      2.71       9.06       8.40
Column amplitudes =
      5.89       16.5       11.5


Foveon X3 Unfiltered: LUM by FF Method, Projected into v2-v1 and v2-v3 planes
LUM of Foveon X3 without filter, proj. into v2-v1 plane.
LUM of Unfiltered Foveon X3, proj. v2-v3 plane.

In the graphs below, the thicker functions on the left are the basis for the camera's LUM, shown above by spheres. The thicker functions on the right are the basis for the best fit curve, shown above as the tips of arrows.
Foveon X3 Unfiltered: Orthonormal Basis and Fit to 2º Observer
Foveon X3 Orthonormal Basis by FF method
Foveon X3 best fit to human 2-degree observer

Links:

Further Examples of Camera Design ... Web Page
"Camera Design Using Locus of Unit Monochromats," paper for CIC 14 in pdf form
Jim Worthey Home Page

Page last updated 2006 October 2, 12:44