Further Examples of Camera Design ... Web Page
"Camera Design Using Locus of Unit Monochromats," paper for CIC 14 in pdf form
 Quan Optimal Sensors

 Locus of Unit Monochromats for Quan Optimal Sensors Locus Derived by "Fit First" Method
 Locus of Unit Monochromats for Quan Optimal Sensors 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
Nikon D1, DiCarlo's data
Quan's Optimal Sensors
Y = inv(OrthoBasis'*rgbbar) =

 0.0725 0.267 0.0376 0.0447 -0.31 -0.0543 0 0 0.138

Y = inv(CamOmega'*rgbSens) =

 0.0614 0.151 0.0375 0.198 -0.107 -0.0865 -0.0221 -0.0345 0.227

Y = inv(CamOmega'*rgbSens) =

 0.164 0.413 0.0748 0.393 -0.303 -0.118 -0.0221 -0.068 0.648

Column amplitudes =
0.0852      0.409      0.153
Column amplitudes =
0.208      0.189      0.246
Column amplitudes =
0.426      0.516      0.663

 Quan Optimal Sensors: LUM by FF Method, Projected into v2-v1 and v2-v3 planes

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.
 Quan Optimal Sensors: Orthonormal Basis and Fit to 2º Observer