Digital Camera Linearity
Bertho Boman


This report is the result of measurement discrepancies found during evaluation of a system to produce accurate camera profiles. In the process of verifying the setup I discovered a non-linearity problem.  Some difference between the channels is to be expected but not a sharp change in only one of the channels. I do not know if this problem is only occurring in my test camera or if I am seeing a basic problem that are common to many users.  As I learn more, I will update this article. It will be very helpful if readers can provide feedback on these problems.

Equipment and Setup

Camera Nikon D2H SLR
Lens Nikon AF NIKKOR 50mm  F 1.8 ”prime”
White Standard Optical standard traceable to NIST, 99% reflective from 400 to 900nm
Black Standard An opto-mechanical design with light traps and non-reflective internal surfaces”
Light Source Bowens Espirit 500 UV coated monolights with small 150mm reflectors
Computer Custom built PC running Windows-XP

Measurements and Data
For information about the "Perfect" black and white standards and measurements see the related report at: www.vinland.com/contrast.html The 50mm diameter White Standard was surrounded with a 150mm by 150mm white painted frame.   There was a black background completely filling the rest of the picture. The measurements were taken at night to avoid bright daylight conditions.  The target was illuminated with two strobes that were positioned at a 45 degrees angle to the target, 1.5 m from the target and the power setting was ¼.

The camera’s aperture was adjusted using the camera’s blinking high light warning.  It was set to just blink on the White Standard. The result was F18.  Then the aperture was changed to F20 before taking the pictures to make sure that no data was clipped.  The lights and settings were kept identical for the rest of the pictures. Speed and sensitivity was set at ISO 200 @ 1/125 second.  The camera sensor to target distance was 850mm.   The viewfinder shutter was closed for each picture to avoid any light leakage.

The pictures were taken in NEF format and converted to reduced size jpg and Tiff images in Phase One’s Capture 1 software using AdobeRGB workspace and white balancing on the White Standard and applying that setting to all remaining pictures.  They were slightly cropped.

All measurements were done in PhotoShop CS on the Tiff samples and after a 10 pixel Gaussian blur was applied to average any possible pixel to pixel variation.  The calculated average of the RGB values were used for the percentage calculations.

The White standard was measured and that value of 243/243/243 was used for the rest of the measurements as the 100% reference value.

Black + White
#1. GretagMacbeth Gray Scale Balance Card
White 232/ 236/ 235 96.4%
Gray 111/ 117/ 117 47.3%
Black 37/ 38/ 38 15.5%

Black + White
#2. DGC-150 Gray Card from Robin Myers Imaging
Gray 156/ 164/ 165 66.5%

Black + White
#3. GretagMacbeth ColorChecker
White 235/ 237/ 236 97.1%
Gray, Light 159/ 167/ 167 85.5%
Gray, Light/Medium 203/ 210/ 210 67.6%
Gray, Medium 111/ 119/ 120 48.0%
Gray, Dark 70/ 74/ 74 29.9%
Black 36/ 39/ 40 15.8%

#4. RGB Data Chart from the ColorChecker

The measured RGB values were plotted against a normalized X-axis of 16 to 96. Either the Green & Blue channels are compressing at the high end or the Red channel is peaking.

There is a significant change in white balance between the white targets and the gray ones.  It appears that something is non-linear in at least one of the channels.  I do not know if that is happening in the camera or the subsequent conversion from NEF to a picture.  I do trust the White Standard and it agrees well with the ColorChecker white patch.  Similarly, all the gray cards show a shift in white balance so I do not believe that it is caused by a defective gray card.
No further work has been done at this time to resolve this error but as time permit, I will do some further tests to understand the problem better.

This problem ought to significantly affect the accuracy of camera profiling.

Further Testing
My next step in the quest for accuracy is to finish the testing of an optically correct illumination system to be used while creating camera profiles and to write a description of profiling procedure. There are so many variables in profiling cameras and they often get mixed up or misunderstood. As a consequence there are claims that it does not work well to profile a camera or that it is useless.  I think that is because the variables are often not sufficiently controlled and the result is in some cases poor.

Bertho Boman
Vinland Corporation
11600 NW 20th Street
Fort Lauderdale
FL 33323
(954) 475-9093
Email: boman33 at vinland dot com