The CCD Image Sensor

CCD image sensors are linear, they have only a small non-linearity of a few percents.

Their transfer function on a log-log chart is always a straight line at 45 degree angle, 45 degree on the log-log chart is the same as gamma 1.0.

In the actual, physical values the transfer function of the CCD imaging sensor looks like this.

The slight difference in red, green and blue response show the effect of color-temperature, another color-temperature of the illumination would cause the lines to map on top of each other, the yellowish light from the normal incandescent lightbulb would give very strong response for red, much lesser response for green and very small response for blue channel.

The Chrome (color reversal film, slide)

Here is the transfer function of Kodak Professional Ektachrome E100s color-reversal film as a log-log chart, it was digitized from the sensitometry curve (pls see the gif, opens in another browser window) using Grafula3 software to numeric data for Excel.

In the actual, physical values the transfer function of the E100s chrome looks like this (the curves in reality are smooth, the ripple is from the digitizing process).

The x-axis of the linear chart is linearly related to the scene reflectances and scene luminances. It is linearly scaled by the exposure of the camera (exposure time and aperture).

The y-axis of the linear chart is linearly related to the RGB levels (of a linear working-space), it can be linearly scaled e.g. by the Levels dialog of scanner driver.

The inverse function of this curve will linearize the image data so that the full capture range (dynamic range of the chrome will be properly utilized.

As can be seen the chrome boosts up the midtones while compressing both the dark-end and the light-end.

Here is a closer view to the compression at the the dark-end, (again the curves in reality are smooth, the ripple is from the digitizing process).

Rather high quality scanner (low noise, high dynamic range) is required in order to extract the full range of the chrome.

The Negative film

Here is the transfer function of Kodak Professional Supra 100 color-negative film as a log-log chart, it was digitized from the sensitometry curve (pls see the gif, opens in another browser window) using Grafula3 software to numeric data for Excel.

In the actual, physical values the transfer function of the negative film looks like this, it has an extremely steep curvature, there is enormous compression in the light end and similarly enormous expansion in the dark end.

This is the reason why scanning of the negative film can not success, this is an extremely steep transfer function for the CCD image sensor that maps its linear capture range over this.

Again the inverse function of this curve will linearize the image data so that the full capture range (dynamic range of the film is properly utilized. Photographic paper has approximately such an inverse transfer function, it will convert this transfer function rather easily to a decently linear viewable image.

When the negative film is underexposed by about 2.5 f/stops there will be slight change for a CCD scanner to extract something useful from the negative film.

The higher exposure range that has almost a horizontal zero slope can be extracted only with the very best drum scanners.

As can be seen the blue information has the most flat transfer function, it explains the high blue channel noise experienced when scanning negative film.

The Photographic Paper

Here is the transfer function of Kodak Professional Supra III photographic paper as a log-log chart, it was digitized from the sensitometry curve (pls see the gif, opens in another browser window) using Grafula3 software to numeric data for Excel.

In the actual, physical values the transfer function of the Supra III paper looks like this.

Naturally the image information on the paper does not have this transfer function but the product of the transfer functions of the negative film and the photographic paper.