The Linear Intensity Space

The words "linear" and "calibrated" are or should be synonyms when the best possible accuracy is the target. But somehow the meaning of the word "calibrated" has deteriorated as one can set up an image manipulation system in several ways. 

One could also calibrate a clock in many ways but only one calibration setting will keep the clock on time. It is the same with image manipulation systems,  only one calibration setting will produce the images accurately, it is the linear intensity setting. 

This is basically dictated by the way the colors are handled, by mixing the primary- or secondary colors according to the linear tri-stimuli theory that all digital color imaging is based on. If the intensity distribution of these primary colors (or secondary colors in the printer)  is non-linear then the result of their mix will have non-linearity that affects to the whole color gamut. 

In addition all the tools and filters of every image manipulation software that affects to the intensity assumes that the system has been set up linearly. 

For instance if you create an gradient from pure white to pure black over e.g. 1000 pixel area, then the 50% gray level (level 128) will be put at the location of pixel 500 in the image-file. If your monitor is not linearly calibrated then you will see the 50% gray level elsewhere on the monitor. And when you print the image the 50% gray level is not there where you saw it on the monitor. This goes for all the tools and filters that affects to the intensity. For example the effect of UnsharpMask is not applied correctly on uncalibrated system. 
  
The Linear Intensity Space Requires that:

• the system is either ICC color-managed and a linear working space ICC profile is specified as the working-space in the editing software or in lack of the ICC color-management that the display of the image manipulation system is calibrated for linear reproduction of intensity.
  
  This way there will be no monitor compensation nor publishing channel related compensations buried into the image-file. The image-files produced on such system is said to be linear.
  
  
• the transfer characteristics of the various input devices needs to be known. If they are non-linear devices a compensation curve needs to created (and saved) in the appropriate dialog of the image manipulation software. For ICC color-managed system this is just an device profile.
  
  
• each image that is acquired from a non-linear input device needs to be brought into the linear intensity space as the first step of the image manipulation. For ICC color-managed system this is means either to Assign the device profile or to Convert from the device profile to the working-space profile.
  
  
• the transfer characteristics of all the different distribution channels or devices needs to be known. In some cases like printers they can be accurately measured by the human eye with the aid of a suitable calibration image. In other cases like Web distribution some average compensation curve for monitors needs to be selected. For each of the distribution channels a compensation curve needs to created (and saved) in the appropriate dialog of the image manipulation software.  For ICC color-managed system this is means to create the required profiles.
  
  
• as the last step of image manipulation and enhancement, each image has to be published for the distribution channel it is intended. In other words a copy of the image is created and the required compensation is then applied to this copy using the appropriate dialog of the image manipulation software, using the previously created compensation curve. 
For ICC color-managed system this is means to Convert from the working-space profile to the publishing space profile.
 
Shortly it looks like this:

Often the input device linearization is not needed since high-end digital cameras and scanners are linear already. They may have an adjustable gamma setting that needs to be set to 1.0 (linear). It is highly recommended to verify that the camera or scanner really has the linear mode before purchase.

Required Calibrations and Compensations Curves

The display unit

The display unit of the image manipulation system needs to be calibrated for linear representation of intensity levels. 

Cathode ray monitors (CRT) require Gamma correction that is done using the display driver card and its software or in absence of such system wide control the corresponding dialog of the image manipulation software has to be used. 

Liquid Crystal Displays There is no calibration mechanism specially for LCD's and TFT's so Gamma correction facility has be used if calibration is attempted. Some of the manufacturers try to tweak the transfer characteristics of these displays with some average gamma, some leave it without any consideration and some calibrate them linearly. There is no general rule for these display units, a gamma image can be used to measure the characteristics of these. 

Input devices

High-end CCD-cameras and scanners should not need any correction curves. They may have software controlled gamma control that should be set to 1.0. 

Consumer grade cameras and scanners may or may not have compensation for uncalibrated monitor. Often there is no option for the user to set the gamma space in these devices.
 

If a camera or a scanner only provides gamma compensated images then they are not suitable for accurate digital imaging. Such images are only good for direct viewing on CRT monitors, image enhancement of such images create difficult errors.

It is possible to remove the gamma compensation from the image but the original quality of the images is deteriorated already by the gamma compensation that was applied at acquire time. 

Even in case the acquire device only provides gamma compensated images the linear calibration can recommended. However before purchase of these devices it is important to verify that the device really has the linear mode (so that they can be set to gamma 1.0 and that this space actually is linear).
 

CCD devices have a property called black-current that is leakage current in the CCD well and can be (usually is) visible in weakly illuminated pixels. It is possible that the software of a CCD appliance is made to suppress the output of weakly illuminated pixels in order to reduce this noise. One should not try to compensate this since only the black-current induced noise would be revealed. 

Calibration (or measuring the transfer curve) of scanners and cameras can be done with a color input target such are the Kodak Q-60. Below is a scanned image of a target (Q60R1 Color Input Target, Kodak catalog #190-7914, about $30), it is a silver halide 5" x 7" print and it is a L*a*b target. (This target is also known as a reflective IT8 target). 



linear Q-60 scan compensated for gamma space 2.5 viewing.

Video-cameras, most often have built-in Gamma compensation. That is to say that even if they have a linear CCD-sensor the output signal has compensation for the television gamma. Images from video-cameras are usually acquired using a video grabber that can be set remove the gamma compensation. Some high-end video cameras can be set to gamma spaces 1.0,  1.67 and 2.22.

Video-grabbers should have a software control for adjusting the gamma, this is usually the "gamma" or "picture" setting, however it may be that the scale of this setting is not the actual amount of gamma. In this case it is rather difficult to find the value that produced linear images. If a calibration chart is available one can grab pictures of it and change the setting until a good match is achieved.

Output Devices and Distribution Channels

Dye-sublimation printers have usually versatile selection of compensation and color management settings and software. One may find out that these are good only for wasting the extremely expensive printing material. On a linearly calibrated system the color Management setting "linear" or "none" is most often the best starting point for calibrations for dye-subs. Calibration of dye-subs is rather specific for each brand/model so it is difficult to outline a general procedure. 

The dye-sub suffers from slight non-linearity (not Gamma) and from mis-registration of the three or four different printing layers. Part of the non-linearity of dye-subs is due to the dot gain, even if they are continuous tone devices. At lower saturation the dot only fills the center of the pixel area leaving the white paper surface on view at edges of the pixel area. Fully saturated pixels cover the whole pixel area but even then pixels do not have even intensity over their are, the center of the pixel area is more saturated than the edges, see some images about it. 

Lasers, ink-jet printers, offset-printing and all the other printing systems that produce different intensity levels by halftoning are in theory linear systems, halftoning just puts numerically determined distributions of pure color pixels and no color pixels next to each other (in a form of printing element) and the eye then does the averaging. In other words halftoning or dithering is a process of cheating the eye by changing the distribution of only two kind of basic elements (pixels), black and light. The human eye then averages this, producing the illusion of continuous intensity levels. 

Halftoning however suffers from the dot gain. Dot gain is the bleeding of the printing ink (dry or liquid) on the printing surface (paper or transparency foil) so that the dots are gaining more area than what is expected by mathematical calculation from the printers resolution. The value of the dot gain depends on the movement tolerance of the printing head, roughness of the printing surface, ambient humidity and on many other technical issues. 

It is easily understood that when then dot size changes from what was expected then the intensity level that is averaged by the human eye/brain changes also.  

Dot gain is typically in the range of 5% to 20% depending on the printer or printing method. Dot gain for a particular dot is either effective or masked, depending on the case if it lands over a white area or over on another dot.

Instructions for creating accurate dot gain compensation curves are provided on the Compensating the Dot Gain of Printers page. 

Sad to say most commercial grade printers usually have built in tweaking of their transfer curve in the printer driver software so that images that are viewed on uncalibrated monitors will print more acceptable. This tweaking deteriorates the image quality similarly or more than is the case with gamma compensated images.

On-Line publishing

On-Line publishing (like the www) is troublesome area since the monitor gamma of different brand/models/platforms varies greatly and chances also are that the images will also be printed where the dotgain should be compensated. 
Monitor gamma compensation is by rule employed for images that are meant for on-line publishing because the images are most often viewed on an uncalibrated monitor.

For PC platforms images needs to be compensated by gamma 1/2.5.
For Mac platforms images needs to be compensated by gamma 1/1.72.

Sometimes an average gamma of 1/2.2 is used for WWW publishing in attempt to enable viewing on both the PC and Mac platforms.

Some compensation curves for Photoshop

Below packet contains quite accurate Gamma compensation curves for Adobe Photoshop: Gamma correction curves for Photoshop, (gamma_curves.zip, 80kb) 
There are 211 gamma curves and 211 inverse gamma curves (*.acv) for gamma values from 1.00 to 3.10 in step of 0.01. They were written directly from Excel, from calculated data. However *.acv files allows only 16 control points. 

The Curves dialog also supports the file type "Map Settings" (*.amp) that allows the control for all the 256 levels. These are mathematically exact curves for the same range of gamma, from 1.00 to 3.10 and their inverse curves, as above. Gamma correction curves for Photoshop, (gamma_maps.zip, 246kb) 

With the inverse gamma curves a known gamma compensation can be easily embedded into an image file, this is useful when images that are created on a linearly calibrated system are to be published for on-line viewing, like on the web. 

Gamma curves can be used for linearizing an image that has a known file-gamma (in case images were created on an un-calibrated system the correct curve is gamma 2.5).