Accurate Image Manipulation for Desktop Publishing

Gamma Terminology and Calculations

The gamma is sometimes a bit difficult to understand because there are a many different terms in use but most importantly because of the over an half-century old convention:

Most often the higher than 1 value is mentioned even if the reciprocal value is actually meant.

This is done simply because it is easier to speak about the higher than 1 values than their reciprocal value and there is usually no possibility for confusion.

So, for people who are new to the wonderful world of digital imaging the below table may offer some help.

After the table there is some examples about calculating the with gammas, but first one needs to know what a gamma value in various places means.

This:	Means:
Gamma function or gamma equation or gamma formula	In the normalized form the gamma function is: output = input ^ gamma Gamma is the exponent of the above power-law function. When gamma=1.0 the function returns output=input, so there is no changes to the image, gamma 1.0 is the same as linear. When gamma > 1.0 image turns more dark. When gamma < 1.0 image turns more light. Normalized form means a range from 0...1. So e.g. for the 8-bit/color images the levels are divided by 255.
Gamma correction	an image processing system or a display is said to be gamma corrected when it has been calibrated linearly (to gamma 1.0). Note that the term "gamma correction" is sometimes incorrectly used where "gamma compensation" should be used.
The native gamma of CRT monitor is 2.50	the CRT monitor applies the gamma function with gamma=2.5 over the data (makes images darker). This is the electrical property of the CRT tube, all of them. In order to show images properly on the CRT monitor the gamma function with gamma=1/2.5 has to be applied over the data, somewhere in the imaging path. The look up table in the display driver is usually used for CRT calibration but an application can also modify the image data itself. CRT monitors are said to be in gamma-space 2.5.
Gamma-space	the gamma value is told but the user needs to understand how to take it, either as it is or as the reciprocal value. There usually is no problem in understanding this.
Image-gamma or File-gamma	it is said that an image has an image-gamma when the image data has been gamma compensated, in other words the gamma function with some gamma value is applied over the data. When the gamma function with gamma=1/2.5 is applied over the image data (makes image lighter) that image is said to have image-gamma or file-gamma of 2.5. Also that image is said to be in gamma-space 2.5.
*Gamma compensation*	Same as the file-gamma. Image is said be gamma compensated when the gamma function is applied over the image data. When the gamma function with gamma=1/2.5 is applied over the image data then the image is said to be gamma compensated for gamma-space 2.5 viewing.
*The gamma value in the acquire dialog of scanners*	the scanner applies the gamma function with gamma=1/gamma over the data. If the gamma value in the scanner acquire dialog is 1.0 then it applies the gamma function with gamma=1/1.0 (does not change the image data, provides linear images). If the gamma value in the scanner acquire dialog is 2.5 then it applies the gamma function at gamma=1/2.5 (makes the images lighter).
*The Desired Gamma* in AdobeGamma utility**	The look up table in the display driver is adjusted so that the monitor (or the system) appears to have the Desired Gamma instead the native CRT Gamma 2.5. When the Desired Gamma is 1.0 then the system is calibrated (linearly). When the Desired Gamma is 1.72 then the system is calibrated to the Mac default gamma space.
The gamma value in Photoshop RGB setup	Photoshop is set into that gamma-space instead of the native CRT gamma-space or to the Desired Gamma space that is set by AdobeGamma utility. Gamma 1.0 in Photoshop RGB setup means that Photoshop is linearly calibrated no matter how the system is calibrated by the AdobeGamma utility. (be aware fo the slope limiting issue). Gamma 2.5 in Photoshop RGB setup means that Photoshop in set to the native gamma-space of CRT monitors no matter how the system is calibrated by AdobeGamma utility.

Gamma calculations

Since the gamma function is power law fucntion it is easy to calculate with it. Subsequent gamma transformations can be combined by simply multiplying all the the gammas on the workpath. But, one needs to use the correct, actual values, not the colloquially mentioned greater than one values.

The product of all the gammas in any imaging path must produce linear representation of light intensity in order the images to appear naturally. So the result must be 1.0. We will now see how it goes by examples:

*Typical gamma space workflow on uncalibrated PC.* Not recommended please see the gamma errors section
1.	Acquire with gamma 2.5 in scanner driver	The scanner driver applies gamma 1/2.5 over the data.
2.	edit in gamma 2.5 space	the gamma-space of the image is not changed due to the editing.
3.	output to CRT monitor on PC	CRT monitor applies gamma 2.5.
		*Product = 1/2.5 2.5 = 1.0**

*Typical gamma space workflow on uncalibrated Mac.* Not recommended please see the gamma errors section
1.	Acquire with gamma 1.8 in scanner driver	The scanner driver applies gamma 1/1.8.
2.	edit in the uncalibrated Mac gamma space (1.72)	the gamma-space of the image is changed to 1.72 by image editing since Mac gamma actually is 1.72.
4.	apply output compensation	since it is going to CRT on PC system gamma 1/1.45 is applied over the image data.
3.	output to CRT monitor on PC	CRT monitor applies gamma 2.5.
		*Product = 1/1.72 1/1.45 * 2.5 = 1.0**

*Typical Linear Space workflow*
1.	Acquire with gamma 1.0 in scanner driver	The scanner driver provides linear (gamma 1.0) images.
2.	edit in Linear Space (gamma 1.0 space)	the gamma-space of the image is not changed due to the editing.
3.	apply output compensation over a copy of the final image	since it is going to CRT on PC system gamma 1/2.5 is applied over the image data.
3.	output to CRT monitor PC	CRT monitor applies gamma 2.5.
		*Product = 1.0 1/2.5 * 2.5 = 1.0**

*Accurate and actual Linear Space Workflow in General*
1.	Acquire linear images (when ever possible).	Some acquire devices particularly the consumer grade digicams do not provide linear images (they do not provide any possibility to change their transfer function). In addition they do not provide images in any gamma space either, their transfer function is arbitrary. Such images are linearized in step 2.
2.	Apply input calibration to bring the image accurately into the working-space (gamma, color-space and color-temperature).	This could happen automatically by an ICC/ICM profile but is most often applied by an Action (with predefined Curves, Channel-Mixer and Hue-Saturation operations that are created with a Color Input Target).
2.	Edit in The Linear Space (gamma 1.0, known color-space and known color-temperature) like Trinitron, D6500.	The gamma-space of the image are not changed due to the editing.
3.	Save the final original.	Important for re-use and sending to a different output device, for further editing etc.
4.	Apply output compensation over a copy of the final image.	if it is going to CRT on PC then gamma 1/2.5 is applied over the image data. If the working-space is Trinitron, D6500 then color-space and color-temperature need no conversion because Trinitron, D6500 is what most of the the monitors use/have. if it is going to CRT on uncalibrated Mac then gamma 1/1.72 is applied over the image data. If the working-space is Trinitron, D6500 then again color-space and color-temperature need no conversion. If it is going to a peripheral printer then output compensation could happen automatically by an ICC/ICM profile but is most often applied by an Action (with predefined Curves, Channel-Mixer and Hue-Saturation operations that are created with a Color Input Target).

Accurate Image Manipulation for Desktop Publishing