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Looking at the EXIF tags on my photos, it seems most of them have a tag for "Gain Control". It seems this is set as either Low gain up or High gain up, or sometimes None.

The value of the tag seems to vary, even on photos taken in similar conditions, or even photos taken one after the other. I am usually using auto or P mode, but sometimes aperture priority or shutter priority, does this affect it?

So what does the "Gain control" mean? What effect does it have on my photos?

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The Gain Control is for "Control of CCD signal amplification" (so it's close to what ISO rating is for).

In EXIF 2.2, you have:

Gain Control 
Value             Abbrev       Num          Meaning 
-------------------------------------------------------------------- 
none              n            0            "None" 
low-gain-up       lgu          1            "Low Gain Up" 
high-gain-up      hgu          2            "High Gain Up" 
low-gain-down     lgd          3            "Low Gain Down" 
high-gain-down .  hgd          4            "High Gain Down" 
--------------------------------------------------------------------

Source

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Gain is the analog amplification of the voltage from the sensor before it is digitized. In a CMOS sensor a particular gain level can be applied to each line of pixels as they are read. The EXIF field is supposed to represent the "average" gain applied to all lines.

"low gain" means that the native optimal sensitivity of the sensor is being used and the dynamic range of the sensor is maximized. Up or Down is whether the average low gain setting is above or below the optimum.

"high gain" means that the sensitivity of the sensor is being boosted. For example, if the sensor has a native ISO of 200 and the amplifier is increasing this to anything above 200 (300, 400, 600, etc), then high gain is in use. When high gain is active, then the potential dynamic range of the sensor is reduced. Note that in a low light situation, using high gain may effectively increase the dynamic range of the captured image. As with the "low gain" setting, "up" or "down" refers to whether the average adjustment over all the lines is over or under the norm.

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On page 43 of the Exif 2.2 specification you can see the following description of the GainControl tag:

This tag indicates the degree of overall image gain adjustment.

Tag     = 41991 (0xA407)
Type    = SHORT
Count   = 1
Default = none

0 = None 
1 = Low gain up
2 = High gain up
3 = Low gain down
4 = High gain down
Other = reserved

Curiously, earlier in the specification (page 25) the same tag is defines as having type RATIONAL rather than SHORT. I'm not sure why that is. It may be a mistake in the document, or that the format was changed in different versions of the spec, or even that the format changes depending upon the IFD.

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