Dynamic Range Compression
Dynamic range is the ratio of the largest to the smallest value of a measured signal. In photography it commonly refers to the ratio of the brightest element of a scene to the darkest. An outdoor scene on a very foggy day commonly has very little difference between the brightest and darkest elements, which is known as a low dynamic range scene. In contrast, an indoor scene with a visible sunny sky through a window is known as a high dynamic range scene.
The dynamic range of a scene can easily exceed the dynamic range of the "sensor" that captures the scene. The human visual system has an adaptive and wide dynamic range (you can see faint stars at night but also bright skies during day). This is very different from the fixed, lower dynamic range of your camera sensor and the (usually even lower) dynamic range of your monitor. As such, photography and image processing needs to deal with mapping high dynamic ranges to lower ones.
In general there are two ways to handle dynamic range changes: either discard a portion of the data outside the destination range (e.g. clipping highlights), or compress the data so that it fits the destination range. The Dynamic Range Compression tool uses the latter approach based on the Gradient Domain High Dynamic Range Compression algorithm developed by R. Fattal and coworkers. This algorithm is often simply referred to as "Fattal", e.g. in Luminance HDR.
The algorithm uses two parameters to control the compression (α and β) which can be tuned by the "detail" and "amount" sliders of the tool, respectively. The tool operates in RGB space and is applied right after Noise Reduction and Haze Removal, but before other tone curve adjustments such as the Exposure controls.
N.B. There are alternative ways of compressing the dynamic range using other tools. The simplest would be a negative contrast value in the Exposure tool to reduce (or rather to redistribute) the dynamic range, however the effect would most likely appear flat and unappealing. A curve gives more control over the process, but may need a lot of fine-tuning.
Use this tool when the dynamic range of the photographed scene is too high to be reproduced on your monitor in an aesthetically pleasing way, that is when you find that the difference between the dark tones and the bright tones (the contrast) is so strong that there is a lack of detail in those areas.
Heads-up panorama stitchers! The effects of this tool depend on the dynamic range (and histogram) of the image being edited. If you are processing a series of images intended for stitching, where each image contains a section of a scene adjacent to the one before it, even if you were to apply identical parameters to these images using this tool, the end results would not be consistent - there would be sudden changes in brightness between adjacent images. Do not use this Dynamic Range Compression tool on the source images. If you need to compress the dynamic range across a series of images in a consistent way, use a curve instead. You can, however, use this tool on the stitched panorama.
Sets the strength of the compression. Higher values lead to a narrower dynamic range (you can easily see the effect by observing the histogram).
Sets how much local contrast is preserved. Positive values reduce the compression in favor of more contrast, negative values reduce the contrast.
Biases the compression towards the shadows or highlights, effectively functioning as an exposure compensation.