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Multi Slope

Linear exposure: the dark parts are underexposedLinear exposure: the dark parts are underexposed
Linear exposure: the bright parts are overexposedLinear exposure: the bright parts are overexposed
Exposure with two different times: dark and bright regions are correctly exposed.Exposure with two different times: dark and bright regions are correctly exposed.

Multi Slope - The idea

The monochrome cameras that are typically used in everyday image processing offer a graylevel dynamic of 8 bit/pixel. A graylevel of zero usually means 'black', while 255 represents 'white'.

The graylevel of a pixel represents the number of photons ('luminance') that are collected by the image sensor at this position. The user-defined exposure time determines the period in which the image sensor is photosensitive.

All CCD image sensors - as well as many CMOS images sensors - have a liner relationship between the number of photons and their graylevel. This is a desirable feature for many applications.

If the luminance difference across an image is larger than the usual graylevel dynamics of 8 bit, we run into the problems shown in the images on the top right hand side. Adapting the exposure time to the dark image parts leads to overexposure of the bright ones and vice versa.

Multi-Slope image sensors detect pixels that could easily become overexposed. They reset their graylevels back to a user-defined value to re-expose these pixels only. The length of the second exposure must also be defined by the user. Ideally, it should stop just before the brightest pixel becomes overexposured. In this manner, we obtain the results shown in the third image shown on the right hand side.

Multi Slope - The realization

To understand the Multi-Slope procedure we only need to have a closer look at the exposure of one image line (see image at the right hand side). The line simply consists of 8 pixels with an index from 0 to 7. These pixels are encountered by a constant flow of photons with intensities from 12.5 per cent to 100 per cent.

Let us assume that after an exposure time of 200µs, the pixels hold graylevels from 50 to 400. But since we only have a graylevel dynamic of 8 bit, pixel 5, 6 and 7 are not able to achieve the correct graylevels. They are saturated with the graylevel 255.

Therefore, the first step of the Multi-Slope procedure defines a reduced exposure time (basic exposure time). In case of our example we stop the exposure after 150µs. Now only pixel 6 and 7 are saturated.

The second step defines the graylevel as of which the second exposure is to start (reset value). Graylevels that are higher than this reset value are set back to it. In case of our example we choose the reset value 180.

The third step continues the exposure of the pixels that have been reset. In doing so we have to choose the time at which the brightest pixel remains just below the saturation (35µs in our example).

Naturally, it would also be possible to reduce the exposure time even more and to follow with two or more reset steps. For many applications, however, one reset step is adequate (as it has been shown in our example). In such case we also use the term 'Dual Slope'.

Please note: The reset value as well as the exposure time have to be adapted by the user to the lighting conditions. Hence, they have to be static. Moving scenes or triggers with variable exposure times are therefore not suitable for a Multi-Slope procedure.

Pixel index:Pixel index
Number of photons ('luminance'):Number of photons ('luminance')
Graylevels after an exposure time of 200µs:Graylevels after an exposure time of 200µs
Graylevels in case of a dynamics of 8 bit:Graylevels in case of a dynamics of 8 bit
Graylevels after an exposure time of 150µs:Graylevels after an exposure time of 150µs
Reset of all graylevels > 180 back to 180:Reset of all graylevels > 180 back to 180
Graylevels after another 35µs of exposure:Graylevels after another 35µs of exposure
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