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Every negative has certain base color, i.e. the color of unexposed areas. I want to know how to fraction this number out of my scans.

In pure math, this is nothing particularly strange, I assume that all colors are coded in RGB values between 0 and 1 and that in my scan result the base color B is multiplied with the color information C of the photograph. So to retrieve the original value C all I have to do is a pixel- and channelwise division by B.

Unfortunately, I don't know how to easily achieve this in PhotoShop. Is there any blending mode acting as division on the RGB values? Or any other operation doing so?

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https://helpx.adobe.com/photoshop/using/blending-modes.html

Divide

Looks at the color information in each channel and divides the blend color from the base color.

https://helpx.adobe.com/photoshop/using/channel-calculations.html

Channel Calculations

The calculation commands perform mathematical operations on the corresponding pixels of two channels (the pixels with identical locations in the image) and then combine the results in a single channel. Two concepts are fundamental to understanding how the calculation commands work:

Each pixel in a channel has a brightness value. The Calculations and Apply Image commands manipulate these values to produce the resulting composite pixels.

These commands overlay the pixels in two or more channels. Thus, the images used for calculations must have the same pixel dimensions.

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