Flat-field correction

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20.309: Biological Instrumentation and Measurement

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Figure 1: Illustration of the effect of nonuniform illumination. The image appears darker at the edges because the illumination is not uniform.

Before you record any images, it is a very good idea to adjust your microscope optics to make the illumination is as uniform as possible. But even if you adjust everything perfectly, the intensity of the illumination will not be exactly the same everywhere in the field of view. In most cases, the illumination is brightest in the middle of the image, with a steady decrease toward the edges. Dirt or other flaws in the illumination system can also cause variation in the illumination. In a fluorescence image, the amount of light coming from a point in the sample is proportional to the fluorophore concentration multiplied by the illumination intensity: $ I_i = L_i C_i $. In other words, the recorded image is equal to the actual image multiplied by the illumination intensity at every point.

Another source of non-uniformity is the detector itself. The characteristics of every pixel are not identical. A reasonable model for the camera's response is $ P_i = R_{i} I_i + D_i + \epsilon_i $, where $ P_i $ is the pixel value recorded by the camera for the ith pixel; $ R_{i} $ is the responsivity of the ith pixel; $ I_i $ is the intensity of light incident on the ith pixel; and $ D_i $ is the dark level of the ith pixel; and $ \epsilon_i $ is a noise term that represents random observational error. The dark level and responsivity of each pixel are slightly different, so the camera will produce a range of output values even if the image is perfectly uniform or even completely dark.

These problems can be largely eliminated through a technique called flat-field correction or shading correction.

Correcting an image

The value of each pixel in the image is equal to $ R_i $ combines the effects of nonuniform illumination and pixel-to-pixel variation in the camera's response.

The goal of flat-field correction is to find $ I_i $ for each pixel. The formula for the correction is: $ I_i = \frac{P_i - D_i}{R_i} $. In order to do the correction, you need to find $ D_i $ and $ R_i $.

$ D_i $ can be found empirically by recording a dark image with the illuminator turned off. Because dark level depends on the exposure, gain, and binning settings, temperature of the detector, and so on…, it is important to take the dark image with identical settings as the source image. It's a good practice to record the dark image just before or after the source image. In order to reduce the noise in the dark image, it's a good practice to take multiple dark images and average them.