What is Flat Field Correction?

This correction is achieved by applying the following operation to each pixel of the raw image:

CorrectedPixel = (RawPixel - Offset) * Gain

where both Offset and Gain coefficients are specific values for each pixel.

The calibration procedure evaluates the Offset and Gain FFC coefficients of each pixel by computing pixel data of two reference images: the Dark Image and the Flat Image

Important: the calibration procedure must be redone if any part of the system is changed, including the camera unit, lighting or optics equipment.

Dark Image Acquisition

The dark image (a.k.a. dark frame) is an image captured in the dark. Such image represents the dark current of the sensors, and is considered as a fixed bias that we want to eliminate when acquiring images in normal conditions. To obtain the dark image:

1.

Cover the lens with a cap.

2.

Acquire several images and compute the average response for each pixel of the array

Flat Image Acquisition

The flat image is an image of a uniform target covering the whole field-of-view. To obtain the flat image:

1.

Place a uniform target (white for color cameras) wide enough to cover the whole field-of-view

2.

Adjust the lens aperture and the illumination intensity to obtain the brightest possible image providing that no pixels are saturated.

3.

Acquire several images and compute the average response for each pixel of the array

FFC Offset Coefficients Calculation

For each pixel, the Offset coefficient is actually the pixel value of the Dark Image.

Note: This correction is also called dark-frame subtraction.

FFC Gain Coefficients Calculation

The Dark Image and the Flat Image provide enough data to compute the Gain coefficients of the FFC.

For this we define CorrectedPixel as the pixel value we consider to be correct for the flat image. Let's set this value as the average pixel value of the flat image (average(Flat)), corrected by the average of the dark image (average(Flat)). In the FFC terms, this gives:

average(Flat) - average(Dark) = (FlatPixel - DarkPixel) * Gain

This leads to the Gain value

Gain = (average(Flat) - average(Dark)) / (FlatPixel - DarkPixel)

The same computation is repeated (width * height) times, to cover all pixels of both flat and dark images. This results in a specific correction for each pixel of the image.

For color pixel formats, we have several ways of computing the value of average(Flat). In all cases, the Gain computation is repeated (width * height * componentsPerPixel) times to cover all pixel components, which results in specific corrections for each pixel component of the image.