1 Flat Field Correction

The Flat-field correction (FFC) is a method used to correct:

the differences of light sensitivity between the pixel sensors of a camera
some artifacts related to the optical system (e.g., non-uniform lighting and vignetting)

The goal is to correct the pixels of the captured (raw) images in such a way that when a uniform background is captured by the system (camera & lens), the resulting output image is uniform.

1.1 Formula

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

CorrectedPixel = (RawPixel - Offset) * Gain

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

The evaluation of the coefficients Offset and Gain requires a calibration procedure explained in the next paragraph.

1.2 Calibration

The calibration procedure to compute the coefficients is done in two steps:

Dark image acquisition

A dark image is acquired¹ by the system. This is typically achieved by covering the lens with the cap. The captured 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. This correction is called dark-frame subtraction.

CorrectedPixel = RawPixel - DarkPixel

For each pixel, the DarkPixel value corresponds to the Offset in the above FFC formula.
Flat image acquisition

A flat image is acquired² by the system. For example by capturing a flat (uniform) background, not too bright to avoid saturation and not too dark.

From dark and flat acquisitions, we have enough data to compute the Gain value of the FFC formula.

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)), corrected³ by the average of the dark image (average(Flat)). In the FFC formula 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.

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

1.2.1 Color Pixel Formats

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.

1.2.1.1 Handling pixel components individually

I.e. in RGB:

using average(Flat[Red]) for computing the Gain values of Red components;
using average(Flat[Green]) for computing the Gain values of Green components;
using average(Flat[Blue]) for computing the Gain values of Blue components.

1.2.1.2 Handling pixel components together

I.e. in RGB, using average(average(Flat[Red]), average(Flat[Green]), average(Flat[Blue])) for computing the Gain values of Red, Green and Blue components.

This way of computing the average (i.e. over the pixel components) results in FFC coefficients that also correct the balance between components. Therefore, depending on the quality of the uniform background used to acquire the flat image, the FFC can effectively perform a white balance correction.

2 Coaxlink

Some cameras have a built-in FFC module while other cameras do not implement this feature. The devices without that functionality can however be corrected by the FFC core of the Coaxlink card⁴.

The FFC core of the Coaxlink firmware corrects the pixels directly coming from the camera by applying the FFC formula using the coefficients (Offset and Gain) corresponding to their locations in the image. Because the correction happens at a very early stage in the Coaxlink pixel processing chain, the other pixel processing functions such as RedBlueSwap, LUT, and Bayer Decoding are performed on corrected pixels.

2.1 Coefficient format

The coefficients calculated in the calibration procedure can be loaded into the Coaxlink card, provided they are encoded as follows:

Offset and Gain values for one pixel component are packed together into a 16-bit little-endian value:
- Gain is encoded in UQ2.8 on bits 9..0
- Offset is a 6-bit unsigned integer on bits 15..10
Coefficients related to pixel component values are treated separately in the same sequence as the pixel components of the image. For example in RGB8 format, one pixel is encoded as 3 successive 8-bit values (Red, Green, Blue), therefore we need 3 successive 16-bit packed coefficients to correct one RGB8 pixel.

If the 16-bit packed coefficients are stored (in sequence) in a binary file (let’s say 'path/to/coefficients.ffc'), they can be easily loaded from a Euresys script by calling

require("egrabber://ffc/load")(grabber, 'path/to/coefficients.ffc');

where grabber is the script variable referencing the grabber to configure.

Note: such a binary file can be created by the Euresys sample application presented in the next paragraph.

3 Sample program (ffc-wizard)

Euresys provides the source code of a sample application, called ffc-wizard, that computes the coefficients and packs them in a binary file targeting the Coaxlink cards.

The purpose of this sample code is threefold:

guide the user through the calibration procedure;
provide a technical and practical translation of what’s described in this document;
provide building blocks for developing custom applications.

3.1 Building

The source code lies in a single source file: src/ffc-wizard.cpp. Building the application should be straightforward;

for Windows, there is a Microsoft Visual Studio project file ffc-wizard.vcproj;
for Linux and macOS, a Makefile is provided.

3.2 Usage

The wizard is a console application. The help message is displayed when the flag -h (or --help) is given:

> ffc-wizard.exe --help
Flat Field Correction Wizard
fcc-wizard [OPTIONS]

Options:
  --if=INT                 Index of GenTL interface to use
  --dev=INT                Index of GenTL device to use
  --ds=INT                 Index of GenTL data stream to use
  --average=INT            Number of images to average (default: 10)
  --roi_x=INT              Horizontal offset in pixels of ROI upper-left corner (default: 0)
  --roi_y=INT              Vertical offset in pixels of ROI upper-left corner (default: 0; ignored for line-scan)
  --roi_width=INT          Width of ROI (default: whole image)
  --roi_height=INT         Height of ROI (default: whole image; ignored for line-scan)
  --balance                Compute flat image average on all components rather than on each component
  --linescan               Force line-scan mode i.e. average image lines (automatically enabled for line-scan cards)
  --dark-setup=SCRIPT      Path to setup script for dark acquisitions
  --flat-setup=SCRIPT      Path to setup script for flat acquisitions
  --timeout=MS             Maximum time in milliseconds to wait for an image (default: 1000)
  --dark-histogram=FILE    Path to histogram html page of average dark image to output and open
  --flat-histogram=FILE    Path to histogram html page of average flat image to output and open
  --output-ffc=FILE        Path to coefficients output file (Coaxlink ffc binary format)
  --load-ffc=FILE          Load coefficients into Coaxlink coefficients partition (default: computed coefficients)
  --no-interact            Skip user interaction
  -h  --help               Display help message

Note: the ROI options allow defining a rectangular region to consider while computing averages,
      this is useful to eliminate pixels close to borders in images subject to vignetting.

Options details

Flags	Details
`--if`, `--def`, `--ds`	the indexes of the GenTL modules that identify the data stream to use (and/or to configure)
`--average`	the number of images to acquire for dark and flat acquisitions; only the average of those acquisitions is further used in the calibration procedure
`--roi_x`, `--roi_y`, `--roi_width`, `--roi_height`	an optional rectangular region to consider when computing the average pixel value of the flat image (`average(Flat)`); this impacts the evaluation of the gain value for each pixel
`--balance`	enables the white balance; i.e. whether the coefficients of color pixel components are computed to balance the component values or not; obviously, this requires the flat background used to acquire the flat image(s) to be as close as possible to a true gray (for which all RGB components would have identical values)
`--dark-setup`, `--flat-setup`	optional configuration scripts to run before dark and flat acquisitions
`--dark-histogram`, `--flat-histogram`	optional; path to output file showing the histogram of dark and flat image pixel components; this gives a visual overview of the dark current variations as well as the variations in the flat image
`--no-interact`	normally the wizard waits for the user to setup the system before starting the dark and flat acquisitions; when this flag is used, the wizard does not wait for the user (nor does it open the created histogram html pages)

3.2.1 Example

Here is an illustrated example that generates FFC coefficients (written to the file coefficients.ffc) using the white balance functionality. The command to run from a console window is the following:

The program starts and tells you what to do:

You can prepare your setup for the dark acquisitions and press Enter when you are ready. It will then acquire the series of dark images and display the instructions for the next step

You can prepare your setup for the flat acquisitions and press Enter when you are ready. It will then acquire the series of flat images, compute the corresponding coefficients and write them to the file coefficients.ffc

Later on you can load the coefficients from the genicam-browser for example, by running the load-ffc script as follows:

Then you can select the previously created file coefficients.ffc

From that moment, the coefficients are loaded into the Coaxlink memory and the FFC processing is enabled.

3.3 Design

The calibration procedure as well as the packing of the coefficients is controlled by the main function ffcWizard.

ffcWizard tasks

Task	Done by function
acquiring a series of dark images to build an average dark image	`acquireImages`
acquiring a series of flat images to build an average flat image	`acquireImages`
computing the `gain` values for each pixel component	`computeGain`
using the dark pixel component values as `offset` values	`computeOffset`
packing `offset` and `gain` values into 16-bit little-endian values	`packCoefficients`
writing the packed coefficients into a binary file	`savePackedCoefficients`

3.4 Customization

The sample application already supports a few common pixel formats: Mono, RGB, RGBa and Bayer.

Limitation: to limit the complexity of the sample application, we consider (for pixel formats with several components per pixel) that all components have the same size. Supporting pixel formats with different component sizes is still possible by updating the functions addImage and addComponents.

To support a new pixel format (under the condition of the previous limitation), we need to modify two functions:

Image::getComponentsPerPixel, to return the number of components per pixel for the new format identified by its PFNC name
Image::getComponentFilters, to return a std::vector of ComponentFilter objects describing how the pixel components of the new format (identified by its PFNC name) are positioned in the image

The ComponentFilter objects are used to separate the processing of the different pixel components while evaluating the Gain and Offset values. For example, in RGB format (as described in Color Pixel Formats), the FFC coefficients related to the Red components are computed using the Red components from the dark and flat images.

Please see the source code of Image::getComponentFilters for details about pixel component layout configuration.

It’s recommended to use the average of several dark acquisitions↩
It’s recommended to use the average of several flat acquisitions↩
dark-frame subtraction ↩
Available in some Coaxlink card types and firmware variants↩