Flat-field correction

It is a standard calibration procedure in everything from personal digital cameras to large telescopes.

Flat fielding refers to the process of compensating for different gains and dark currents in a detector.

For handheld cameras, the screen could be a piece of paper at arm's length, but a telescope will frequently image a clear patch of sky at twilight, when the illumination is uniform and there are few, if any, stars visible.

The dark-current is the amount of signal given out by the detector when there is no incident light (hence dark frame).

The gain and dark-frame for optical systems can also be established by using a series of neutral density filters to give input/output signal information and applying a least squares fit to obtain the values for the dark current and gain.

The photographer typically takes 15–20 light frames and performs median stacking.

It may stem from beam inhomogeneity, gain variations of the detector response due to inhomogeneities in the photon conversion yield, losses in charge transport, charge trapping, or variations in the performance of the readout.

Also, the scintillator screen may accumulate dust and/or scratches on its surface, resulting in systematic patterns in every acquired X-ray projection image.

In X-ray computed tomography (CT), fixed-pattern noise is known to significantly degrade the achievable spatial resolution and generally leads to ring or band artifacts in the reconstructed images.

Fixed pattern noise can be easily removed using flat field correction.

While conventional flat field correction is an elegant and easy procedure that largely reduces fixed-pattern noise, it heavily relies on the stationarity of the X-ray beam, scintillator response and CCD sensitivity.

Indeed, detector elements are characterized by intensity dependent, nonlinear response functions and the incident beam often shows time dependent non-uniformities, which render conventional FFC inadequate.

In synchrotron X-ray tomography, many factors may cause flat field variations: instability of the bending magnets of the synchrotron, temperature variations due to the water cooling in mirrors and the monochromator, or vibrations of the scintillator and other beamline components.

A linear combination of the most important eigen flat fields can then be used to individually normalize each X-ray projection:[3]