Non-Uniformity of Sensitivity Response (Flat-Field Correction)

(Note: The approach described to calibrate and correct for the flat-field response has been shown at the ESRF to be able to produce high quality data when used in conjunction with a technique to produce smooth flood-field illumination. Such a technique has been suggested by Jean-Pierre Moy using fluorescence from elements held in an amorphous lithium borate glass [23].)

Owing to geometry, and artifacts of manufacture, the sensitivity of different areas of the detector may vary. This variation may be a low frequency effect e.g. geometry effects, or may be high frequency e.g. pixel to pixel sensitivity differences in a CCD chip. With the assumption that the effect of the point spread function is not important, this can be calibrated by uniform exposure of the detector [35]. It is necessary that the error owing to counting statistics is less than the required accuracy of the calibration e.g. if 1% accuracy is required in the calibration image, then a minimum of 10000 true counts per pixel are necessary.

In practice it is quasi impossible to satisfy the two requirements. Any source which is close enough to give a reasonable flux will not give completely uniform response. If the source is an isotropic point source then the non-uniformity may be a simple geometrical effect. In many cases a point source is required as the sensitivity of the detector will change not only as a function of the detector position, but also as a function of (3-D) source position. In such a case the way to calibrate the detector for a diffraction experiment is to have a point source at the sample position.

Unfortunately, we have not found convenient X-ray sources which are isotropic at the 1% level. Thus, we need to characterise the source distribution. With the assumption that the sources are at least circularly symmetric the intensity distribution of the sources has been characterised using a zero-dimensional detector on the two-theta arm of a diffractometer.

Three different types of flood-field ³⁵sources have been used, each with advantages and disadvantage:

• Radioactive sources give a reasonably smooth distribution and are easily portable, allowing source rotation to ensure circular symmetric intensity distribution. They offer only low count rates and are only conveniently available in a limited range of energies. Over-night exposures are necessary.

• Amorphous diffuse scatterers can give reasonable count rates at the required energy provided a synchrotron source is available, but often contain unwanted structure in the angular intensity distribution.

• Fluorescent cells containing a solution of the fluorescent material can be very nearly isotropic sources at $90^{o}$ to the illumination and can give reasonable count rates with a synchrotron source. However, the energy will always be slightly lower than that of the incoming radiation. We have found that Bragg scattering structure can be minimised by using lithium borate glasses doped with the fluorescent material [23]. These glasses may be thin and machined parallel, and may be mounted in the sample position, orthogonal to the beam. As they are solid, there is no problem of evaporation, and there emission distribution does not change with time.

With synchrotron sources polarisation will cause the distributions of any Compton scattering component not to be circularly symmetric, but this effect can be calculated and corrected. Having calibrated the source intensity distribution, the recorded flood-field image may be corrected for source anisotropy, polarisation, geometrical $\frac{1}{r^2}$ fall-off, and any absorption effects.