The Transfer Curve

The transfer curve is a plot of the square of the noise (variance) in an image after correction for flat-field effects versus the mean counts. It was first developed as a tool for investigation of CCD properties by Janesick (1987) and is used to measure the CCD conversion factor in electrons/ADU.

At illumination levels less than saturation, the variance of the signal in electron units, is given by:

where is the noise in the signal and is the readout noise in electrons. Assuming Poisson statistics, is the signal in electrons and is equal to the illumination level in electrons, which is the illumination level in ADU, , multiplied by the CCD conversion factor (or, imprecisely, the gain), g, in electrons/ADU. Similarly, is the standard deviation of the signal in ADU, , multiplied by g. Thus:

or

Therefore, the slope of the plot of the variance of the signal in ADU, , versus the mean counts, , is the inverse of the CCD conversion factor.

The readout noise is obtained from the square root of the y-intercept, which is simply the variance of the signal in a bias frame, divided by the conversion factor.

Note: at high count levels, the transfer curve levels off and may turn over. This is because the system has become saturated. Saturation may be defined in either of two ways.

• Digital saturation - the CCD, while still accumulating charge in linear proportion to the illumination level and delivering it to the output amplifier upon readout, is producing signals which are above the dynamic range of the analogue-to-digital converter. Such pixels will be measured to have a content equal to the maximum value delivered by the converter (32768 ADU in a 15-bit converter), but will have contained more charge. The variance of a fully saturated image is 0.
• Analogue saturation - individual potential wells of the CCD are filled to their limit. Any further charge generated by incident light will spill over into neighbouring pixels of greater well depth, primarily in the vertical direction (an effect known as ``blooming''). Note that the response of the CCD may still be apparently linear, but the variance no longer increases linearly with signal as the unconstrained, excess charge is smeared across the image. The response will start to level off and the variance to decrease with increasing signal when the majority of potential wells (pixels) are filled with signal electrons.

Normally, the system gain should be set so that digital saturation is encountered at signal levels less than analogue saturation.

• Transfer curves: Data Required
• Transfer curve: Reduction Procedure