# GainImaging Topics

## Gain

In CCD imaging, gain refers to the magnitude of amplification a given system will produce. Gain is reported in terms of electrons/ADU (analog-to-digital unit). A gain of 8 means that the camera digitizes the CCD signal so that each ADU corresponds to 8 photoelectrons.

The system gain of a Teledyne Photometrics camera is typically set so that the full well of the CCD matches the full range of the digitizer (at 1x gain). The camera’s gain can also be selected under software control to meet the needs of a given application. For example, the gain can be increased to 4x when the application is photon starved and a high-sensitivity mode is required. Alternatively, the gain can be reduced to 1/2x when the application is photon-shot-noise limited and a high SNR mode is required. Because gain refers to the amplification of a system and the gain reported in CCD imaging is actually inverse amplification, the meaning of gain is not entirely intuitive. As gain increases, the reported gain value decreases. For example, if the system gain (1x) is 8e-/ADU, then the high-gain (4x) mode would be 2e-/ADU.

A simple method to calculate the system gain is shown below:

1. Collect a bias image (zero-integration dark image) and label it “bias”.
2. Collect two even-illumination images and label them “flat1” and “flat2”.
3. Calculate a difference image: diff = flat2 – flat1.
4. Calculate the standard deviation of the central 100 x 100 pixels in the difference image.
5. Calculate the variance by squaring the standard deviation and dividing by 2 (variance adds per image, so the variance of the difference image is the sum of the variance of flat1 and flat2).
6. Calculate a bias-corrected image by subtracting the bias from one of the flat images and label it corr: corr = flat1 – bias.
7. Obtain the mean illumination level by calculating the mean of the central 100 x 100 region of the corr image.
8. The mean divided by the variance equals the gain: gain = mean /variance.

A more rigorous method is that of Mortara and Fowler (SPIE Vol. 290 Solid State Imagers for Astronomy (1981) pp. 28-33), which essentially involves repeating the above procedure for a series of illumination levels over the full range of the CCD full well. In addition, their method recommends collecting four or more flat images at each exposure level and averaging them to improve the precision of the measurement. The authors also provide the theory supporting the method. Another rigorous, excellent method that can be used to calculate gain is the photon-transfer technique of Janesick et al. (Optical Engineering Vol. 26 (10) (1987) pp. 972-980).