In reality, dark frames contain the unwanted baggage of a bias frame. To get at the thermal electrons, you must make a bias frame and subtract it from the dark frame:

When you perform the subtraction, the bias level, Bx , the fixed-pattern bias, (BFP)x y, and the thermal electrons that accumulate during readout, tROdxy, are indeed removed. However, a real-world thermal frame contains not only thermal electrons and thermal noise but also readout noise from two readouts plus noise from two doses of unpatterned interference. The noise adds in quadrature; so, for example, two readouts produce Jl times the noise of a single readout:

(THERMAL)^ = ~{tdx,y +<5^+ J2gko + Jl(<5m)x,y} . (Equ.6.12)

When the integration time is long enough for several thousand thermal electrons to accumulate, oTE dominates the other noise sources, and it is possible to obtain high-quality measurements of the dark current.

However, a thermal frame is scalable, meaning that you can multiply its pixel values to recreate a dark frame with an arbitrary integration time. A normal dark frame is not scalable because of the bias value that it contains. If you can create a scalable dark frame, you can match its dark current to the dark current in image frames taken with different integration times. Standard and Scalable Dark Frames

There exist two widely employed strategies for creating master dark frames. The first strategy is used to create master dark frames for the standard calibration protocol, and the second is used to create scalable master dark frames for the advanced calibration protocol.

• The standard protocol requires dark frames that are made from multiple dark frames having the same integration time as the raw images taken by the observer; because in the standard calibration protocol, the dark frame is subtracted directly from the raw images, without the use of a bias frame.

• The advanced protocol can use dark frames with any integration time—that is, scalable dark frames. Ideally, these are corn-

Figure 6.10 Opposite: "If you've seen one dark frame, you've seen them all." Not true!

Even though dark frames are similar, they are by no means identical. Every dark frame is unique. The left column contains greatly enlarged sections of five 60-second dark frames; if you inspect them closely, you will see the differences. At right, the differences are highlighted: from each dark frame, the average of all of the dark frames has been subtracted, leaving the residual dark noise.

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