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In the context of GAIA, time-delay integration is the clocking of a CCD's charge shift register at a frequency such that it matches the linear speed across the focal plane of the actual image. So even though the image and data are moving continuously, their rates are locked together and the data coming out the end of the row is un-smeared.

As background only, the first time I'd seen this speed-matching technique on a 2D imaging sensor used was in semiconductor wafer and mask inspection tools produced by KLA. Here is a patent filed in 1988 US4877326A

TDI uses the fact that, as charge packets are transferred from photosite to photosite by cycling clock voltages as described above, the photosites are still sensitive and photons entering a new photosite will create electrons that add to the charge packet located at that photosite at the time. In TDI the charge packets are moved across the array at the same speed the image is moving across the array so that, as a feature's image moves across the array, the charge generated by that feature is adding to the same charge packet.

Question: What was the first use of time-delay integration (TDI) in Astronomy? Are there instances before GAIA?

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This is usually referred to in astronomy as the "drift scan" technique, and has actually been used with ground-based telescopes since the early 1980s (e.g., McGraw, Angel, & Sargent 1980, Wright & Mackay 1981). Gibson & Hickson (1992) have a summary of work done in the 1980s and early 1990s in the Introduction section of their paper; this includes references to interesting things like early drift-scan work done at 10 microns using a linear array of HgCdTe photodiodes, scanned perpendicular to the array direction (Bloemhof, Townes, & Vanderwyck 1986).

The imaging part of the Sloan Digital Sky Survey was done using this technique.

Here is an example of a high-end amateur-astronomy setup from the late 1990s for doing drift-scan observations.

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