*********** Square Rooter ************

[roger smith x294]

Posted to CCD-world:
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Jim Janesick wrote...

"Unfortunately nonlinear encoding such as a square-rooter is difficult to
 implement in practice. Logarithmic amplifiers do not exhibit a perfect
 response leading to camera linearity problems when CCD data is mapped back
 into the linear domain. Also, nonlinear circuits used are inherently slow and
 show instabilities in offset level. The latter characteristic is important
 because an offset change implies a gain change which must be taken into
 account when reducing CCD data. A compromise in making the square-rooter
 useful for scientific applications is to encode the CCD linearily and employ a
 digital square-root look-up table to compress bits. For example, the output of
 a 12-bit converter can mapped into 8 bits without loss of information
 (employed on the Cassini mission to Saturn)."

Many years ago, Bruce Atwood (then at CTIO, now at Ohio State) built a
cute ADC with a square root tranfer function to optimally encode shot
noise limited data.  he did this by inserting a squaring circuit in the
feedback loop of a successive approximation converter.  These were the
days when ADC were mostly hybrids and had such pins available.

This can be done digitally before the DAC, or using an analog squaring
circuit between the DAC and the comparator. I can no longer remember
which method Bruce used.  Clearly the digital method is accurate but
the DAC which follows it has to have at least as much dynamic range as
the CCD!  These days I would go for a commercial ADC and digital data
compression, since getting the ADC to work really well is of primary
importance.

>From time to time we hear of someone worrying about their CCD having
more dynamic range than ADC's with the appropriate speed, but in my
experience there is very little astronomy that requires anything more
than programmable gain prior to linear 16 bit conversion (ie. gain
selected before each readout).   I'd be interested to hear of any
examples where more than 16 bit dynamic range is needed in a single
image....

Roger Smith

Cerro Tololo Inter-American Observatory
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