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Re: Mark IV noise and sky noise

Thanks to Michael for the sky noise computations.  I assume the numbers
below are sigmas in electrons, not electrons as stated. i.e. you have
already taken the SQRT of the computed number of electrons.  Hmmmm!  I don't
get very close by my estimate.  Perhaps you can tell us the photons per sq
cm per second used, the bandwidth assumed, etc., and I will check it.
Michael, it is really a little better than you have computed.  The 442A
pixel size is 15 microns, not the 9 microns that I think you used in your
computations.  This is 15/400000 radians with the 400 mm lens.  Or 7.7
arseconds per pixel.

But we have a lot of real data, and we can use that to make predictions.  A
good night with the Mark III gives a sky sigma of 50 counts at my location.
This is a sigma of 125 electrons at 2.5 electrons per ADU or a charge of
15625 e-.  From memory this is about right.  We use up about 20 per cent of
the full well with the sky.  This is why I still want to try to get the Mark
IV to run in non-MPP mode.  One gains a factor of 4 in full well capacity.  

OK, here is the way I see it for the Mark IV when compared to the Mark III:

The pixel is half the dimension in arcseconds of sky.  This reduces the sky
photons by a factor of 4.  The lens is twice the diameter.  This increases
the light by a factor of 4 and increases the sky photons by a factor of 4
for the same exposure.  The net gain is thus a factor of 4 or 1.5 mag at 470
seconds exposure.  When we go to a shorter exposure we lose only by the sqrt
of the exposure length because of the sky background.  The Mark IV should
have a better focus.  No 9x9 psfs, I hope.  This should help the faint stars
to stick up out of the noise.  If we take 3 minute exposures followed by 1
minute read out, then a single Mark IV lens can cover a band of 16 degrees
in the sky.  The shorter exposure than the Mark III loses 0.5 mag.  

Going from mag 13 (the Mark III) to mage 14 from the above computation, we
pick up a factor of 2-3 in stars and have 4x as many pixels to put them in,
about right.  

I really hope that the improved focus will gain 1 mag.  This is not too much
to expect for a good instrument.  The Mark IIIs have never performed to
close to the limit of theory.

The bottom line is that my goal for the Mark IVs is a 16 degree wide sky
sweep at mag 15.  I think it is possible.  We will be pretty crowded at the
galactic equator, so we will probably not be so sensitive there.  But we
should get a good map of the rest of the sky.

Tom Droege

With optimism, the Mark III can  

At 08:18 PM 10/27/98 -0500, you wrote:
>  Tom has beaten the Mark IV electronics down to a readout noise
>of 14 e- per pixel.  Is this small enough that it does contribute
>the majority of the noise in a stellar measurement?
>  Let's see:  I have calculated the number of electrons one expects
>from the sky itself at two different sites:
>          dark site: (similar to Apache Point, NM)
>                    V = 21.5 mag / sq. arcsec
>                    I = 20.0 mag / sq. arcsec
>          suburban site: rough guesses
>                    V = 19.0 mag / sq. arcsec
>                    I = 17.5 mag / sq. arcsec
>  Given these values for sky brightness, and 
>       + an assumed overall quantum efficiency of 0.4
>       + a pixel size of 4.7 arcseconds per pixel
>       + exposure time 60 seconds
>  I find the number of electrons due to sky noise per pixel to be
>          dark site:      V band       9.5 e-/pixel
>                          I band      17   e-/pixel
>          suburban site:  V band      30   e-/pixel
>                          I band      53   e-/pixel
>  From which it follows
>        - from a suburban site, the sky noise will overwhelm the chip's
>          readout noise (unless one takes very short exposures)
>        - from a really dark site (like Arne's), the chip's readout noise
>          is about the same as the sky noise for 1 minute exposures
>  The conclusion?  The Mark IV electronics will do the job just fine
>in their current form.  No need to go chasing after another factor
>of 20% in noise reduction.  If someone wants to use the Mark IV for
>spectroscopy, or very short exposures, he may get slightly less than
>optimal results.  Big deal.
>                                          Michael Richmond