Here are a few analyses of ghost images in the SV data. Many thanks to the Eyeball Squad for assembling Ghost Gallery: http://www.phys.susx.ac.uk/~mm610/des/Ghosts/
First, here is a ghost image of R Doradus, for which the in-focus image is located on an F/A sensor. The ghost is formed by a double-reflection inside C5 as shown in the drawing (magenta lines on the right). Exposure 157554, i-band.
My very rough guess at calculating the intensity is as follows. I assume the following:
Mirror 3.8 m diameter
30% of light is blocked by secondary
Throughput is otherwise 75%
CCD gain is 4.5 e- per ADU
I-band sky brightness is 20.2 mag/arcsec^2
Pixel size is 0.263 arcsec
I calculate that the sky should produce 7 ADU/pixel/sec. As a check, exposure 135130 is an I-band exposure taken with moon down near zenith - the measured sky is 6.7 ADU per pixel. Close enough. The ghost image in 157554 has an intensity of 0.4 ADU/sec, or 23.31 mag/arcsec^2. The diameter is about 0.8*2048 pixels. This gives an integrated mag. of 10.8.
The I-band magnitude is ~1.5 (?). This means that 1/5000 of the flux is reflected into the ghost image. If I split the reflectance of the front and back of C5 equally, this means that the reflectivity is ~1.4% per surface. That is close to the spec for the antireflection coating.
Next up, the ghost image of Mira in r-band exposure 150983. This ghost is formed by a reflection between the CCD in the focal plane and the backside of C5.
I estimate that the ghost image has a brightness of 26 mag/arcsec^2, with an integrated total mag of 13. The R brightness of Mira is ~5 (?). If I assume the CCDs reflect 10% of light in the r band, the reflectivity of the back of C5 is ~1%.
These calculations are rough, since both stars are strongly variable. But they show that the ghosting performance is about as expected.
Next up, another ghost image of R Doradus, this one in exposure 157556. The star is now on S28.
The origin of this ghost was a mystery at first. In fact, it is a reflection between the focal plane and the front surface of C4.
Finally, here are 6 scattered light images in the g, r, i, z, u, and Y filters of the original SN-X1 position. Mira is 1.67 degrees away from the center from the focal plane, but scattered light is being directed back. The next 6 images are arranged by filter in the order that they are loaded in the Filter Changer Mechanism.
Mira-g (149251) Mira-i (149253)
Mira-r (149252) Mira-z (149254)
Mira-Y (149713) Mira-u (149710)
Here are two more images in the z band with Mira at different distances from the center of the focal plane:
Mira-z (1.45 deg) (153975) Mira-z (1.79 deg) (149807)
Note that the pattern varies significantly from one filter to the next. Multiple surfaces are involved. The scattered light can be classified into three categories.
Type Ia Spray: This pattern is best seen in the Y filter (149713) and is light being scattered off the side wall of the shutter box. It is repeated in z and i, but is too faint to see in the bluer filters because Mira doesn't emit much light there. The z band image 153975 also shows this spray when Mira is closer to the focal plane; the central gap is caused by occultation of rays due to the central "chimney" (primary mirror baffle).
Type II Spray: My conjecture is that the incoming beam for Mira passes through a clear, uncoated section at the edge of a filter and reflected off the side of the filter, the "rim" that supports the bottom of the filter, the top of the filter, and back down towards the focal plane.
Arc: The origin is still unclear. The pattern is as if there were a rim of radius 310 mm about 15 mm above the u and Y filters. The filter cage might work except it is radius 305 mm, which is too small (the larger radius is needed in order to ensure that the arc does NOT show up in the u and Y filters.)
The following figure shows how a ray in a Type II spray would work, and the resulting spot diagram corresponding to 149251:
The following figure shows the lightcurve of Mira during this time period (generated from data collected by the AAVSO):
The following figure shows the arc in the z and Y filters for Mira at a radius of 1.82 deg. The arc just makes it into the Y filter at this radius; it is not visible for smaller
radii. This combination of images nails down the geometry of the reflecting surface to a narrow envelope.
Quantitative Tests of Scattered light¶
Exposure 201461 z band is 1.67 deg away from Gamma Crux, 100 sec exposure. I measure a peak brightness in the "spray" from the shutter wall of 1000 ADU per pixel. The sky itself is about 2300 ADU/pixel. Converting to AB, I get AB ~ 19.9 mag/arcsec^2.
From Simbad, I get the Johnson mags V=1.63 and J=-2.00. I find a good interpolation is Mag(Johnson) varies as log10(lambda). Interpolating to z band, I get mag -0.7. Conversion to AB I add ~0.6. So the final AB mag at z is -0.1.
Thus, a 0th mag star creates peak scattered light of 20 mag/arcsec^2.
The requirement for ghosts is that a 0th mag star create a ghost no brighter than 19 mag/arcsec^2. Thus, we are below the ghosting requirement. However, the spray covers a much larger area.
Natural sky in z band is about 18.9 mag/arcsec^2.