Ghost Busters: Subaru/HSC Ghost Analysis&Removal (2) Arc Ghosts
Satoshi Kawanomoto, Yutaka Komiyama, Masafumi Yagi (NAOJ)
email: kawanomoto.satoshi@nao.ac.jp
Abstract
We have investigated the optical ghosts generated on the images of Hyper Suprime-Cam (HSC). In this presentation, we focus on the arc-shaped (or mustache-shaped) ghost which is located near the edge of the field of view of HSC.
The standard ray tracing on HSC model can not predict this feature, however, we finally identified that the ghost is constructed by the ray which goes through the rim of the 3rd lens (G3) of the wide-field corrector. In order to hold G3
in ceramic lens holder, there is narrow unpainted flat glass surface at the rim of G3. This gap does not affect in small incident angle up to about 0.88 degree from optical axis. But, in the case of incident angle range 0.89-0.99 degree, asmall amount of light can pass this gap and reach the detector surface. So if a bright star is located little bit apart from the field of view of HSC, the arc ghosts will appear. Now we understand the principle of constructing arc ghosts, wecan predict their appearance, position, and size. We show how well the optics model including unpainted flat surface of G3 reproduces the position and the shape of the ghost. Image masking process will be introduced into the HSC
pipeline as an optional function.

1. Introduction
Hyper Suprime-Cam (HSC) is a powerful CCD camera on the Subaru
Telescope which covers the 1.5 degree diameter field of view. In earlyphase of HSC observation, we noticed that many arc-like ghosts appear nearthe edge of HSC field of view (see Fig 1 (left)). It was easy to find thesource star of these ghost (Fig 1 (middle)), however, the mechanism forcreating these ghosts can not be found for long time.
These arc ghosts have these properties: (1) field angle of source stars are
distributed between 0.88 and 0.99 degrees, (2) larger field angle source star
makes a ghost which is more distant from the optical axis, (3) all ghosts
have central gap. Property (1) says there are some strict positional condition
to make the ghost on the CCDs, property (2) suggests that there are evennumber reflections in light path of ghosts, and property (3) might be due tothe central obstruction of the POPT2.
Imag~7

We finally found the mechanism and reproduce arc ghost well by the ray
tracing (Fig1 (right)).
Fig.1: (Left): Arc ghost examples located near the edge of HSC FoV. (Middle): An arc ghost and corresponding (source) star. (Right): Ghost reproduced by ray tracing is overlayed as green circles.

2. Arc Ghosts
The rim of the HSC wide-field corrector (WFC) lenses are polished andunpainted in order to be held by the ceramic lens holders. In the case of thethird lens of WFC (G3), it has relatively wide clear rim in its front side
because of strong concave surface. The G3 retainer ring has a stop to hide
the clear rim of G3 from incident light and the diameter of the stop is
smaller than the inner edge of the G3 rim. However, the diameter of the stop
is not sufficiently small.
In the case of large field angle, incident light has some positive radial
component at the G3 retainer. So some potions of rays can reach the G3
clear rim (see Fig 2 left). These rays are not affected by the negative powerof G3 front surface that refract rays toward outside of G4, and advance toG4, G5, … and finally the CCDs (see Fig 2 middle and right).
Since we don't have precise measurement of the radius and deviation fromthe circular form for the inner edge of G3R1 clear rim, there are someuncertainty in our simulation.

Fig. 2: Field angle 0.92 degree point source beam on the front surface of G3 lens(left), side view of the beam on the bisection of the optics(middle), and simulated image on the CCDs (right).

3. Removal Method
The method to remove the ghost is very simple as is described below.
Calculate the parameters (Arc center distance, arc radius, arc length, andgap length) of the ghost as a function of the field angle of the source star() and central wavelength of a filter () using the optics model.
1. For a certain exposure (visit), search candidate stars in a star catalog bycriteria of a star located in a range from the optical axis of telescope.
2. Calculate  and ghost image by using of pre-calculated parameters inorder of the brightness of candidate stars.
– Stop process if the ghost level becomes sufficiently low.
3. Mask the relevant pixels in the exposure according to the prediction.
4. Coadd masked exposures (Note that this method assumes that thedataset is composed of dithered exposures with appropriate intervals).
Fig 3-1 shows the predicted position and shape of the ghosts for HSC-i2. Fig. 3-1: The simulated shape of the arc ghosts as the function of Note that these position and shape are depend on filters. Fig 3-2 and 3-3 for HSC-i2 filter. The obscuration of the prime focus structure isshow the parameters of arc ghost as a functions of .
included in the calculation. Non-axisymmetric features (stacker offilter exchanger, spiders of telescope) are not included.

Fig. 3-2: The predicted arc center distance and arc radius of theghost as functions of . Data in [0.88,0.94] range can be fitted
well in a function a+b/[um]+c*[deg]. Fitting results for thearc center distance and arc radius are:c(,)[mm]=-60.487+3.864/ + 493.185* andr(,)[mm]=+66.559+6.101/ + 102.998*, respectively.

4. Application to the Real Images

Fig. 3-3: The predicted size (arc length (1,2,3), gap length (4,5,6)) of
ghost as a function of . Both length are normalized by corresponding
arc radius. The data points are fitted with square root (1,5,6), linear(2,3), and quadratic (4) function. Wavelength dependency seems to besmall. Fitting results are:f1()=0.74774+0.87603*sqrt(), f2()=0.066128+0.11285*,f3()=0.46512-0.30564*, f4()=0.039944-4.7459*(-0.93117)**2,f5()=0.76672+0.96272*sqrt(), and f6()=1.3041+0.97663*sqrt().

5. Issues to be resolved
Typical width of arc ghosts are about 80pixels. The positional
error of prediction is several tens of pixels. So now we aremasking twice area of real ghost regions for a tolerance.
We should:
1. Introduce non-axisymmetric structure Filter stacker of the filter exchanger
 Telescope spiders
 Alignment error of POPT2
 Alignment error of HSC camera unit
 Atmospheric dispersion compensator
2. Introduce astrometry and correct the telescope pointing
A few arcsec error between commanded and obtained
position in HSC / Subaru telescope.
3. Introduce band width of filters
4. Introduce Fresnel diffraction
5. Improve star catalog
Especially in HSC-i2, HSC-z and HSC-Y filter,
unexpected bright IR star and its ghost frequently
appeared in a image.

Fig. 4: Sample image of the arc ghost removal. Left panel shows arc-ghost removed image. Right one shows original image.
Ghost removed image is generated by clipped coadding of 5-dither raw imags in HSC-pipeline. The most significant arc ghost corresponds to HD135905(Rmag=7.4),
the second one is created by HD135676(Rmag=8.1). The remaining arc ghost might relate to TYC-4186-347-1(Rmag=9.5).