Bruce Truax
Calypso Telescope
btruax@home.com
860-276-0450
August 18, 2000
In January of 2000 we used the "I" filter (725nm to 900nm) on the HRCam for the first time. We immediately noticed large, donut shaped ghost images northwest of the image of brighter stars. Measurements with IMEXAM showed that the size of the ghost was about 90 unbinned pixels and the average intensity of the ghost image was only a factor of about 1,000 below the parent star. This was quite a shock since we had designed and specified the HRCam optics to keep the ghost images to a much lower level. A quick geometric analysis based on the size of the image and the f-number of the optics indicated that the ghost reflections were caused by light reflected from the CCD and then off one of the two surfaces of the filter and back to the CCD.
After observing this bad reflection and also observing what might have been other suspicious spots of light it was decided that we should perform a more detailed ghost analysis and categorize all of the brighter ghosts by size and, if possible, by brightness. This would allow astronomers to quickly determine if small, bright spots were real or ghosts.
The HRCam optical system was originally designed using the lens design program CODE V. It has since been transferred to ZEMAX which has a nice feature for analyzing the source and size of ghost images. By telling ZEMAX which surfaces to analyze, it will create a table showing the ghosts caused by reflections from those surfaces and every other surface in the system. Since we are interested in the appearance of ghost images in the image plane, there are two types ghost image formation which must be considered.
Type 1 ghost images are caused be reflection of light from the CCD detector back into HRCam optics. At each optical surface, some of this light will be reflected back to the CCD plane to form a ghost image. See Figure 1. Because the backside thinned CCD in the HRCam has very high quantum efficiency, it has a relatively low reflectivity compared to bare silicon, and this is particularly true in the blue-green portion of the spectrum where the QE is the highest. As the QE drops off towards the red end of the spectrum, the reflectivity of the CCD increases and can get as high as 25%-35%.
Type 2 ghost images are formed when incoming light reflects off an optical surface and some of this reflected light is reflected yet again back towards the image. These double reflections can occur between any two pair of refracting surfaces in the telescope. Each of these double reflections will form a ghost image. See Figure 2.
The shape of both types of ghost images are similar and identical to any out of focus telescope image. Some of the slightly out of focus ghost images will appear as circular rings with a slight dip in the center. As the images get very far out of focus they change into a donut shaped ring with a dark hole in the center. These very out of focus ghost images are easy to recognize but the slightly out of focus images can look like a star, or they may be misinterpreted as an extended object. It is therefore important to categorize these ghost images by size and intensity so that suspicious objects can be identified and eliminated from the images.
The lens design program ZEMAX was used to compute the diameter of the two types of reflection ghost images at the image plane using the Ghost tool. The relative intensity of the ghost images compared to the primary image was computed using a very simple formula and some rather elementary assumptions regarding the reflectivity of the various surfaces. First, it was assumed that the primary image and the ghost image were simple flat top disk images (this turns out to be a conservative assumption). The size of the primary image was given by the atmospheric seeing and set at a value of 0.7 arc seconds. The relative area ratio of the two images was computed and then this was multiplied by the product of the reflectivity of each of the two surfaces. The CCD reflectivity was assumed to be 5%. The transmissive glass surfaces were assumed to have broadband AR coatings with an average reflectivity of 1%. A parameterized model was created in Excel such that these reflectivity values could be varied to test the effect of different reflectivities for both the CCD and the glass surfaces.
Table 1 summarizes the results of the analysis. There are two sections in the table. The CCD Reflection section shows a summary of the Type 1 Ghosts which are reflected from the CCD and then from one of the other optical surfaces in the system. The second section labeled "Other Ghosts" shows the worst Type 2, double reflection ghost for each surface. The reported ghost image size is the size of the ghost image reported by ZEMAX and is simply a geometric computation based on ray tracing. The actual ghost image size is approximately equal to this number, plus the radius of the actual image. This corrected radius is used in the relative intensity computation. For each ghost image, the diameter of the ghost image in unbinned pixels (corrected for the size of the primary image) and the intensity of the ghost image relative to the primary image are given. For reference, 24 unbinned pixels represents 1 arc second.
Ghost Analysis Summary
Table 1
The two, highest intensity Type 2 ghost images come from internal reflections in the dewar window and the beamsplitter. These two ghosts have the highest intensity because they are the smallest, both of which are actually smaller than 1 arc second. Once they are corrected by adding the size of the primary image, they are still quite small and only slightly larger than the size of the primary image. Depending on their location, they could be difficult to distinguish from a real star. The location of these ghost images depends on the angle of the surfaces relative to the optical axis. The Dewar window is likely to be very perpendicular causing this ghost to fall very close to the primary image. The filter, on the other hand, is a moving piece of glass and is probably not very perpendicular to the optical axis, and the angle of the filter can vary slightly each time it is inserted. An another comment on these Type 2 ghosts is that the ghost intensity can vary considerably over the CCD sensitivity spectrum. In some areas of the spectrum, the coatings are better than 0.5% reflectivity where in other areas the reflectivity can be as high as 2%. This variation will cause the relative intensity to vary 4x in both directions around the average value in the table depending on the filter used. The worse performance will be at the ends of the spectral range (U and I filters).
The brightest expected images for Type 1 ghosts are caused by reflections from the dewar window. These reflections are about 2 arc seconds in diameter and have intensities, which are down 25,000 to 30,000 times from the primary image. As with Type 2 ghosts, the location of the ghosts depends on the perpendicularity of the surfaces to the optical axis. Also, as with Type 2 ghosts, the intensity is dependent on variations in reflectivity of the surfaces, which are greater for both the CCD and the AR coated glass at the ends of the CCD sensitivity spectrum.
Table 1 can be used to identify the source of ghosts, which are observed in images. To do this, measure the size of the ghosts in unbinned pixels and then look in the table for a ghost of that approximate size. Once you know the source of the ghost, the next step is to measure it's average intensity and compare the results with the peak intensity of the primary source. If the observed intensity ratio is more than 4x different from the values in the table, then there is something abnormal, which should be investigated further.
Note that relative intensity of the ghost images will increase as the seeing deteriorates. This is because the peak of the primary image will decrease as the seeing deteriorates but the total energy in the primary image, which is what determines the average level of the ghost image dose not change. Conversely, better seeing will reduce the relative intensity of the ghost images.
Table 1 by itself does not explain the cause of this investigation, the large 90 pixel ghost observed in the I images of bright stars. There is a ghost image of the proper size in the table, the Type 1 ghost from the first surface of the filter but the intensity of this ghost should be down by over 70,000x. The size is correct and the fact that the ghost image is offset from the primary image is indicative of a tilted surface (Figure 3), a likely problem with the filters because of the mounting and the mechanical tolerances of the filter changer. If this is the source of the ghost, then it is necessary to explain the 70x increase in intensity from what it predicted in the table. Examination of the CCD response and the filter response help to shed light on the discrepancy. The peak filter transmission has an average of about 85%. The average of the base RG-9 glass in this band is 93% therefore the Dielectric coating used to modify the passband must be rejecting an additional 8%. Since the coating is a dielectric stack, it must be reflecting the energy, therefore there is an average 8% reflectivity from the filter. In addition, the reflectivity of the CCD QE in this area is 65%, of which 30% is probably due to an increase in reflectivity. This is an increase of a factor of 6 over the 5% estimated in Table 1. The combination of these two increases in reflectivity accounts for a factor of 50x change in the ghost intensity. The next question is, how can these ghosts be eliminated. One method is to simply use RG-9 filter glass with no dielectric coating, in fact, the dielectric coating should be replaced with an AR coating. This change would reduce the intensity of the ghost image by about a factor of 20 since a relatively narrow band AR coating can probably be better than 0.4%. While such a filter would have a low ghost image intensity. The disadvantage of this approach, and the reason why the coating is on the filter in the first place, is that the lack of the dielectric coating moves the long wavelength cutoff out from 900nm to about 975nm. This change in filter bandpass would make it significantly different from the standard "I" filter.
I-Band Ghost Images
Figure 3
Table 1 indicates that some other ghost images may be detectable, particularly with stars which are at or above saturation. As of the time of the writing of this report, no such images have been noticed. Once possible reason is that many of the Type 2 ghost images caused by the parallel plates which are parallel to the optical axis (Dewar Window, Beamsplitter) would cause ghosts which fall directly on top or very close to the primary image. The result would be a distorted PSF which would be difficult to discern.