Quick and dirty summary:
This brief Note examines the properties of a few images from the Mark IV CD-Rom number 3, all taken on March 28, 1999.
Below I will discuss
For the most part, I limit my analysis to the central portion of each image. For reference, here's the 200-second V-band image in its raw form: the box marks the area around the star HD 139088 (J2000 RA = 15:36:03.49, Dec = +06:11:00.7) on which I concentrated. The image has been rotated 90 degrees clockwise from its natural orientation, so that North is up and East to the left.
When I first examined these images, I was surprised by the sky values; using the images as supplied on the CD-Rom, I measured:
If one obeys the BZERO directive in FITS header ...
V-band I-band
mean sigma mean sigma
----------------------------------------------------------------------------
20-sec dark -23,790 11 -24,010 9
20-sec night-sky +9,657 51 +10,561 47
200-sec dark -23,720 - -23,950 -
200-sec night-sky +15,692 93 +26,923 153
This makes no sense -- why should the difference between a dark frame and 20-second night-sky exposure be so large, but the difference between a 20-second and 200-second night-sky exposure be so small?
Tom Droege indicated that he didn't see any such strange behavior. So, I looked at the files again.
The dark frames have no BSCALE and BZERO keywords in their FITS headers. So the data values in those files should be interpreted as falling in the range (-32768 to +32767). I was doing this properly.
The night-sky frames do have BSCALE=1 and BZERO=32768 in their FITS headers. This means that one is supposed to add 32,768 to each pixel value immediately as one reads it from the data file. My software did so ... and therefore found a big jump between the dark and night-sky background values.
If I ignore these directives in the FITS header, then the sky values make much more sense: consider this fixed table:
If one ignores the BZERO directive in FITS header ...
V-band I-band
mean sigma mean sigma
----------------------------------------------------------------------------
20-sec dark -23,790 11 -24,010 9
20-sec night-sky -23,111 51 [ +679] -22,207 47 [ +1,803]
200-sec dark -23,720 - -23,950 -
200-sec night-sky -17,076 93 [+6,644] -5,845 153 [+18,105]
The values in square brackets show the amount by which the night-sky brightness exceeds the dark frame's background. It all makes sense now: the 200-second exposures have sky values which really are about 10 times larger than the 20-second exposures.
I examined the pixel values in a 300x300 pixel box near the center of the frame, roughly centered on the star HD 139088. A histogram of the pixel values ought to form a nice Gaussian distribution, with a small tail of high values. While this was true for the short (20-second) exposures from each camera, I discovered some very peculiar features in the long (200-second) exposures. The long dark exposures showed multiple peaks in the histogram.
The 20-second V-band dark, and 20-second V-band night-sky image are shown below. I have shifted the night-sky image values downwards to match the dark image values (so they could appear on the same plot). No major problems here. The night-sky distribution looks as if it has one or two parallel tracks; note the low value every 16 (?) data numbers. That means the A/D converter may have a small problem: no big deal.
The 20-second I-band dark and 20-second I-band night-sky image likewise appear fine (but again note the minor features introduced by the A/D converter):
However, when I plot the distributions for the long (200-second) exposures, I find several peaks in the histogram of pixel values in the dark frames. This I do not understand at all! The night-sky frames don't look too bad -- the noise in the night sky probably overwhelms whatever is causing the multiple peaks in the dark frames.
First, the V-band images:
Now, the I-band images:
David Morris of EEV CCD Sensors sent the following message to the CCD-World mailng list on April 30, 1999:
I'm not familiar with the device you are using, but I would guess that it is operated in an MPP mode. The sort of structure that you are seeing in the dark signal is common in such devices, and is believed to be due to the fact that the dark signal is 'quantised'. This comes about from the fact that the dark signal is generated from subtle defects in the silicon crystal lattice, or from contamination decorating these defects. There are only a few (preferably none) of these per pixel. Each has a characteristic charge generation rate and activation energy. The peaks that you see in the dark signal histogram represent the number of pixels with 0, 1, 2...... defects in them. Assuming the distribution is random on the device, the numbers of pixels should follow a poisson distribution. If you compare the spacings of the peaks vs temperature, you can calculate the activation energy, which will indicate what type of defect (mid band or close to the conduction band) you have in the device.
The effect you are seeing is what is usually expected in MPP devices. If you have a good non-MPP device your dark signal is dominated by the surface states, which are (hopefully) very uniformly distributed over the device, and are present in very high numbers per pixel, you see no structure in this.
Peter Pool of EEV Sensors sent the following message to the CCD-World mailing list on April 30, 1999:
The effect you describe sounds very much like the effect of heavy metal contamination in the silicon. This has been observed by several workers, but one of the first references I can remember is:
Self-Analysis of CCD Image Sensors using Dark Current Spectroscopy. W.C.McColgin et al (Kodak) 1993 IEEE Workshop on Charge Coupled Devices and Advanced Image SensorsThe idea is that the heavy metal gives rise to a characteristic generation centre and that a pixel contains an integral number of these centres, the probability decreasing with number of centres.
These guys deliberately contaminated with Au, Co and Ni and were able to discriminate Au from the other 2 by the generation rate. I believe more work has been done since, so you may be able to identify the culprit !!
Images taken with the I-band camera shows bands which run across the chip from north to south: that is, in the original orientation, perpendicular to the direction in which charge is transferred across the CCD.
To show the bands clearly, I co-added pixels in each column to form an average in each row. We expect to see a periodic variation in the averages along each row -- that's what the eye detects as bands. To check on the size of the effect, I also formed averages along each column (which should show no such variation). Here are values from the 20-second I-band dark frame (I offset the vertical scale arbitrarily -- sorry):
As expected, there are no big variations if we average along columns. But in the row direction, there is a variation of amplitude about 6 DN peak-to-peak with period about 5 rows.
I think the problem lies in the electronics. If so, we should expect it to become less significant if more random noise is added. The 200-second dark frame has a higher average value, and more noise, than the 20-second dark frame. Let's compare the two of them, averaging over the same central rows:
Yup, just as expected: the same periodic variations are present, but they are beginning to be overwhelmed by random noise.
One would expect that night-sky frames would have so much random noise due to the sky that this periodicity would disappear. And it does disappear -- but another one takes its place! Look at the 200-second I-band image below: there is a pattern of bands along the rows, but it has a longer period -- more like 16 rows, instead of 5 rows. Perhaps this is a different sort of noise, due to interference from power supplies or something?
I did not clean up these images at all: no dark subtraction, no flatfielding. I believe that using the raw images will have no large effect on the limiting magnitude one can derive for point sources.
Again, I concentrated only on a small subsection of each image, about 300x300 pixels, centered on HD 139088. Here's an image of the field taken from the Digitized Sky Survey, oriented with North up and East left (as all TASS images will be shown).
Note that there are two small galaxies which can be identified on the TASS images -- I have marked them with squares. The large rectangle at bottom left shows the western edge of NGC 5964, a big galaxy which shows up nicely in the H*R1265.926 images.
Let's look at the V-band images first. I show below images of the central sub-section with a zoom factor of 2 -- so that each pixel appears as a 2-by-2 block.
First, the 200-second V-band image:
And now the 20-second V-band image:
When I examine the stars in these raw images, I find the following properties: the first row for each star in the table refers to the 20-second image, the second row for the 200-second image.
(peak-sky) FWHM 5-pix aper 5-pix aper
Star DN pix flux instr mag cat mag
----------------------------------------------------------------------------
A 23,000 1.89 132,000 12.20 7.30 HD
sat - - -
B 16,000 1.79 72,300 12.85 8.10 HD
sat - - -
C 2,800 1.60 9,990 15.00 10.3 T
17,000 1.94 90,622 12.61
D 160? 2.6 840? 17.69? 12.92 G
1,700 2.02 9,040 15.11
E invis 13.47 G
1,300 1.96 6,540 15.46
F invis 13.66 G
1,100 1.70 3,903 16.02
G invis 14.60 G
400 2.06 1,460 17.09
------------------------------------------------------------------------------
Key to Catalogs: HD = Henry Draper (not sure of magnitude source, actually)
T = Tycho
G = Guide Star Catalog
The I-band images clearly show many more objects than V-band images of the same exposure time. Here is the 200-second image: note the "stripes" that run across the image, north-south. They occur at intervals of roughly 16 or 17 rows. Recall that this image has been rotated by 90 degrees -- the "stripes" are perpendicular to the scan direction. These features also appeared in earlier images taken with the same image. Why?
Note added later: Tom Droege thinks that he understands the source of these features, due to some of the electronics. As Tom Droege pointed out, these bands have very low amplitudes. I doubt that they will make any difference in the data we can extract from the frames.
And now the 20-second I-band image:
I can make a table for measurements of the same stars in the two raw I-band images.
(peak-sky) FWHM 5-pix aper 5-pix aper
Star DN pix flux instr mag cat mag
----------------------------------------------------------------------------
A barely sat - 208,000 11.71 7.30 HD
sat - - -
B 22,000 2.30 164,000 11.96 8.10 HD
sat - - -
C 5,400 1.81 27,000 13.91 10.3 T
barely sat - 102,000 12.47
D 650 1.98 3,800 16.05 12.92 G
5,200 1.93 32,000 13.74
E 480 1.79 2,030 16.73 13.47 G
5,000 1.94 24,000 14.07
F 420 1.85 2,430 16.53 13.66 G
3,500 1.63 17,000 14.41
G 180? 2.54 1,220 17.28? 14.60 G
1,700 2.21 11,600 14.84
------------------------------------------------------------------------------
Based on these measurements, I can make a very rough table of limiting magnitudes in these images:
V-band I-band
--------------------------------------------------
20-sec mag 7 to 12 V = 8 to V = 14
200-sec 10 to 15? V = 10 to V = 16?
A few comments:
The design specs for Mark IV lenses call for them to place about 85 percent of the light inside a radius of 25 microns -- that is, inside a radius of about one pixel -- even near the corners of the field. The actual Mark IV lenses, as delivered to Tom, put only about 50 percent of the light inside a radius of 1 pixel on axis. That's not bad. But what is bad is that the this fraction decreases to about 15 percent near the corner of the field. Details below.
The PSF is pretty good at the center, with Full Width at Half Maximum (FWHM) about 1.8 pixels. As one moves away from the center of the image, however, the stellar images become comatic: they look like little comets with their heads pointed away from the center of the field.
One way to quantify the effects of this distortion is by the curve of growth: define a set of concentric circular apertures, and see how much flux falls within each aperture. A good, tight PSF will hold nearly all its light in the innermost aperture, while a bad one will throw much of the light outwards, away from the center.
I created a small set of circular apertures, with radii
First, the V-band image V1265_920.
Next, the I-band image I1265_920.
The figures show clearly just how bad the distortion is: it reduces the fraction of light within a 1 pixel = 7.3 arcsec = 24 micron radius around the centroid from about 50 percent (near field center) to about 15 percent (near field edge). The effect is about the same in V-band and in I-band.
Is there a dependence on angle? Not much of one. Below are plots showing the manner in which the fraction of light inside a given radius depends on angle: the size of the "star symbol" is proportional to the fraction
(light inside 1 pixel radius) / (light inside 10 pixel radius)
and the size of the "circle symbol" is proportional to the fraction
(light inside 2 pixel radius) / (light inside 10 pixel radius)
First, the V-band image V1265_920.
Next, the I-band image I1265_920.
If the size of the distortion depended on angle, these plots would show symbols which changed size as one moved vertically (i.e. at the same radius, but at a different angle in the image). I see a small variation: the images are slightly better in the South-West and North-East corners.