A Discussion of Issues Related to Digital Imaging Resolution
Here is a glimpse of my view about digital imaging. I should point out at the start that I have an ST-7 and love it and I hope to have an ST-8 some day. I have the AO on order and I love digital imaging. More recently I have purchased and used an Olympus Digital Camera which has a full resolution frame of 1280 by 1024 for a file of 1,410,000 bytes. The color images from this camera are quite good in my opinion. I feel that full screen images have almost photographic quality. The camera has two lesser resolutions as well. Thus, the following comments have to be put into perspective. I am comfortable with the discussion but want to point out that my complaint about astrophotography CCD chips is mainly that they are too small. The ST-8 comes very close to the quality I would like to see for general purpose astrophotography. With these comments in mind, here is my diatribe against CCD (Digital) Imaging ( Down with pixels they are nothing more than big fat grain particles.)
Digital imaging has become a modern rage in the area of astrophotography. Why is this? It certainly has nothing to do with the quality of the images. This is obvious if you just take a look at what has happened to astrophotography quality in the past few years. The great images of today are taken by people like Malin, Ware, Wallis and Provin and a few others. They are all taken on photographic film. Even the images from the Hubble are spectacular for what they image and not for the quality, resolution, of the images. They are mostly quite "pixelated."
General purpose digital cameras have been somewhat of a bust as they try to encroach on film cameras. They are now just approaching a more reasonable price range but still do not give results as good as the 35 mm format film much less 6 cm format. The images have only fair resolution and modest tonal range and color. They are "pixelated." This is not to say that digital imaging in general has been a bust. In the area of PC cameras there has been considerable good news. Direct digital imaging for web and similar publication is taking off. In this case, they digital images are good enough. Good enough is all that is required. Will CCD images ever have true photographic quality? I think the answer is a reserved "well maybe some day." The limits of current digital technology are now and will for a considerable time simply not allow for photographic quality, high resolution imaging. The closest one can come is the $10,000 attachments to the Canon and Nikon cameras. The best of the current lower priced cameras is the $1200 Olympus D-600L. It takes single frames of 1.4 Meg.
A study of the numbers reveals the following tough facts. A $2000 CCD camera has 390 K pixels. The PC screen I am looking at has 480 K pixels and it is certainly not photographic quality by any means. I can boost it to 1.2 or 1.6 pixels easily. The quality of the highest resolution image is quite nice to look at. An $8000 CCD has about 1.5 M pixels. This is equivalent to a good quality image on my PC screen. A TV screen has 400 K pixels. The new HDTV will have something like 2 M pixels. Digital technology has a way to go. We need 2000 by 1600 pixel chips (3.2 Meg) at a reasonable price before digital will really replace photographic film I believe. The digital files get large in a hurry.
Digital imaging at this time is, I think, more about what can be done with a reasonable amount of equipment and who can do it than it is about the quality of the images. Film based astrophotography is extremely difficult. It requires long exposures and specialized film handling techniques. But the result can be images that are high resolution and of "photographic" quality. The highest standard is to attain photographic quality. CCD imaging is attractive because it is possible to get nice images with relatively short exposures. It is quick, it is fun and it is interactive to a great extent. It fits with digital, computer control and with our view of everything going more and more digital. I have no problem with this trend. I am part of it. ;-]
The problem currently is that CCD chips are not at this time large enough nor do they have enough pixels to approach photographic quality. What set me off about these issues was the discussion about over-sampling and under-sampling. When you can see the pixels in the final picture that you look at with your eye interfering with the image then it is under sampled. With today's technology all digital cameras tend to under sample when referenced to the final print. (screen or hard copy)
We need to face the fact that the CCD chip is simply a small imaging surface with rather poor resolution. It is like a small piece of film with bad grain. With a given imager chip a certain, fixed number of pixels, will appear in the image of whatever final size we establish. If it is a PC screen we will typically see the pixels individually even for an image from a 510 by 765 pixel chip. The larger 1020 by 1530 pixel chip will give a PC screen image that is apparently quite good. But if it is printed to 11" by 17" size it will show significant pixelization. A 35 mm film print can easily be made into a 16" by 20" print and still retain good photographic quality.
My philosophy of what must be done to get the best image of a given object is this. In every case it is best to make the image size fit the chip. This can only be done by choosing the correct focal length for the telescope or lens. The correct focal length is in turn the one that places the image of the object onto the CCD chip and fills the area of the chip.
Adjusting the focal length of the telescope, and of course the image size, is exactly what can be done. With focal reducers of 0.63 or 0.33 strength and the choice of the right focal length telescope you establish the range of celestial object sizes that fill the chip. A 3000 mm focal length might be almost long enough for M57, but a 100 mm lens is more appropriate for M 31. In the sense of pixel/angular resolution this is over sampled. But in an 8X10 inch print it is not over sampled at all. It is very nice and the best that we can do with current technology. Unless we can afford the 1040 by 1570 pixel chip.
I point I am trying to make is that it is quite useless to talk about over- or under-sampling when almost all digital images are under sampled in some sense with current technology. (see discussion below about the details of the over/under issue) The main issue at this stage of the discussion is image size. The rule that must be followed is to use the CCD chip fully and effectively by filling the chip area with the desired image. There is, at this time, absolutely no resolution to spare with any CCD chip regardless of the cost. A list of interesting objects and the focal length, image size relationships is given elsewhere on this web site.
I admitted at the beginning of these comments that I liked CCD imaging. The CCD chip has some really great advantages over film. Control of the process and immediacy of results are some. But the principal one is speed and lack of reciprocity failure. The speed advantage for the single exposure gray scale image is probably several thousand. Still when doing three color imaging, some of this advantage vanishes. My sky background limits me to about 45 minutes to 1 hour at a telescope speed of f10 with film of 400 to 1000 speed. With the CCD imager I can get the green image in about 5 minutes but when doing the whole color image it still takes about an hour. These are very approximate numbers. They give some idea of the conditions one must face. Never-the-less, the CCD has it all over film for sensitivity and versatility. Now if only we could get the 2 K by 2 K class 1 imager for under $3000, that would be a more attractive solution.
A few more technical comments are in order. There are two distinct issues in the discussion of resolution in CCD imaging and making high quality hard copy prints. (or viewing on a PC screen)
One issue is that of the resolution of the CCD imager, the telescope
optics and the atmosphere. This issue is about capturing an image of a
celestial object. There are three parts to capturing the image.
One is the transparency or resolution or call it the seeing of the atmosphere.
Stars are point sources of light which are smeared out by the atmosphere,
optical aberrations and the size of the pixels. Each of these elements
has a resolution which can be described by a transfer function. This
is called in optics a modulation transfer function. The three transfer
functions must be multiplied in some way. For example if the
transfer
function of the atmosphere is 1 arc second and the telescope's is one
arc second and the CCD's is also 1 arc second then the result of the combination
is about 1.6 arc seconds. The transfer functions can be combined
like power, the square root of the sum of the squares. If any
one of the transfer functions of the total imaging path is a larger number
it will dominate the final value. The implications are that one should
work on the weakest link in the total transfer function. Of course,
the best system will be if all the transfer functions are small numbers
in terms of the normalized angular measure I have chosen, arc seconds.
I find that when there is a good imaging night, I can always, easily separate
the double-double or equivalent doubles. Thus the seeing on a night when
imaging is possible at all has resolution of about 1 arc second.
So the optics and the atmosphere together are about 1 arc second resolution.
I do not claim the telescope pointing is that good and it too is a serious
factor in resolution. But I will assume for this argument that the
telescope mount and guiding are as good as the seeing. With a really
good telescope mount this will be close to the truth.
Some transfer functions can be controlled and some can not. The atmosphere can only be controlled by selecting a good night, the telescope by buying an optically good one, and the CCD chip by using one with small pixels. The pixel size does relate to the focal length of the telescope and the angular seeing functions of course. My point is that I feel the resolution of the CCD chip in arc seconds should be as good as, or better than, the rest of the optical path unless there is some very good reason to reduce it.
The arc second resolution of the pixels is naturally related to the focal length of the telescope. Pixels of 9 microns with a 2000 mm telescope subtend about 1 arc second. So for my typical good imaging night, all three transfer functions are about the same and about as small as practical. But still it would be mice to reduce one or two of the elements involved in the total transfer function if possible. Star images that have 4 pixels are more like little mosaics than star images. I feel that 9 or 16 or even 25 pixels per star image would be much nice, that is, more photographic.
I have no brief with those that would reduce the resolution for one of the links in the resolution chain. I only wish they would say that they are doing this for some real reason and not wave the Nyquist flag. We are with current technology stuck with doing the best we can. I still believe that the best choice of telescope focal length is to have an image size that fits the chip and that it should fill the chip as much as possible. I would forget the discussion of Nyquist frequency or satisfying some transfer function criterion or the PDF function or whatever. The idea is to use what you have and use it to the best advantage. Even well composed images taken with the tiny, low resolution 256 by 512 chips can be quite attractive and satisfying.
Another issue I want to discuss is that of the basic adequacy of the current CCD chips when it comes to creating the final image that we view on the screen or on a hard copy. My many years of experience with large, medium and small format photography has taught me what a good photograph should look like from a resolution standpoint. When viewing a print the resolution of the print should be good enough so that it looks continuous to the viewers eye. (That is not taking into account artistic license.) A normally accepted standard was that an 8 by 10 inch print should have about 10 lines per mm of resolution when viewed from a normal viewing distance of 16 inches. When this criteria is reflected to the 35 mm frame we need to have about 80 lines per mm resolution on the film. (this due to the 8 times enlargement from 35 mm to 8 by 10)
Now consider the CCD chip. The CCD chip with 9 micron pixels has a basic resolution if 55 lines per mm. (one might argue for 110 but I think that is not correct) In either case, this sounds like a good number. It is comparable to film but still 2 to 3 time less than fine grained films. The problem is that a medium size CCD chip has only 510 by 470 pixels and is 4.5 by 6.8 mm in size. In order to make an 8 by 10 print from a full frame, an enlargement of 37 times is required. The final print has only 2 pixels per mm. This "graininess" is clearly visible. Even if the next size chip is used (1020 by 1540 pixels) there are only 4 pixels per mm. This is better but still shows quite perceptible pixelization. To match 35 mm film the chip would have to have about 2400 by 1700 pixels.
In summary, I am arguing that for the most satisfying, photographic like, images it is not only ok, but desirable to over sample. The price you pay is somewhat inefficient use of resources. Second I am pleading for more resources. Finer grained and faster film and finer grained CCD chips. That is not to mention more rational costs of the chips. A 2400 by 1700 pixel chips with only 16 bit resolution requires an 8M file. Three color image goes to 24M. But that is why we have 24G drives on our PCs, isn't it. :-)
For a nice technical analysis of image processing see:
CCD Astronomy by Christian Bull, William Bell 1991 Ch. 4.5.11
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