The Great
Pixel Debate

Comments by Tom

A book entitled "FOSTER" was written in 1994 by Michael Palermitti of Jupiter, Florida, and published in 1995 by Software Bisque. At that time FOSTER started a heated debate among CCD imagers about what is the best pixel size to use for what telescope. The following document addresses some issues that were raised during this often "heated" debate.

Remember, this debate was started in 1994, before there was widespread use of CCD cameras by amateur astronomers and there was a very limited number of off-the-shelf CCD cameras to choose from.

At the time of this writing the SBIG ST-9E is now on top of my list for a cost effective large detector/larger pixel camera well suited CCD camera for SCT's, Ritchey-Chrétien's, or other similar "optical systems employing larger f-numbers and/or longer focal lengths.

This 512 by 512 20 micron pixel Kodak KAF-0261E detector with reasonably low noise, good sensitivity, extremely fast read-out - USB interface, two stage cooling, employing a nearly 1/2 inch square detector and built in auto-guider has replaced my older ST-6 (which is still a very good CCD camera and used by many!). An even better choice albeit more expensive camera is the 1 inch square KAF-1001E from SBIG using 24 micron pixels and a full 1 inch in size well suited for the commercial SCT's.

The ST-9E At a list price of under $3500, is a very cost effective camera that is well matched for most of my, as well as many other amateurs', optical systems. Especially those scopes employing 60 inches or more of focal length and all systems that are f/6.3-f/10 or larger f-numbers, regardless of focal length! This is where the heat begins.

I am arguing that the airy disk of a star is F-NUMBER dependent not focal length dependent. Yep the Focal ratio is directly related to the focal length but read on.

An example of an SBIG ST-9E image taken with a Celestron C-11.

M81 Bode's Nebula

4 - 2 minute exposures
Older Paramount GT-1100S Unguided

The above image is well over sampled using 69 inches of focal length at f/6.3, hence nice round stars. The image was taken with the moon 106 degrees away and 93.48% full. The mount is the Paramount GT-1100 and the telescope is the Celestron C-11 focal reduced to f/6.3. Also, Denver Colorado is 15 minutes away (pop. ~2 million). Note that even at 20 microns the stars are nice and round indicating plenty of sampling in the image. This is why I always bin my ST-8 two by two or 3 by 3 when used with a Schmidt Cassegrain telescope.

F-Number

Regarding pixel size being "focal length dependent" I do not agree with the statement. However, I do agree that matching the scale of the scope (arcseconds/pixel) to the pixel size is important. This term is what Software Bisque has coined "pixel matching" in the FOSTER text.

Example, take a 1/2 inch focal length f/10 optic and a 9 micron pixel. You cannot generate any contributing data in the 9 micron size even with effectively no focal length (only 5 inches!). In my opinion it is not worth employing a detector which yields less than about 1.5 to 2 arcseconds/pixel given normal imaging conditions with compromised optical systems like commercially available SCT's or Ritchey's. This is a realistic number to shoot for. The claims of resolution present in CCD images with amateur scopes that have better than 1 arcsecond/pixel are hard for me to understand.

Personally, I still will not buy into the claims of sub arcsecond resolution in any amateur CCD images that are 10 to 20 minutes long. Taking LONGER and LONGER exposures with smaller and smaller pixels is not an advantage, on the contrary, it is a disadvantage for most amateurs since the accumulated seeing, tracking, and guiding errors, will negate any effective gain in resolution. But the key here is very setups can even create any actual contributing data in anything smaller than about 20 microns unless very good quality optics are used AND a small f-number.

1 Micron Pixels?!?- Are you kidding?!

To this day I still chuckle at a statement I once heard from a "professional" where it was stated that a one micron pixel camera would ALWAYS yield the very best resolution. LOL!

I mean, if that were truly the case wouldn't you think the new digital cameras out there being used by millions of normal everyday users (not astronomers) would employ such a small pixel!? Simply put they DON'T!

Why is it that the smallest pixel that exists today in any Cannon, Nikon, Olympus, etc. digital camera on the order of 4 to 6.5 microns, and not smaller?  Simple. FOSTER lives.

The optical design of the lens will simply not take advantage of extremely small pixel detectors, nor does it have to, or they would.

Regarding the general statement that "smaller pixels are always better." 

Remember, stars are not resolvable objects in the first place so covering more and more pixels with the same data does not give you an immediate "gain" in resolution. Regardless of how many pixels you want each star to cover you cannot claim more resolution by simply employing the use of smaller pixels, say 0.5 arcseconds/pixel resolution.

More pixels may be esthetically more pleasing to some because the stars are nicely rounded but this is not a gain in actual resolution. The spot size (airy disk if you will) is governed by the f-number of the optic and is a function of the wavelength of light. Simply put an f/10 airy disk is larger than an f/5 airy disk (does anyone want to argue this?).

Note the above simple statement is governed by the laws of physics and is not subject to any "qualifiers". Although to this day I am still told this simple statement does not hold water and many do not agree with the statement. Oh well.

Of course, there are advantages to using more than one optical system and more than one CCD camera, but most of us cannot afford 2 well built telescopes, two CCD cameras, two focusers, and so on.

I am a proponent of good raw data and recommend striving to get the best raw data results rather than relying on image processing techniques or "magic" to produce what some consider a good end result. A CCD camera is not film and should not be treated the same. And there are many things you can do with a CCD camera beyond just taking pretty pictures that you cannot accomplish with film.  After many years (15+ in my case) of taking thousands upon thousands of images you will probably ask yourself "what is next?" 

Examples of what can be done  include, but certainly are not limited to, astrometry, photometry,  and variable star monitoring, minor planet light curves, and so on.  For pretty pictures I prefer film which in many cases is actually a lot less work than tri-color imaging with the CCD  camera and more often than not yields equal to or better end results WITH A LOT LESS WORK or digital magic.  I find it surprising that anyone can be proud of 1 hour plus exposures with a CCD camera (or days worth) and several hours of processing time?  Sounds like a lot of work to me.

Software Resembling A baaad example

In my opinion, it is unfair to resample an image and claim the end result is the same as using a CCD detector with a larger pixel. For example, I have seen several web pages simulating the use of larger pixels by software re-sampling an image from say 9 microns to 25 microns. Below I will compare a raw untouched image of the same object M33 by using small and large pixels in the detector.

The image on the left was taken with an ST-6 having 23 by 27 micron pixels!  The telescope was a high resolution Genesis 4" f/5.4 refractor not well matched to the larger pixels of the ST-6. But...

And I will not argue that the M33 image taken with the ST-6 and the Genesis refractor is under sampled since Image Link gives my scale as 10.34 arcseconds/pixel but you cannot ignore the raw data (DON'T BOTHER ME WITH THE FACTS!).
 

Yes a smaller pixel can be justified in this case as governed by the small f-number and very short focal length as per FOSTER. No argument here. But notice the difference between re-sampling the image with software from above and what reality is. Now that I have the ST-8 CCD I will be using it on my 5" f/3.7 Wright Schmidt astro-graph because the ST-6 pixels are not well matched. FOSTER.
 

I want the raw ST-6 image above.

Keep in mind the ST-6 image is only 2.6 minutes. Other equally misleading examples describing the use of a larger pixels can be found on many home pages on the web. I will refrain from putting any of these links here. Just bear in mind that any type of software "re-sampling" does not achieve the same results as imaging with the larger 25 micron pixels and bears no resemblance to reality. See 25 micron images below demonstrating a completely different story. Please note that I prefer raw unaltered images taken on average nights with no special modifications to my equipment to make my case.

Furthermore, anyone that claims a full-width, half-max, of any certain value, especially those under an arcsecond/pixel, after spending considerable processing time on the image is misrepresenting the data. Many individuals will run heavy convolution routines (those that like more and more pixels) and claim an increase in resolution and/or an increase in signal to noise ratio. Hence the misconception that smaller and smaller pixels are always better. The absurd claim is that smaller pixels always means more resolution. In my experience this simply does not hold true. Case and point. Even though my 20" f/4 with 80 inches of focal length can fully take advantage of a "gain in resolution" using a 9 micron pixel, on rare occasions, i.e. imaging the Trapezium 4-8 stars in a .01 second exposure during nights of great seeing, the limiting factor to resolution becomes seeing, tracking, focus, and quality of the optics.  When I have to take a 5-20 minute image of M51 to get a good signal to noise ratio my accumulated seeing and tracking errors have negated any effective gain in resolution by employing a smaller pixel. Now consider the following RAW data.

Now let's take a worst case example of binning a 24 micron pixel camera 2 by 2 or 48 micron pixels.  Is this what you would expect?

 48 MICRONS! 
Are you crazy!?

2 x 2 Binned 24 micron  AP-7

The above scenario uses an image that was "binned" 2 by 2 to the equivalent of a 48 micron pixel and yet it stills shows a completely different story when compared to other misleading images on the web that have been "software" re-sampled to demonstrate this.

A far cry from other "simulated software re-sampled" examples I have seen on the web!  Again nothing but the facts and raw data to consider here. I will always argue that 1 minute of seeing and accumulated tracking error is always better than 5, 10 or 20+ minutes of accumulated seeing and tracking error. PERIOD.  Even with the use of "corrective optics" or anything else you want to throw into the equation.

This is why I prefer shorter exposures. If I can get to 18th magnitude in 1 minute with an Apogee AP-7 or SBIG ST-6, SBIG ST-9E, with a 1 and half to 2 minute exposure, why would I take longer exposures with smaller pixels, rely on an auto-guider, or $900.00+ for more equipment to minimize poor pixel matching in the first place.  Personally I like to image 100 to 200 images a night or more.

To those that claim more resolution after heavy processing has been applied to the image I ask why bother processing the image?  Just calculate your scale in arcseconds/pixel and start claiming this is the actual resolution present in the image. For example, my C-11 at f/10 with 110 inches of focal with 9 micron pixels yields .66 arcseconds/pixel resolution.  Wow, that is better than the professionals on Kitt Peak can get using a 36" telescope with better than average seeing.  How can anyone maintain sub-arcsecond seeing and maintain .66 arcseconds/pixel tracking for 10-20 minutes or longer as many claim or seem to be able to justify?

Even with or without the any type of "corrective optics". I use corrective optics rather than what I would say is a misnomer, "ADAPTIVE OPTICS", which is technically used by the "professionals" but is a is an entirely different method of imaging that involves matching the mirror wave front to that of the seeing conditions by deforming physically deforming the mirror(s).

The reasons for focal reducing are simple. Less focal length, smaller spot size, and larger field of view to help take advantage of the smaller pixels which are not well matched to with larger f-numbers or longer focal length scopes. I will also argue that a focal reduced Schmidt Cassegrain telescope to f/3.3 is not a clean smaller spot yielding a "HIGH RESOLUTION" optical system.

Celestron now has the right idea with the FaStar systems. They designed the f/2 - 8 inch, 11 inch, and 14 inch telescopes in an attempt to match the small chip small pixel CCD detector like that found in the ST-5. How do you take advantage of small pixels?  Smaller f-number and shorter focal lengths, that's how.  An 8 inch f/2 is only 16 inches of focal length. No seeing or tracking issues here. But, why by an optimally designed longer focal length scope and then cripple it with more and more glass to use the smaller pixels?  To bin or not to bin, that is the question?  Keep in mind that most of if not all of the best 9 micron pixel images are now being taken by shorter focal length smaller f-number scopes, and these are not commercial off-the-shelf OTA's!

The use of smaller pixels with less sensitivity will always require more exposure time. The larger pixel gathers more light than a smaller pixel. This is a simple concept. A large bucket in a rainstorm will collect more rain than a smaller bucket due to the larger area. I bigger mirror gathers more light than a smaller mirror. The same holds true for the size of a pixel.

With an average Schmidt Cassegrain at f/6.3 or f/10 you are much better off binning 2 by 2 or even 3 by 3. Do the tests to convince yourself. If there is no more information in the final image, i.e. count both images star for star. If the same amount of data exists in both images you are wasting exposure time and hard drive space for no gain.

Compare the results from a Schmidt Cassegrain focal reduced to the results achieved with a low f-number Newtonian or low f-number shorter focal length color corrected APO refractor and you will see a noticeable difference in the image quality. You simply cannot start with a compromised optical design and then compromise it further with additional optics and expect a good clean small stellar image to justify the use of smaller pixels. To think that one can justify 1 arcsecond/pixel of resolution or better scale with smaller pixels after factoring in the longer exposures, average users optics, is not a reasonable conclusion. Expensive high-resolution shorter focal length scopes like Maksutov Newtonians, APO refractors, and Astro-graphs employing smaller f-numbers will be better matched to the smaller pixels.

The best results I have seen with the smaller pixels are short focal length, small f number optical systems, mounted on above average mounts.  Mounts that employ the Byers series of gears will always give superior tracking results.  High resolution telescopes include the Astrophysics and Tele-Vue series of refractors and Peter Ceravolo also makes great shorter focal length high quality Maksutov optical systems yielding an effective gain in resolution. This is how to generate "HIGH RESOLUTION" images that can often rival film. 

In 1995, Software Bisque offered the FOSTER CCD Imaging CD-ROM (this product is no longer sold). The FOSTER text was controversial in some respects but nothing being said or done by amateurs armed with CCD cameras and telescopes of varying focal lengths with or without the glorified tracking systems contradicts the information presented. See the Hires ST-8 image below taken by Mike Palermiti demonstrating how to take full advantage of 9 micron pixels.

Example Image - Show me the Data!

The ST-6 image was taken with 80 inches of focal length and the ST-8 image was taken with only 50 inches of focal length. The smaller focal length and smaller f-number is better matched to the smaller pixels so one would expect a "gain" in resolution. The ST-8 image was cropped down to the approximate the size of the ST-6 image. The ST-6 image was re-sampled square to make the aspect ratio correct by compensating for the 23 by 27 micron pixels. One image is 4 one minute exposures the other is 7.5 minutes. Guess which was shorter. Also, the ST-8 image was binned two by two to shorten the exposure time by a factor of 4.  Had the image been taken at 9 microns the exposure would have been about 20 minutes. Where is the gain in resolution by employing smaller and smaller pixels?  Does employing smaller pixels always mean more resolution?  I think not, in this case. GET THE RAW data for anyone who would like to evaluate it. If you need software to read the raw SBIG file formats click here.

By the way, the one on the right was imaged with the ST-6 having 23 by 27 micron pixels. Surprised?   Again, GET THE RAW data and see for yourself. The advantage of short exposures are simple, fewer tracking errors, less seeing problems and less chance of unforeseen problems like satellites, airplanes, clouds, bumps in the gear train, wind, etc. I can generate 100 to 200 images of the above ST-6 image quality a night. How many super novae, comets, variables stars and minor planet discoveries are missed by amateurs fiddling with their equipment?

Pixel Matching

Another great example of Pixel Matching is below. The following image is an SBIG ST-6 taken with a 20" f/12 on a Byers series III mount in Florida skies. This image yields 0.9 arc-seconds/pixel resolution. Great optics, great seeing and great tracking allowed this resolution to be obtained. Would a 1 micron pixel help gain any more resolution. Of course not that is simply absurd!

20-inch f/12 sub arcsecond resolution M3 Globular Cluster ST-6 image Mike Palermiti of Jupiter Florida

Would 4 or 10 or 1000 more pixels/star increase the resolution of the above image?  OF COURSE NOT!!!! The scale of the above image of M3 is just under 1 arcsecond/pixel. The use of a smaller pixel could not have increased resolution. In fact, due to the longer exposure time needed to justify the use of the less sensitive smaller pixel the accumulated seeing and tracking errors would have resulted in an image with LESS resolution. Round stars that cover many superfluous pixels is not always an advantage nor does it always mean a "gain" in resolution. Take the ST-6 versus ST-8 image above. Since the ST-8 image has many more pixels covered by the data one could claim more resolution. It does not work this way. Take the two images and match them star for star. Where is the additional gain in resolution?  Simply put, there isn't any gain.

Remember that stars are not resolvable objects. Another big misconception is that smaller pixels yielding better resolution allows for more accurate astrometry. Again WRONG. Note that the limiting factor when performing astrometry is the accuracy of the stellar data being used in the solution and the number of stars used. In the case of the GSC data it is only good to 2/10ths of an arc-second.  Assuming a realistic scale of 2 to 2.5 arcseconds/pixel the use of a smaller pixel yielding sub-arcsecond resolution will not improve the astrometry.  The key to accurate astrometry is scale. If you cannot get enough stars in your field to perform astrometry consider buying a bigger detector camera or focal reduce, but only if you have to.  How about photometry??  Why is a photometer better suited for photometry than a CCD detector?   Is a photometer broken down into very small discrete units. No.

The use of smaller pixels with less sensitivity always requires more exposure time. Hence the need for the auto-guider and consequently the introduction of the new corrective optic methods to overcome the issue of using to small of a pixel that is not well matched to the telescope. Of course the reasons for focal reducing are simple, less focal length, (arguably) smaller spot size, and a larger field of view, all to help take advantage of the smaller pixels. However, I will also argue that a focal reduced Schmidt Cassegrain to f/3.3 is not a "HIGH RESOLUTION" optical system. Compare the results from a Schmidt Cassegrain focal reduced to f/3.3 to the results achieved with a low f-number like an 8 f/4 Newtonian or low f-number short focal length color corrected refractor or Mak Newt and you will see a BIG difference in the image quality. You simply cannot start with a compromised optical design and then compromise it further with additional optics and expect a good clean small stellar image as needed to justify the use of a smaller pixel. To think that one can justify 1 arcsecond/pixel of resolution or even better scale with smaller pixels after factoring in the longer exposures necessary, with our without guiding, is achieving the impossible especially with larger f-numbers (f/8 or larger). Shorter focal length scopes with smaller f-numbers will be better matched to smaller pixels.

Resolution??

When the optical system is matched to the pixel size you will get optimum results. For an example of good pixel matching with the smaller 9 micron pixels showing an actual gain in resolution here is a sample ST-8 image taken with a 5" f/3.8 Wright Schmidt. This is a small f number, short focal length scope, yielding roughly 3.4 arc-seconds/pixel resolution. Notice that high resolution optics that are pixel matched to the 9 micron pixel results in high resolution imagery. Here an even smaller pixel could have been used effectively to gain resolution.

Note that only 1/4th of the data is presented in the above image. For the full 1536 x 1024 image click here. For the untouched raw 16 bit ST-8 data click here.

More 25 micron images!

Hi-res Moon Mosaic
TIE. 24-inch Mt. Wilson scope Mosaic

Courtesy Colleen Gino ST-6

M83 showing good detail
|
One from down under C-14 f/7
Good day mate

Steve Williams Grove Creek ST-6 120 seconds

 C-14 f/7
on Paramount GT-1100

AP-7 CCD Mt. Wilson
Click on the image for actual size
No guiding needed!

The above image was taken from Mt. Wilson using an AP-7 (24 micron pixel camera) and a Celestron C-14 at f/7 telescope mounted on our Paramount GT-1100. Nice match at 2 arc-seconds/pixel. Average seeing. No processing, no guiding, and 120 second exposure.  Somewhere someone said that "time is money".  So little time so many objects to image.

M83 Only 3 minutes
B,V,R

Courtesy James McaGaha and Tim Hunter
Grasslands Observatory

Above is another image showing what can be done with a 25 micron pixel. Imagine 3 to 5 minute exposures in the red, green, and blue. No color balancing required. For detailed information on basic CCD related terms and related concepts please visit the CCD University here for great well explained CCD related topics  Since a picture is worth a thousand words here are some other images which say a lot for the use of a large pixel.

Imaging the planets with large pixels - Absurd!!!

Another very common misconception is that the smallest pixel available will give better results when imaging the planets. Again LOL! Why then do so many of the best planetary CCD imagers  use larger than 9 micron pixel cameras when imaging the planets?

Because, as stated above, the f-number is the governing factor. If you wish to resolve detail on planets you must have a tremendous amount of scale. How do you get good scale for the planets?  The use of a Barlow lens 2x, 3x, or more or better yet eyepiece projection. So what happens to the f-number?  The f-number is increased.  Larger f-numbers that yield the best planetary results are often f/50 or more.

ST-6 Planetary Images - How can this be??

Celestron C-14 OTA 23 by 27 micron pixels

Images courtesy Ed Grafton. Please see Ed's web page for examples of excellent planetary imaging with the 25-micron ST-6 CCD camera

http://ww.ghgcorp.com/egrafton/
 

Again, would a smaller pixel have increased the resolution on the above images?  No absolutely not and is exactly the reason why the best planetary imagers in the world do not use the "SMALLEST" pixel they can find.