10 replies to this topic

[asaint]

Yesterday's CCD Imaging Gear

[Tom T]

Very nice article John. Personally, I'd like to see more in this vein.

[Rusty]

Well done, Sir!

[jrcrilly]

Thanks, Rusty.

I do notice a couple of things to fix when time permits. I'm sure someone will point out to me that the ST-6 used RS-232 serial communications with a PC rather than parallel as I mis-stated. They switched to parallel when the chips got larger and downloads slower. Also, the chart showing pixels/chip size/FOV got scrambled in conversion.

[Tom T]

Hey John

The ST-6 used RS-232 serial communications with a PC rather than parallel. They switched to parallel when the chips got larger and downloads slower.

And just so you know - looks like the chart showing pixels/chip size/FOV got scrambled in conversion.

Well, now that's out of the way...



T

[wilash]

What do all these numbers mean? The pixel matrix array is pretty simple to understand; it defines the overall size of the image created by the camera. The chip dimensions determine the field of view the camera can see with a telescope of a given focal length. This can be calculated by the formula, 57.3/Focal Length of Objective (mm) * chip size in mm. The pixel size determines the resolution attained for a given focal length; smaller pixels result in higher resolution. Oversampling occurs when the pixels are so small relative to the focal length that the resulting resolution exceeds the limitations of seeing or of the optical system. This wastes camera performance but does take advantage of all the resolution the optical system can deliver. Undersampling results when the pixels are too large, failing to take advantage of the available resolution of the instrument. Imagers usually try to select a camera and telescope which will deliver on the order of 1 to 2 arcseconds of resolution. For a 1000mm telescope, this would require pixels of about 3.5 to 7 microns.

Well, there is some strange stuff here. John where did you get that formula for calculating angle of view? What is wrong with angle of view = 2 arctan (d/2f) where d is the dimension of the image plane?

Secondly, why are you using angular resolution rather than resolving power to calculate "sampling"? Focal length by itself is not a good indicator of this. There seems to be a lack of discussion of the inverse of the resolving power of the optics and media are additive. Also, pixel size alone is not a good indictaor of the quality of an image - or do you believe a QVGA sensor that has half the pixel pitch of a 5 megapixel CCD somehow produces "high resolution" images? I feel there is a confusion between angular resolution and resolving power and neither of these address the subjective issue of sharpness and detail of an image (the end result) which tends to be far more important.

Sorry, but I find this whole conclusion very confusing.

[jrcrilly]

Hi, Will!

The formula I used for FOV is the form most commonly seen. When performing calculations on the fly and in one's head it's easier for me to do arithmetic than geometry.

I evaluate angular resolution in my camera analysis because that's a characteristic of the camera and varies only with focal length. Instrument resolution is a different analysis using variables not known in the context of the article (I don't know what your seeing is, or what telescope you'll be using). It's desirable to use an angular resolution which approximates the resolving power of the attached instrument; folks attempt to choose an appropriate combination of focal length and pixel size for a given setup (or as close as they can get while achieving the desired FOV). That's why I mention oversampling and undersampling.

I don't discuss image quality in the article but I can address it briefly here. The highest image quality can be achieved when the angular resolution (arcseconds per pixel) of the camera matches or is smaller than the resolving ability of the instrument under the conditions existing at the time the image is taken. As stated above, oversampling (pixels too small) wastes imager capability but doesn't compromise the resulting image. Undersampling (pixels too large) throws away data to the detriment of the final image.

[wilash]

Hi, Will!

The formula I used for FOV is the form most commonly seen. When performing calculations on the fly and in one's head it's easier for me to do arithmetic than geometry.

I evaluate angular resolution in my camera analysis because that's a characteristic of the camera and varies only with focal length.

John, the focal ratio also affects this. That is why a 1000mm telescope with an 8" aperture has a higher angular resolution (and hence a higher resolving power) than a 4" scope of the same focal length.

Instrument resolution is a different analysis using variables not known in the context of the article (I don't know what your seeing is, or what telescope you'll be using). It's desirable to use an angular resolution which approximates the resolving power of the attached instrument; folks attempt to choose an appropriate combination of focal length and pixel size for a given setup (or as close as they can get while achieving the desired FOV). That's why I mention oversampling and undersampling.

Because you do not know the conditions for imaging, resolving power is preferred over angular resolution. Because both the optics and media can be defined by resolving power, it makes determining the abilities of the imaging system simple.

I don't discuss image quality in the article but I can address it briefly here. The highest image quality can be achieved when the angular resolution (arcseconds per pixel) of the camera matches or is smaller than the resolving ability of the instrument under the conditions existing at the time the image is taken. As stated above, oversampling (pixels too small) wastes imager capability but doesn't compromise the resulting image. Undersampling (pixels too large) throws away data to the detriment of the final image.

Why does "oversampling" "waste" the capability? I don't understand. Resolving power of the componants of a system are additive. You cannot acheive the resolving power of any individual componant. Higher resolution optics allow to to get closer to the resolving power of the media. If you make the optics and media resolving power the same, the final resolving power is half of both. There is a reason that high-quality imaging optics out resolve the media it will be used with because it lets you approach the resolving power of the media itself.

"Oversampling" is dependant on the size of the media, not just the pixel pitch. What is "oversampled" on a small chip, is not "oversampled" on a large one with equal pixel pitch - this is why small digicams are limited to minumum apertures of f/8 whereas larger chips can use effective aperture of f/22 or smaller. So media dimensions will impact how far you can push an optical system.

I am sorry John, but it seems you are trying to define imaging on an absolute scale. That won't work. Ultimately, the process comes down to a final image. As far as your discussion goes, that is a combination of chip size, pixel pitch, and the resolving power of the optics all working together. Individually, these qualities have no real meaning.

[jrcrilly]

I am sorry John, but it seems you are trying to define imaging on an absolute scale. That won't work. Ultimately, the process comes down to a final image. As far as your discussion goes, that is a combination of chip size, pixel pitch, and the resolving power of the optics all working together. Individually, these qualities have no real meaning.

Hi, Will.

We don't disagree but are looking at two different things. Your discussion is focused on analysis of an optical imaging system and deriving some figure of merit to describe the resulting image. Mine (and the topic of the article) is about camera selection. If I choose a focal length and pixel size which results in .5 arcseconds/pixel resolution I know I'm oversampled. If I choose a focal length that results in 5 arcseconds/pixel resolution I know I'm undersampled. Knowing this helps me select which camera/telescope combination to use for a desired image scale. I'm just trying to share this with folks needing to make a similar decision.

In-depth analysis of how to evaluate the degree of harm or lack thereof caused by either condition and/or methods of alleviating the harm would be a topic for a different (and much longer) paper which would be best written by someone else; I'm just helping folks choose a camera.

[wilash]

John:

I am not really talking about something different. When matching a camera to optics, it would be very strange to base it only on focal length and pixel pitch ("pixel size" is not really the size of the pixel). (Especially since it is focal ratio that determines the Airy disk size at the image plane.) Also the idea you can "over-" or "undersample" is not real nor can even be determined by those two factors alone. And if the resulting image is not good, what is the point of this method?

I guess we can beat our heads together over this. But thank you for the effort you put into answering my questions.

[jrcrilly]

Here's a corrected version of the chart which didn't survive reformatting!

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