View Full Version : The Kell Factor And Why You Should Care

01-09-2006, 11:09 AM
My wife doesn't understand me; no really, when I slip and talk engineering, she has NO IDEA what I'm saying. Lately when I'm lost in my own little world talking about bandwidth and -3dB points, she uses ASL (American Sign Language) to snap me out of it. It only takes 2 signs; (Don't Know) (Don't Care), for me to realize that I'm talking in a foreign language, engineering. It's not easy for an engineer to come back to the real world and talk in plain English, but I'll do my best to explain the Kell Factor in simple terms.


Assume we have a CCD with a 4:3 aspect ration and a resolution of 640h x 480v. We also have the best lens and the best circuits to obtain the maximum resolution. The Kell Factor tells us what is the best resolution we can expect. There's more to it than that, but I'll cover that later.

There are 2 ways of measuring the horizontal resolution. The first is to measure across the whole horizontal width. This measurement would provide the highest number because there are more pixels and more width than the vertical direction. The second way is to limit the horizontal direction to the maximum vertical distance. This places both directions on the same scale and allows us to compare the 2 resolutions.

The classic definition is the lines must fit in the biggest circle on the device. This definition works very well with tubes where the corners of the image were cut off. Today, with CCDs and LCDs, every pixel is visible and we could say the biggest SQUARE that fits on the device.

In the case of a 4:3 aspect ratio, 640h pixels x (3/4) = 480h pixels. Thus, the measurement is made on a 480h x 480v area.

If all the lines on resolution chart aligned exactly with the elements of the CCD, we should have a total of 480 lines. Where a black line equals 1 line and a white line equals another line. However, if we shift the lines by 1/2 a pixel, every CCD element has 1/2 a black line and 1/2 a white line. This would result in all the CCDs rendering a solid gray output. When the Kell Factor is 1, every CCD element must render a different line. It could happen, but don't count on it.

Let's assume that the Kell Factor is 0.5; in that case 480 pixels x 0.5 = 240 lines. In other words, 2 CCD elements results in 1 line. 1/(Kell Factor) = Number of CCD elements per line. In the best case alignment, we would see 2 black pixels followed by 2 white pixels. In the worst case alignment, we would see: Black Pixel, Gray Pixel, White Pixel, Gray Pixel. This may not be perfect, but the lines are clearly visible.

When the Kell Factor is 0.6666..., 3 pixels are trying to resolve 2 lines. In the best case we have: Black, Gray, White. In the worst case we have: Black, Gray, Gray (OR Gray, Gray, White).

As the number of lines increases or I could say as the Kell Factor is increased, we have a lowering of the contrast between the lines. The detail is still there, but the lower contrast makes it harder to see. There is a way to increase the contrast, but it comes at a price.

In the analog days, we called it peaking. That is, the gain for the higher frequencies is increased, while the gain for the frequencies below that point is the same. At the point where the signal is starting to drop, we increase the signal. This improves the contrast of the fine detail.

The problem with increasing the high frequency detail is NOISE. It turns out that noise in the tube and CCD sits exactly at the same point where we want to increase the gain. Another problem is that too much gain can result in over sharpening the edges and create a weird outline effect.

In the digital world with DSP (Digital Signal Processing) we have tighter controls over what we can do to the signal compared to analog control. Still, every system has its limits and the correct setting is a balance between 2 extremes.

Taking into account what we can do with digital compared to analog, what is the correct number for the Kell Factor? The answer depends on who you talk to. Most give a number around 0.70 (give or take a little). This seems to be the standard number we use, but you can make a case for a number like 0.80 and 0.85; however 0.85 seems to be pushing the limits.


Someone reported that the Canon had a horizontal resolution of 800 lines. This can NOT be correct! First we need to convert the 800 lines into the full width of the 16:9 frame.

800 lines x (16/9) = 1422 lines

1422 lines / 1440 horizontal pixel count = Kell Factor = 0.988

Yes, if things line up exactly, you can get that, BUT no engineer worth their salt will ever agree to a Kell Factor of 0.988 all the time!!!

Based on the recorded pixel resolution and a Kell Factor for 0.7 to 0.85, (written as xx - yy lines), here is what we would expect to see for resolutions. This does NOT take into account loss in sharpness due to the lens and other factors. The resolution could be about this high or lower.

Canon and Sony 1440h x 1080v:
. horizontal 567 - 689 lines
. vertical 756 - 918 lines

JVC 1280h x 720v
. horizontal 504 - 612 lines
. vertical 504 - 612 lines

Panasonic 1280 x1080v
. horizontal 504 - 612 lines
. vertical 756 - 918 lines


Depending on how the test is performed, different results will occur. We would want the test chart to be well lit and the camera set for the optimum image.

One critical thing is that the F Stop setting can have a major impact on the sharpness of the image. In general closing the lens One F Stop from the widest opening is the sharpest image you can get from the lens. The test should never be performed with an F Stop greater than F 4. At higher F Stops, like F 11, the sharpness of the lens drops.

Another issue is that with zoom lenses, there can be a point in the zoom where the image is the sharpest. To understand the lens sharpness you may need to do 5 different tests at 5 different points in the zoom range.

Even under ideal conditions, there are points in the image where the lines match the CCD elements and appear. Yet, other points in the image, the lines end up in the worst possible placement and the resolution looks worse. Because of this effect, taking a reading from just one point in the chart is not accurate. To be very accurate would require several readings. If the chart does not have the resolution in several different places, you may need to move the camera a little to the left/right/up/down to take additional readings.

The readings may be a bit subjective. It's easy to count the lines when you clearly see black and white lines, but do you count black and gray OR light gray and dark gray?

Last of all with most lenses, the corner of an image is never as sharp as the center of the image. Most readings should be taken from around the center of the image. The ideal test is when you compare several cameras, that way the readings can be taken from the same spot in the frame with each camera.




Bob Diaz

01-09-2006, 11:52 AM
Thanks Bob, this is all new to me. I am the sponge trying to soak it in. Of course, you could tell me the net res is my IQ times my shoe size and I couldn't argue the point.


01-09-2006, 12:03 PM
Once again Bob!

Man, you should get together with Barry and Jarred sometime.

You have a lot to offer to this forum.

Everyones hyped about 1080 resolution, but what will the end result be if the lens falls short.

As you mentioned, the center of the lens has the least aberrations.
I wonder if engineers could come up with a solution that will focus
on gaining the benefits of using the center of the lens. Obviously they have to
some extent, maybe more than I realize depending on imaging surface, focal length and chosen glass.

I work in the photolithography field and this is exactly how the
last six years of photolithography have benefited.

We now scan the masked image (reticle) through the lens over the exposure area.
This way we can scan through a slit within the center of the lens.
We have better control of astigmatism, distortion, coma, SA, and TFD.
We're able to resolve lines <100nm. Intel is driving 65nm technology now.


01-09-2006, 01:12 PM
great post...! i wish it had some little illustrations to go with it... :)

01-09-2006, 03:00 PM
That's da bomb, very clearly explained. It's very important to remember that the numbers are only measuring the verticle equivalent in the horizontal! Then again, that means the CCD's in the 450 are oversampling like nobody's business, with 850 lines. If only you could get the raw output of those CCD's and get them to tape somehow... Sigh.

01-09-2006, 03:43 PM
One critical thing is that the F Stop setting can have a major impact on the sharpness of the image. In general closing the lens One F Stop from the widest opening is the sharpest image you can get from the lens. The test should never be performed with an F Stop greater than F 4. At higher F Stops, like F 11, the sharpness of the lens drops.
Awesome information, Bob. I noticed exactly what you said (above) while testing my new JVC GY-HD100 this weekend. The lens looked sharpest around F2.8 - F4. The shots I posted in the JVC section were shot around F8, a tad soft for what the lens is capable of.

01-09-2006, 06:04 PM
Geeeezzzzz...Bob !

I perfectly understand now !
I perfectly understand !!!

...i...perfectly...understand...why i am a musician and not an engineer !

...but i get the idea.

I understand that if we take 10 different readings from the same camera from the same rez chart, but with a very very slight pan from shot to shot, the different alignment of the pixels with chart's lines could lead to different readings ?

Do i undertand correctly ?

(sorry for my poor english)

thanks a lot !

01-09-2006, 07:20 PM
First, if possible do NOT shoot with any of the 1/3" HD cameras with an F Stop higher than F4. Maybe F5.6 if shooting 720p. At F8 and higher there will be a loss in sharpness. If you must shoot in sunlight, use the highest N.D Filter to allow you to open the F Stop up.

Second, if one shoots a resolution pattern. Then pans the camera a little to the left, takes a shot, a little to the right, take a shot, a little up, take a shot, a little down, ... If you do this for a total of 10 readings, many readings will aggree, but the readings will fall into groups. For example, xx readings say 625 lines, yy readings say 650 lines...

Bob Diaz

01-09-2006, 07:44 PM
Bob for president!

01-09-2006, 09:17 PM

Good info bob. But maybe she wants something else... hopefully. Man, how do you keep that in your head and then want it out. I got into this biz so I wouldn't have to do math... better to write up a script and shoot somethin and let that stand for what counts. I think one of the best films I've ever seen, the celebration, was shot on a 900 dollar mini DV cam.