Let's Talk About Optics Downticks

You might not have noticed that neutral-density filters are our friends. But first, you also might not have noticed that OConnor introduced some HDTV camera mounts at April's NAB show. I am not making this up.
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You might not have noticed that neutral-density filters are our friends. But first, you also might not have noticed that OConnor introduced some HDTV camera mounts at April's NAB show. I am not making this up.

Now then, I happen to believe that OConnor makes fine camera mounts, and I can understand how they might think that the adjective HDTV makes them seem extra stable, but there ain't anything HDTV about them. OConnor's marketing types are just following in the footsteps of folks like the founder of Videssence, who once described the output of his products as "high-definition light."

There ain't any such thing as HDTV light. There ain't any such thing as an HDTV tripod or panning head. There ain't HDTV wires, cases, equipment racks or gaffer tape.

I'm ticked off by OConnor's recent misuse of HDTV on account of it diluting the real meaning of HDTV--that is, if it still has one. Yes, you guessed it. In this lunar cycle's rant, I'm going to delve into optics.

Let me get the put-off stuff out of the way right up front. I'm going to mention Airy disks and the Rayleigh criterion. Don't panic! I promise you can forget all about them the instant you finish this column.

Imagine you're a commanding officer, you've got a line of a thousand soldiers side by side in a field, and you tell them to charge straight ahead. Chances are, unless they hate your guts, they'll pretty much charge straight ahead.

Now imagine the same thing, except this time, there's a gigantic wall halfway down the field and it has a slit in the center of it, big enough for maybe a few soldiers to fit through. This time, when you give the order to charge, some of the folks who get through the slit will continue straight ahead, but some will head left or right after they get through.

Light does the same thing. Stick it through an aperture, and some will go straight ahead, but some will spread left or right. That's called diffraction.

Now then, light being wavelike (when it isn't particular), a straying ray could end up with a wave trough superimposed over a wave peak of another ray, canceling it out. The resulting interference pattern from a circular aperture would have a bright center dot, falling off to a black surround, with some other stuff surrounding that.

That bright dot is an Airy disk. Are you with me so far? The Rayleigh criterion says that if two Airy disks are at least half their diameter apart, they can be perceived as two dots, not just one. Still with me?

On account of I'm such a swell masked engineer, I've pre-done most of the math for you. I've got just one small, simple equation. The radius of an Airy disk is 1.22 times the wavelength of the light you're interested in times the f-stop of the optical system. Piece of cake, eh?

So now let's move into the real world. Suppose you've got a 1080i HDTV camera with 2/3-inch imagers. A 2/3-inch imager has an 11-millimeter image diagonal (on account of old camera tubes with 2/3-inch outer diameters having 11-millimeter image diagonals). Apply the 16:9 aspect ratio and the Pythagorean theorem, and you end up with an image height of around 5.4 millimeters. So 1080i HDTV's 1,080 lines have got to fit into that 5.4 millimeters. That means each line is 5 µm.

If the radius of the Airy disk of the optical system is 5 µm or less, everything's cool--at least as far as diffraction is concerned. So, let's pick blue light with a wavelength of 475 nm and an aperture of f/2. Stick that into the handy-dandy equation, and the Airy disk radius is just 1.159 µm. The 1,080 lines have nothing to fear from diffraction.

Now then, take the same camera, pick red light at a 630 nm wavelength and an aperture of f/11, and the Airy disk radius is about 8.45 µm. That means you can't get a totally clean 1,080 red lines out of the camera. If you want the full 1,080-line HDTV, you've got to be wider open than f/8. If you're most interested in green at maybe 510 nm, f/8 will just make it, but f/11 would be diffraction limited.

You folks who shoot indoor events at f/4 or less are probably filing this away in the Esoteric Knowledge file, (which is often circular and sits close by on the floor so it can be more easily filled). But give me another moment or two.

The big news at NAB2005 was 1/3-inch HDTV cameras. That's what was at the front end of HDV camcorders from JVC and Sony as well as the P2 HDTV camcorder from Panasonic.

A 1/3-inch camera has a 6-millimeter image diagonal. In 16:9 HDTV, that's about a 2.9-millimeter image height. That means the Airy disk radius has got to be about 2.7 µm or less to get all the resolution of 1,080 lines.

So let's keep that 510 nm green wavelength and try f/5.6. So sorry! The Airy disk radius is about 3.5 µm, so the 1,080 lines will be diffraction limited. At f/4 you're okay on green, but red is still a small problem.

If you take one of those new HD camcorders out to shoot in broad daylight, you're in trouble. (The JVC, with 720-line HDTV, is less affected.) If you stop down for exposure, you hit diffraction softening. If you use a shutter, you get motion judder.

What to do? Neutral-density filters are our friends! With enough neutral density, you can stop down to f/2.8 so even red isn't diffraction limited. With the small-format imager, you'll still probably have as much depth of field as you need, (which'll have to be the subject for a different rant).

"But, Mario, what about single-chip cameras with color filtering?"

Ah, yes. My rant on the divided-loyalty optical low-pass filter will also have to wait for a different lunar cycle.