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The Digital Shot Calculator
April 4th, 2005 Posted in Schubin's Greatest Hits by sfelix | Print This Post Print This Post
Originally published in Videography April 2005

A man stretches out both arms, hands with fingers together, thumbs stretched out and touching, as though framing a shot. He wears a cap backwards and squints. It seems a cliché of Hollywood pretentiousness. Is it?

Microsoft Word offers truism as a synonym for cliché. Merriam-Webster offers “an undoubted or self-evident truth” as a definition for truism, “especially one too obvious… for mention.”

Perhaps there was a time when what the man was doing with his arms, hands, fingers, thumbs, squint, and even cap were too obvious in image capture to mention. Perhaps today, with a new generation of videographers, it’s worth mentioning again.

The cap may be explained quickly. It’s usually sunny in southern California, so it makes sense to protect one’s scalp with a head covering. The cap is backwards because otherwise its brim would get in the way when pressing one’s eye to a camera’s viewfinder.

The squint is even more specific to shooting. It’s not caused by the sun but is an intentional mechanism for viewing a scene the way less adaptive imagers than the eye (such as film and television cameras) might.

The human visual system is tremendously adaptive. As one squints, however, uneven lighting becomes quickly apparent. Areas that need to be toned down become obvious. Those that need additional light rapidly disappear. Those differentiated by color alone become less saturated and indicate any need for different ways to make them stand out.

As for the arms, hands, fingers, and thumbs, a bit of background is required. Consider the word foot. It refers to (among other things) both the body part at the bottom of a human leg on which a person stands and a unit of length.

Is there a relationship between the two? Take a common 12-inch ruler, and measure your foot. Unless you have exceptionally large feet, you’ll come up short. Certainly, adult human feet are closer to a foot in length than to an inch, a yard, a meter, or any other common unit of distance. But they don’t match.

There was a time when more feet matched a foot. Humans weren’t bigger; the measurement unit was smaller. But it wasn’t easily divisible by other human-body-based measurement units.
So a longer measurement foot was created, defined as the same as three hands (a term that survives in the measurement of horses), four palms, 12 inches (thumb widths), or 16 digits (finger widths). Of course, people still came in different sizes.
The ancient Greek foot was a little over a foot (about 12.1 inches). The ancient Roman foot was about 11.7 inches. The foot we know today was once called the “foot of St. Paul,” not because he had exceptionally large feet but because that distance was carved into a pillar at St. Paul’s Cathedral in London, where everyone could come to measure it.

The foot is a measurement of distance. So is the light year, the distance light travels through a vacuum in a year, almost six trillion miles. That might seem like a lot when you’re measuring scene widths and shot distances, but it’s small for some astronomical measurements, so there’s also the parsec.

Parsec is simply an abbreviation of the words parallax of a second. Second, in this case, refers to an angular measurement, a sixtieth of a sixtieth of a three-hundred-sixtieth of a circle (an arc-second). Parallax is a term for angular displacement based on the position of an observer.

Close your left eye. Hold your right index finger in front of your right eye and position your left index finger behind the right so that it’s hidden from view. Now, without moving the fingers, close your right eye and open your left. The left index finger is now clearly visible due to parallax.
A parsec, about 3.3 light years, is the distance to a star that would shift in position by one arc-second as you opened and closed each eye if your eyes were separated by the average distance between the earth and the sun. A star with a parallax of a tenth of an arc-second would be ten times farther away.

If it’s possible to measure a distance (a parsec) with a known other distance (earth-to-sun) and an angle, it should also be possible to measure an angle with two known distances: the distance to an object and the size of the object. That’s what the squinting person with the backwards cap and extended arms is actually doing.

The ancient Greeks and Romans may have had different lengths of standardized feet, but the human feet within either civilization varied even more. A tall person’s foot was almost certainly longer than a short person’s.

If the length of an adult male foot were divided by his height, however, the result would be the same for most people. That proportionality was described by the Roman architect Marcus Vitruvius Pollio in ancient times. Leonardo da Vinci’s famous drawing of a man in a circle and a square with limbs in different positions is sometimes called “Vitruvian Man” based on that earlier work (Charles Francis Jenkins, the motion-picture and television pioneer who founded the engineering society known today as SMPTE, credited Vitruvius-contemporary Lucretius with the concept of sequential frames depicting motion).

So, although people have different sized arms, hands, fingers, and thumbs, if a person extends the arms forward, palms facing outward, fingers together pointing upward, thumbs pointing at each other and touching, the angle described by the distance from the eyes to the hands and the distance between the index fingers will be about 15 degrees.

What good does knowing the angle do? Fifteen degrees horizontally translates to about an 85-mm lens for a cinematographer shooting with a standard 35-mm movie camera. For a videographer shooting with a 4:3-aspect-ratio, 2/3-inch imager, it corresponds to a lens focal length of about 33 mm.

Suppose you’re going to be shooting in an office, and you want to know if you’ll need a wide-angle lens. Position the left index finger at one edge of the desired shot and find something corresponding to the right index finger position. Reposition the left index finger to that point. Repeat. Repeat again. You’ve now measured 45 degrees, comfortably within the wide end of most normal video zoom lenses. If what you want fits in that angle, you won’t need the special wide angle lens. If it doesn’t, you might (for an alternative method of angular measurement, see sidebar “The Origami Shot Calculator”).

What about narrower angles? Remove one hand. The angular distance from the tip of the thumb to its base is half as much — about 7.5 degrees and twice the lens focal length. Need a tighter shot? Hold up two fingers. Their combined width covers an angle of about four degrees. Want to go tighter still? Hold up just your thumb. It’s about 2.5 degrees wide under the nail, equivalent to about a 200-mm lens for a 4:3 2/3-inch imager, tighter than most normal zoom lenses for shoulder-mount cameras.

Are you shooting with a longer zoom lens and want to know if the face of someone speaking at a rostrum at the other end of a ballroom will fill the shot? Hold up just your little finger, and see if the width of its nail covers what you want. That’s just about one degree, equivalent to about a 500-mm lens on a 4:3 2/3-inch imager, roughly the tight end of a 55:1 zoom.

What if your camera uses a different size imager or you’re shooting in a widescreen 16:9 aspect ratio? The angles remain the same. All you need to do is multiply the focal-length results by a factor.

For most brands of 16:9 cameras with 2/3-inch imagers (exceptions are some BTS, Grass Valley, Philips, or Thomson models), the factor is 1.1. For those same 2/3-inch 16:9 cameras operating in 4:3 mode, the factor is 0.82. For 4:3 cameras with half-inch imagers, the factor is 0.73. For most half-inch 16:9 cameras, the factor is 0.79. For those half-inch 16:9 cameras operating in 4:3 mode, the factor is 0.6. For 1/3-inch 4:3 cameras, the factor is 0.55. For most 1/3-inch 16:9 cameras, the factor is 0.6.

Thus, a little-finger nail width on a 16:9 2/3-inch camera would be about a 550-mm lens (500 x 1.1) — a bit too much for a 55:1 but fine for a typical 60:1 lens. Four thumb-to-thumb framings on a 4:3 half-inch camera would require about a 6-mm lens (33 / 4 x 0.73) — a little too wide for a normal zoom, but well within range of wide angles. And two fingers on a 16:9 1/3-inch camera would need about a 75-mm lens — not that tight in the grand scheme of things, but perhaps a bit more than some lenses that come with 1/3-inch cameras can handle. The solution, in that case, might require moving the camera closer — to three fingers, four, or a fist.

Naturally, digital shot calculators and orbital contrast comparators aren’t the only tools every videographer was given at birth. The auricular distortion analyzer works better and faster than any electronic test equipment and can perform in-service measurements. And the olfactory over-current detector can identify burned-out components in non-contact testing (see sidebar “The Nose Knows”).

Of course, the digital shot calculator seems to work best on cop shows. That’s where the police are armed, suspects are fingered, and, when the bad guys are nailed, the good guys sometimes get a hand.

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The Origami Shot Calculator

Take a piece of paper. It can be of any size or shape, as long as it’s square or rectangular.
Fold it diagonally at one corner. As the paper was originally square or rectangular, the corner was 90 degrees. Folded, it’s 45 degrees, the nominal wide end of a normal lens.

Stick the pointy end against the skin under your eye (don’t poke yourself in the eye). Sight along the outer edges of the folded paper, and you see approximately the view that the wide end of a normal lens can capture.

Now unfold the paper. Fold one of the previously folded edges to the crease formed by the original fold. The angle from that side to the crease is now about 22.5 degrees (“about” only because your folding skills might not be perfect). Add the unfolded side, and the total angle is 67.5 degrees, roughly equivalent to a 6.5-mm lens on a 2/3-inch 4:3 imager, close to the wide end of many wide-angle lenses.

There is, unfortunately, one big drawback to the origami shot calculator. You can’t call it digital.

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The Nose Knows

The engineer in charge rushed into the audio room when told the sound had gone dead. He sniffed the air and announced, “It’s a distribution amplifier.” But which one failed?

Like a bloodhound on the trail, he stuck his nose up against the equipment rack. He popped the cover off one frame of circuit cards, scanning them with his nose.

He pulled one card and replaced it with another. The sound was restored. The good card looked the same as the bad. He sniffed again and pointed to one resistor. “This one,” he announced.

His nickname was based on both his skill at sniffing out the problem and the speed with which he attacked it. He was proud to be known as the Running Nose.

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