One time, a few years ago, I was flying from LAX to Tokyo. Now, if you looked at a Mercator map, you would think a direct route would go near Hawaii on a "straight line." But of course, a proper Great Circle route goes nowhere near Hawaii, but rather closer to Alaska—and Siberia. After several hours, I looked out the window and saw an odd angular object. Was it a Russian airplane? An Optical Ilyushin? Or was it just an Optical ILLUSION? No—it was a perky volcano on an island. It was just an Optical Aleutian.
A few months back, I was drinking a beer with a former National engineer, Bill Gross. He made some observation that audible sound covers a very wide dynamic range. A whisper is at around 20 dB; the smallest sound you can hear is around 0 dB. The sound of a jet engine at full power is 100 to 130 dB, which is getting painful. Thus, a dynamic range of 130 dB is a very wide dynamic range indeed.
I immediately rebutted: "But the dynamic range of light that you SEE is, surely, even wider." He did not want to agree with that. So I looked up some numbers. I read somewhere that the limit of the human eye's ability to see a faint object is equivalent to the light you get from a candle 20 miles away.
Right now, I do not want to get into the question of how many photons per second the eye can see. Let's just talk about the relative energy flow, comparing a candle 20 miles away versus direct sunlight. (Let's leave nuclear explosions out of this. They are very bright—and also very LOUD....)
I jumped into my 40-year-old CRC Handbook of Chemistry and Physics and was immediately socked with a bewildering array of terms. How do you compare lamberts, foot-lamberts, candles, foot-candles, steradians, lux, and other forms of light/flux? And what about candelas, milliphots, and stilbs? In general, you don't, and I couldn't. These terms were all cooked up a century or two ago by scientists who used the terms or dimensions that were most convenient for THEM in their own little experiments—not necessarily convenient for us.
I spotted one comparison: The brightness of a candle (as you look at its brightness) is about 3.1 lamberts, whereas the brightness of the sun at noon is about 519,000 lamberts. What does that mean? How can we compare? Let's say the sun subtends an arc of about 0.5°. A candle might have a flame 0.2 by 0.5 in. If that candle is placed about 3 ft. away, it would subtend a similar (solid or spherical) angle.
Thus, the amount of light falling on a surface might be in the ballpark of a ratio of 170,000:1, comparing a candle's light at 3 ft. away versus sunlight. Then if we move the candle back from 3 to 105,600 ft. (20 miles), its intensity would drop by a factor of 35,2002. Using these numbers, the ratio of sun-light, as we see it, to the minimum signal is about 2 * 1014—or about 143 dB.
So this is comparable to the range of sounds the ear can hear. I didn't feel all that comfortable with this estimate, so I went about it another way: The total energy from sunlight falling on the earth is 1000 watts per square meter per second, according to Fink and other handbooks. Let's assume the visible part is half of that, 500 W/m2, or 0.05 W/cm2. What is the LIGHT output of a candle? You cannot use a watt to make 621 lumens, but you can use 621 lumens to make a watt. Thus, 31 lumens/cm2.
A candle puts out 12.57 lumens. If you average this over the area of a 1-ft.-radius sphere, that's 1 lumen per square foot. As there are 930 square centimeters in a square foot, that is 1/930 lumen per square cm. Now increase the radius of that sphere to 3 ft.: There is 1/8370 lumen per cm2 at that radius. The ratio of sunlight to candlelight is about 259,000:1. That seems like a reasonable approximation that's similar to the earlier data. Again, expand that sphere from 3 ft. to 20 miles, and the light-density ratio becomes 3.2 * 1014, or about 145 dB.
So the dynamic range for the ear and eye are both OUTRAGEOUSLY large. It's true that a 100-MW generator at a power plant is BIGGER than the 0.01-pW signal that your radio can pull in by a bigger factor than that (perhaps 220 dB?). But it's still pretty impressive, considering that when it comes to eyes and ears, just about everybody's got two of each. Good redundancy.
Let me see how many photons per second are falling on my eye. (Assume 0.5 cm2.) If we have 1 volt * 1.6 * 10-19 per second (assume 1 electron volt * 1 photon per second), that's a small number. The candle is putting out 1.6 mW of visible light, total. That would be 127 µW/ft.2, or 0.136 µW/cm2, at a 1-ft. radius. At a 20-mile radius, that density is about 150 * 1019/cm2, or 38 * 1019 falling on each eye. This is comparable to 25 electrons per second. Not too silly after all.
Remember, if we knew some of these physical constants, this would all be back-of-the envelope work. Calculators aren't really required for high accuracy. After all, I don't want to claim that one can SEE a 1-dB change in the intensity of a candle 20 miles away. Nor can one DISCERN a 1-dB change in the brightness of sunlight, or HEAR a 1-dB change in the amplitude of a very faint (0 dB) sound. Nor can someone DETECT a 1-dB shift in the roar of a jet engine. Still, that is the ballpark of the signals we're talking about.
One time, I bought 100 LEDs from Poly-paks (long ago located in Lynnfield, Mass.). I also got 600 LEDs from a barrel of factory rejects that National Semiconductor was giving away. In each case, I was hoping to find some weak LEDs to see what range of output light they covered. In each case, I was disappointed, as none of them seemed to be any weaker in output than the others.
I soon realized that this is partly because the human eye has a HUGE dynamic range—but not very good resolution for less than 1 or 2 dB of brightness. Still, these days, you sometimes pull up behind a car that has a long row of LEDs used as tail lights. Sometimes there are some OBVIOUS dim bulbs in there!
Of course, you have noticed that when you walk into a dark room with a LED-readout clock, the LEDs seem quite bright. As you turn on the room's light, the LEDs become MUCH less bright. Of course, that is due to the eye's iris closing up automatically as the room's light levels come up.
Here's a related phenomenon that I saw recently and never noticed before: When you stare out a window into a bright area, and close your eyes, everybody knows that the eyes retain that shape of brightness. NOW—do that—and then quickly put your hand over your eyes. The bright area gets darker, and the dark area gets darker, too. I'm not sure why or how it does that. The hand is a fairly good attenuator of light. Perhaps 80 or 100 dB? But it is not really OPAQUE. Nor are your eyelids.
Neither is the glass seal around the leads of a metal-can transistor. In the old days, when 8-lead TO-5 cans (TO-99s, really) were popular, we used to have to explain to the test engineers that you can't read picoampere currents accurately when bright light is shining around the package. The photons would come through that glass and rattle around inside the metal can, and then get detected by the silicon junctions.
Now we have some new op amps that are packaged in free air. We call it a micro-SMD package. It's die-scale packaging, so the complete dual op amp is just 1.35 by 1.35 by 0.9 mm. There's even a coat of opaque epoxy on the back of the die. Fine. But what's to stop the light from coming in the side of the die? Nothing. The test guys did not think this was a big deal, but I was worried that users might find it a significant problem in ambients where lights might fluctuate.
I set up a couple of test circuits and got some data as I rotated the DUT in full sunlight. The delta VOS was always less than 0.3 mV, worst case. Not so bad. Although the bias current was never worse than 10 nA, the offset current was only about 1/10 or 1/20 of that. So in typical circuits where the impedances at the + and - inputs are balanced, you would barely have to worry about a nanoampere—even in full sunlight!
In a more realistic situation, such as when the devices are a couple of feet away from a 100-W incandescent bulb, these photocurrents are reduced by a factor of ~40 or 60. If you had a fluorescent lamp right down near the IC, just 4 in. away, the ripple current at 120 Hz could be as small as a few dozen picoamperes.
That light sensitivity might make some people nervous. But hey, any 1N914 or 1N4148 glass diode can generate photocurrents TWICE as bad as that! So long as engineers are aware of this small problem, they shouldn't be worried or confused. For further technical information on these small op amps, you could look up AN1112 at NSC's web site, http://www.nsc.com.
All for now. / Comments invited!
RAP / Robert A. Pease / Engineer
Mail Stop D2597A
P.O. Box 58090
Santa Clara, CA 95052-8090