‌Chapter 3

Digital Photos: The Patent Clerk’s Heuristic

My social media feeds are full of the usual overnight fare—morning news from Europe and Africa, evening stories from Asia and Australia, digital photos of the kids and cats of friends around the world …

As someone who writes regularly about historical discoveries in science, I’m often struck by how few photos exist of major scientists of the past. These image collections also tend to be skewed toward later life, after the subject became famous, which distorts our perception of scientists somewhat. Photos of Einstein taken around the time he was revolutionizing physics show a well-groomed young man—a far cry from the iconic images of him taken later on, with rumpled clothes and wild, white hair. The scarcity of images is complicated by copyright issues, of course, but even professional archives tend to have only a few dozen photos of great physicists of the twentieth century.

This paltry number is especially shocking from a modern perspective; over the last few decades digital photography has become ubiquitous, leading to an explosion in the number of images created. I’ve long been interested in photography, but the expense of purchasing film and having it developed presented enough of an obstacle that I have only a few hundred pictures from before 2004, when I first got a digital camera. Since then, I’ve taken tens of thousands of digital photos, nearly all of which I have stored on the hard drive of my computer. I probably have more photos of my children (who’ll be ages ten and seven when this book comes out) than have been taken of my parents in their entire lives. And that only counts those captured with my dedicated camera, not quick snapshots grabbed with my phone.

The incredible ease of digital photography, particularly thanks to the spread of cameras in phones, has had a revolutionary impact on everyday life. Today there are billion-dollar companies that do nothing but process, store, and share photos taken by users, and whole new cultural phenomena like “selfies” that have grown up around the technology. And the ready availability of cameras has transformed all manner of interactions between the general public and various authority figures. Incidents that would have been “he-said, she-said” disputes in the days of film seem invariably to be caught on cell phone video these days, with consequences for society that are still working themselves out.

Digital cameras made the transition from rare and expensive gadgets to integral parts of everyday life impressively quickly, but the science underlying these devices remains underappreciated. The sensor your phone uses to take pictures of your kids, cats, or your breakfast to post on Twitter is, at a fundamental level, quantum mechanical, relying on the particle nature of light. There’s no small irony, then, in the fact that the discovery of the physics essential to this technology was merely a byproduct of an experiment proving light’s wave nature.

Hertz’s Experiments

As mentioned in the last chapter, experiments by Thomas Young and Francois Arago in the early 1800s—demonstrating that light waves show interference effects when passing around obstacles—conclusively showed that light behaved like a wave. And in the middle of that century, Maxwell’s equations answered the question “What is waving?” by predicting the existence of electromagnetic waves moving at the speed of light.

One of the implications of a theory of light as an electromagnetic wave is that it ought to be possible to create such waves using electric currents. In the late 1880s, the young German physicist Heinrich Hertz decided to do just that, and put Maxwell’s equations to a direct experimental test. Hertz devised an ingenious apparatus involving “spark gaps,” pairs of metal knobs separated by a few millimeters of air. One spark gap was attached to an antenna connected to a battery system, which applied an oscillating high voltage between the knobs. This produced a bright spark in the gap as the electric field broke down the air between the knobs, allowing a current to flow at a frequency determined by the oscillating voltage (which Hertz could set to a value of his choosing). As electrons rushed back and forth across the gap, according to Maxwell’s equations, their motion should generate electromagnetic waves traveling outward from the gap, oscillating at the same frequency.

The other spark gap—the knobs on either end of a wire ring placed some distance away—served as the detector. The arriving electromagnetic wave from the transmitting spark gap induced a smaller voltage in the detector and produced a much smaller spark. The distance between the knobs on the detector was adjustable, and would be tuned until the arriving waves just barely created a spark across the gap. More intense arriving waves induced a higher voltage in the detector, increasing the distance the spark could jump. Using this detector, Hertz was able to map out the intensity of the waves produced and show that the results exactly matched Maxwell’s predictions—both for traveling waves leaving the detector and standing waves formed by reflecting the initial waves off a metal sheet on the far side of a lecture hall. Hertz’s apparatus generated waves at extremely low frequencies compared to visible light, but he showed that they traveled at the same speed, confirming that light is an electromagnetic phenomenon.

Principle of the spark gap apparatus used by Hertz. A large oscillating voltage creates sparks across a gap in a loop of wire, generating electromagnetic waves at that frequency. At the detector gap, the wave induces a voltage that can make a spark if the gap is small or the wave is large enough. The size of the largest gap the spark can jump is a measure of the size of the wave.

Asked about the significance of his experiments, Hertz demonstrated the business acumen of a great physicist by cheerfully responding, “It’s of no use whatsoever. This is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there.” Only a few years later, however, the same principles used in Hertz’s spark-gap experiment were used to generate radio waves for “wireless telegraphy,” eventually leading to broadcast radio, television, and cellular phones.

Hertz’s experiment demanded enormous care and precision, plus the investigation of many possible confounding factors. In the course of this investigation, Hertz noticed that the size of the detector gap possible for a given configuration was slightly larger when there was a direct line of sight from the source to the detector. When he blocked the light from the initial spark from falling on the detector, it reduced the size of the gap across which a spark could jump. He thus discovered what’s now called the “photoelectric effect”: that ultraviolet light falling on a metal surface produces a charge on the metal, making it easier for weak incoming waves to induce a spark between the knobs of his detector.

For Hertz, the discovery of the photoelectric effect was of little consequence, merely a systematic quirk to be explained along the way to demonstrating the wave nature of light. Unbeknownst to him, though,1 this minor digression would prove to be an essential bit of evidence for light’s particle nature, just a few decades later.

The Patent Clerk’s Heuristic

Hertz’s accidental discovery of the photoelectric effect drew the attention of a number of prominent physicists of the day, who began shining ultraviolet light on a variety of materials and investigating the results. From the way the ejected particles responded to electric and magnetic fields, they determined that the charges ejected by the light were electrons, which had recently been identified as negatively charged subatomic particles by the British physicist J. J. Thomson (who would eventually win the 1906 Nobel Prize for discovering the electron).

When combined with the wave model of light, the knowledge that the photoelectric effect involves the ejection of electrons, which are components of atoms, allowed physicists to construct an appealingly simple model of the process. Electrons are bound into atoms, and an incoming electromagnetic wave shakes those electrons back and forth. This shaking transfers energy to the electrons in a way that physicists expected would depend on the intensity of the light. The higher the intensity, the greater the displacement of electrons, so high-intensity light should deposit enough energy to knock electrons loose quickly, but as electrons will continue to absorb energy as long as the shaking continues, even low-intensity light should eventually shake a few electrons free.

The light’s frequency was another experimental factor that could affect the ejected electrons, though how the electron properties should depend on frequency was less obvious. In the classical wave picture of light, the amount of energy carried by the wave depends on the size of the wave, not its frequency, so any dependence on frequency would be more complex than the intensity dependence. There might be some resonance effects—shaking at some characteristic frequency associated with a particular atom might deposit energy more efficiently, in the same way that gentle shaking of a pendulum at just the right rate can produce dramatic oscillations. Lower frequency might also lead to a delay in emission, as electrons shouldn’t be ejected until they’ve had time to be shaken back and forth a few times, but the frequency of visible light is so high there’s no real hope of measuring this.

The simple model favored by physicists made four basic predictions about the behavior of the ejected electrons that can be tested in experiments:

This simple model ties together the best knowledge of the day concerning the physics of light and electrons, and thus was very appealing to physicists. Unfortunately, it was also a miserable failure.

In particular, careful experiments by the German physicist Philipp Lenard (who had worked with Hertz for a time) failed to show the expected relationship between the intensity of the light and the energy of the electrons. Brighter light did, as expected, increase the number of electrons emitted (measured by the current flowing between two metal plates inside a vacuum tube when one of the plates is illuminated), but the energy of those electrons (measured by the voltage associated with the current in the vacuum tube) was the same regardless of the intensity of the light used.

An even more puzzling outcome of Lenard’s experiment was the discovery of a surprisingly simple relationship between the energy of the ejected electrons and the frequency of the light. Across all the materials Lenard tested, the energy of the electrons increased as the frequency increased, in an apparently linear manner. This was a completely unexpected and deeply mysterious result.

As in the case of thermal radiation, the simple and universal behavior discovered by Lenard seemed to point to simple underlying physics, but nobody could construct a convincing model. Lenard himself spent many years working on the theory that the electron energy was determined by the motion of electrons within the atoms, with the light serving only as a trigger for the electron ejection, but this proved untenable and he eventually had to abandon it.

The explanation that would eventually become the accepted model for the photoelectric effect was first proposed in 1905 by an obscure patent clerk in Switzerland by the name of Albert Einstein. In a paper with the rather cautious title “On a Heuristic Viewpoint Concerning the Production and Transformation of Light,” Einstein suggested taking Max Planck’s quantum hypothesis, which associated each light-emitting “oscillator” in a material with a characteristic energy that depended on the frequency of its emitted light, and applying it to the light itself. In this “heuristic viewpoint,” a beam of light is not a wave, but a stream of particles (now called “photons,” though that term wasn’t coined until years later; Einstein preferred “light quanta”), each carrying a single quantum of energy: Planck’s constant multiplied by the frequency of the light. If the energy of a single photon exceeds a characteristic energy for the material being illuminated, called the “work function,” each photon can knock loose a single electron, which carries off the rest of the photon’s energy.

This particle model of light was a radical departure from well-known physics, but it worked brilliantly to explain the observed features of the photoelectric effect. A more intense beam of light contains more photons, thus enabling the increase in the number of emitted electrons. The energy of the electrons, though, does not depend on the intensity, because only a single photon is needed to knock loose an electron. And the increase in energy with increasing frequency simply reflects the increasing energy of a single photon following Planck’s rule relating energy to frequency; if the photon energy is greater than the work function, the electron carries off the excess, which increases as the frequency increases.

Eisntein’s photon model is simple and elegant, but also completely incompatible with Maxwell’s equations—which only work for waves, not particles—and was thus wildly unpopular when first introduced. Planck himself, in nominating Einstein to the Prussian Academy of Sciences, wrote: “That he may sometimes have missed the target in his speculations, as for example, in his hypothesis of light quanta, cannot really be held too much against him, for it is not possible to introduce fundamentally new ideas, even in the most exact sciences, without occasionally taking a risk.”

However unpopular it was, Einstein’s heuristic model made very clear and unambiguous predictions about what one should expect to see in photoelectric-effect experiments, and as a result attracted a considerable amount of attention. The situation remained a little murky, though, until Robert Millikan, one of the finest experimental physicists of the day, took up the question. The experiments are very sensitive to contamination of the metal surfaces and small voltage shifts arising from contacts between different metals, but Millikan and his team2 tracked down and resolved all these issues, and provided an extremely convincing experimental confirmation of Einstein’s model in 1916, producing a measurement of Planck’s constant that was consistent with previous values but with much improved precision.

This does not mean, however, that Millikan was a fan of the photon model. In fact, the introduction of his first paper on the subject is a masterpiece of the passive-aggressive style in scientific writing:

Einstein’s photoelectric equation for the maximum energy of emission of a negative electron under the influence of ultra-violet light … cannot in my judgment be looked upon at present as resting upon any sort of a satisfactory theoretical foundation. Its credentials are thus far purely empirical…

I have in recent years been subjecting this equation to some searching experimental tests from a variety of viewpoints, and have been led to the conclusion that, whatever its origin, it actually represents very accurately the behavior… of all the substances with which I have worked.

Millikan’s grudging acceptance of the accuracy of Einstein’s model in spite of his personal reservations is fairly representative of opinion at the time. The photon model was too radical a departure to be easily accepted, but it worked too well to be easily cast aside. Over time, the particle view of light became more accepted, though concerted efforts to find an alternative explanation continued until the mid-1920s. In a strict technical sense, incontrovertible experimental proof of the existence of photons was only achieved in 1977,3 but as a practical matter, light as a particle was an accepted part of quantum physics by 1930 or so.

Both Einstein and Millikan made out well as a result of the photoelectric effect. While he’s best known for relativity, the photoelectric effect is the only specific result mentioned in Einstein’s citation for the 1921 Nobel Prize in Physics.4 And Millikan’s own Nobel Prize, in 1923, mentions both the photoelectric effect and an earlier experiment to measure the charge on an electron. And as we shall see, this new understanding of light paved the way for many technologies that have become central to modern life.

Photoelectric Technologies

The dual particle and wave nature of light is one of the classic examples of the weirdness of quantum physics, a phenomenon with seemingly contradictory properties. This is evident in the photoelectric effect itself, which relates a particle property (the energy content of a single photon) to a wave property (the frequency of the light), leading to some potential confusion as to what, exactly, it means for a particle to have a frequency. Even today, physicists continue to argue about the best language to describe the nature of light, and how best to teach the core concepts.

As such, the idea of photons may seem too bizarre to make everyday use of. In fact, however, it is central to essentially any technology used to convert light into an electronic signal.

Admittedly, the device that shows the clearest connection to photoelectric physics is a bit arcane: it’s what’s known as a “photomultiplier tube,” consisting of a series of metal plates with a high voltage (generally a few hundred to a thousand volts) applied between them. A photon of light falling on the first of these will eject a single electron through the photoelectric effect. The high voltage then accelerates this electron toward the next plate in the series, where it collides and knocks loose several more (ten to twenty) electrons.5 Each of these is then accelerated toward the next plate, and the next, and so on. By the end of the tube, a single photon has triggered a cascade of millions of electrons, producing a tiny pulse of current that can readily be detected. Photomultiplier tubes can be extremely sensitive, able to detect even a single photon, and they are at the heart of many experiments investigating the quantum nature of light. While used in some older “electric eye” systems, these days, photomultiplier tubes are generally found only in physics labs.

The same essential physics, however, is at the heart of a digital camera. Each pixel in a digital camera’s sensor consists of a tiny chunk of semiconductor material that is exposed to light for some period of time. In this case, incoming photons do not completely eject electrons from the material, but they do promote an electron from a state in which it is unable to move to one where it can flow freely (more about this in Chapter 8). When the camera shutter is open to take a photo, all the electrons within a given pixel that are promoted to a freely flowing state are collected,6 building up a voltage that gives a measure of the brightness of the light hitting that pixel. At the end of the exposure time, these pixel voltages are read out to produce an image.

Silicon-based photosensors offer the great advantage of small size and ready integration with the digital information processors they work alongside. Today, a camera chip small enough for use in a cell phone will contain a number of pixels that rivals the resolution of a professional-quality digital camera. The camera of my current smartphone has 16.1 million pixels (the default image is 5344 x 3006 pixels), while my good DSLR camera has 24 million (6000 x 4000). The primary limitation on the quality of cell phone photography these days is optical, not electronic: a lens package small enough to incorporate into a phone has more limited capabilities than the larger lenses of a standalone camera. For most people who are not serious photography buffs, though, these limits are not particularly noticeable.

To make color sensors, a grid of red, green, and blue filters is placed over the top of the pixel array, so that each pixel is detecting light of a single color. To make the final image, the voltages from nearby pixels of different colors are combined to determine the mix of red, green, and blue colors that best approximates the light at that point in the image.

Digital cameras can get away with measuring only three colors because this closely matches the way the human eye processes light to determine color. When a photon strikes a light-sensitive cell in the retina, the energy from the photon triggers a change in the configuration of a protein molecule, which sets off a chain of chemical reactions that eventually sends a signal to the brain to inform it that this particular cell detected some light. There are three varieties of these cells, each sensitive to a different range of photon wavelengths, and the brain uses the different responses from each type to produce the color that we see. The peak sensitivities are at wavelengths corresponding to blue, green, and yellow-green light, though all three are sensitive to a broad range. Our brains infer color from the mix of activity levels of these cells: red light triggers only the longest-wavelength receptors and blue light only the shortest, while green light triggers all three. Televisions and computer monitors use a mix of the three colors to trigger these receptors in the right proportions to duplicate our response to the spectrum of light from some real-world object and trick the brain into thinking it sees a rich variety of colors.

While it takes only a single photon to trigger the light-detecting process, a typical digital camera sensor does not offer single-photon sensitivity because the random thermal motion present in any material at temperatures above absolute zero can spontaneously generate free electrons inside the sensor. To have confidence that the signal recorded by a particular pixel reflects actual light, the number of photoelectrons must exceed this “dark current” to register a response within the sensor, which limits the sensitivity at low light. This effect depends strongly on temperature, so professional scientific cameras used by astronomers and in quantum-optics experiments generally have their sensors cooled to reduce the dark current to a level that allows reliable detection of single photons.

The same issue of “dark current” affects your eyes—in principle, the photosensitive chemicals in your retina can detect a single photon, and in carefully controlled laboratory experiments, human volunteers can sometimes detect pulses of light containing only a handful of photons. In more typical situations, though, it takes something like one hundred photons entering the eye within a few milliseconds for a human to reliably detect a faint flash of light—and, of course, cooling the retina of the human eye to reduce dark current and improve sensitivity isn’t advisable.

However, the limits of dark current are a practical issue, not a fundamental one. The process that enables commercial digital cameras is fundamentally quantum: a single photon enters the sensor and knocks loose a single electron. Our ability to understand this process—and to build these devices that take advantage of it—traces directly back to Heinrich Hertz’s chance discovery of the photoelectric effect, and Albert Einstein’s radical suggestion in 1905 that light might be a particle after all.

Notes

1 Around five years after his pioneering experiments on electromagnetic radiation, Hertz died of a vascular disease at only thirty-six, a tragic loss for physics.

2 As was common in that era, Millikan is listed as the sole author on the resulting papers. His acknowledgments, however, make clear that other people (he credits A. E. Hennings and W. H. Kadisch for assistance with the experiment, and he thanks Walter Whitney for spectroscopic measurements to determine light wavelengths) contributed at a level that by modern standards would rate an author credit. He also gives a rather generous acknowledgment to “the mechanician, Mr. Julius Pearson,” for helping design and make the evacuated glass tubes used for the experiment.

3 In the 1960s, Leonard Mandel and colleagues developed a “semi-classical” model for the photoelectric effect, where the metal surface is treated quantum-mechanically but the light is considered as a classical wave. In 1977, an experiment by Jeff Kimble, Mario Dagenais, and Mandel demonstrated a clear delay between the emission of consecutive photons by single atoms, an effect that can only be explained with a particle model.

4 This came about through tedious and petty academic politics.

5 As a material particle with mass and charge, an electron colliding with a surface delivers energy to the material more effectively than a massless photon does.

6 In an older “CCD” type camera, the electrons build up in each pixel, and after the exposure is finished, they are shifted along the rows of pixels to a sensor at the edge of the chip. The “CMOS” sensors on most newer cameras include a small amplifier associated with each pixel, and directly produce a voltage signal that’s read out to make the image.