circa 2004
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AN OPTICAL CONNECTION TO LIGHT
I believe the Aleph [one of the points in space that contain all points…the place where, without admixture or confusion all the places of the world, seen from every angle, coexist…there too will be all stars, all lamps, all sources of light] of Calle Gara was a false Aleph. Let me state my reasons. In 1867, Captain Burton was the British Consul in Brazil; In July of 1942, Pedro Henríquez Ureña discovered a manuscript by Burton in a Library in Santos, and in this manuscript Burton discussed the mirror attributed in the East to Iskandar dhu-al Qarnayan, or Alexander the Great of Macedonia. In this glass, Burton said, the entire universe was reflected. Burton mentions similar artifices—the sevenfold goblet of Kai Khosru; the mirror that Tāriq ibn-Ziyād found in a tower (1001 Nights, 272); the mirror that Lucian of Samosata examined on the moon (True History, I:26); the specular spear attributed by the first book of Capella’s Satyricon to Jupiter; Merlin’s universal mirror, “round and hollow and … [that] seem’d a world of glas” (Faerie Queene, III:2, 19)—and then adds these curious words: “But all of the foregoing (besides sharing the defect of not existing) are mere optical instruments...--- Borges, The Aleph
-- From “Star Testing Astronomical Telescopes” by Harold Suiter.The Point Spread Function which describes, roughly, what one can, or rather cannot, see of the lighted universe by way of an optical device. [This will make more sense later...]
When I am fortunate enough to have a well-corrected telescope; a warm night; clear, stable, dark skies; and a big, fat softly-powered eyepiece, I am graced with what I consider to be among the most beautiful views in the universe: seemingly infinite and opulent fields of shining-white and impossibly small pinpoint stars. It is one of the reasons I entered the hobby of amateur astronomy and it is often what I think about on the cold or cloudy nights when I am not indulging my only other know hobby down in my wine cellar. I have been looking at and thinking about these fields of stars on and off for more than thirty years. I was astounded and disoriented, then, when it was finally revealed to me at age 45 that what I was seeing was not impossibly small pinpoint stars but rather a mere effect of optics, an interaction between the telescope aperture and the wave-front of light coming from the star that looked like a star but was, I now understand, not.
When I uncovered this little surprise at an age when I was surprised I would be surprised about something, I knew that I would have to dig a little deeper into the question of light and optics. I had been operating on assumptions about astronomy and telescopes and light that needed an update. I couldn’t use the old ones since they were fractured and I couldn’t go forward without new ones because I felt I needed to understand what I was looking at to make it meaningful. I needed to know what I was seeing. Fortunately, my new revelation was not really new and is well understood by physicists, optical designers, and most if not all moderately advanced amateur astronomers. In fact, many of the astronomy and optical books already on my shelves made some reference to it, a reference I had, to date, glossed over completely. But I took another look now and in looking I quickly learned that to understand what I was seeing optically of stars required that I understand something about light. And understanding light – which, with the exception of seeing it with our eyes, is usually apprehended indirectly – is an act of interpretation, mathematically or otherwise, if not an act of faith. And since interpretation is always filtered by way of culture and history, I had to look back before I looked forward to understand what I was seeing. So here is my short history of light:
Chapter 1: Light is created. If you have a religious turn of mind, the first chapter of light needs to be about its creation otherwise skip to Chapter 2. Since references to Genesis and “Let there be light” seem clichéd at times, I like Bacon who called light “the first creature of god”:
The first creature of God, in the works of the days, was the light of the sense; the last was the light of reason; and his sabbath work ever since, is the illumination of his Spirit. First he breathed light upon the face of the matter or chaos; then he breathed light into the face of man; and still he breatheth and inspireth light into the face of his chosen.-- Bacon, Of Truth
Theories of light after the beginning and before chapter 2
are either unspoken or incoherent or wrong (by way of our hindsight). Light
is viewed at this point as “one thing” rather than the “many” we know today (as
the color components of light, for example) and it always arrives from its source instantaneously.
Chapter 2: Light is a Wave, Part I. In 1678
Christiaan Huygens pitches to the world a wave theory of light in "Traite
de la lumiere." The basic idea is that light is like a wave
which spreads out from the source and each point on the wavefront propagates a
new wave-front. By this model many optical behaviors like
reflection, refraction, interference, and diffraction (discovered by Jesuit
priest Francesco Maria Grimaldi in the 17thC) are explained well enough. This modern-ish theory, however, was briefly overrun by …
Chapter 3: Light is a Particle. Isaac Newton, in
his treatise Optiks (1704), articulates a theory of corpuscular light which
then dominates thinking about light for a long time:
“Are not the rays of light very small bodies emitted from shining substances?”
- Newton , Optiks, Query 29
Chapter 4: Light is a Wave, Part II. Thomas Young and Augustin Frensel
rehabilitate Huygen’s theory. Light is a wave again. (Let’s ignore for the moment, though , folks
like 1790’s renaissance man George Lichtenberg whom Jacque Barzun describes as
having “the ultramodern notion that the wave theory of light and the
corpuscular might both be true…”). But
this time it propagates through something called luminiferous ether.
Chapter 5: Light is a Wave, Part III. Light is still a wave
but now it looks more like something called an electromagnetic wave (Faraday) after
James Clerk Maxwell puts light in the context of an electromagnetic energy
spectrum – e.g., from radio to gamma rays – and helps us visualize waves
through svelte new mathematical equations like:
Chapter 6: Light is a Wave, Part IV. Light is still a wave, but this time without
the ether (Michelson, Morley 1880’s; Einstein 20C).
Chapter 7: Light is a Packet of Energy, Part I. Oops, light behaves like a particle again (Einstein,
Planck) or rather more like a little “packet of energy”; let’s call it a
photon, or maybe a boson. But it is
still like a wave, too; in other words it has “dual nature” or “wave-particle
duality” which is to say, I guess, that it is not fully understood except to
the extent that the two modes together explain a lot about what we see…for now. In fact, we are at a point where a standard
optical text can, in the space of half a page, say both that we know and that we don't:
“A consistent and unambiguous theoretical explanation of all optical phenomena is furnished jointly by Maxwell’s electromagnetic theory and the quantum theory. Maxwell’s theory treats the propagation of light, whereas the quantum theory describes the interaction of light and matter… the combined theory is known as quantum electrodynamics.”
and
“The question as to the “true” or “ultimate” nature of light, although as yet unanswered, is quite irrelevant to our study of optics.”
- Fowles,
Modern Optics
All the content of all my little chapters on the history of
light, though, are so far only about models or guesses at ways of seeing light
intellectually; math in particular provides a uniquely satisfying way of seeing
light and waves (in which respect I am blind, I suppose).
But like many epistemological things, these models, with or without the
math, all have problems of inference (all I see are grey ducks therefore all
ducks are grey). They describe what is
seen based on what is known so far but in the end they are only proxies for
reality that are ready to change with the next contradictory datum. They break
or shrink when new information comes into the picture and then a new model is
created to replace or subsume the old. Is
there, then, anything ultimate or definitive we can say about light at this
point? In the world of science, the
answer is “yes, of course.” But most
honest sources will tip their hat to the current unknowability of light in any
fundamental sense. Fowles calls light an
“unanswered question.” ACS van Heel, in “What
is Light,” compares the question of light to asking the question “what is
truth?” and suggests either that poets might have a better short answer to the
question or perhaps that one can only say “it is what you see.” So, sticking with the science – but without
getting into the hard core parts of it (at which I am not qualified) and
ignoring aspects of light that are not directly relevant (read “I don’t get it
yet”) – there are in fact a few concrete things that can be said about light at
this point, things that might actually apply to the topic in this essay. Here is a short list of what I have taken
away from my readings so far:
- The current scientific model of light is called quantum electrodynamics (QE)
- Light’s speed, a constant, is independent of the motion of the light source
- Light has no mass but can, evidently, exert pressure
- The QE model says that light acts like a particle and a wave at the same time
- Light’s propagation (motion) and its optical manipulation are best understood using the wave model
- Light bends (refracts) or reflects when interacting with optical media
- Light “waves” can bend around edges (diffract) and its waves can interfere
- Visible light wavelengths are tiny, about 20 millionths of an inch (~500nm)
- Wave oscillations are fast, about 310 million million oscillations per second
- Wave propagation speed is high, about 300,000 kilometers per second
- Light waves are part of a broader electromagnetic spectrum of waves
- Light waves are made up of separate color waves, each with its own wavelength
- Color wavelengths refract differently in optical media but they reflect the same
- The eye is sensitive to the EM spectrum at about what we call green-yellow light (~550nm)
- The eye’s peak sensitivity shifts a bit towards shorter green-blue wavelengths when it is adapted to the dark(~510nm)
- Optics, one of the few ways of “touching” light, is a very complex science...and art
Let’s pick up the thread with this last item. Since we are
taking a look at why stars are not really stars when we “touch light” with
optical devices and we are not articulating the finer details of quantum
electrodynamics, we should to shift our gaze to the light-touching optical
device we call a telescope. Almost any
entry level astronomy book will describe the varieties and workings of optical
telescopes which will not be repeated here.
In effect, though, there are only a few types: those that bend light to a focus through a
glass lens (refractor), those that reflect light to a focus by way of a mirror (reflector),
and those that are some combination of the two (cadiotropic). All of them take light waves coming from a
distant point source like a star and manipulate them through refraction or
reflection towards a focus. At the focus
(focal point) the telescope creates a small but bright facsimile of the light
source called an image. This
concentrated light, the bright image, is then magnified by an eyepiece – think
of the eyepiece as a fancy magnifying glass used to inspect the image. This sounds simple enough of course, but
given the complexity, scale and speed of light waves, all optics, in order to
successfully manipulate light and create the image as well as possible, must be
extraordinarily precise and reflect a deep understanding of the nature of light. For example, errors in the surface of a lens
or mirror more than ½ or ¼ of the wavelength of light (let’s say green light) can
create observable, negative effects. That’s
about 0.000005 inches which is pretty small.
Here’s how Harold Suiter put it in “Star Testing Astronomical Telescopes”:
“The objective…element of an astronomical telescope contains the most accurate macroscopic solid surfaces yet shaped by humans…[if] the surface of a common 8 inch telescope mirror [were] expanded to 1 mile…the optical error tolerable on such a surface [for] premium optics would be only 1/100 inches – a playing card thickness error on a disk a mile across and 300 yards high.”
Not only that, the potential for error in making the optics
and deploying them in a telescope, an otherwise simple thing to make, seems
almost infinite. Mirrors, which can be
spherically surfaced if small and paraboloidal if large, could be misshaped by
only tiny amounts and fail. There can be
bubbles or imperfections in glass lenses.
Surfaces can be rough. Lenses and
mirrors can sag. They can be mis-aligned.
Off axis light can be difficult to bring to a best focus. Mirrors can be obstructed by things in the
way like other mirrors. Glass lenses,
without some seriously complex engineering and in the end unsuccessful effort, bring light of different colors to different foci.
Objects that are flat in real space can become curved in the image space (think
of having to take pictures with curved film rather than flat, which is what
they do in Schmidt cameras...and the back side of human eyeballs). In the end one can conclude that perfect
optical systems cannot be created. The
errors can only be minimized or pushed around to optimize for some particular
optical function or purpose.
“In this way a three dimensional figure is always distorted by a lens or mirror. By using several lenses in a row, in such a way that they compensate for each other’s errors as much as possible, it is possible to make an image of a particular area, with only a few small aberrations. Here begins the singular field of the design or optical systems. This complicated work demands not only a thorough knowledge of mathematics and optics but also a certain artistic insight.”
ACS van Heel,
“What is Light”
But even if one can artfully manage the aberrations, it gets
worse still. Optical aberrations are
only one link in a chain of potential problems between star and brain. There
are factors both between a star and telescope and between the telescope and the
brain that can vitiate the image in a million infuriating ways. Suiter lists some of these in a useful
diagram not reproduced here but which includes some of the following: outside
the telescope there can be turbulent air, ground turbulence, light pollution,
and dust, dirt or dew on the lens; inside the lens and beyond, there can be alignment
problems, tube currents, obstructions, internal reflections and stray light,
eyepiece problems, mis-focusing, eye problems, and even perception and mental
processing errors.
In other words it is literally impossible to achieve a
perfect optical image even with a perfect telescope. Let’s say we can, though. Let’s wave a magic wand and have all our
optical design aberrations and environmental context problems disappear. Now we have clean, perfectly shaped,
aberration free, well aligned pieces of glass or mirror in a well baffled
telescope on a clear night in a vacuum. Surprisingly
we are still not looking at a star. And
the reason we are not looking at a star is because we are looking at light or
at least the diffraction effects of light created by the [now perfect] telescope
itself out of the wave front of light arriving from the star and its own (the telescope's) aperture. Let’s take a look at what this means.
To explain this diffraction effect, those who write about
optics often use Huygens’s model of light paired with a comparison to water
waves. Waves have a source. They move in an outward direction, circular
for water and spherical for light; a wave front’s motion is perpendicular to
the circle-sphere. Each point on the
light wave front creates a new spherical wave front (wavelets, perhaps? I can’t
find the technical term). Among the
implications of this model as it relates to the manipulation of light are that:
1) light will bend around a corner (i.e., it diffracts) just like water waves
bend when they enter a harbor, and 2) the wavlets will interfere with each
other at certain points to create areas that are dark rather than light. The interference here is often compared to
what waves from two pebbles will do when dropped in water near to each other. In other words, since each light wave
creates new wavelets along its surface (like the two pebbles example) then at
any point past the telescope aperture, and especially at the focal plane, waves
that are observed at that point will have arrived from more than one of the “source”
wavelet/pebbles and they will have traveled to that point over different
distances and time durations. Like water
waves, if one wave crest meets another wave crest (“in phase”), they add to
each other and, alternatively, if one wave meets the trough from another
slightly delayed wave from a more distant source – let’s say its slower by ½ wavelength
(where the trough is) i.e., out of phase – the waves will cancel; water becomes
flat, light becomes dark. For our
telescope and our star, that means we will have a bright spot in the center
focal point of the star image that represents the center of the light wave -- and
its overlapping wavelets – at its maximum intensity. As one moves away from the center focal point
the time lag difference of waves coming from their various sources, or sides of
the lens, will grow and at some point the peak of one wave will meet trough of
another and there will be a dark spot (actually a dark circle around the image). A little farther away still from center and
the time lag is such that a peak meets peak again and there is light again but
dimmer this time.
The net implications for us of this diffraction effect are
that the image of a star will be much bigger and fuzzier than the "real" angular
size of the star due to the bending of light around the corner of the telescope’s
aperture and that the image will look not like a real disc of a real star but
more like a circle, intensely bright in the center and dimmer towards the edge
and surrounded by increasingly dim rings that are attributable to the
interference of the wavelets. The
mathematical description of the resulting image is called the point spread
function (see the formula in the epigraph above). The rings around the center are called
diffraction rings. The central region is
called the Airy Disk (after Sir George Airy). The simple formula for the airy
disk is:
ADrad = 2.44l/D
l is the wavelength of light
D is the diameter of the telescope aperature
and it will look like Figure1:
Figure 1. Diffraction of light into
an Airy Disk.
Just to get my point across and to actually make use of the
math, let’s look at the difference between a real star and its image using the
formula. The airy disk in one of my
telescopes would be, for green light, 0.0000103231 radians. On the other hand, A.C.S. van Heel describes
a Orion (Betelgeuse) as having an interferomically measured diameter of 47
thousandths of an arc second which is 0.0000002279 radians, an order of
difference of about 45 times. This is a
huge difference and it is not an effect of magnification. In other words we are not, evidently, looking
at a real star, we are looking at something else.
But the comparison is absurd and I am not really trying to
teach diffraction which is done better elsewhere. So here is the point. It’s a matter of emphasis. While most texts will speak about diffraction
in order to describe why a star is a bit fuzzy and why it has rings around it
or to describe how a telescope works, they never tell you with the proper
emphasis that you are not really looking at a star. The disparity comes out with more force when
you go back and take a close look at the absurdity of the comparison I made
between the angular diameter of a star and its airy disk. At no time in doing the math for the Airy
disk in my telescope did we ever ask, with one exception, anything about the
star: not its real size, not its angular size, not its distance, not even its
name. It could be any star. The only thing we ask about the star is the
wavelength of its light and the size of the aperture(2.44l/D). The
Airy disk, it seems, is merely an artifact of the diameter of the telescope and
the wavelength of light. Wave front meets circle. That’s all.
In fact, the disk actually gets bigger as you decrease the aperture. Without the math, it doesn’t make any
intuitive sense. In other words, we are
not looking at a star (if I haven't made that clear yet).
“We know that a perfect telescope under perfect atmospheric conditions never sees more of a star than the Airy diffraction pattern. The origin of this disc is not to be ascribed to the star but to the telescope.”
ACS
van Heel, “What is Light”
While this is child’s play for scientists and optical
experts, to me this is nothing short of astonishing and, as I mentioned
earlier, disorienting. I used to think
of the phrase “optical illusion” only in the context of parlor tricks and
amusements, now it’s a tautology and fundamental. I also used to like looking at stars,
thinking I could actually see them -- but maybe now I know too much. They are still there of course, but it’s an
illusion and not as much fun as it used to be.
Perhaps its things like this that explain why the Hindu concept of Maya,
the world as illusion, makes so much sense to many people. I suppose it’s also why one gets kicked out
of paradise for knowing too much and why the cliché “ignorance is bliss” is
often true and why literary deconstruction can be such a downer. Knowing too much, except from a strictly
analytical point of view, diminishes the mystery and the joy. Walter Benjamin touched on this effect with
respect to optics back in the 20s:
"If one had to expound the teachings of antiquity with utmost brevity while standing on one leg...it could only be in this sentence: 'They alone shall possess the earth who live from the powers of the cosmos.' Nothing distinguishes the ancient from the modern man so much as the former's absorption in a cosmic experience scarcely known to later periods. Its waning is marked by the flowering of astronomy at the beginning of the modern age. Kepler, Copernicus, and Tycho Brahe were certainly not driven by scientific impulses alone. All the same, the exclusive emphasis on an optical connection to the universe, to which astronomy very quickly led, contained a portent of what was to come. The ancients' intercourse with the cosmos had been different: the ecstatic trance [Rausch ]. For it is in this experience alone that we gain certain knowledge of what is nearest to us and what is remotest from us, and never of one without the other. This means, however, that man can be in ecstatic contact with cosmos only communally. It is the dangerous error of modern men to regard this experience as unimportant and avoidable, and to consign it to the individual as the poetic rapture of starry nights."
-- Walter Benjamin, “To the Planetarium”
In other words, an optical connection to the universe is
superficial illusion compared to what was formerly essential and it diminishes
the observer, or observers, in some important way. I don’t know much about ecstatic trances but
I think this is, however, in the end, wrong.
I’ve seen the star illusion for what it is – and for a while the fun was
gone – but my optical connection to the universe is stronger since my [un]certainty
in seeing stars has been replaced by the vertigo of leaning over an abyss of
light. The sad day, it turns out, is not
when we optically connect to the universe it is when there is some final
certainty about light. I have perhaps lost the "real" stars in my back yard (there is still some hope, the Hubble space telescope has
been able to image some part of star disks and ground-based advances like
speckle interferometery and adaptive optics can open the turbulent sky) but in
a way I’ve enhanced the mystery by wondering about light and that makes it much more interesting.
2004
Some sources used in this essay:
- “Star Testing
Astronomical Telescopes,” Harold Richard
Suiter
- “What is
Light,” A.C.S. van Heel,
- “Modern
Optics,” Grant R. Fowles,
- “Telescope
Optics,” Rutten and Van Venrooij
- McMillan
Encyclopedia of Physics
- “StarWare,” Phillip
Harrington
- “Build your
own Telescope,” Richard Berry
- “From Dawn
to Decadence, 1500 Years of Western Cultural Life,” Jacques Barzun
- J L Borges, misc.
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