(Radio sources / Radio antenna / Resolving power)
The three
interesting concepts discussed in this section are radio sources in the sky,
radio antenna, and resolving power of a telescope.
1. Radio sources:
“Now let us consider
another problem in resolving power. This has to do with the antenna of a radio
telescope, used for determining the position of radio sources in the
sky, i.e., how large they are in angle (Feynman et al., 1963, p. 30–6).”
According to Feynman, a problem in resolving power
is related to the antenna of a radio telescope that is used for determining the
position of radio sources in the sky. In
a sense, the phrase “radio sources in the sky” may be
misleading because it takes about 23 hours and 56 minutes (a sidereal day due
to the Earth’s rotation relative to the stars) for extraterrestrial radio
sources to be periodically detected by the radio telescope. One should realize
that radio sources can be any “warm” objects that emit radio waves. In
addition, we need not criticize Feynman for not mentioning radio sources such
as pulsars, quasars, active galactic nucleus, black holes, radio galaxies, or
Jupiter. The term quasar was coined in May 1964 for quasi-stellar radio sources (Chiu, 1964), whereas black hole was used by Ann Ewing (a
journalist) in January 1964 in an article titled Black Holes in Space.
“We are very
interested to know whether the source is in one place or another. One way we
can find out is to lay out a whole series of equally spaced dipole wires on the
Australian landscape (Feynman et al., 1963, p. 30–6).”
In his Nobel lecture titled Radio Telescopes of Large
Resolving Power, Ryle (1975) explains: “…the forerunners for this
type of instrument were realized in the early days when observations in both
Australia and England with aerial elements having a range of separations were
used to determine the distribution of radio brightness across the solar disc.” Interestingly, Feynman says that one way to locate radio sources is
to lay out equally spaced dipole wires on the Australian landscape (instead of
England landscape). One may
clarify that radio telescopes cover a region of the sky ±45o from zenith, that is, mostly
the southern sky if they are in Australia (northern sky if they are in
England). Historically, Hanbury Brown’s research
proposal was not accepted by the referees, thus he left
England. Subsequently, Hanbury managed to find support
and build an observatory in Australia.
2. Radio antenna:
“Some radio antennas
are made in a different way… we may arrange them not in a line but in a curve,
and put the receiver at a certain point where it can detect the scattered
waves … This is an example of what is called a reciprocity
principle. (Feynman et al., 1963, p. 30–7).”
Feynman explains a reciprocity principle of radio antenna as “the receiving pattern of an
antenna is exactly the same as the intensity distribution we would get if we
turned the receiver around and made it into a transmitter.” He adds that this
principle is generally true for any arrangement of antennas, angles, and so on.
However, one may elaborate that the essence of reciprocity principle is similar
to action and reaction are equivalent, but Newton’s third law of motion
does not always hold. Better still, this principle should include a condition
of validity because it relates two possible solutions in a linear system
(or linear medium) where the radio sources and radio receivers are
interchanged. It is worth mentioning that Rayleigh
formulates the principle of reciprocity in
acoustic and electromagnetism.
“The arranging of the
antennas on a parabolic curve is not an essential point. It is only a
convenient way to get all the signals to the same point with no relative delay
and without feed wires (Feynman et al., 1963, p. 30–7).”
Feynman clarifies that we may arrange radio
antennas on a parabolic curve, but this is not an essential point. However, extraterrestrial radio
signals are extremely weak because the wavelengths could be 100 kilometers and
longer (or billions of times weaker than the signals used by communication
systems). We can apply the
principles of Hanbury-Brown-Twiss effect by connecting two radio antennas to analyze the
correlation between the fluctuations of radio signal intensities. In his book
titled QED: The Strange Theory of Light and Matter, Feynman (1985)
writes: “[t]his phenomenon, called the Hanbury-Brown-Twiss effect, has been
used to distinguish between a single source and a double source of radio waves
in deep space, even when the two sources are extremely close together (p. 75).”
This effect has helped to develop quantum optics and it is related to Dirac’s incorrect dictum on interference: “Interference
between two different photons can never occur.”
Many physicists including Feynman had difficulty in
accepting the Hanbury-Brown-Twiss effect. In Radhakrishnan’s (2002) words: “I was present at a Caltech
colloquium at which Hanbury talked about it, and Richard Feynman jumped up and
said, ‘It can’t work!’ In his inimitable style, Hanbury responded, ‘Yes, I
know. We were told so. But we built it anyway, and it did work.’ Late that night,
Feynman phoned and woke Hanbury up to say ‘you are right.’ He also wrote a letter in
which he magnanimously admitted his mistake and acknowledged the importance of
this phenomenon that, at first sight, appears counterintuitive, even to quantum
theorists (2002, p. 76).”
3. Resolving
power:
“Now we are
describing a telescope mirror, of course. We have found the resolving power
of a telescope! Sometimes the resolving power is written θ = 1.22λ/L, where L is the diameter of the
telescope (Feynman et al., 1963, p. 30–7).”
It may seem strange that the discussion of radio
antenna is changed to the resolving power of a circular telescope within a
paragraph. However, a side-view of the circular telescope is parabolic in
shape, but there could be a new paragraph to explain the resolving power formula
θ = 1.22λ/L (what if you substitute the wavelength of radio signals l = 100 km into the formula?). To be specific, the magnified image of a star seen through the
telescope is not the star’s physical body, but it is a diffraction pattern (or “moving”
diffraction pattern due to the Earth’s rotation). The resolution of image seen depends on the sky conditions as well as the diameter
of the eyepiece and the size of the pupil. One may explain that the resolving power or
resolution is based on at least three mathematical concepts: “Abbe’s diffraction
limit,” “Airy disk diameter,” and “Rayleigh’s criterion.”
“… thus we can
appreciate that the effective diameter is a little shorter than the true
diameter, and that is what the 1.22 factor tells us. In any case,
it seems a little pedantic to put such precision into the resolving power
formula (p. 30–7).”
Feynman feels that it is pedantic to put such precision into the resolving
power formula. However, one may argue that it is not strictly pedantic because we can theoretically
compare Rayleigh’s criterion with Houston’s criterion, Abbe’s criterion, and
Sparrow’s criterion. From a practical perspective, we can compare the resolving
power of different telescopes such as a refractor telescope and reflector
telescope, or other optical systems. On the other hand, the diffraction limit of the eye can be calculated
using Rayleigh’s criterion where D is the diameter of the eye’s pupil. If you are
wondering about the factor “1.22,” it is based on the Bessel function (of the first
kind) of order one, J1(x).
Review Questions:
1. How would you describe the radio sources in the sky?
2. How would you explain a reciprocity principle of radio antenna?
3. Does the factor 1.22 seem pedantic to be included in
the resolving power formula?
The moral of the lesson: The diffraction patterns
of radio sources are so weak that we cannot simply rely on the Rayleigh’s
criterion, but it is important to apply the principles of Hanbury-Brown-Twiss effect.
References:
1. Chiu, H. Y. (1964).
Gravitational collapse. Physics Today, 17, 21–34.
2. Feynman, R. P. (1985). QED: The strange theory of light and matter.
Princeton: Princeton University Press.
3. Feynman, R. P.,
Leighton, R. B., & Sands, M. (1963). The
Feynman Lectures on Physics, Vol
I: Mainly mechanics, radiation,
and heat. Reading, MA: Addison-Wesley.
4. Radhakrishnan, V. (2002).
Obituary: Robert Hanbury Brown. Physics Today,
55(7), 75–76.
5. Ryle, M. (1975). Radio
Telescopes of Large Resolving Power. Reviews of Modern Physics, 47, 557–566.
