Astronomical Instrumentation and Statistics

This figure is a nice summary of the impact of new technology on new discoveries. It plots the time the necessary technology was available prior to making a major discovery with it. Before ~ 1950, discoveries were driven by other factors as much as by technology, but since then technology has had a discovery shelf life of only about 5 years! Most of the physics we use is more than 50 years old, and a lot of it is more than 100 years old. You can do good astronomy without being totally current in physics (but you need to know physics very well). The relevant technology, in comparison, changes rapidly.

But is that how it really happens?????

Coblentz developed the vacuum thermocouple (thus reducing the heat losses and substantially improving both the stability and the sensitivity). In 1914, he measured the infrared fluxes of more than 100 stars and a few planets. He used these measurements

to derive temperatures of the stars, a “hot” topic at the time!

The Birth of Infrared Astronomy

Pettit and Nicholson continued (~1922) with an infrared photometer on the 100-Inch. The photometry looks quite good. They used a water cell to block the infrared, so its strength was deduced by the amount by which this cell reduced the signal. (Coblentz had introduced this approach) Also note that even with the infrared blocked, they got a nice signal on R Hydrae at 8th magnitude visually!

…….but nothing more happened. Fellgett tried infrared photometry with a PbS cell in 1951 …….but nothing more happened.

Modern infrared astronomy started in the 1960s led by Harold Johnson, Frank Low, Gerry Neugebauer, Martin Harwit, and Ed Ney.

Here is Harold “maintaining the photometric system” at the Catalina 28-Inch telescope of the UA Lunar and Planetary Laboratory

Why did the field not take off until the 60s and 70s??

Early infrared astronomy was dominated by physicists: Physicists: 11 Astronomers: 1 As was early X-ray astronomy: Physicists: 9 Astronomers: 0

It wasn’t because astronomers got interested:

Jarrell (2005)* summarizes a study of citation rates: “To be sure, several important optical and theoretical astronomers….showed interest in the early radio work. But, for most of their colleagues, radio data were simply irrelevant to their research. In fact, radio results were as likely to be of as much value to atmospheric scientists as to astronomers.” * “’Radio astronomy, whatever that may be’: The marginalization of early radio astronomy,” Astrophysics and Space Science Library, 2005

Non-astronomers had opened up radio astronomy also

Physicists and engineers: 82 Astronomers: 11

It wasn’t because of an advance in accuracy: Fellgett’s PbS Index agreed with Pettit & Nicholson’s Heat Index with a scatter of only 8%!!! Both sets of measurements were

quite accurate.

Nor a breakthrough in sensitivity: Because Pettit and Nicholson had a large telescope (100”), their measurements were just as sensitive as Johnson’s (28”).

Nor was it the opening of the non-stellar Universe with radio astronomy: Vasilii Ivanovich Moroz started an infrared program in the USSR at the same time almost exclusively on non-stellar targets, but it died out and he migrated to planetary studies.

Correct answer here:

And now: radiometry, basic optics, noise

A long, long way away…….. a stream of photons was launched in our direction.

To quantify this process, we need to define carefully what is happening at the source. We will assume that the source is Lambertian, that is it has no limb darkening or brightening. In general, we will deal only with grey body sources. The spectral radiance is then: and the flux density is with similar expressions for wavelength units. Here, k is the Boltzmann constant, c the speed of light, h Planck’s constant, T the temperature, the emissivity, the frequency, A the area of the source, and r its distance. The simple form for the flux density validates very simple calculations.

These photons encounter little resistance (except maybe for a little scattering) until they hit the atmosphere of the earth.

Scale height ~ 2km

The submillimeter is very sensitive to “precipitable water vapor. ” These two curves are for 0.5 and 2 mm of PWV. The overall atmospheric scale

height is about 8 km, but for water it can be only 2 km (and widely variable with the site).

In the near infrared, OH airglow adds a lot of extra photons.

Here comes our photon (it got through all that atmosphere). We have to remember that it has phase as well as

wavelength/frequency. We can write its electric field as

or as

To manipulate light we need to collect it so that it interferes constructively, requiring that it arrive at the image having traversed paths of identical length from the object. This requirement is expressed in Fermat’s Principle, which is stated in a number of ways including:

“The optical path from a point on the object through the optical system to the corresponding point on the image must be the same length for all neighboring rays.” The optical path is defined as the integral of the physical path times the index of refraction of the material that path traverses.

The drawing to the right shows the wavefronts converging. The condition that they interfere constructively can be written as

In a perfect optical system, entendue is conserved (A is the area of the beam and

the solid angle) : A =C

But ℓ max then corresponds to D /2 where D is the optic diameter and is the FWHM of the image

Thus, = /D, so the best we can do is the diffraction limit!

These days, all fancy optics designs are generated in computer ray-trace software, so we can be very simple. Just looking at the definition of focus, and noting that a central ray is not deflected, we can derive

the thin lens formulae.

A mirror does the same thing as a lens, just folded back on itself, so it will often be convenient to represent optical systems by simple lenses.

The Abbe sine condition states that any two rays that leave an object at angles a1 and a2 relative to the optical axis of the system and that are brought to the image plane at angles a1’ and a2’ must obey the constraint

That is, the sine of the angle with which the ray approaches the image plane is proportional to the sine of the angle with which it leaves the object.

The thin lens formula is fantastically useful, but for good optics there are other constraints. For example:

Failure to satisfy this condition results in the aberration of coma.

Of course, modern optical systems are designed with elaborate computer “ray trace” programs rather than explicitly applying these design rules. However, the design rules are important to understand the principles behind optical systems.

How much light gets to the detector? Ignoring absorption, it is the amount emitted by the surface area on the source within the field of view of the telescope, emitted

into the solid angle subtended by the telescope as viewed from the source. The formula for the flux density is simplified because it assumes that all of the

source lies within the field of view of the telescope.

In photon detectors, the light interacts with the detector material to produce free charge carriers photon-by-photon. The resulting miniscule electrical currents are amplified to yield a usable electronic signal. The detector material is typically some form of semiconductor, in which energies around an electron volt suffice to free charge carriers; this energy threshold can be adjusted from ~ 0.01 eV to 10eV by appropriate choice of the detector material. Photon detectors are widely used from the X-ray through the mid-infrared. In general, except in the X-ray, a single mobile charge carrier is produced per absorbed photon. In a simple sense, the performance of the detector is then characterized by its quantum efficiency, the proportion of incoming photons that are absorbed to produce charge carriers. The performance of photon detectors in the far ultraviolet and particularly in the X-ray has another dimension. The energy of the individual photons substantially exceeds that required to produce a single free charge carrier. The absorption of a photon therefore can yield multiple charge carriers, whose average number is termed the quantum yield. In the X-ray, the number of charge carriers produced by an absorbed photon is a useful indicator of its energy, allowing low-resolution spectroscopy.

We have three basic technologies to detect the photon once we have collected it at the focus of the telescope.

In thermal detectors, the light is absorbed in the detector material to produce a minute increase in its temperature. Exquisitely sensitive electronic thermometers react to this change to produce the electronic signal. Thermal detectors are in principle sensitive to photons of any energy, so long as they can be absorbed in a way that the resulting heat can be sensed by their thermometers. However, in the ultraviolet through mid-infrared, photon detectors are more convenient to use and are easier to build into large-format arrays. Thermal detectors are important for the X-ray and the far-infrared through mm-wave regimes. The ultimate limit to the performance of a thermal detector is determined by two parameters: 1.) its absorption efficiency; and 2.) thermal noise. The role of absorption efficiency is straightforward, although optimizing this parameter is a demanding goal in detector design and fabrication. Thermal noise arises from the basic physics of the devices. They must be connected to a low-temperature heat sink by a low-conductivity thermal link so the absorbed photon energy can raise the temperature of the detector element. Thermal noise is generated due to thermodynamic fluctuations across this thermal link. Minimizing it requires that these detectors be operated at very low temperatures. Since photon detectors work very well in the optical and infrared, and do not require such low temperature operation, they are strongly preferred for these spectral regions.

In coherent detectors, the electrical field of the photon interacts with a signal generated by a local oscillator (LO) at nearly the same frequency. The interference between the electrical field of the photon and that from the LO produces a signal with an amplitude that increases and decreases at the difference frequency, termed the intermediate frequency (IF). If this signal is passed through an appropriately nonlinear circuit element, this amplitude variation can be converted to a real signal at the IF (rather than just the amplitude variation in a higher-frequency signal). This signal encodes the frequency of the input photon and its phase. The phase of the photon is equivalent to a timing constraint, so the detectors are limited by the Heisenberg Uncertainty Principle; it is not possible to determine the phase and energy of the photon with unlimited accuracy. This limit is termed the quantum limit. Coherent detectors must also be illuminated in a way that preserves the electrical wave nature of the photons, which translates into a requirement that the photons must strike the detector sufficiently normal to its sensitive area that there is insignificant change of the phase across that area. This requirement translates into a field of view on the sky of no larger than /D where is the wavelength of the photon and D is the telescope aperture diameter. In general, for similar reasons, coherent detectors are only sensitive to a single polarization. The restrictions in field of view and polarization together are called the antenna theorem. In addition, coherent detectors have relatively narrow spectral response (if measured in frequency units, which are appropriate given their principle of operation) and have limited sensitivity to continuum emission at high frequency (due to the quantum limit).

That’s how we get signals, but they come with noise.

Ideally, the noise would just be the intrinsic noise in the photon stream. Simple statistics would claim that the noise in n photons is √n. However, photons are bosons (like rental car buses) and tend to arrive correlated. Thus, a corrected relation is

Here, is the emissivity of the source, is the transmittance of the optical system, and is the quantum efficiency of our detector (the fraction of photons it absorbs). The product of these terms is typically significantly less than 1, so the correction term can usually be ignored. We will generally take the simple relation, that the noise in n photons goes as √n. In fact, a general way to characterize noise is in terms of the loss of information in the process of capturing and detecting photons. If (S/N)(in) is the intrinsic S/N of the photon stream and S/N(out) is what our instrument delivers, then the detective quantum efficiency, DQE, is

Confusion Noise

• Modern detectors can often reach detection levels such that the dominant noise is just the crowding of sources.

• Suppose that your sources have a power law distribution in flux density: • Then a rough estimate of the confusion is • Here is the “beams per source” and q is the desired signal to noise level. • For example, with = 2.5 (“Euclidean”) and q = 3 (three standard deviation measurements), = 18.

Spectrum of SgrB2 (N) near 246 GHz, taken in position-switching mode, with a total integration time of 30 minutes with almost 2 GHz instantaneous bandwidth. The rich chemistry of this region is striking, with the weakest lines detectable at a 3 sigma level of 15 mK. Spectrum obtained with U of AZ Submillimeter Telescope.

Confusion can be a problem in spectroscopy also!

What can be done about confusion??

• Idea 1