---
title: Telescopes and Detectors Across the Spectrum
draft: false
module: Observational Foundations
moduleNumber: 2
lessonNumber: 3
order: 203
summary: >
  A telescope collects light in proportion to its collecting area and resolves
  detail down to the diffraction limit set by its aperture and the observing
  wavelength. The atmosphere blurs and blocks large parts of the spectrum, which
  drives the choice between ground and space and between refractors, reflectors,
  and radio dishes. CCDs record the light with high quantum efficiency, and
  interferometry synthesizes an aperture as large as the separation of two
  telescopes.
topics: [Observational Foundations]
sources:
  - book: Carroll & Ostlie
    ref: "Ch. 6 — Telescopes; §6.1 Basic Optics, §6.2 Optical Telescopes, §6.3 Radio Telescopes, §6.4 Infrared, Ultraviolet, X-ray, and Gamma-ray Astronomy"
  - book: Maoz
    ref: "Ch. 2 — Basic Physics of Stars"
---

Every measurement in the previous two lessons — a flux, a color, a spectrum —
depends on collecting photons and forming an image. Two properties of a telescope
set what it can do: how much light it gathers, which fixes the faintest object
detectable, and how finely it resolves, which fixes the smallest detail
distinguishable. Both scale with the aperture, and both are limited by physics the
observer cannot escape: diffraction from the finite aperture, and, on the ground,
the turbulence and opacity of the atmosphere. This lesson works through
light-gathering power, the diffraction limit, seeing, the reflector and radio
designs that beat the refractor, the CCD detector, the atmospheric windows that
push astronomy into space, and the interferometry that synthesizes apertures larger
than any single mirror.

## Light-gathering power

A telescope intercepts the flux falling on its aperture and concentrates it onto a
detector. The energy collected per second is the flux times the collecting area,
and for a circular aperture of diameter $D$ that area is $\pi (D/2)^2$. The
**light-gathering power** therefore scales as the square of the aperture,

$$
P \propto D^2,
$$

so a mirror twice the diameter gathers four times the light and reaches objects
$4\times$ fainter, a gain of $2.5 \log_{10} 4 = 1.5$ magnitudes. The faintest
detectable magnitude climbs steadily with aperture, which is the single strongest
argument for building ever-larger mirrors. Comparing two telescopes,

$$
\frac{P_1}{P_2} = \left( \frac{D_1}{D_2} \right)^2.
$$

A $10\ \text{m}$ mirror gathers $(10/0.1)^2 = 10^4$ times the light of a
$10\ \text{cm}$ amateur telescope and about $10^6$ times the light entering the
dark-adapted human eye.[^co-optics]

## Diffraction and the resolution limit

An aperture of finite size diffracts. A point source imaged through a circular
aperture does not form a point but an **Airy pattern**: a bright central disk
surrounded by faint rings. The angular radius of the first dark ring, from the
theory of Fraunhofer diffraction, is

$$
\theta_{\min} = 1.22 \frac{\lambda}{D},
$$

with $\theta_{\min}$ in radians, $\lambda$ the wavelength, and $D$ the aperture
diameter. Two point sources are just resolved when the center of one Airy disk
falls on the first dark ring of the other — the **Rayleigh criterion** — so
$\theta_{\min}$ is the smallest angular separation the telescope can distinguish.
Resolution improves with larger aperture and shorter wavelength.

$$
% caption: Two point sources are resolved by the Rayleigh criterion when the peak
% of one Airy pattern falls on the first minimum of the other, at 1.22 lambda over D.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (9.4,0) node[right, black!70] {angle};
\draw[->, black] (0,0) -- (0,3.9) node[above, black!70] {intensity};
% first Airy peak centered at x=3
\draw[acc, very thick] (0.6,0.1) .. controls (2.2,0.1) and (2.6,3.4) .. (3.0,3.4)
  .. controls (3.4,3.4) and (3.8,0.15) .. (4.6,0.15)
  .. controls (5.0,0.15) and (5.1,0.5) .. (5.4,0.5)
  .. controls (5.7,0.5) and (5.8,0.15) .. (6.2,0.12);
% second Airy peak centered at x=4.6 (its peak at first minimum of the first)
\draw[black, thick, dashed] (2.4,0.12) .. controls (2.8,0.15) and (2.9,0.5) .. (3.2,0.5)
  .. controls (3.5,0.5) and (3.6,0.15) .. (4.2,0.15)
  .. controls (4.6,0.15) and (4.6,3.3) .. (4.6,3.3)
  .. controls (4.9,3.4) and (5.4,0.1) .. (7.0,0.1);
% markers of the two peaks and separation
\draw[black, dashed] (3.0,0) -- (3.0,3.4);
\draw[black, dashed] (4.6,0) -- (4.6,3.3);
\draw[<->, black] (3.0,3.6) -- (4.6,3.6);
\node[black!70, anchor=south] at (3.8,3.6) {lambda over D};
\end{tikzpicture}
$$

For a $2\ \text{m}$ optical telescope at $\lambda = 550\ \text{nm}$, the diffraction
limit is $\theta_{\min} = 1.22 (5.5\times10^{-7})/2 \approx 3.4 \times 10^{-7}\
\text{rad} \approx 0.07''$. In principle such a telescope resolves detail seven
hundredths of an arc second across. In practice a ground-based optical telescope
almost never reaches its diffraction limit, because the atmosphere blurs the image.

## Seeing and the atmosphere

Turbulent cells in the atmosphere have slightly different refractive indices and
bend starlight by small, fluctuating angles. Over an exposure the image of a point
source is smeared into a blob typically $1''$ across at a good site, far larger than
the diffraction limit. This atmospheric blur is **seeing**, and it, not diffraction,
sets the resolution of a large ground-based optical telescope. Above about
$D \approx 10\text{--}20\ \text{cm}$ at optical wavelengths, increasing the aperture
buys light-gathering power but no resolution, until adaptive optics or space
removes the atmosphere. **Adaptive optics** measures the wavefront distortion with a
reference source (a bright star or a laser-excited sodium beacon) and corrects it
with a deformable mirror hundreds of times per second, restoring something near the
diffraction limit over a small field.

## Refractors, reflectors, and optical design

Early telescopes used a lens objective — a **refractor** — but lenses suffer
**chromatic aberration**, focusing different wavelengths at different points because
the refractive index varies with $\lambda$, and a large lens can be supported only
at its edge, sags under its own weight, and absorbs light in its bulk. Every modern
research telescope is a **reflector**, using a curved mirror as the objective. A
mirror has no chromatic aberration (reflection is achromatic), can be supported
across its whole back, and can be made segmented and lightweight. A single paraboloid
suffers **spherical aberration** only if made spherical, and **coma** off-axis; real
designs combine mirrors to widen the corrected field. The light path is folded to
bring the focus to an accessible location:

- **Prime focus** — the detector sits at the focus of the primary mirror, giving
  the widest field but a cramped, obstructing instrument position.
- **Cassegrain focus** — a convex secondary reflects the light back through a hole
  in the primary, giving a long effective focal length in a compact tube.
- **Nasmyth / coudé focus** — a tertiary flat sends the beam out the side (Nasmyth)
  or down the mounting axis (coudé) to a large, stationary instrument.

$$
% caption: A reflector folds the light path: the primary focuses to prime focus, a
% secondary sends it to Cassegrain, and a tertiary diverts it to a Nasmyth platform.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% primary mirror as a concave arc at the bottom, on the optical axis x = 2.5
\draw[very thick] (0,0.2) .. controls (2.5,-0.5) .. (5,0.2);
\node[anchor=east] at (-0.1,0.0) {primary};
% incoming rays from top
\foreach \x in {1.0,2.5,4.0}
  \draw[black, ->] (\x,5.0) -- (\x,4.1);
% converging rays toward prime focus high on the axis
\draw[black] (1.0,4.1) -- (2.5,4.6);
\draw[black] (4.0,4.1) -- (2.5,4.6);
\fill[black!70] (2.5,4.6) circle (1.6pt);
\node[black!70, anchor=west] at (3.0,4.6) {prime focus};
% secondary below prime focus, reflecting light back down through the axis
\draw[thick] (2.05,4.1) -- (2.95,4.1);
\node[anchor=east] at (2.0,4.1) {secondary};
\draw[black] (2.5,4.1) -- (2.5,-0.9);
% Cassegrain focus below the primary (through a central hole)
\fill[black!70] (2.5,-0.9) circle (1.6pt);
\node[black!70, anchor=west] at (2.7,-0.9) {Cassegrain focus};
% tertiary flat diverting the beam to the side
\draw[thick] (2.2,1.7) -- (2.8,2.1);
\node[anchor=south] at (2.5,2.15) {tertiary};
\draw[black] (2.5,1.9) -- (5.6,1.9);
\fill[black!70] (5.6,1.9) circle (1.6pt);
\node[black!70, anchor=west] at (5.7,1.9) {Nasmyth};
\end{tikzpicture}
$$

## Detectors and quantum efficiency

The detector converts collected photons into a recorded signal. The **charge-coupled
device (CCD)** is a grid of silicon pixels; an incident photon frees an electron by
the photoelectric effect, the charge accumulates in a potential well during the
exposure, and the wells are read out row by row. The key figure of merit is the
**quantum efficiency** — the fraction of incident photons that produce a counted
electron. Photographic emulsions reach only a few percent; a modern CCD reaches
$80\text{--}90\%$ across the optical and near-infrared, so it records nearly every
photon. High quantum efficiency, a linear response over a wide dynamic range, and
direct digital output are what let CCDs replace photographic plates entirely.
Detector noise sets the faint limit: **read noise** from the readout electronics and
**dark current** from thermally freed electrons both add spurious counts, and
cooling the detector suppresses the dark current.

## Atmospheric windows and observing from space

The atmosphere is transparent only in limited **windows**. It transmits the optical
band ($\sim 300\text{--}1000\ \text{nm}$) and a broad radio window
($\sim 1\ \text{cm}$ to $10\ \text{m}$), with partial infrared windows between water-
and carbon-dioxide absorption bands. It is opaque to the ultraviolet (absorbed by
ozone and molecular oxygen), to most of the infrared (absorbed by water vapor and
carbon dioxide), and to X-rays and gamma rays (absorbed high in the atmosphere).
Everything outside the optical and radio windows must be observed from above the
atmosphere, from balloons, aircraft, or satellites. This is why ultraviolet, most
infrared, X-ray, and gamma-ray astronomy are space-based.

$$
% caption: Atmospheric opacity versus wavelength: the atmosphere is transparent in
% the optical and radio windows and opaque to UV, most IR, X-ray, and gamma-ray.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (10.4,0) node[right, black!70] {short to long wavelength};
\draw[->, black] (0,0) -- (0,3.4) node[above, black!70] {opacity};
% opacity profile: high at gamma/X, dip in optical, high in IR, dip in radio, rising far IR-ish
\draw[acc, very thick]
  (0.3,3.0) -- (2.4,3.0)
  .. controls (2.7,3.0) and (2.8,0.2) .. (3.2,0.2)
  -- (4.0,0.2)
  .. controls (4.4,0.2) and (4.6,3.0) .. (5.2,3.0)
  -- (6.6,3.0)
  .. controls (7.0,3.0) and (7.2,0.2) .. (7.8,0.2)
  -- (9.5,0.2)
  .. controls (9.9,0.2) and (10.0,2.6) .. (10.2,3.0);
% window labels
\node[black!70, anchor=north] at (3.6,-0.05) {optical};
\node[black!70, anchor=north] at (8.6,-0.05) {radio};
\node[black, anchor=south] at (1.3,3.0) {X-ray, gamma};
\node[black, anchor=south] at (5.9,3.0) {infrared};
\node[black, anchor=south] at (10.0,3.0) {ionosphere};
\end{tikzpicture}
$$

## Radio telescopes and interferometry

Radio waves have wavelengths $10^5$ to $10^7$ times longer than optical light, so a
single radio dish has terrible angular resolution: at $\lambda = 21\ \text{cm}$, a
$100\ \text{m}$ dish gives $\theta_{\min} = 1.22(0.21)/100 \approx 2.6\times10^{-3}\
\text{rad} \approx 9'$, worse than the naked eye. The escape is
**interferometry**. Two telescopes separated by a **baseline** $b$ combine their
signals; the phase difference of a wavefront arriving at the two dishes encodes the
source position, and the effective resolution is set not by the dish size but by the
baseline,

$$
\theta_{\min} \approx \frac{\lambda}{b}.
$$

An array with baselines of kilometers to thousands of kilometers achieves
resolutions of milliarcseconds, far beyond any single aperture. As Earth rotates,
the projected baseline sweeps through many orientations, and combining the data —
**aperture synthesis** — reconstructs an image as if from a telescope the size of
the whole array. Very-long-baseline interferometry links dishes on different
continents; the Event Horizon Telescope, an Earth-sized synthesized aperture,
resolved the shadow of a supermassive black hole.

$$
% caption: Two dishes separated by baseline b combine signals; the extra path to
% the far dish encodes the source direction, giving resolution set by b, not by D.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% incoming wavefronts as slanted parallel lines
\foreach \s in {0,0.9,1.8}
  \draw[black] (0.5+\s,4.4) -- (3.5+\s,2.0);
\node[black, anchor=south] at (1.6,4.3) {wavefronts};
% two dishes on a baseline
\draw[very thick] (1.2,0.4) arc (200:340:0.6);
\draw[very thick] (6.4,0.4) arc (200:340:0.6);
\node[anchor=north] at (1.5,0.35) {dish 1};
\node[anchor=north] at (6.7,0.35) {dish 2};
% baseline
\draw[<->, black] (1.5,0.0) -- (6.7,0.0);
\node[black!70, anchor=north] at (4.1,0.0) {baseline b};
% extra path length to dish 2
\draw[black, dashed] (1.5,0.6) -- (5.9,2.4);
\draw[black, dashed] (5.9,2.4) -- (6.7,0.6);
\node[black, anchor=west] at (5.9,2.4) {extra path};
\draw[->, black] (1.5,0.6) -- (6.7,0.6);
\node[black!70, anchor=west] at (7.0,0.6) {correlate signals};
\end{tikzpicture}
$$

## The multiwavelength view

Each band of the spectrum probes a different physical regime, set by the temperature
or energy of the emitting process. A rough map of what each band reveals:

| Band | Wavelength | Traces | Site |
| --- | --- | --- | --- |
| Radio | $> 1\ \text{mm}$ | cold gas (21 cm H I), synchrotron, pulsars, CMB | ground |
| Infrared | $1\text{--}300\ \mu\text{m}$ | dust, cool stars, protostars, redshifted galaxies | space, high sites |
| Optical | $0.3\text{--}1\ \mu\text{m}$ | stellar photospheres, most galaxies | ground, space |
| Ultraviolet | $10\text{--}300\ \text{nm}$ | hot young stars, accretion disks | space |
| X-ray | $0.01\text{--}10\ \text{nm}$ | million-kelvin gas, accretion onto compact objects | space |
| Gamma-ray | $< 0.01\ \text{nm}$ | nuclear transitions, blazars, gamma-ray bursts | space |

An object looks different in each band because different mechanisms dominate: a
galaxy cluster is a swarm of galaxies in the optical, a diffuse glow of
million-kelvin gas in X-rays, and a faint distortion of the microwave background at
millimeter wavelengths. Combining bands is what turns a picture into a physical
diagnosis.

The instruments of this lesson set the resolution and sensitivity of every
observation that follows, and they define the reach of each rung of [the cosmic
distance
ladder](/astrophysics-cosmology/observational-foundations/the-cosmic-distance-ladder):
parallax needs the astrometric precision of a space telescope, and standard candles
in distant galaxies need the light-gathering power of the largest apertures. The
next lesson assembles those rungs into a single scale from the nearest stars to the
edge of the observable universe.

[^co-optics]: Carroll & Ostlie, §6.1-6.2 — Basic Optics and Optical Telescopes: light-gathering power, the diffraction limit and Rayleigh criterion, seeing, aberrations, reflector designs, and CCD detectors.