Telescopes and Detectors Across the Spectrum

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,

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,

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.¹

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

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.

For a $2\text{m}$ optical telescope at $\lambda =550\text{nm}$, the diffraction limit is ${\theta }_{\min }=1.22(5.5\times 10^{-7})/2\approx 3.4\times 10^{-7}\text{rad}\approx 0.07^{\prime \prime }$. 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 $1^{\prime \prime }$ 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.

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.

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 ${\theta }_{\min }=1.22(0.21)/100\approx 2.6\times 10^{-3}\text{rad}\approx 9^{\prime }$, 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,

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.

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:

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: 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.