Simple Spectrograph. grating. slit. camera lens. collimator. primary

Simple Spectrograph slit grating camera lens collimator primary Notes: 1) For ease of sketching, this shows a transmissive system (refracting telescope, transmission grating). Most telescopes use a reflecting system. 2) The focal ratio (f L /D) of primary and collimator must be matched!

Single Slit Diffraction Take the light from a star or galaxy and disperse in wavelength to create a spectrum. Typically done using transmission or reflection gratings rather than prisms. Let s think about diffraction and interference. Pass a wave through a single slit aperture and you ll get a diffraction pattern: θ = projected angle from center of peak a = slit width λ = wavelength Condition for nulls (zero intensity): α = integer (m, order ) or sin(θ) = mλ/a

Two Slit Interference Now think about two-slit interference: θ = projected angle from center of peak d = distance between slits λ = wavelength

Two-slit interference pattern Combine diffraction and interference: single-slit diffraction two-slit interference θ = projected angle from center of peak a = slit width d = distance between slits λ = wavelength

Multi-slit interference Keep adding slits: single-slit diffraction multi-slit interference θ = projected angle from center of peak a = slit width d = distance between slits λ = wavelength N = number of slits

Dispersion in wavelength So far, we have considered monochromatic light (single fixed λ). Now consider a mythical light source that produces light at two wavelengths only, a blue line and a red line. Peaks and nulls will happen at different places because of the λ-dependence of the diffraction: So to resolve (separate) lines, you can either 1. increase N (which makes lines narrower), or 2. go to higher order (which gives a bigger wavelength spread). Pros and cons of doing either? m = order number

Diffraction gratings Etch grooves in either a reflecting surface or a transmitting film, and diffraction via the groove spacing (d) produces a reflected or transmitted diffraction pattern. Transmission Grating Reflection Grating

Spectroscopic Instrumentation: Diffraction gratings Now put a continuum (white light) source through a diffraction grating: a transparent medium (film/glass) with fine grooves etched in it. transmission grating monochromatic continuum showing m= -1,0,+1 showing m= -3,-2,-1,0,+1,+2,_3

Spectroscopic Instrumentation: Diffraction gratings Alternatively, look at light diffracting off a reflective grooved surface: The Grating Equation α = angle of incidence β = angle of refraction d = groove separation m = order λ = wavelength

Spectroscopic Instrumentation: Diffraction gratings The Grating Equation for either reflection or transmission gratings! α = angle of incidence β = angle of refraction d = groove separation m = order λ = wavelength Simplifying checks: zeroth order : m=0, so sin(α) = sin(β) specular reflection or direct transmission normal incidence : α = 0, so mλ = d sin(β) pattern symmetric around m=0

Free Spectral Range Look at diffracted light in different orders. For simplicity, let s sketch normal incidence (α=0). At any given β (outgoing angle), there can be light overlapping from various orders. λ 1 = 8000 Å λ 2 = 4000 Å λ 3 = 2667 Å Free spectral range: region of spectrum free from overlapping orders How do we get rid of this problem of overlapping orders?

Cross-dispersed Echelle Spectrograph cross dispersal to separate overlapping orders: Echelle dispersion Cross dispersion

Diffraction grating laser lab

Blazing A grating spreads light out into many orders, much of which is wasted by not projecting onto the detector. Blazing concentrates ~ 70% light into a particular order and wavelength. Tilt the grooves by an angle θ so that the face of the groove points in the direction of the diffraction ray you want to maximize in intensity: d condition at blaze peak: blaze wavelength (λ b ):

Spectral Resolution Depends on many things, both spectrograph design, observing mode, and slit width. Typically characterized by R = λ / δλ ( = c/δv via Doppler equation) where δλ is the wavelength difference of two spectral lines that can just be distinguished separately. High resolving power: R > 50,000 at Hα (λ=6563å), so δλ < 0.1Å, or Δv < 6 km/s. Low resolving power: R < 10,000 at Hα (λ=6563å), δλ > 0.7Å, or Δv > 35 km/s.

Low Resolution (R ~ 1000)

High Resolution (R ~ 50,000)

Spectral Dispersion Remember β is the outgoing angle of diffraction. At fixed spectrograph setup (i.e, for fixed spectograph tilt (α) and grating (d)), the spectral dispersion tells you how broadly dispersed the spectrum is: δβ/δλ Start with the grating equation: Differentiate with respect to λ: and solve for spectral dispersion: this is angular dispersion: units are radians/angstrom, for example

Simple Spectrograph slit grating camera lens collimator primary Notes: 1) For ease of sketching, this shows a transmissive system (refracting telescope, transmission grating). Most telescopes use a reflecting system. 2) the focal ratio of primary and collimator must be matched!

Linear Dispersion Coming off the grating, the light has to be refocused onto the detector via a camera lens. This maps the angular dispersion onto linear dispersion (Å/mm) on the detector. Remember imaging: the imaging plate scale was determined solely by the focal length of the telescope: S = 1/f L (in radians/mm). The same thing holds for the spectrograph camera: S cam = 1/f cam. Conversion via unit analysis: Linear dispersion (Å/mm) = plate scale (radians/mm) divided by spectral dispersion (radians/å) this is linear dispersion: units are Angstroms/mm, for example then given the physical pixel size you can turn that into Angstroms/pixel

Slitless Spectroscopy

The Spectrograph Slit The width of the slit determines the range of angles that get into the spectrograph. A wide slit allows a broader range of incoming angles, so it blurs the outgoing dispersed light and limits the spectral resolution. Characterizing slit width Physical size (linear): true size of slit, ω Projected width on the sky (angular): just like image size, it depends on the focal length of the telescope, ω θ = ω / f L (remember, if ω and f L are measured in the same units, this will come out in radians!) Projected width on the detector (linear): depends on the focal length of the camera and collimator lenses: ω = ω(f cam /f col ) also possibly a term due to anamorphic (de-)magnification (Schweizer 1979): r = dβ/dα = cos(α)/cos(β) Projected width on the detector (wavelength): use linear dispersion to convert microns to Angstroms: ω λ = ω d cos(β) / (m f cam ) Width in velocity (speed): use Doppler equation: ω v = ω λ (c/λ) Caution: always work through unit analysis when using the expressions to make sure you re using consistent units!

GoldCam Spectrograph (KPNO 2m)

Longslit Spectroscopy Point source (distant galaxy) Spatial direction à Spectral direction à

Longslit Spectroscopy Extended source (nearby galaxy)

Multi-object spectroscopy: Slitmasks

Multi-object spectroscopy: Slitmasks Metal plate with slits cut at the position of stars. Put at focal plane of telescope; star light passes through slit onto grating. Forms a series of spectra, one for each star. Spectra are offset in wavelength from each other, due to different X-positions of slits. Slits must not overlap in Y! (otherwise spectra will overlap)

Multi-object spectroscopy: Slitmasks

Multi-object spectroscopy: Fiber fed spectrographs Metal plate with holes cut at the position of stars. Put an optical fiber in each hole to carry the light down to the spectrograph. Produce many spectra, no constraints on fiber positions (other than they can t be too close spatially).

Multi-object spectroscopy: Fiber fed spectrographs

Multi-object spectroscopy: Integral Field Units (IFUs)

Multi-object spectroscopy: Integral Field Units (IFUs) Dithering to get full coverage

Spectroscopic Throughput

Spectroscopic Sky Subtraction

Spectroscopic Sky Subtraction M51 (B) M51 (Hα)

Spectroscopic Sky Subtraction WIYN/Sparsepak pointing

Spectroscopic Sky Subtraction