# Spectra

## 1.0 Light can be dispersed into colors

White light is really the sum of many different frequencies.

We can use a dispersing element to analyze the amount/intensity of light at each wavelength (this is called a spectrum)

a nice image of prism from here

The reason a spectrum is made is due to light slowing down in the denser glass so it must take a more direct route. This is know as Snell's law

Snell's Law:
n1sinθ1 = n2sinθ2

so as we can see how Snell's law applies to a prism. from here

This shows that since n is a function of lambda we get a spectrum! from here  this site has nice images for basic optics

## 2.0 Dispersion grating

While prisms are fine for very low resolution spectra in astronomy we usually need higher spectral resolutions.

In optics, a diffraction grating is a reflecting or transparent element, whose optical properties are periodically modulated. Most commonly the diffraction gratings are realized as fine parallel and equally spaced grooves or rulings on material surface. When light is incident on a diffraction grating, diffractive and mutual interferencediffraction orders. Because of their dispersive properties, gratings are commonly used in monochromators and spectrometers.

a cartoon of a transmission grating from here

A typical reflective diffraction grating from here

what are these orders physically? -- constructive interference!

one way of thinking about these orders from here

2.1 The grating Equation

where: n is the order of diffraction, λ is the diffracted wavelength d is the grating constant (the distance between successive grooves) θi is the angle of incidence measured from the normal and θd is the angle of diffraction measured from the normal.

The diagram above shows the orders of the diffracted wavelength. As well as positive orders, light can also be diffracted in the opposite direction (i.e. n = -1, -2 etc.) Higher orders may also appear but these decrease in intensity. Usually the first order lines (n=1 or n=-1) are the most intense.

## 3.0 Spectrographs

Once we have a grating we need to use a spectrograph to produce a spectrum

A more "real" design looks like that below from the Carbon Observatory satellite

SLITS --- why do we need them?

By use of slit we can keep light from the seeing disk from overlapping from here

The end result is a nice spectrum
See this site for background on stellar spectra

the spectra of stars look like

This is how astronomers classify different stellar types (in order of decreasing effective temp)

Usually astronomers only plot the spectra as lines
from here

## 4.0 Spectrographs

What does the spectra really look like on our CCD?

Clearly a lot of processing is required before we can extract
the spectrum. Compare to the calibrated B5V spectrum above...

RESOLUTION of a Spectrograph

R = Lambda / Delta_Lambda = c/Delta_v

where Delta Lambda is the smallest difference the spectrograph can resolve
and c = speed of light, and Delta_v is the smallest velocity difference that can be measured.

example

(STIS) can distinguish features 0.17 nm apart at a wavelength of 1000 nm, giving it a resolution of 0.17 nm and a resolving power of about 5,900

The STIS example above then has a spectral resolution of 51 km/s

5.0 SPECTROGRAPH DESIGN (lecture 15)

see here for the rest of the lecture on spectrograph design
from Dennis Zaritsky's lecture.

6.0 SPECTRAL DATA REDUCTION (lecture 16)

See here for notes on how IRAF can reduce spectroscopic data
(lecture notes from M. Bote lick obs.)