# Spectrographs/Lecture

A spectrograph is an apparatus for photographing or otherwise recording spectra.
"The spectrograph [on the right] (named MERIS, for MEdium Resolution Imager Spectrograph) is attached directly to a small telescope. So, the entrance slit of the spectrograph coincides with the focal plane of the telescope."
"The CCD camera is a 768 x 512 pixels Audine - (KAF-0401E Kodak CCD - pixel of 9x9 microns). The CCD is Peltier-cooled. For 768 pixels along the dispersion direction the mean reciprocal dispersion is approximately 1.4 Å/pixel (1200 groove/mm grating used for this Vega observation) and 2.9 Å/pixel (for an optional 600 groove/mm grating). We use 30 mm x 30 mm gratings from Edmund Industrial Optics with a 5000 A blaze (ref. NT46-077 for the 1200 g/mm and ref. NT46-077 for the 600 g/mm). The width of the grating is greater than the projected beam diameter for F/D telescope faster as 6.5. The grating is mounted on a rotating stage with a fine adjustment for center wavelength (it is possible to observe zero-order image for field identification and center the target). We use 35 mm photographic camera lens for the collimator and camera objective functions. The collimator is a Nikkor 135 mm focal length objective f/2.8 model. We select a Nikkor 50 mm f/1.4 model for the camera objective. The entrance aperture size of the lenses is matched to the diameter of the optical beam for unvignetting with a F/D=6.5 telescope. The distance between the grating surface and the entrance pupil of the camera objective is about 60 mm and the angle between collimator axis and camera axis is 38°. The entrance slit is adjustable by the use of a micrometer. Onto the telescope the spectrograph is mounted with its long slit oriented north-south (optimal for spectral resolution and flux consideration relative to the periodic error of the RA drive). The total spectrograph weight is of 3.1 kg (CCD camera included)."
"The measured spectral resolution is 1900 @ 6000 Å (i.e. 3.2 angstroms FWHM) for the 1.4 Å/pixel dispersion (this present work) and 1000 @ 6000 Å for the 2.9 Å/pixel (i.e. 6 angstroms FWHM). The chromatism of the optical layout is reasonably low from 4500 to 6800 Å. Refocus is necessary for spectral band outside this spectral range."

## Spectrograms

Def. a "visual representation of the spectrum of a celestial body's radiation" is called a spectrogram.
On the right is a spectrogram of dolphin vocalizations: chirps, clicks and harmonizing visible as Λs, vertical lines and horizontal striations, respectively.
Spectrograms are used extensively in the fields of music, sonar, radar, speech processing, and seismology.

## Spectrometers

Def. an "optical instrument for measuring the absorption of light by chemical substances; typically it will plot a graph of absorption versus wavelength or frequency, and the patterns produced are used to identify the substances present, and their internal structure" is called a spectrometer.

## Spectrometry

Def. a "measurement of the wavelength of electromagnetic radiation, especially any of several techniques used to analyze the structure of molecules; the measurement of spectra of things other than radiation, such as the masses of molecules and their breakdown products" is called spectrometry.

## Theoretical spectrographs

Def. a "machine for recording spectra, producing spectrograms" is called a spectrograph.

## Spectrography

Def. a "process of using a spectrometer to produce a spectrograph" is called spectrography.

## Prisms

A "prism is a transparent optical element with flat, polished surfaces that refract light [over a range of wavelengths]. At least two of the flat surfaces must have an angle [α] between them. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type."
"Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. For the prism shown at right, the indicated angles are given by"
    ${\begin{aligned}\theta '_{0}&=\,{\text{arcsin}}{\Big{\frac {n_{0}}{n_{1}}}\,\sin \theta _{0}{\Big )}\\\theta _{1}&=\alpha -\theta '_{0}\\\theta '_{1}&=\,{\text{arcsin}}{\Big{\frac {n_{1}}{n_{2}}}\,\sin \theta _{1}{\Big )}\\\theta _{2}&=\theta '_{1}-\alpha \end{aligned}}$.
"For a prism in air $n_{0}=n_{2}\simeq 1$. Defining $n=n_{1}$, the deviation angle $\delta$ is given by"
    $\delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{arcsin}}{\Bign\,\sin {\Big\alpha -{\text{arcsin}}{\Big{\frac {1}{n}}\,\sin \theta _{0}{\Big )}{\Big ]}{\Big )}-\alpha$
"If the angle of incidence $\theta _{0}$ and prism apex angle $\alpha$ are both small, $\sin \theta \approx \theta$ and ${\text{arcsin}}x\approx x$ if the angles are expressed in radians. This allows the nonlinear equation in the deviation angle $\delta$ to be approximated by"
    $\delta \approx \theta _{0}-\alpha +{\Bign\,{\Big{\Big\alpha -{\frac {1}{n}}\,\theta _{0}{\Big )}{\Big ]}{\Big )}=\theta _{0}-\alpha +n\alpha -\theta _{0}=(n-1)\alpha \ .$
"The deviation angle depends on wavelength through n, so for a thin prism the deviation angle varies with wavelength according to"
    $\delta (\lambda )\approx [n(\lambda )-1]\alpha$.

## Spectroscopy

Def. an "optical instrument used for spectrographic analysis" is called a spectroscope.
Def.
* a "scientific study of spectra" or
* a "use of spectrometers in chemical analysis"
is called spectroscopy.

## Hypotheses

* A spectrograph that uses something to replace a prism exist.