# Spectrographs/Lecture

The image shows a cap-off view of the insides of a spectrograph. Credit: Buil/AstroSurf.

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."[1]

"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)."[1]

"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."[1]

## Spectrograms

Cacaphony of dolphins are visually represented in this spectrogram of their clicks, whistles, and whines. Credit: Spyrogumas.{{free media}}

Def. a "visual representation of the spectrum of a celestial body's radiation"[2] 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,[3] 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"[4] is called a spectrometer.

In the image on the right is a spectrogram of dolphin vocalizations: chirps, clicks and harmonizing are visible as Λs, vertical lines and horizontal striations, respectively.

Spectrograms are used extensively in the fields of music, sonar, radar, speech processing,[5] and seismology.

## Spectrometry

Def. a "measurement of the wavelength of electromagnetic radiation, especially any of several techniques used to analyze the structure of molecules;[6] the measurement of spectra of things other than radiation, such as the masses of molecules and their breakdown products"[7] is called spectrometry.

## Theoretical spectrographs

This is a schematic of a spectrograph which names the parts. Credit: Buil.

Def. a "machine for recording spectra, producing spectrograms"[8] is called a spectrograph.

## Spectrography

Def. a "process of using a spectrometer to produce a spectrograph"[9] is called spectrography.

## Prisms

The image shows a plastic prism. Credit: D-Kuru.
A ray trace through a prism with apex angle α is shown. Regions 0, 1, and 2 have indices of refraction ${\displaystyle n_{0}}$, ${\displaystyle n_{1}}$, and ${\displaystyle n_{2}}$, and primed angles ${\displaystyle \theta '}$ indicate the ray angles after refraction. Credit: NathanHagen.

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."[10]

"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"[10]

{\displaystyle {\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 ${\displaystyle n_{0}=n_{2}\simeq 1}$. Defining ${\displaystyle n=n_{1}}$, the deviation angle ${\displaystyle \delta }$ is given by"[10]

${\displaystyle \delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{arcsin}}{\Big (}n\,\sin {\Big [}\alpha -{\text{arcsin}}{\Big (}{\frac {1}{n}}\,\sin \theta _{0}{\Big )}{\Big ]}{\Big )}-\alpha }$

"If the angle of incidence ${\displaystyle \theta _{0}}$ and prism apex angle ${\displaystyle \alpha }$ are both small, ${\displaystyle \sin \theta \approx \theta }$ and ${\displaystyle {\text{arcsin}}x\approx x}$ if the angles are expressed in radians. This allows the nonlinear equation in the deviation angle ${\displaystyle \delta }$ to be approximated by"[10]

${\displaystyle \delta \approx \theta _{0}-\alpha +{\Big (}n\,{\Big [}{\Big (}\alpha -{\frac {1}{n}}\,\theta _{0}{\Big )}{\Big ]}{\Big )}=\theta _{0}-\alpha +n\alpha -\theta _{0}=(n-1)\alpha \ .}$

"The deviation angle depends on wavelength through n, so for a thin prism the deviation angle varies with wavelength according to"[10]

${\displaystyle \delta (\lambda )\approx [n(\lambda )-1]\alpha }$.

## Spectroscopy

Def. an "optical instrument used for spectrographic analysis"[11] is called a spectroscope.

Def.

1. a "scientific study of spectra"[12] or
2. a "use of spectrometers in chemical analysis"

is called spectroscopy.

## Hypotheses

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

## References

1. Buil (4 July 2002). "Vega Spectrum Atlas". AstroSurf. Retrieved 2015-06-29.
2. Keffy (5 March 2006). spectrogram. San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2014-03-24.
3. JL Flanagan, Speech Analysis, Synthesis and Perception, Springer-Verlag, New York, 1972
4. SemperBlotto (7 April 2005). "spectrometer, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-06-29.
5. JL Flanagan, Speech Analysis, Synthesis and Perception, Springer- Verlag, New York, 1972
6. SemperBlotto (29 January 2006). "spectrometry, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-06-29.
7. SemperBlotto (4 February 2012). "spectrometry, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-06-29.
8. "spectrograph, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. October 8, 2013. Retrieved 2014-03-24.
9. SemperBlotto (18 April 2013). "spectrography, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-06-29.
10. "Prism". San Francisco, California: Wikimedia Foundation, Inc. March 21, 2014. Retrieved 2014-03-25.
11. SemperBlotto (13 December 2005). "spectroscope, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-06-29.
12. SemperBlotto (7 April 2005). "spectroscopy, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-06-29.