Basics on prisms and diffraction gratings. Part 1

1.  Purpose

The purpose of this page is to summarise the descriptions and the equations of prisms and gratings used as dispersive elements. Most of the topics are clarifications issued from discussions with colleagues and astronomy amateurs.  For a detailed description of concepts and principles on dispersive elements, please consult the classical Optics textbooks like Hecht, Pedrotti,  Born & Wolf, Fowles, Jenkins, etc. This summary is aimed to use these parameters and equations  for designing spectrographs for astronomical observations.

Contents of Part 1

  • Introduction
  • Resolving power
  • Prisms
  • Diffraction gratings

Part 2 (in preparation):

  • Échelles
  • Grisms
  • Holographic
  • VHPs: Volume Phase Holographic gratings

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Spectra of solar corona and prominence during July 2nd 2019 solar eclipse

Figure 2. The spectrum of the prominence

We had the opportunity to take spectra of the corona and of one prominence of the sun during the eclipse of 2 of July 2019. We observed the eclipse from the ESO La Silla Observatory in Chile. The results are shown in Figures 1 and 2.


The corona shows the “classical” iron (Fe-XIV and F-X)  and H-alpha lines. The He line at 587.6nm is barely visible.

However, in the spectrum of the prominence, we found interesting features: the calcium Ca II were well detected with BACHES. Five Helium lines and the four hydrogen lines (Balmer series) are also well present.


The spectra were recorded with a BACHES spectrograph attached to a 11 inches Celestron telescope as shown in Figure 3.

Figure 3. BACHES spectrograph attached to a 11″ telescope

Telescope: Celestron 11″, F/10, equatorial mount

Spectrograph: BACHES from Baader-Planetarium, F/10, 50 x 125 microns slit (3.7 x  9.2 arcsec sky aperture),  Resolving power 11 000, Spectral range: 393 – 707 nm

CCD camera: SBIG ST1603ME. CCD temperature set to -10C,

Calibration unit: RCU from Baader-Planetarium, Thorium-Argon hollow cathode and halogen lamps linked with a 300 microns optical fiber for spectral calibration and for order identification respectively.


Before the totality of the eclipse, the telescope was covered with a filter density film (Mylar sheet) with an optical density of  OD-5 to protect the instrument and our sight.

In total 13 exposures of 5 seconds, each  (plus 3 seconds download) were taken during the totality of the eclipse. The duration of the totality of the eclipse was only 1 minute and 50 seconds!

We placed the slit of BACHES close to the north pole of the Sun.  Some pointing adjustments were needed to correct the drift of the telescope due to poor South Pole alignment of the equatorial mount.

3 of these 13 exposures showed partial illumination of the slit of a solar protuberance. The remaining 10 exposures recorded only the much weaker corona spectrum.

Echelle format was composed of 25 orders covering a continuous wavelength range of 393-707 nm. Results of both, protuberance and corona spectra were reduced with ESO-MIDAS software.


Carlos Guirao

Gerardo Avila

European Southern Observatory

Creative Commons License
“Spectra of solar corona and prominence during July 2nd, 2019 solar eclipse ” by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at

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Simulated White Laser: a tool for optical alignment


A way to simulate a white laser is to combine three lasers: red, green and blue. The superposition of the three colors gives the appearance a of a white laser.

Our basic motivation to make such a device is to have a practical tool to align optical systems such as spectrographs, optical setups and measurements of optical efficiency.

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FLECHAS Opto-mechanical Components

FLECHAS is a breadboard Echelle spectrograph. Its name stands for Fiber Linked ECHelle Astronomical Spectrograph.

The article is aimed to distribute, with as much detail as possible, each FLECHAS subsytem and their components. With the help of the document Integration and alignment of FLECHAS we believe you are in the best condition to build your own breadboard spectrograph.

Good luck!

The CAOS team.

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Dual-laser beam


Lasers are widely used to align optics. In most cases a unique laser beam is enough for alignment of “open” optics as shown in Figure 1 and Figure2. However, there are cases where the optical set up does not allow the use of a single laser beam in one direction as for example in collinear mirrors (Figure 3). In this case a device with two laser beams travelling in opposite directions on the same axis is extremely useful for alignment of the optics in opposite directions.

This article describes the design, integration and alignment of a Dual-beam laser.

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Linking a telescope to a spectrograph through an optical fibre. Part III


This post discusses how spectrograph features such as the resolving power and the “size” of its optical elements are affected when the spectrograph is linked to a telescope with an optical fibre.

The main aim of the post is to help in the design of a spectrograph taking into account the features of any given telescope together with the specifications of the required spectrograph. The basic parameters of a telescope are its size (aperture diameter), the focal ratio (F/#) and the average seeing at the observing location. For the spectrograph, on the other hand, the specifications are usually the required resolving power, the spectral range and the optical efficiency.

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Injecting a laser beam into an optical fibre


Injecting  a laser beam into an optical fibre is a very common task in optical  laboratories. For example it is extremely useful for the alignment and collimation of optical components in instruments like fibre-fed spectrographs.  Our youtube video Injecting a laser beam into an optical fiber describes this process.
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Building a spectroscopy high resolution experiment


This article describes a simple laboratory spectroscopy test bench to obtain resolving powers as high as R = 150 000. The optical set up is basically composed of an échelle diffraction grating, a doublet achromatic lens, a beam splitter, an optical fibre and a CCD camera. Among others, this experiment allows to  discern and study the longitudinal emission modes of  diode lasers. Our 20′ video Building a spectroscopy high resolution experiment explains in details the bench implementation

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Alignment of an on-axis parabolic mirror


The purpose of this post is to show the alignment procedure of an on-axis parabolic mirror. The methodology has been applied to align the collimator of two of our fibre linked spectrographs:

  •  LECHES which uses the full parabola and
  • FLECHAS where the collimator works in an off-axis parabola. In this case we have used a full parabola because it is cheaper than a dedicated off-axis mirror.

An off-axis parabolic (OAP) mirror consists of a small section cut out  from a larger, so-called “parent” parabolic mirror
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BESOS: a prism spectrograph


We present here our based prism low resolution spectrograph baptized BESOS or BEst Simple Optical Spectrograph (kisses in spanish). Designed in 2003, the spectrograph was proposed to overcome the  low throughput of our previous instrument LOROS (coming soon to this blog) which was an instrument based on an on-axis dispersion prism obtained from a commercial spectroscope. The total efficiency of LOROS was only 25% in the visible spectral range.  BESOS was built with only two doublets and a prism. This configuration reached almost 87 %  at 620 nm. With such efficiency and low resolution, we expected to measure the red shift of the most bright galaxies and quasars.

In this post we provide a description of the instrument, features, performances and the set of mechanical drawings.

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