Basics on dispersors

1. Diffraction gratings

Sign conventions

Anamorphic ratio


Free spectral range

Resolution and resolving power

2. Blazed gratings

Shift of efficiency

Blazed equation

In a practical way, as shown in Figure 1, the spectrograph is not working in the Littrow configuration and the slit is not a line-like source but it has a width w.


Fig. 1. Layout of a simple grating spectrograph

In this case and assuming a free aberration optics (just “geometrical” collimator and camera) the resolving power is given by

Resolution general                                                                            (eq. 2)

where is the focal distance of the collimator, the slit width,  ø the angle between the camera and collimator and θ the grating angle (the angle between the grating normal and the bisector of the camera-collimator angle).

Note that the resolving power is higher when ø is positive. This means that the angle of the incident ray must be bigger than the angle of the diffracted ray with respect to the normal to the grating.

3. Prisms

Minimum deviation


Resolution and resolving power


Equation + approximation

Prism contribution (Zemax 3D plot)

5. VPHs

New post: Spectrograph designs

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Resolving power for rectangular and circular slits

The purpose of this post is to find an equation for the resolving power of an spectrograph with a circular slit.

The resolving power of an spectrograph working in Littrow configuration for a rectangular slit is given by:

Littrow equation        (eq. 1)

where is the focal distance of the collimator, the slit width and θ the Littrow angle (the ray incidence angle and diffracted angle with respect to the grating normal are the same). This equation is valid for spectrographs including free aberration optics. However, in a more realistic situation, the image profile of the slit on the CCD is not a perfect rectangular function. Due to aberrations and specially for narrow slits, the profile approaches a gaussian function. In this case, the slit width is represented by the FWHM of the gaussian function. The same reasoning applies to a circular slit but a different FWHM.

In order to find the resolving power for a circular slit, we need to find the variation of the FWHM between a rectangular and circular slits. In Figure 1 we have superposed the two profiles. For simplicity we consider only the half of a circle. The result is the same for the whole circle.


Figure 1. Rectangular and circular slits. Only the half is shown for simplicity in the calculations

For the rectangular slit, the FWHM is simply the width of the slit. In Figure 1 is 2R. As for the circle, we have to find the profile of the PSF. During the data reduction, the columns of pixels perpendicular to the dispersion are binned to find  the PSF. Assuming an evenly illumination of the circle, each pixel will contain the same number of electrons No. If Yi is the number of pixels for a given pixel position Xi, the flux of that column will be YiNo. We can see that the profile of the circle is the circle function y = (R^2 – x^2)^1/2

By doing y = R/2,  we find x = R√3/2, therefore the FWHM = R√3

By replacing the FWHM of the circle and slit in equation 1, the resolving power by a circle is

Rcircle = √3 /2 Rslit ~ 1.15 Rslit

Figure 2 shows the spectrum of the sodium doublet obtained with FLECHAS spectrograph using a fibre and a rectangular slit. Note the elliptical shape of the image of the fibre due to the anamorphic magnification of the spectrograph configuration. In order to find the FWHM at different pixel samplings, the fibre and slit were wide opened (400 um) to cover a large number of pixels.

NaFibre NaSlit NaSlitFibreCombined

Figure 2. Sodium doublet with a 400 um fibre and with a 400 um slit

The FWHM were

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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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