DeVeny Grating Angle Calculator

Status: Completed 2021-01-26

Overview

The Grating Equation

The angles at which the diffracted light reflects off the grating are given by the grating equation:

\[\begin{equation} m\lambda = d(\sin \theta _{i}-\sin \theta _{m})~, \end{equation}\]

where \(d\) is the spacing between adjacent grooves on the grating, \(\theta_{i} = \theta_{\rm grangle} + 10^{\circ}\) is the incident angle, and \(\theta_{m} = 55^{\circ} - \theta_{i}\) is the outgoing angle for light with wavelength \(\lambda\) diffracting into order \(m\) (see the DeVeny user manual for a description of the physical layout of the spectrograph). The DeVeny gratings are typically operated in 1^st order (\(m = 1\)), although use of \(m=2\) would possible with the proper short-pass order-blocking filters to remove 1^st-order light.

This tool computes the necessary tilt \(\theta_{\rm grangle}\) by numerically solving the equation below for a given grating. The computation uses the groove density (in g/mm) in place of \(d\), and finds \(\theta_{\rm grangle}\) for a specified 1^st-order central wavelength (\(\lambda_c\)) in Angstroms on the spectral CCD.

\[\begin{equation} \lambda_c~({\rm \mathring{A}}) = \frac{\sin(\theta_{\rm grangle} +10^{\circ}) - \sin(45^{\circ} - \theta_{\rm grangle})}{ {\rm groove~density~(g/mm)} }\times 10^7 \end{equation}\]

Usage

The script usage can be displayed by calling the script with the -h option:

$ deveny_grangle -h
usage: deveny_grangle [-h] [--cli] [--max]

DeVeny Grating Angle Calculator

options:
  -h, --help  show this help message and exit
  --cli       Use the command-line version of this tool (default: False)
  --max       Use the MAX version of the GUI (compute wavelength from angle)
              (default: False)

In its default mode, the tool launches a GUI window as in Fig. 1.

Fig. 1 – The `deveny_collfocus` GUI at startup.

Select your grating from the dropdown menu (this selects the groove density), and enter your desired central wavelength (in angstroms). When you click “Compute”, the bottom half of the GUI is populated with the needed grating tilt value from the equation above and the computed slit demagnification value (see the DeVeny user manual for a brief discussion of grating physics). See Fig. 2.

GUI after clicking "Compute" — Fig. 2 – The `deveny_grangle` GUI after clicking “Compute”. The needed grating tilt angle and computed slit demagnification values have been populated.

There are two optional modes for running this tool:

--cli: A command-line version of this tool, which looks and functions identical to the old IDL routine with the same name.

--max: The GUI will have the option to compute the central wavelength from \(\theta_{\rm grangle}\) in addition to the forward calculation done in the default mode.