Commissioning an Inexpensive Off-the-shelf Spectrograph for Radial-Velocity Studies

TL;DR

This work presents a low-cost, remotely operable off-the-shelf echelle spectrograph (the Shelyak eShell II) integrated with a dedicated enclosure, autofocus, and Python-based data reduction to enable time-domain radial-velocity studies on a modest 0.5 m telescope. Resolution exceeds $10^4$ across most of the spectral range (roughly $3900$–$8200$ Å), with a nightly drift of about $2\,\text{km s}^{-1}$ mitigated by periodic ThAr calibrations to achieve residuals near $250\,\text{m s}^{-1}$. The authors validate the setup with RV measurements for binaries (e.g., 21 Cas, GK Cep) and a planet-hosting star (τ Boo), showing results consistent with literature and demonstrating the instrument’s effectiveness for high-cadence RV monitoring and educational use. Technically, the system combines remote INDI-based control on a Raspberry Pi, an autofocus mechanism, a CERES-based data-reduction pipeline, and automation of calibrations and observing sequences, offering a practical path to accessible, remotely operated RV instrumentation on small telescopes.

Abstract

We present a way to set up an inexpensive out of the shelf spectrograph at a local observatory. Stability and resolution of the spectrograph are high enough for radial velocity determination of binary stars or determination of stellar characteristics. Even some exoplanets might be detectable via the radial velocity method.

Figures (11)

• Figure 1: Sketch of the Shelyak eShel spectrograph. The stellar light is fed into the spectrograph by an optical fiber on the right side (not shown). The light is then dispersed by a blaze grating, with the echelle orders being separated by a prism. The light beam is then projected onto a camera sensor using a camera lens. Image credit: Shelyak Instruments
• Figure 2: Sketch of our enclosure. At the top one of the fans (1) is visible. To the left, the power supply for the ThAr lamp (2) and the calibration unit (3) are displayed. In the middle the spectrograph (6) with camera (4) and lens (5) is shown. Both the control unit and the spectrograph are placed on top of a styrofoam plate (7) to mitigate vibrations. The electronics chamber (8) is displayed on the right. Temperature sensors are highlighted in red. In total, the enclosure measures 76 cm x 56 cm x 61 cm.
• Figure 3: The autofocus hardware: On the left side the stepper motor (1) and the attachment of the motor to the spectrograph (2) are visible. This attachment is a U-shaped aluminium plate, made in the department's precision engineering workshop. On the right side the camera (3), the camera lens (4) and the toothed belt between motor and lens (5) can be seen. The spectrograph (6) comes in view below.
• Figure 4: Overview of the autofocus routine. Left: At the top a cross-dispersion cross-section of the flat spectrum can be seen. The single orders are clearly visible and are fitted with a Gaussian, each. The median of the widths of these fits over the subsequent iterations is shown below. Provided the median width is decreasing, the direction of the focus change remains unchanged. When the median increases the focus direction is reversed and the step width of the autofocus motor decreased. The routine iterates as long as the number of motor steps per iteration is not smaller than 6. Right: Strip of the flat spectrum, where the orders can clearly be seen. Calculating the median of this strip in the dispersion direction generates the 1D-spectrum used for the autofocus routine.
• Figure 5: Resolution of the eShel II spectrograph in different orders or wavelengths, respectively. The resolution drops near the edges of the spectral range due to optical errors in the system, which increase towards the edges of the image sensor.