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Geometrical optics is a fundamental pillar for engineers and physicists specializing in optics and photonics. However, traditionally, this discipline is taught mainly in a theoretical manner, leaving students without the practical experience of building optical instruments and analysing their limitations in real-life situations. This can be problematic, as future optical engineers will face these challenges in their professional careers.
On the other hand, optical instruments are not only essential in industrial and academic applications, but it is also important to know the crucial role they have played in the history of Humanity, especially helping to change our conception of the world around us, extending our senses and illuminating the scientific revolution of the 16th and 17th centuries, with the advances they made possible in the fields of astronomy and biology. Today, scientists and engineers around the world continue to work on higher quality optical systems; Examples include the astronomy projects that our colleagues at Sener are working on or have worked on: the WEAVE corrector, the cells of the secondary, tertiary and fifth mirrors of the Extremely Large Telescope (ELT) of the European Southern Observatory (ESO), or the secondary mirror of the Gran Telescopio de Canarias (GTC), among other projects.
Many of the discoveries and advances in the fields of astronomy and biology are due to improvements in the quality and magnification capacity (that is, the ability to produce an enlarged image of the object to be observed) of these instruments. However, resolution, defined by diffraction, is also an agent to be considered in the performance of imaging systems, and aberrations can deteriorate the resulting image, limiting the information available to scientists.
To address these issues, a laboratory experience was designed in the Master’s degree in photonics taught in Barcelona, which we taught with Professor Santiago Vallmitjana a few years ago. This practical exercise was used to introduce students to practical aspects of geometric aberrations, resolution and optical design, while allowing them to recreate Galileo’s first observations of the rings of Saturn, demonstrating the historical importance of resolution and performance of optical instruments. The experiment was recently published in SPIE’s Optical Engineering journal and is described in this short article.
Historical context and motivation

In August 1609, Galileo Galilei introduced his telescope, an instrument that allowed him to magnify the apparent size of distant objects by up to 20-30 times. In 1610, he observed Saturn accompanied by two curious bulges around the main body, which led him to think that the planet was a “triple” system. Today we know that what he saw were Saturn’s rings, but at that time, the resolution of his telescope did not allow him to clearly distinguish them.
Two years later, in 1612, Galileo observed that the planet was “perfectly” round, without the bulge-like companions. In 1616, he again observed Saturn’s “bulges” in a different position. These changes are due to the relative positions between Earth and Saturn.
It was not until March 1655 when the Dutch astronomer Christiaan Huygens, with a telescope of better optical quality and a magnification capacity of up to 50 times, solved the mystery of Saturn’s “bulges”, revealing that they were rings surrounding the planet’s equator.
Theoretical background
Telescopes are optical instruments designed to observe distant objects. Keplerian and Galilean telescopes are basic configurations that use different lenses to collect light from stars. Resolution, the ability of an optical system to distinguish between two nearby objects, is affected by diffraction and aberrations, so the quality of the system and its components is vital to allow us to “see” details with it.
Galileo and Kepler telescopes

Galileo and Kepler telescopes are basic configurations that use convergent and divergent lenses to magnify images.
A Keplerian telescope uses two convergent lenses, the objective and the eyepiece, separated by the sum of their focal lengths. This design inverts the image and magnifies it.

A Galilean telescope uses a convergent lens as the objective and a divergent lens as the eyepiece. This design does not invert the image, but the magnification is lower than in the Kepler telescope.
Resolution and Aberrations
As we have already indicated, the resolution of an optical system refers to its ability to distinguish between two nearby objects. It is influenced by diffraction and optical aberrations. The lab includes the use of resolution test charts, such as the USAF 1951, to measure the actual resolution of the telescopes built by the students.

Lab Description

In the photonics lab course, students first worked with JavaOptics software to practice the imaging process. They designed Keplerian and Galilean telescopes and then performed more realistic simulations using thick lenses.

In the lab, students used a frontograph to measure the power of various lenses and built Kepler-type telescopes with the desired magnifications. Then, they placed a diaphragm in different positions to analyse its function and discuss partial compensation for some aberrations.
Recreating Galileo’s Observations
Students recreated Galileo’s observations both with computer simulations and experimentally. Using a photo editing program, they simulated the type of images Galileo might have seen with his instrument. They then built a telescope with features similar to Galileo’s and observed a photographic sample of Saturn and a resolution chart placed at a considerable distance.

Results
In recreating Galileo’s observations, students used a Keplerian telescope with an approximately +30D ocular lens and a 500mm objective lens, achieving a theoretical magnification of approximately 15x. This configuration made it possible to distinguish the space between the main body of Saturn and the rings, just as Galileo did in his early observations.


Conclusion
The hands-on experience in the photonics lab allowed students to experiment with telescope design and construction, understand the importance of resolution and aberrations, and appreciate the historical impact of advances in optical instruments. Recreating Galileo’s observations not only provided a hands-on educational experience, but also connected students to a pivotal moment in the history of astronomy.
I hope that the work will be of interest to colleagues at Sener, and that the resources and references included will be helpful in projects related to optics.
Acknowledgements
I would like to thank all the students who have participated in the course throughout the different editions of this course, with special mention to those who allowed their images to appear in Fig. 13. I would also like to thank Ms. Siobhán Henry for reviewing the text of the original article and Dr. Matthew Jungwirth for the invitation to present this work in this special section of Optical Engineering. I would also like to thank the reviewers for their corrections and suggestions; and finally, my colleague Raúl Soriano from Sener, for inviting me to share this work on our corporate blog.
Code and data availability
The data used in this study were obtained by the students and its authors, Antonio Marzoa and Santiago Vallmitjana, during the practical workshop described in the article. The data are available on demand, and the full article can be found in SPIE’s digital library at the following link.
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Antonio Marzoa
Antonio es físico experimental, con Máster en Fotónica y Máster en Astrofísica. Ha trabajado en áreas tan diversas como las pinzas ópticas, el procesado de materiales con láser, metrología óptica, el análisis de poblaciones estelares y la dinámica molecular. Su actividad principal en Sener se ha desarrollado entorno a proyectos de I+D en las Áreas de Ciencia y Espacio, especialmente en sistemas ópticos para Astronomía. Compagina su actividad profesional en Sener con la investigación y docencia en la Universitat Politècnica de Catalunya.