Telescopes are instruments used to observe and study celestial objects such as stars, planets, galaxies, and nebulae. The word telescope comes from the Greek words tele, meaning “far off,” and skopein, meaning “to look at.” The basic principle of operation for all telescopes is to gather and focus light from a distant object. The two main types of telescopes are refracting telescopes and reflecting telescopes.

Refractive telescope

Refracting telescopes use a lens to gather and focus light. The lens is usually made of glass and has two curved surfaces, one convex and one concave. When light passes through the lens, it is bent or refracted, and the image of the object is magnified. Refracting telescopes are often used for observing planets, stars, and other bright objects. The optical elements, which are oriented toward the far object are called objective, and the optical elements, which are closer to the eye or the camera are called eyepiece. 

Telescopes can be classified based on their size and the wavelength of light they are designed to observe. Large telescopes with primary mirrors or lenses that are several meters in diameter are often used for observing distant objects in visible light. Radio telescopes, which are used to observe radio waves emitted by celestial objects, can be even larger, with primary mirrors or lenses that are several kilometers in diameter.

In addition to their primary optical components, telescopes often include accessories such as eyepieces, filters, and cameras. Eyepieces magnify the image formed by the telescope and allow observers to see more detail. Filters can be used to block unwanted light or enhance specific wavelengths of light. Cameras can be used to record images of celestial objects for later analysis.

The first type of telescope is known as the Galilean  telescope and it is based on a large positive objective lens and a negative eyepiece, as shown in Fig. 1. The magnification is calculated according to the ratio between the focal distances of the two lenses as:


Where the focal distance of the objective isf_{obj} and the focal distance of the eyepiece is f_{eye} and the distance between the lenses is f_{obj\;}-\;f_{eye}. This is shown in Fig. 1, where the telescope magnifies the incident angle. Thus, a small input incident angle is mapped into a large angle shown in the widget. In this type of telescope, the image is magnified and is not inverted, which is idle for using in terrestrial schemes. 

Fig. 1. Simulation of a traditional telescope with a positive objective and a negative eyepiece. 

Another type of telescope is Fourier telescopes, which are based on two positive lenses where the distance between the two lenses is f_{obj\;}+\;f_{eye}.  In a Fourier telescope, the incoming light from the object is first passed through a lens that focuses the light onto the Fourier plane. A spatial filter, such as a pinhole or slit, is placed at the Fourier plane to filter out unwanted spatial frequencies. The filtered light is then passed through a second lens that focuses the light onto a detector, which records as an image. The image in such telescopes is inverted, so it is more suitable for observing objects in space, where the orientation is less important. 

The main advantage of Fourier telescopes is that they can achieve higher spatial resolution than traditional telescopes. This is because Fourier telescopes are not limited by the size of their apertures but rather by the spatial resolution of the detector and the properties of the spatial filter. Fourier telescopes are also capable of measuring the spectral content of astronomical objects, making them useful for spectroscopic observations.

One example of a Fourier telescope is the Fizeau interferometer, which uses a 4f configuration to combine light from two or more telescopes to form an interferometric image. The Fizeau interferometer can achieve very high spatial resolution by using the interference between the two beams to extract information about the object.

Overall, Fourier telescopes based on two positive lenses are a powerful tool for astronomical observations, particularly in applications where high spatial resolution and spectral information are required. They have the potential to revolutionize our understanding of the universe and provide new insights into the nature of astronomical objects.

We show a simulation of the telescope in Fig. 2, where the objective lens has a focal length of 500 mm and the eyepiece lens has a focal length of 50 mm, therefore, the magnification in this system is X10. We insert into the telescope two parallel beams in two slightly different orientations, and as evident, the filter blocks beams that are not oriented parallel to the telescope.

 Fig. 2. Simulation of a Fourier telescope with a filter at the Fourier plane.

Chromatic aberrations in a refractive telescope

Chromatic aberration is an optical phenomenon that occurs when a lens or a lens-based telescope fails to focus different wavelengths of light to the same point. Such aberrations result in colored fringes or halos around the edges of objects in the image and reduce the overall sharpness and clarity of the image.

Chromatic aberration is caused by the fact that different colors of light have different wavelengths and refractive indices, which refract differently when passing through a lens, resulting in a failure to converge at the same point and causing the colored fringes. As a result, the lens’s focal length is different for different light colors, leading to chromatic aberration.

There are several ways to mitigate chromatic aberration in lens-based telescopes. One common method is to use multiple lenses made of different glass types with different refractive indices. By combining these lenses in a specific configuration, the chromatic aberration can be minimized. This is commonly used in apochromatic telescopes, which use three or more lenses to achieve high-quality images.

Another method to minimize chromatic aberration is to use a specialized lens called an achromatic lens. Achromatic lenses are made of two different types of glass, which are selected to have different refractive indices and dispersions that cancel each other out. This allows achromatic lenses to focus different colors to the same point, reducing the chromatic aberration.

In modern telescope design, more advanced solutions such as using mirrors and sophisticated coatings can be used to minimize chromatic aberration. However, it remains a challenge for lens-based telescopes in certain applications, particularly in the visible light spectrum.

Exercise 1: 

Finding the spectral aberrations of a refractive telescope. 

  • Load the file “telescope_ex1.opt”
  • Run the simulation and find the correct position for the eyepiece for obtaining parallel beams at the output. To find the focus, run the simulation and find the focus of the first lens, then place the eyepiece at a focal length from this focal point. 
  • Change the input wavelength and find the new position for the eyepiece, and fill in the following table:

Input wavelength

Measured theta






Reflecting telescopes

Reflecting telescopes use a curved mirror to gather and focus light. The mirror is usually made of glass and is coated with a thin layer of aluminum or another reflective material. When light reflects off the mirror, it is focused onto a secondary mirror or a detector. Reflecting telescopes are often used for observing faint objects, such as galaxies and nebulae.

The benefits of mirror-based telescopes, in addition to the lower chromatic aberrations, are that they are easier to scale in size and can be lighter than large glass lenses Such a telescope is demonstrated in Fig. 3.

Fig. 3. Simulation of a reflecting telescope based on a curved primary mirror and a small eyepiece lens.

Exercise 2: 

Chromatic aberrations in reflecting telescope

  • Load the file “telescope_ex2.opt” and run the simulation

Input wavelength

Eyepiece location






Spherical aberrations in telescopes

Spherical aberration is another common optical phenomenon that can affect the image quality of telescopes. It occurs when the spherical shape of a lens or mirror leads to a failure to focus all the light rays to a single point, resulting in blurred or distorted images. Spherical aberration occurs because the curved surface of a lens or mirror cannot focus all the light rays to the same point, as the rays near the edge of the lens or mirror have a different focal point than those near the center. This results in a blurred image with reduced contrast and resolution.

Spherical aberration can be particularly problematic for telescopes with large apertures, as the larger the aperture, the greater the effect of spherical aberration. However, it can also occur in smaller telescopes if the lens or mirror is not properly designed.

One way to mitigate spherical aberration is to use a lens or mirror with a non-spherical shape, such as a parabolic or hyperbolic shape. These shapes allow all the light rays to be focused to the same point, resulting in a sharper and more focused image.

Another approach to reducing spherical aberration is to use multiple lenses or mirrors in a telescope, which can be designed to compensate for each other’s aberrations. This is commonly done in modern telescopes, which use a combination of lenses and mirrors to achieve high-quality images.

The Hubble Space Telescope (HST) is a highly advanced telescope that has revolutionized astronomy with its ability to capture incredibly detailed images of astronomical objects. However, despite its advanced optics, the HST is not immune to spherical aberration.

In fact, when the HST was first launched into orbit in 1990, it was discovered that its primary mirror had a spherical aberration problem. This was due to a flaw in the manufacturing process that resulted in the mirror being too flat by just a few microns. As a result, the mirror could not focus all the incoming light to a single point, resulting in blurry images. To correct the spherical aberration, NASA engineers developed a fix known as the Corrective Optics Space Telescope Axial Replacement (COSTAR) system. The COSTAR system installed new optics and mirrors that corrected the spherical aberration in the HST’s primary mirror.

However, in 2009, a new set of instruments called the Wide Field Camera 3 (WFC3) was installed on the HST. These instruments were designed with advanced optics that were specifically engineered to reduce spherical aberration and provide sharper and more detailed images. In addition, the WFC3 instruments also include built-in correction software that can further improve the image quality by correcting for any residual spherical aberration.

Exercise 3: 

Spherical aberrations in the HST

  • Load the file “telescope_hst.opt” and run the simulation.
  • Here we simulate a scaled version of 1/100 of the Hubble space telescope and its primary mirror in addition to all the aberrations in the mirror. To evaluate the telescope’s aberration, we need to measure the focal distance of the mirror as a function of the distance between the two light sources.  Fill the Focal distance as a function of the distance between the sources in the following table:

Distance between the sources

Focal distance







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