Magnifico’s Optical System

Introduction

At the Magnifico, we want to provide a new tool for people passionate about astrophotography. An optical system which allows for taking high-quality images of the night sky with an application of a smartphone. The lens will be also a great add-on for smartphone owners interested in wildlife photography.

To revolutionize the market and to reach our goal, we have developed an optical system based on a catadioptric telescope design. Every telephoto adapter for smartphones available on the market has been designed on the refractive scope principle (is a refractor). This type of design has some limitations and creates challenges when it comes to minimizing the chromatic aberrations in the whole field of view. Especially for long focal length lenses.

Usually, refractive designs have to incorporate expensive glasses and complex lens shapes (aspherical lenses) in order to give high-quality images. Therefore manufacturing costs are largely increased. There are no shortcuts, especially when you need to feed the image from a telephoto adapter into smartphone’s camera wide field of view. Every attempt to save on quality of optical elements ends with a terrible image like the one presented in Fig. 1.

Fig. 1. This is a low-quality image from one of telephoto adapters available on the market. Note how the image is blurry and with a large portion of chromatic aberrations (red circle). The only sharp region is located at image center.

With catadioptric systems, the situation is different because mirrors do not add chromatic aberrations. Minimizing chromatic aberrations coming from an eyepiece only is a much easier task.

Our design

Engineers from Magnifico have designed a small and reliable telescopic system based on 8th order polynomial aspherical mirrors. Magnifico’s optical system allows for reducing the overall dimensions, without sacrificing large optical magnification (30X). With the rigid mechanical design based on our experience in designing military optical equipment, our lens can survive daily shocks and vibrations that might occur during everyday usage and transportation.

Diffraction limited resolution

Our optical system gives diffractive limited image quality. The spot diagrams representing our design are presented in Fig. 2. The spot sizes are below diffraction limit described by the Airy disc in a whole field. The Airy disc is a description of the best-focused spot of light that a perfect lens with a circular aperture can make. Its size is limited by a diffraction of light. The disc size is defined by the wavelength of light and lens f-number. The images presented in Fig. 1A, describe the spot size at the image sensor for different field of view (from the center to the edge). As can be seen, the spots are within the Airy disc diameter, which means diffraction limited system performance.

The images presented in Fig. 1A, describe the spot size at the image sensor for different field of view (from the center to the edge). As can be seen, the spots are within the Airy disc diameter, which means diffraction limited system performance.

Fig. 2. Spot diagram from our telephoto adapter. The dark circle shows the limit of how small the spot can be in Magnifico’s optical system.

Chromatic aberrations and distortion

The curves describing chromatic aberrations of Magnifico’s optical system are presented in Fig. 3. The plot contains a characteristic of chromatic aberrations in so-called cross-section view. Each line represents different wavelength from visible spectrum (blue, green and red). The black lines describe Airy disc diameter. If the system is well designed like in the case of Magnifico’s design, the lines representing each wavelength should be located within the Airy disc. The vertical axis represents the distance from the image center to the edge.

Fig.3. A lateral color diagram is showing how the chromatic aberrations behave regarding distance from the optical axis to image corner.

Next, very important feature of the 0ptical system is minimized distortion of the image. It’s challenging to feed the image to a smartphone’s camera without distorting it. The images from distortion analysis are shown in Fig. 4. Telephoto adapter designed by the Magnifico introduces minimal distortion (below 2.5% from the center to the corner).

Fig. 4. Simulated image showing distortion and chromatic aberrations of Magnifico’s optical system.

Comparison with a badly designed optical system

In order to have a good comparison between a well and poorly designed optical system, check the images presented in Fig. 5a-c. Please note how each spot size at Fig. 5a is small but apart from each other. The separation between each spot size represents specific wavelength from a visible spectrum. It is increasing with increase in a distance from the optical axis (from the image center). It is also clearly visible in Fig. 5b that the lines representing wavelengths are also diverging from the optical axis. The consequences of this are shown as a simulated image in Fig. 5c. The distortion grid is no longer white but separated with different colors. In reality, due to a continuous visible spectrum, this image would be blurred like presented in Fig. 1.

The consequences of this are shown as a simulated image in Fig. 5c. The distortion grid is no longer white but separated with different colors. In reality, due to a continuous visible spectrum, this image would be blurred like presented in Fig. 1.

Vignetting

Vignetting is another important feature of an optical system. Image vignette is causing a decrease of energy reaching to the detector plane with an increase in a distance from the optical axis. When observing evenly illuminated white test plane you can see a decrease in intensity (from white to dark) towards the image corner if vignetting is present in the optical system.

In astrophotography, this effect can have a tremendous influence on the final image quality because the user will not be able to achieve homogeneous sensor exposure (the intensity of the stars will faint when getting nearer to sensor borders). That is why the Magnifico reduced this effect to almost zero during the adapter development (Fig. 6a and Fig. 6b). The secondary mirror is specially located at aperture stop hence it does not cause any intensity gradients.

In comparison, if vignetting is present in the optical system (like in many available on the market telephoto adapters) it is noticeable that the image is getting darker towards the sensor’s corners (Fig. 7). This effect can be avoided when using larger optics. But the larger optics tends to generate bigger aberrations which are harder to balance. Therefore lenses with small f-number and good image quality are much more expensive.

 

Authors: Szymon Korotko (CEO), edited by Slawomir Tomczewski

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