Removing the background

Posted on April 24, 2023 by malcolmfairbairn

Written by Matin Sharkawi

Why do we need to remove the background?

Unfortunately, London is plagued by a constant orange haze of light pollution. For the purposes of our project, light pollution harms our data as it adds a seemingly random value to all areas of the image, making it impossible to read the actual brightness of celestial bodies.

In order to remove the noise pollution, there are a few possible methods one could take. We tried two methods with varying degrees of success.

When taking the photos of each celestial body, we included an extra offset shot of the nearby sky. This shot was to provide us with a reference from which we could determine values to remove from our main photos, in order to remove the noise.

Method 1 – Minima removal

The simplest method of using the offset image is to compare each image with the offset image and generating an array of minima between the two images, as shown below.

Code in order to generate a "mud" and remove it from the original image. — Figure 1 – Code in order to generate a “mud” and remove it from the original image.

As described, the code generates an image showing the minima between the main images and the offset image, then subtracts this ‘mud’ from the original image to remove the noise pollution. The function backround_removal also needs error handling for underflow errors, as when values go below zero, they wrap back around to the maximum 32 bit integer. This can be avoided by implementing an if statement that checks if any values drop below zero, and returns them to zero.

However, as is now visible, artifacts in the form of dark holes appear on the image with the mud removed that line up with the stars visible in the offset image. In an ideal scenario, you would attempt to find a patch of sky with as few stars as possible in order to avoid this.

Image 1 - The "Mud". Note how the holes line up with the brightest stars in Figure 2 below. — Figure 2 – The “Mud”. Note how the holes line up with the brightest stars in Figure 2 below.

Figure 3 – The offset image, which lines up with the holes in the mud

Method 2 – Gradient Removal

n order to get rid of the artifacts, we instead found the gradient between the offset image and the 10 images, and from this we generated a noise map that represented the background in each image. Adding another error handler to avoid underflow errors, we then subtract the noise map from the original image, resulting in a clean, artifact free image from which we can extract data.

Figure 4 -The alternate method, generating a 2D background image that can then be subtracted from the original.

The noise map generated by Fig. 3 — Figure 5 – The noisemap generated by figure 3. As you can see, there are no visible stars left to cause artifacts, just a map of the skies brightness levels.

Figure 6 – One of the final images with no background.

Star clusters and their HR diagrams

Posted on April 13, 2023 by malcolmfairbairn

Written by Elvi Haaramaki and Sof Hachem

Star clusters

In this project, we are looking at objects called star clusters, which are groups of stars that are gravitationally bound together. There are two types – globular clusters and open clusters.

Globular clusters are large collections of thousands of millions of red stars, most of which are population II stars formed a few million years after the Big Bang. The stars are densely packed together, and the shape of the cluster is roughly spherical¹.

Open clusters are made up of a few hundred stars which are much less densely packed together than globular clusters, and are without a distinct shape. These stars are younger blue stars, tens of millions of years old, and are weakly gravitationally bound². For this project we took pictures of M35, M36, and M37, which are all open clusters.

Open clusters are ideal for the purposes of the project, since the stars are further apart from each other, making them easier to resolve individually. This is necessary to be able to find the apparent magnitudes of the stars. Additionally, it is assumed that all the stars in the cluster are the same distance from us, allowing us to calculate the absolute magnitudes.

Figures 2 and 3: Open clusters M36 and M37.

HR diagrams

HR diagrams are a useful tool in astronomy, as plotting stars within a cluster based on their magnitude and colour-temperature allows the study of the stars’ relative stellar evolutionary stages and provides an idea about the age and the relative distances of given clusters³, which was also the objective during the project.

For the data here, green and blue filters⁴ were used to attain the difference in the magnitudes corresponding to a colour index in the observational HR diagram, being plotted against the apparent (green) magnitude.

Figures 4 and 5: HR diagrams for M36 and M37.

The upper left region in the diagrams corresponds to the bluer and brighter stars, while the redder and dimmer stars are located at the bottom right. The stars in a HR diagram for a relatively young open cluster, which mostly contains stars burning hydrogen into helium, are expected to lie along the main sequence branch – this is seen in the HR diagram for M36. In older clusters, the main sequence cut-off becomes more visible as the more massive stars burn hydrogen at faster rates and are consequently spending less time in the main sequence, leading older clusters to have more prominent red-giant branches. In globular clusters, more stellar evolutionary stages are present due to the clusters age, which can be seen in the HR diagram for M3.

Figure 6: HR diagram of M3, showing more distinct branching and stars in variety of evolutionary stages⁶.

Identifying the turnoff point from the diagram and comparing the mass and brightness of the most massive remaining star in the main sequence, allows us to further estimate the age of the star and – as stars within the cluster are estimated to have formed around the same time – the age of the cluster⁵.

References:

1: https://www.britannica.com/science/globular-cluster

2: https://www.schoolsobservatory.org/learn/astro/stars/clusters/openclus

4: https://www.astronomik.com/en/photographic-filters/deep-sky-rgb-colour-filters.html

3: https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram

5: https://www.scientificamerican.com/article/how-do-scientists-determi/

6: https://jila.colorado.edu/~ajsh/courses/astr1120_03/text/chapter4/l4S8.htm (Figure 6)

Removing the Hot Pixels

Posted on April 12, 2023 by malcolmfairbairn

Written by Stylianos Spyrou

In this post, the concept of the hot pixels will be analyzed, the importance of removing the hot pixels from the FITS files will be emphasized and parts of the coding and the reasoning behind the steps followed will be explained.

What are the hot pixels and how are they obtained?

Hot pixels are single sharp pixels located at random locations of common images taken by digital cameras. They are points that do not react linearly to incident light captured by the lens. An important feature of the hot pixels is that they appear in the same location regardless the frame. This means they do not move, and they remain at a fixed position.

Hot pixels are caused due to electrical charges which appear into the sensor well of the camera’s lens. Since they are very sharp, and they are individual extremely bright pixels, they cannot be observed while looking at the image taken. However, they are very easy to determine while zooming at the images closely during processing, especially if the background of the image is very dark, such as the images taken from a telescope. They can also be visible when the sensor’s temperature increases or at very high ISOs[1]. The weather conditions during the photoshoot also have impact on the existence of the hot pixels since, if the temperature of the surroundings is high, it is ideal for their formation of hot pixels on the lens during the shoot. Finally, they tend to appear far more often in long exposure images. The reasoning behind the formation of the hot pixels is that while capturing less light from the scenery in the given moment, the patterns obtained by the camera sensor are comparatively stronger in that specific moment. Lenses and camera sensors get hotter and hotter as they use long exposures.

Why & how to remove hot pixels?

It is very important to remove the hot pixels from an image. The main reason is that it affects the image significantly during close viewing or printing. The only way they can be removed is by following a processing method after the image is taken. This can either happen through photo editing or coding. In this particular article, the second method will be analyzed and explained in detail.

Figure 1- defining the function that will find the hot pixels of the FITS files. In this part of the code, median filter is being used, however, it can be replaced by a gaussian filter instead.

On Figure 1, the function that determines the hot pixels of each FITS file must be defined. In the first part of the code, the edges must be ignored, and they will be found separately later on. In order to understand the purpose behind it, we need to imagine the filter being a square with the center passing from every point of the image obtained. As the detector approaches the edges of the image, the corners of the square filter will exceed the limits and therefore the values they will obtain will be set by Python to zero, which affects the rest of the data (median/Gaussian filter).

Figure 2- Finding the hot pixels at the edges.

As indicated in the Figure 2 above, the next step of the code is to find the pixels on the edges of the image, but not the corners. Repeat the process for the left and right edges, top and bottom.

The next step is to find the hot pixels of the image at its four corners. The code used is very similar to the one used to determine those at the edges and can be indicated in the Figure 3 below:

Figure 3- Finding the hot pixels at the four corners of the image.

Using the previous Figures, the hot pixels can be obtained. Since the code would be required to be repeated for all images in order for them to get stacked, a part that repeats the following method can be introduced, which keeps the code simple and neat. However, the easiest method is to simply repeat the code for each FITS file of each cluster. A suggestion can be found below on Figure 4:

Figure 4 – Removing the hot pixels for or images before stacking.