In the previous post, we built a simple gravitational lens raytracer that simulates how an image would be distorted when seen through a point-mass gravitational lens. That approach was fully numerical: we traced rays from each pixel and observed how they bent. But if we’re working with small, elliptical galaxies and want to understand how their shapes change statistically, we can use an analytical model based on the lensing Jacobian.
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Gravitational lensing is one of the most beautiful predictions of general relativity.
When a massive object, like a galaxy or black hole, lies between a distant light source and an observer, the gravitational field bends the path of light rays, distorting and duplicating the image of the background object. In this post, we’ll build a simple but realistic raytracer that simulates this phenomenon in two dimensions.
When we look at galaxies through a telescope, we see them as ellipses. But real galaxies are 3D disks randomly oriented in space. This post shows how we can simulate that: we start with a random orientation, project a flat disk into the 2D image plane, and extract the observed ellipse parameters. This setup helps us understand what shape distributions we expect to see in the absence of structures like gravitational lensing and clustering.
In research we can analyse and compare the properties of this pure random reference model against real observations to look for subtle distortions
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When we look at an astronomical image, we see a 2D projection of a 3D universe. But suppose we want to simulate the distribution of galaxies behind that image, for example, to generate synthetic data, test detection algorithms, or check if real galaxy distributions statistically deviate from what we’d expect under uniformity. To do this, we need a way to sample galaxies uniformly in 3D space, restricted to the cone of space visible in an image.
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