Unless you’re fluent in German, you might not recognize this phrase.

It means spooky action at a distance.

And even if you do speak German, you might still find it a little strange.

The phrase Spukhafte Fernwirkung, coined by Albert Einstein, refers to a phenomenon now known as quantum entanglement.

Okay, none of that probably helped, so let’s break it down, shall we?

Quantum Entanglement and Early Rebuttles

The term “spooky action at a distance” was first introduced by Einstein in the 1930s to critique the emerging theory of quantum mechanics — a theory hoping to explain the behaviour of subatomic particles. Einstein had trouble with some of the principles of this theory, with the idea that particles could influence each other even if they were separated by vast distances. What constitutes a “vast distance”? Quantum entanglement can occur across distances as small as a few nanometers or as far as other ends of the universe. Seems basic, right?

So why was this concept difficult for Einstein to accept?

Einstein was reinforcing concepts of classical physics. Key concept: It seemed impossible that something could influence another thing at a distance faster than light. Everything was thought to need some form of communication that couldn’t exceed the speed of light, something that Einstein came up with himself with the theory of relativity. He called it spooky action because he was just genuinely surprised by this as it contradicted his theory implying instantaneous influence, regardless of distance. He had problems with quantum mechanics (QM) altogether (even though he did contribute to the creation of the theory) because it introduced the relations of how physics worked under a probabilistic framework, defying clear reasoning to which he famously said, “God does not play dice with the universe.” (Pretty fire quote if you ask me.)

He went as far, alongside physicists Boris Podelsky and Nathan Rosen, to publish the EPR paper (name based of their initials), presenting what would later be called the EPR paradox questioning the completeness of quantum mechanics.

Going Deeper into the EPR Paradox (Realism and Separability Contradictions)

The Einstein-Podolsky-Rosen (EPR) paradox, introduced in 1935, challenges the completeness of quantum mechanics by questioning its alignment with the principles of realism and separability. Realism is the concept that particles possess already determined properties (e.g., position or momentum) independent of observation — they’re not affected by our observation. The EPR argument suggests that if quantum mechanics were complete, it should be able to describe these properties without requiring us to measure them. To illustrate their point, Einstein, Podolsky, and Rosen imagined two entangled particles, measuring one particle’s property, like position, allows the prediction of the other’s corresponding property with certainty, implying that the second particle’s property existed before measurement. This directly targets QM plausibility, which denies any values causing the sync between these particles. This is essentially separability, where the total wavefunction of two distant particles can be expressed as a product of their wavefunctions:

This separability implies that the particles are independent and that no instantaneous connection exists between them. However, in the case of entanglement, the wave function cannot be factored independently — the quantum states (that we’ll discuss later) can’t be seen as separate entities. Instead, the entangled state is described by a single non-separable wave function, influencing correlations between the particles regardless of distance. This non-separability leads to our notable “spooky action at a distance,” where measuring one particle instantaneously influences the state of the other, contradicting EPR’s statement. So now we have two possibilities: either QM is incomplete (meaning there’s some undiscovered factor that’s influencing the correlation between those hypothetical particles) or nature isn’t bounded by the principle of locality — stating that objects can influence each other directly or signals that travel at or below the speed of light. Understanding how quantum mechanics challenges classical expectations is crucial before we explore the experimental proof that solidified entanglement.

To fully grasp why Einstein was so troubled by this concept, let’s take a step back and examine what classical physics expected and why quantum mechanics seemed to break these expectations.

Quantum entanglement is a phenomenon in QM in which the quantum states of two or more particles become so deeply correlated that the state of each particle cannot be described independently of each other, even from other ends of the universe. What does it mean to be deeply correlated?

When quantum states of two or more particles become deeply correlated, it means the properties of these particles — such as their spin, position or momentum are linked in a way you’ll instantly know something about the other, even if they are far apart. This isn’t the same as stating that they have the same properties, they’ve just become interdependent — entangled. When particles become entangled, their independence is lost — properties of particles become intertwined that you can’t describe the state of on particle without knowing the state of another.

Debriefing Quantum States

Quantum states, such as spin, position, and momentum, are fundamental properties of particles in quantum mechanics, and their relationship to probability helps us to understand quantum entanglement. These states are determined on probability and only take a definite value when measured. It’s like they’re water vapour until measured, once measured it’s an ice cube — it takes a value, a form. For instance, an electron’s spin can be described as a superposition of “up.”

Here, α and β are complex probability amplitudes that determine the likelihood of measuring the spin as “up” or “down,” with ∣α∣² + ∣β∣² = 1. This equation reflects the probabilistic nature of quantum mechanics. Before measurement, the particle doesn’t have a definite spin but exists in a superposition of possibilities (we’ll explain the meaning of superposition later). When two particles become entangled, their combined state cannot be expressed as independent probabilities, as mentioned before but here more descriptively, they’re entangled. Instead, their wave function is described as a single inseparable entity, such as:

This means that if particle A is measured to spin “up,” particle B will instantly collapse into spin “down,” regardless of the distance between them. The probabilities for each outcome are encoded in the wave function, but they are perfectly correlated due to entanglement. For example, if you measure particle A with a 50% chance of being “up,” particle B will have a 100% certainty of being “down” once A’s state is determined. The same probabilistic principles apply to other quantum states like position and momentum. Their positions are correlated through a shared probability until one is measured, then we can determine the corresponding value. This probabilistic framework is what makes quantum mechanics different from classical physics. In classical systems, probabilities are derived from not knowing about pre-existing values or facts (e.g., not knowing which side of a coin will land face up). In quantum mechanics, probabilities reflect the uncertainty of nature — properties like spin or position don’t even exist in definite forms until measured. Entanglement makes things even more mind-boggling with this strangeness by linking the probabilities of multiple particles in ways that aren’t easy to understand at first — even Einstein refuted it.

We previously established that the properties of a particle can’t be established unless you know the properties of another — but don’t you have to know at least one particle’s quantum state if you want to figure out others?

You first have to measure a particle’s state before you can get another, and before measurement, they exist in a superposition of states — meaning that neither particles have a determined state until one is measured. My instant reaction?

I had none, I was just confused until I came across this analogy.

To put it simply, you’re acting as if a house has no coordinates until you solve for them — you’re solving for them even though you’re assuming they don’t exist.

There’s a key claim we have to sustain here.

There’s a big difference between classical and quantum objects.

Classical and Quantum Objects

Classical objects have defined properties, regardless if we solve or observe them. A house has a location, even if no one checks if its coordinates exist. A dice roll has a number, even if it hasn’t landed yet — it just hasn’t been revealed to us.

Quantum mechanics is different. A particle’s properties do not exist in a definite form until they are measured. It’s not like you just don’t know them, they don’t exist until you measure. Makes absolutely no sense? Perfect — you got it!

Let’s try to better understand this; imagine a weird house that exists in multiple places at the same time. It’s not like the house is hidden, rather it’s spread out over many locations. When you measure the house’s location, you find it at one specific place, but only because your measurement forced it to be there. Before you measured it was in a superposition of locations — a mix of multiple states. When you measure, you essentially force the system to “choose” a definite state and the entangled partner instantly adjusts.

This may seem boggling to you, but we have a theory that proves this. Bell’s Theorem.

Introducing Bell’s Theorem, the proof of it all.

Bell’s theorem is a cornerstone of quantum mechanics, illustrating that there’s no local hidden variable that can explain the predictions QM offers. It builds upon the EPR paradox mentioned earlier and shows the non-local nature of quantum entanglement — local meaning being affected by its nearby surroundings or things in its’ immediate facility, a principle of classical physics.

What would a hidden variable be? In QM, hidden variables refer to unobserved properties that would help us determine the outcomes of quantum events. Essentially, it would remove the probability aspect of QM by suggesting that the seemingly random outcomes of quantum measurements are determined by hidden factors, so once again we’re trying to operate under a classical physics framework. This is where Einstein developed his famous quote, “God does not play dice with the universe.”

The theorem begins with the assumption that particles have predetermined properties — so we’re trying to work under the constraint that no transmission can be faster than light. If this is true, the relations between the measurements of the entangled particles must attain a Bell’s inequality — a mathematical limit. QM, however, violates this inequality saying at least one of these assumptions must be false.

Experimental Verification: Violating Bell’s Inequality

The theoretical violation of Bell’s inequality has been confirmed experimentally through

Bell tests, which measure correlations between entangled particles under varied detector settings.

1. Aspect Experiment (1982):

• Alain Aspect and colleagues used entangled photons to test Bell’s inequality.
• They observed violations consistent with quantum mechanics, ruling out local hidden-variable theories.

1. Loophole-Free Tests (2015):

• Recent experiments addressed potential loopholes (e.g., detection efficiency and locality).
• These tests provided definitive evidence that physical systems obey quantum mechanics and violate Bell inequalities.

So what does this mean? A violation of Bell’s inequality implies that nature is ultimately non-local — entangled particles influence each other over any distance, and it doesn’t have to be through direct interactions.

To understand why entanglement is so strange, let’s expand more on the idea of locality — stating that objects can only influence each other through direct interactions, or signals travelling at or below the speed of light (things we’ve established before). Quantum mechanics ultimately says — yeah no.

Imagine you’re playing a game with two magical dice. You roll one die in New York, and your friend rolls the other in Tokyo. Every time you roll a 6, your friend also rolls a 6. Every time you roll a 3, your friend gets a 3. It doesn’t matter how far apart you are — the results are always perfectly correlated. In classical physics, this would seem impossible unless there was some kind of prearranged agreement between the dice (hidden variables) or some communication happening between them faster than light.

The Results?

The experiments mentioned before prove that there isn’t any prearranged agreement, no signalling travelling between them, and the correlation is instantaneous. Bell’s Theorem mathematically explains this weirdness. It starts by assuming the constraint we mentioned earlier: that there are hidden variables and any transmitted signals between the particles can’t travel faster than light. If these assumptions were true, the measurements of entangled particles would have to abide by mathematical limits known as Bell inequalities.

Guess what happened? The nature of QM did violate Bell’s inequality, meaning that one of our classical assumptions — locality or realism, has to be wrong. We’ve explained what locality is, but what’s realism? The violation would mean in realism’s case, that particles don’t have definite properties until they are measured.

In other words, realism just means these properties exist objectively, whether or not anyone measures them. The violation of Bell’s inequality challenges this, suggesting that if realism were true, quantum mechanics would not produce the correlations observed in experiments involving entangled particles.

To better understand this, let’s use an analogy. Imagine a pair of socks: one red and one blue. You place each sock into a separate box and send them to two different locations. If someone opens one box and finds the red sock, they instantly know the other box contains the blue sock. This is how realism works in classical physics — the socks’ colors are predetermined before you open the boxes, and your act of opening doesn’t change their inherent properties.

However, quantum mechanics doesn’t follow this logic. Instead, it suggests that before measurement, the “colour” of each sock doesn’t exist in a definite form but rather in a superposition — a mix of red and blue, “both possibilities are possible.” The act of opening one box (measurement) forces the sock inside to “choose” a colour, and this choice instantaneously determines the colour of the other sock, no matter how far apart they are. Mathematically, this is described by an entangled wavefunction:

Here, neither sock has a definite colour until one is measured. The violation of Bell’s inequality confirms this strange behaviour: particles don’t have pre-existing values for their properties — those values only come into existence when measured.

This challenges our basic intuition because it implies that reality itself isn’t fixed until we interact with it. Pretty poetic though. In realism’s case, the violation means that nature doesn’t “store” information about a particle’s properties beforehand; instead, measurement plays an active role in creating those properties. This probabilistic nature of quantum mechanics is fundamentally different from classical physics and forces us to rethink what it means for something to “exist” independently of observation.

Okay.

So now that your brain has been depleted of energy, you’re probably asking why should I care that two particles separated by distances across the universe can do a little telepathy.

Well quantum entanglement, has led us to one of the world’s future leading industries; quantum computing.

A quick tangent to Quantum Computing

Quantum Computing: Entanglement is essential for building quantum computers, which use qubits (quantum bits) that can exist in multiple states simultaneously. It’s quite literally its’ foundation. This allows them to solve certain problems exponentially faster than normal/classical computers.

Unlike classical computers processing information in binary bits (0s or 1s), quantum computers use qubits, which can exist in multiple states simultaneously (thanks to superposition) and influence one another instantaneously (via entanglement). Imagine a quantum computer as a library where every book can be read simultaneously, rather than one at a time — this is the essence of its computational power. This unique capability allows quantum computers to excel in applications like optimizing supply chains, simulating molecular interactions for drug discovery, enhancing AI algorithms, and addressing climate modelling challenges. An exponentially increasing rate of analyzing data exponentially decreases time on previously deemed impossible problems.

At first glance, quantum entanglement seems almost supernatural — it defies intuitive thinking about how objects, fundamentally particles behave. As strange as it may be, it has been repeatedly proven through rigorous experiments spanning over 50 years. Still, many questions remain: Is there a deeper explanation for why entanglement works? Could there be hidden variables after all — non-local ones? Is there another derived theory we need to further explain QM? For now, physicists accept entanglement as one of nature’s prominent characteristics— a reminder that our universe operates in ways on principles that sometimes don’t make sense. And while Einstein may not have liked it, quantum mechanics continues to surprise us with its beauty and strangeness, written through every string that threads the universe.

The Motivation Behind the Project

My interest in optical systems and wavefront sensing sparked the desire to create a simulation that could accurately model how light interacts with various optical elements. Wavefront sensors are crucial in applications such as adaptive optics, which corrects distortions in optical systems caused by atmospheric turbulence or lens imperfections. With the growing accessibility of software like Blender, I saw an opportunity to bridge the gap between complex optical theory and practical simulation.

A while back, I wrote my first article associated with TKS on Medium, my Learnicle, on the Nancy Grace Roman telescope — and its’ methods for tackling space noise distortions. The solution — deformable mirrors; mirrors with fractions of itself being raised and fallen multiple times per second to a custom to different wavefronts. I was captivated by this solution for its’ ingenuity — I remember thinking to myself, “I would’ve never thought of this…wow” So now, as my second project, I’ve decided to simulate a deformable mirror directly interacting with the atmosphere and correcting distortions in real-time!

Theory and Explanation

The technology and mathematics behind adaptive optics (AO) are incredibly advanced and complex, but the underlying concept is quite straightforward. The primary goal of adaptive optics is to eliminate the twinkling of stars. This twinkling occurs due to the Earth’s atmosphere, which distorts the light from stars as it passes through, creating a flickering effect that can make astronomical observations challenging. In simple terms, the atmosphere randomly alters the path of light thousands of times per second, resulting in blurred images of the stars and other space phenomena. To counteract this distortion and achieve clearer images, adaptive optics systems work by “un-distorting” the light before it reaches instruments like cameras or spectrographs within telescopes. This is accomplished using a flexible mirror that can be deformed to create the “negative” of waves detected (will be explained later). By adjusting the mirror in real time to compensate for these changes, astronomers can significantly reduce the noise caused by atmospheric interference, leading to sharper and more detailed images of celestial objects. In space, where there is no atmosphere to cause such distortions, images are typically much clearer. However, ground-based observations must contend with these atmospheric effects. Therefore, adaptive optics plays a crucial role in enhancing our ability to capture high-quality images of stars and other astronomical phenomena by mitigating the impact of atmospheric turbulence.

However, the amount of science and technology involved in doing so is breathtaking! First, we need to “measure” what deformation the atmosphere is applying. Then, we have to apply that deformation (the negative of it) to a deformable mirror. Moreover, we have to do that thousands of times per second!!! For example, the Nancy Grace Roman Telescope has 3000 actuators for each mirror located in the Coronograph and utilizes them accordingly.

Specifically, what’s the goal of an Adaptive Optics System?

The system is crafted to enhance the clarity of light distortions when imaging objects, in our case distortions caused by Earth’s atmosphere.

From this a lot of questions come up, for example here were some of mine: how do the mirrors know how much to alter the mirror, what mathematics are involved, how does the received light translate to actual deformations, how long does it take to render these alterations, how much error is still possible even with tech enhancements — and more…

Now, let’s answer all of this by doing a deep dive into the tech used in the coronagraph replicate. Firstly, the wavefront sensor.

The wavefront sensor (WFS) measures the amount of deformation being caused by a medium (in our case, the atmosphere) that’s being applied to the wavefronts. It’s a camera, a special one but an imaging device nonetheless that’s able to see how light is bent/warped. Wavefronts you can think are kind of like the shape of light waves — connected points in the wave cycle where they’re all at the same point, this forms a line, surface or what you would call a front. Wavefront sensors can measure the deformations of light received once it has reached the telescope.

There are different types of WFSs; the one represented in the simulation is the Shack Hartmann WFS. It works by imaging several “copies” of a point source light (the star) in different spacial positions in a CCD (image sensors) called “sub-apertures” — basically tiny lenses. Each sub-aperture creates a small spot of light on the CCD — a centroid is the exact middle point of that spot — from there we’re able to detect where the spots are located and track how these spots move, we can measure how the wavefronts are being distorted, based on how the light is distributed. Measuring the centroids of each of the “copies” of the source light produces a “vector field” (called slopes) that corresponds to the direction and amplitude of the deformation at each place in space. I tried to get my hands on a Shack Hartmann, but depending on the complexity it can cost between $3000 to $30,000…Yeah, no. If you’d like to fund me, please email me at lovelygebeyehu@gmail.com (Only slightly joking 😭)

So, by discussing the use of the Shack Hartmann, we just answered how our simulation will be able to know what to correct from the light distortions and theoretically, know the steps of what to do with that info… But what will it do with it?

Deformable Mirrors

I encourage you to read my past article on the Nancy Grace Roman Telescope, and how it utilizes deformable mirrors for the same purpose.

A deformable mirror is a mirror with a flexible surface — a.k.a, a wavefront corrector (WFC). As said before, the goal is to deform the light that comes from the atmosphere with the “negative” of the wave’s deformation to make the effect of the atmosphere itself disappear. It is the same with waves, the negative and the positive altitude of the wave with the same absolute value will cancel out! The data gathered by the WFS is then used to reconstruct and correct the wavefront using that logic, this includes calculating the slopes — or deformations of the wavefront at each sub-aperture. From here, we generate a correction signal to adjust the DM creating the “negative” of the wavefront error — the actuators morphing the DM for this to happen.
A deformable mirror (DM) has a flexible surface of small actuators that push or pull on the mirror’s surface to change its shape, cancelling out the atmosphere’s distortions that the WFS has detected. The mirror’s surface shape is adjusted to match the exact inverse of the detected distortions, correcting the light as it passes through. If this wasn’t enough, this all happens before all this information arrives at the telescope or any other optical system, ensuring a clear and sharper image.

If you’re curious about what actuators are, they are tiny devices that physically alter the surface of the mirror to correct for distortions, pulling and pushing specific points of the surface of the DM to change its’ shape.

My projects consist of several key components, each designed to mimic real-world counterparts while allowing for interactive experimentation. It’s a replica of the deformable mirror set up in the Roman Telescope’s chronograph.

With all this info — I thought… Why don’t I make my own?

My project consists of several key components,

My project consisted of a couple of components that I made into assets (reusable data/objects/resources that you can use in multiple projects — in our project, lenses, filters, atmosphere, lasers, deformable mirror with the detector and a corresponding lens apart from the necessary Python script for the change in the DM to be visible.

The first thing I did was create assets — model the different objects, create materials or set up elements appropriately for your purposes; you then those objects “Mark as Asset” and save them as an independent Blender file. You’re now able to use your assets in any blender file — I set up my scene, arranging the layout quite randomly but the results should be the same value as all the data of wavefronts will be simulated through the Python script.

TLDR? It’s all for show — but gets the job done.

Here’s more about the components.

1. Wavefront Sensor (WFS): The WFS is designed to measure phase distortions in incoming light waves. It employs a Shack-Hartmann configuration, which samples light using an array of micro-lenses focused onto detectors.
2. Deformable Mirror (DM): The DM is represented as a highly subdivided plane that can be deformed to correct wavefront errors. Each actuator on the DM corresponds to a vertex on this plane, allowing for smooth adjustments.
3. Atmospheric Medium: Translucent objects are used to simulate atmospheric distortions that affect how light propagates before reaching the WFS.

Here’s my final product with an unaffected DM (for now).

Setting up the environment on Blender

Blender is a 3D open source (and free!) graphics software that allows for modelling, animation, simulations, rendering, motion tracking and even the likes of game creation!

In this project, we use Blender together with Python, Matlab and a bit of (OSL) Open Shading Language to simulate a simple (although quite didactic) AO system. We simulate the starlight, the medium where the light passes through (atmosphere), the wavefront sensor that measures the phase deformation and the deformable mirror that corrects for that deformation. We also compute all the cool math that is used in a real AO system with the data generated by our simulator.

Using the assets I made before and storing them in my Asset Browser, I created the setup and was able to code the necessary instructions for the DM to respond to the simulated light (represented by the reflected light beams).

Two last components bring this project together — the math (Lord have mercy) and the Python script used to calibrate the results (It was a bit easier, but Lord still have mercy).

I created a separate document for the math involved if you’re interested, and a short playlist of videos that introduce you to the main components that made this possible called matrices (no, not the matrix — I thought it was the first time I read it too if that makes you feel better 😎). Matrices are rectangular arrays of numbers, symbols, or expressions arranged in rows and columns — they’re used in Linear Algebra (instant cheat code for me in math class now hehe 😏). They organize systems of linear equations and describe linear transformations; interaction matrices are specific applications of matrices in optical systems. They describe the relationship between the WFS and the DM. They show the mirror’s movements will affect the light. We then use a reconstruction matrix — the reverse of the interaction matrix and if you remember what I mentioned before, the negative attitude of the wave will cancel out the positive attitude of a wave with the same absolute value — it’s the same situation but now with the actual DM and the inverse relationship with the IM and RM.

Check out this if you’re interested in the mathematics of it.

Let’s now talk about the code.

The basic outline of the code was to simulate the light, introduce both the interaction and reconstruction matrix and instruct the mirror to deform accordingly.

All the code was put into Blender’s script editor — here’s how it looked.

1. Import Libraries

import bpy  # gives access to Blender scene + we can manipulate objects through the progra,
import bmesh  #  used for manipulating vertex positions (for simulating DM)
import math  # provides basic math operations for modelling deformations on DM
import numpy as np  # allows for matrix calculations + solving systems + calibration

We need to import these libraries to create functions and use proper functions.

2. Simulate Light Path

def simulate_light_path(beam, dm, detector):
    start = beam.data.splines[0].bezier_points[0].co
    end = beam.data.splines[0].bezier_points[1].co
    beam_dir = (end - start).normalized()
    
    hit, hit_point, _, _ = dm.ray_cast(start, beam_dir)
    if hit:
        normal = dm.closest_point_on_mesh(hit_point)[1]
        reflection = beam_dir - 2 * beam_dir.dot(normal) * normal
        beam.data.splines[0].bezier_points[1].co = hit_point
        
        det_hit, det_hit_point, _, _ = detector.ray_cast(hit_point, reflection)
        if det_hit:
            return det_hit_point
    return None

The Breakdown

The simulate_light_path function simulates how the light beam will interact with the DM and then determines how the light intersects with the detectors. It simulates the path of the light beam as it travels from its origin, reflects off the DM and intersects with the detectors. Looking for the intersection with the detector is important since we’re now able to measure light position, providing information about the distortion in the wavefront.

Explanation of code:

The first line takes the three arguments (beam, dm, detector) to simulate the light beam in the system. The start and end variables access the Bezier spline (defines the shape of the beam) — they retrieve the coordinates of the starting control and ending control point of the light beam.
The beam_dir variable allows us to compute the vector pointing from the start point to the end point of the beam — which we calculated in the start and end variables prior.

We then create an assignment (hit, hit_point, _, _ = dm.ray_cast(start, beam_dir)) — that takes multiple values we’ve constructed into separate variables. We receive four return values from the ray_cast function; where the the ray is being hit, the coordinates of the point the ray and the DM intersect, and the two underscores (“_”) give information about the faces indices and distances.

Deformable Mirror Deformation

def deform_dm(dm, deformation_function):
    for vertex in dm.data.vertices:
        x, y = vertex.co.xy
        z = deformation_function(x, y)
        vertex.co.z += z

The Breakdown

This code sector modifies the geometry of the DM by applying deformation to the vertices calculated by the function “deformation_function.” This function uses the x and y coordinates of each vertex to determine the proper displacement on the z-axis to alter the object's shape on the Blender.

Explanation of code:

The first line defines our function deform_dm containing the 3D object dm (DM), and the deformation function — calculating the needed displacement in the z-axis of each vertex of the (x,y) coordinate.
The second line loops through all the vertices in the dm object, the dm.data.vertices give us access to the vertex data within the mesh allowing us to loop through all of them. The line “vertex.co.z += z is updated by adding the calculated deformation value of z. This modifies the vertex’s position along the z-axis and deforms the DM.

Wavefront Measurement

def measure_wavefront(beam, detector):
    beam_dir = beam.data.splines[0].bezier_points[1].co - beam.data.splines[0].bezier_points[0].co
    hit, location, _, _ = detector.ray_cast(beam.data.splines[0].bezier_points[0].co, beam_dir)
    if hit:
        return location - beam.data.splines[0].bezier_points[0].co
    return None

The Breakdown

The measure_wavefront function calculates the distortion in the light wavefront by finding where the beam interacts with the detectors.

You may ask — didn’t we already do this with the first block of code? They both deal with ray casting, finding intersections, and simulating how the light interacts with the system.
However, they serve different purposes in the pipeline. The first function simulates the full path of the beam, from its origin to the DM and eventually to the detector, calculating the reflection of the DM. The second function measures the wavefront distortion through the calculated intersections from the first block of code. It doesn’t simulate the reflections of immediate interactions, it measures how the wavefronts of the beam interact with the detector.

Explanation of the code:

The first line defines a new function “measure_wavefront,” including parameters beam and detector. Our next line brings out “beam_dir” again, the line calculating the direction of the light beam by subtracting the end from the start coordinates of the Bezier spline. This subtraction gives us a vector pointing in the direction from the start to the end control point. The “ray_cast” function returns different values, “hit” indicating whether the ray hits the detector (a boolean if you’re familiar); location describing the 3D coordinates of if the ray intersects the detector. If “hit” is true, it means the ray has intersected with the detectors and the intersection point is given to us (returned).

Create Interaction Matrix

def create_interaction_matrix(dm, detector, beam):
    num_actuators = len(dm.data.vertices)
    interaction_matrix = np.zeros((num_actuators, 3))
    
    for i, vertex in enumerate(dm.data.vertices):
        original_z = vertex.co.z
        vertex.co.z += 0.01
        dm.data.update()
        bpy.context.view_layer.update()
        
        wavefront = measure_wavefront(beam, detector)
        if wavefront is not None:
            interaction_matrix[i] = wavefront
        vertex.co.z = original_z
    
    return interaction_matrix

The Breakdown

(Here is where it gets interesting — at least for me that is 😅)

This function aims to create an interaction matrix representing the effect of each actuator on the wavefront detected by a detector. We’ll look into how the calibration process of the DM in the next code breakdown.

Explanation of code:

The first line introduces a new function “create_interaction_matrix,” taking three parameters — the dm, the detector, and the beam. The next line calculates the number of actuators on the DM by counting the vertices. These are what’s used to deform the mirror physically. The three in the next lines correspond to the displacement of a 3D vector. Initially, the interaction matrix is filled with zeros, and the matrix stores how the wavefront changes.
The next line begins a loop stating all the vertices on the DM.

The next two lines store the calculated z-coordinate, done by remembering the start position (beam.data.splines[0]), the next line would do the physical moving of the mirror vertex by 0.01 — the deformation. This isn’t actually to scale to what deformations are made to actual deformable mirrors.

The next two lines ensure the updates show up on Blender.

We then call upon measure_wavefront (discussed earlier_ to measure the wavefront displacement caused by the deformation of the vertex (actuator). After the loop finishes, the interaction matrix is returned, containing the wavefront change applied on the DM.

The interaction matrix is vital for understanding how the small changes in the DM surface affect the wavefront and can play out in Blender. The matrix is used in the calibration process to determine the proper adjustments to achieve the desired wavefront.

Calibrate the Deformable Mirror

def calibrate_dm(dm, beam, detector, interaction_matrix, target_wavefront, steps=10):
    for step in range(steps):
        current_wavefront = measure_wavefront(beam, detector)
        if current_wavefront is None:
            break
        
        error = target_wavefront - current_wavefront
        adjustments = np.linalg.lstsq(interaction_matrix, error, rcond=None)[0]
        
        for i, vertex in enumerate(dm.data.vertices):
            vertex.co.z += adjustments[i] / steps
        dm.data.update()
        bpy.context.view_layer.update()
        
        print(f"Step {step + 1}/{steps}:")
        print(f"  Current wavefront: {current_wavefront}")
        print(f"  Error: {error}")
        print(f"  Max adjustment: {np.max(np.abs(adjustments))}")

The Breakdown:

The purpose of the calibrate_dm function is to adjust the DM surface while minimizing the error between the current wavefront and the target wavefront — an undisturbed wavefront before it encounters some kind of medium.

The first line defines the function with most of the prior functions with additional “target_wavefront” and “steps.” The next line begins a loop that will go on for a number of times specified by “steps.” The next lines of code are just precautionary, checking if the light beams are hitting the DM and the detectors or not — this continues until we reach the variable “adjustments.” It stores the results of the computations done by the function “np.linalg.listq” — this function for the NumPy’s linear algebra module (first time using this 🎲), computing the least-squares solution to a linear matrix equation; once again if interested in the math, look here. In this case, it finds the optimum adjustment values that minimize the error between the current wavefront and the target wavefront (ensuring proper manipulation of the DM).

Explanation of the code:

This block contains the “calibrate_dm function.” It does this iteratively by measuring the current wavefront, calculating the difference compared to the target, and adjusting the DM actuators (a.k.a vertices_ to minimize that error).
The first line runs for the specified number of times (“steps.”) Each step refines the DM’s shape further. The next line measures the current wavefront, bringing a previous function “measure_wavefront,” checking if the light heats the detectors and determines the current wavefront. The error variable is the difference between the “target_wavefront” and the “current_wavefront.” The adjustment is an array where each element is related to the calculated displacement being applied to the DM. The updates are done by “dm.data.update()” and “bpy.context.view_layer.update() reflecting the new actuator positions.

Summary

Here’s the overall pipeline.

1. Simulates light paths through the DM: Simulates the light beams path through the system coming towards the DM onto the detectors and looking for the intersections between the detector and the mirror.
2. Apply Deformation to the DM: Modify the shape of the DM by altering the vertices position using the deformation function that calculates how much to move the vertex on the z-axis.
3. Measure the wavefront: Measure how the light beam interacts with the detectors and determine the WF distortion forms the mirror based on a mathematical function. Uses information on the necessary start and end points of the vertex.
4. Creates an interaction matrix: Create a loop so we’re able to reach each DM vertex and apply each small deformation. We use the “measure_wavefront” function to measure the resulted wavefront distortion and correction — store the effect of each actuator in the interaction matrix.
5. Calibrates the DM to achieve a target wavefront: Adjusts the DM actuators to match the target wavefront by measuring the distorted wavefront, calculating the error (different) between the desired and the distorted WF and using the interaction matrix to compute the necessary adjustments using least squares.
6. Update Blender Scene to reflect the changes.

With this, we’re now able to properly deform the DM to correct disrupted wavefronts and have similar results to the figure below.

Challenges Faced

This was in no way seamless… Like not in the slightest. Initially, I was planning to get my hands on a Shack-Hartmann WFS to build the actual system physically — which I had, but for a short period as I had to return them and this was not a weekend project.

And those were just the initial problems 😑.

Other issues included:

• I had no idea what a matrice was, just knew it helped with Linear Alg.
• I initially wrote a lot of precautionary code which I eventually removed as time went on; a.k.a inefficient.
• I had never worked with NumPy’s linear algebra module. So, you can make the guess: I had no idea what I was doing — plus, I still didn’t know what a matrice was.

Conclusion

THIS WAS FUN. REALLY FUN.

Despite how the order of my articles on Medium has been published, this was my first project on Blender (apart from an unfinished doughnut🍩 😋). This is where I discovered my love for 3D simulations and Blender in general. I would say I’m still a beginner to programming so learning what destructive arguments were interesting amongst other sequences and new ways to structure functions, as well as matrices' involvement in calculating displacement in the DM.

This is more than just poking a mirror in a couple of places and calling it a day. Everything I just explained to you through this 15-minute article, is a phenomenon that’d happen multiple times per second. All to correct distorted WF for clearer imaging.

With the high cost of adaptive optics equipment, it’s difficult for a high school student to get access to this tech — trust me, I’ve tried. However, this project allows me to manipulate that space to my will and see the results in real-time, and it’s not just me, you can too — available for a wider audience. By leveraging open-source tools like Blender and Python, I created a simulation that replicates the functionality of a $50000 physics lab for free (probably giving myself too much credit, but you get the gist 😋). Adaptive optics technology has revolutionized ground-based astronomy by correcting for atmospheric distortions, enabling clearer and more detailed images of celestial objects. This simulation not only educates users about the main concepts surrounding adaptive optics systems but also inspires innovation and interest in the field, potentially leading to advancements in telescope design and astronomical imaging.

RESULTS

Here’s the after with the DM appropriately deformed.

Authors Note:

My name is Lovely Gebeyehu, I’m 15 years old and am interested in quantum physics, space exploration and what it holds for our future. Always willing to have a conversation — reach out to me here!

Email: lovelygebeyehu@gmail.com

Linkedln: www.linkedin.com/in/lovely-gebeyehu-155b5632b

References:

• Wavefront Sensing and Adaptive Optics with First Light Imaging Cameras- Oxford Instruments
• Discover how First Light Cameras can be a real game changer for wavefront sensing & adaptive optics applications
• andor.oxinst.com
• https://github.com/ngmsoftware/blender_wavefront_sensor
• https://www.axiomoptics.com/products/haso-swir-fast-high-speed-swir-wavefront-sensor/
• https://www.laserfocusworld.com/optics/article/16548376/adaptive-optics-liquid-crystals-lower-the-cost-of-adaptive-optics
• https://www.thorlabs.com/thorproduct.cfm?partnumber=DMP40-F01
• https://youtu.be/cbzBt60dhY8
• https://www.indiamart.com/proddetail/shack-hartmann-wavefront-sensor-1951930148.html
• https://www.dev-mind.blog/using-blender-to-learn-about-adaptive-optics-part-ii-ii/
• https://www.dev-mind.blog/using-blender-to-learn-basic-adaptive-optics/
• https://arxiv.org/pdf/1909.05224

A bit about the Nancy Grace Roman…

The Goal: The Roman Telescope will be used for space imaging and exploration, with concentrations like dark energy, exoplanet exploration, and the mapping and distribution of galaxies. Different components of the telescope will correspond to its’ mission — the WFI (Wide Field Instrument) with a field view 200x larger than that of the Hubble Space Telescope; it possesses a CGI (coronograph instrument) for high-contrast imaging, for direct observation of exoplanets by suppressing surrounding starlight. The CGI also contains two deformable mirrors that correct wavefronts in real-time through actuators — you can read all about that in my article here!

Now the juice of this article…

Recent Milestones and Progress:

In the past six months, the Roman Space Telescope project has achieved several crucial milestones:

Coronagraph Instrument Integration

On October 28, 2024, the Coronagraph Instrument (CGI) was successfully integrated into the telescope’s instrument carrier

This milestone required:

• Extensive testing at NASA’s Jet Propulsion Laboratory in Pasadena, California
• Careful transportation to NASA’s Goddard Space Flight Center
• Precise alignment and integration with the instrument carrier
• Verification of the CGI’s two deformable mirrors, crucial for real-time wavefront correction

The Coronagraph Instrument (CGI) aboard the Nancy Grace Roman Space Telescope is mounted within the telescope’s optical system, located near its focal plane, where it directly interacts with incoming starlight. It works by employing a combination of starlight suppression techniques (why you may ask? Read here.), adaptive optics, and precision engineering to capture high-contrast images of exoplanets. First, a series of masks and filters within the coronagraph blocks the overwhelming light from a star, isolating the faint light reflected by its orbiting planets. To refine this process, the CGI utilizes deformable mirrors — highly precise, adjustable mirror surfaces with thousands of actuators (essentially tiny pistons under the mirror)— that dynamically correct distortions in the light path caused by imperfections in the optics. This wavefront control ensures near-perfect cancellation of residual starlight, allowing planets billions of times fainter than their host star to be detected.

Optical Telescope Assembly Delivery

On November 7, 2024, the Optical Telescope Assembly, including the 2.4-meter primary mirror and nine additional mirrors, was delivered to NASA’s Goddard Space Flight Center. The delivery process involved:

• Precise manufacturing and assembly of the mirrors
• Extensive testing to ensure optimal performance
• Secure packaging and transportation
• Careful unloading and inspection upon arrival

Instrument Carrier Integration

By December 12, 2024, the telescope and its two main instruments were fully integrated into the instrument carrier

This complex process required:

• Precise alignment of the Wide Field Instrument (WFI) and the CGI
• Careful connection of all electrical and data interfaces
• Thorough testing of the integrated system

The WFI, equipped with 18 HgCdTe detectors (semiconductor devices made from a compound of mercury (Hg), cadmium (Cd), and tellurium (Te) — used to convert infrared light to electrical signals) provides high sensitivity and resolution for capturing detailed images of cosmic phenomena. Its field of view is 200 times larger than that of the Hubble Space Telescope, allowing for more comprehensive surveys of the sky.

Spacecraft Integration

On January 8, 2025, the final integration of the payload with the spacecraft was completed, keeping the project on schedule. This critical step involved:

• Mating the integrated instrument carrier with the spacecraft bus
• Connecting and verifying all power, data, and control systems
• Comprehensive testing of the fully integrated system

Data Management and Scientific Collaboration

Roman is expected to generate 4 petabytes of data annually, or about 11 terabytes per day. All data will be non-proprietary and made publicly available through NASA’s Mikulski Archive for Space Telescopes (MAST) shortly after collection. The mission encourages community-driven science through Core Community Surveys and General Astrophysics Surveys, allowing researchers to propose new observations. (Yay for me!)

Challenges and Future Steps

Despite the progress, the project faces several challenges:

1. Data transmission risks due to the limited capacity of NASA’s Deep Space Network and Near Space Network
2. Funding shortfalls for necessary upgrades to support Roman’s communication needs
3. Ongoing logistical challenges in integrating various sophisticated components

NASA’s Deep Space Network (DSN — NASA’s network of global antennas to communicate with beyond Earth orbit spacecraft) and Near Space Network (NSN — supporting communication within Earth’s orbit) are valuable for enabling communication between Earth and spacecraft operating across the solar system. However, these systems aren’t perfect and present challenges due to processing and storage capacity when handling missions like the Nancy Grace Roman managing 11 TB of received data per day. Additionally, both networks support multiple missions — each competing for time with these two instruments. They weren’t designed for current output of modern mission and their development has outpaced the improvements of the NSN and DSN. These demands far exceed the capacity envisioned during the early development of NASA’s communication infrastructure, creating a substantial risk of data transmission delays or losses.

Another layer of complexity arises from the increasing number of active missions relying on the DSN. With its antennas also supporting Mars rovers, lunar exploration under the Artemis program, and even probes like Voyager, the DSN must divide its limited resources among a growing number of spacecraft. This competition for bandwidth could lead to prioritization challenges, where Roman’s mission data might face delays in transmission or risk lower-quality communication links.

Looking ahead, the project team will focus on:

• Completing the integration of all components
• Conducting extensive testing, including electromagnetic, vibration, and thermal vacuum tests
• Preparing for the launch, scheduled for May 2027
• Developing strategies to manage the massive data output and ensure efficient distribution to the scientific community

The Nancy Grace Roman Space Telescope has made exciting progress within the past six months, reaching goals with integrating the Coronograph instrument, the delivery of the Optical Telescope Assembly achieving critical milestones such as the integration of the Coronagraph Instrument, the delivery of the Optical Telescope Assembly by NASA’s Goddard Space Flight Center, and successful spacecraft integration — all in effort to reach the deadline of launch by May 2027. Approaching challenges include addressing the limited capacity of NASA’s current communication infrastructure with the DS and NS networks to ensure proper management of data output from the Nancy Grace Roman. As the telescope inches closer to launch, it promises to revolutionize our understanding of the cosmos and pave the way for future space exploration.

Authors Note:

My name is Lovely Gebeyehu, I’m 15 years old and am interested in quantum physics, space exploration and what it holds for our future. Always willing to have a conversation — reach out to me here!

Email: lovelygebeyehu@gmail.com

Linkedln: www.linkedin.com/in/lovely-gebeyehu-155b5632b

When most people think of creating a realistic simulation of Earth, they imagine a complex process filled with intricate details and expert designers. Some envision a high-tech lab buzzing with activity as scientists meticulously craft every element of the model. However, the reality is quite different. For many 3D enthusiasts, including myself as a newcomer — building an Earth simulation can be surprisingly accessible and straightforward. By utilizing high-resolution textures and advanced shading techniques, individuals can create stunning representations of our planet from the comfort of their own homes. This democratization of technology allows anyone with a passion for 3D modelling to explore the beauty and complexity of Earth, making it possible to visualize atmospheric effects, dynamic weather patterns, and even the vastness of space — all without needing a team of experts or expensive software. Here’s how I did it!

Personal Experience: The first Blender tutorial I followed was for creating a Donut — although it was fun, the full-length tutorial was 5 hours… If you don’t have the time for that (try to make the time too though), this tutorial I feel was more straightforward. My advice would be to do about an hour of the donut tutorial from the YouTube channel Blender Guru, and then follow this tutorial for the Earth and Atmosphere simulator which uses similar tools.

Setting Up the Scene

To begin, I created a new scene in Blender and set up a basic spherical mesh (UV Sphere) to represent Earth. (Typically, a blender scene automatically imports a cube, a camera, and a light source — delete the cube in the scene collection). I adjusted the sphere’s size (proportional to the Earth’s actual size)and subdivided it (making it smoother) using a modifier to provide enough detail for the upcoming texturing process.

Implementing Textures

I applied multiple high-resolution Earth texture maps to the sphere, which included landmasses, oceans, topography, and ice caps. This provided the foundation for a realistic look.

All images implemented as textures were taken from NASA’s here (thanks NASA!)

The next step would be to go to the shading console and apply each texture image accordingly. As you can see in the screenshot below, each image texture corresponds to different properties, such as colour, and roughness, and soon you’ll see displacement. Try to follow along the nodes to see which image corresponds to which!

Displacement and Bump Mapping

To create topographical detail, I employed both Displacement and Bump mapping:

1. Displacement: I connected a Displacement node to the material output, using a separate height map texture to add depth, and create the illusion of mountains, valleys, and ocean depths to reference Earth’s more three-dimensional appearance.
2. Bump: I used a Normal Map node connected to the Normal input of the Principled BSDF shader.

All maps were implemented using the shading tool on the blender and can be linked using nodes to affect different factors, like roughness, colour, and displacement. Each map, at least for this project, affected a different factor.

And voila! You’ve created your earth!

Atmospheric Effects

To create the atmosphere, I duplicated the current earth we have, changed its transparency and increased its radius so it sits around the earth. You have to delete the first material that’s been duplicated from the Earth model, so we can add new properties (color, roughness — all factors influencing the surface of the mesh).

Now, depending on your interests you might now that the Earth’s oceans aren't actually blue, its influenced by the Earth's atmosphere. So — to make this proper, we need to remove the actual colouring from the oceans so the colour is solely based on the atmosphere.

We can easily do this by adding a Hue/Saturation/Value in the shade editor in between the earth's colour texture and the principle BSDF, connecting the earth's land and ocean image so we can remove the colour from the ocean but not the land.

The next step would be to add our cloud texture. Going back to the earth mesh, we can duplicate it, the size being slightly bigger than the earth, but slightly smaller than the atmosphere. some of your mountains will be higher than your clouds but that's accurate to real-world circumstances so that works out nicely. then you can utilize another image texture — the cloud image sourced by NASA!

It gets it own material, after duplicating it from our Earth object, then all other components visible in the image after the shadowing and placement of the clouds.

One way we can take this to the next level is by improving the dark side of the earth street lights that are probably going off like they usually do in the 21st century. Luckily, NASA provides a map for that too!

You would implement it in the same way, going to the shade editor on the Earth Material, but when connecting to the Principal BSDF, we connect it to emission and can influence the amount through a blackbody.

Rendering and Post-Processing

For rendering, I utilized Cycles with optimized settings for noise reduction and render time. In the Compositor, I applied subtle lens effects using the Glare node and adjusted colour grading with Color Balance and Hue Correct nodes.

Scale Considerations

To manage Blender’s unit system effectively, I scaled the Earth model to 1/10 of its actual size. For the atmosphere, I used the Scale tool to increase the duplicated sphere’s diameter by 20 Blender units. This technical approach to creating an Earth simulation in Blender demonstrates the software’s capability to produce scientifically accurate and visually compelling representations for space exploration preparation.

If you enjoyed this article, be sure to follow these steps to keep in touch with my future projects and articles!

1. Be sure to give my article some claps for support.
2. Connect with me on Linkedin, to hear about my future developments and future projects. Right now I’m currently working on furthering my knowledge of Blender and using it to predict different interactions within space.
3. Feel free to email me at lovelygebeyehu@gmail.com to talk about this project and more!

Thanks for reading this article!

Most people generally know where they’ll live in the next 2–5 years, but here’s the catch: that’s never guaranteed! Earth isn’t exactly a reliable living space anymore. After millions of years, humanity hasn’t ventured even 1% of what lies beyond our atmosphere. The main challenge we face is detecting possible living spaces beyond our planet and how to even go about navigating and understanding these spaces. Now, you might think, “There must be something out there!” And you’d be right! The problem is, we know where to look, but can’t see clearly… Imagine stepping on a planet you think is your new home but instead finding a steaming wasteland — all because we couldn’t analyze its’ atmosphere. Scientists — to great relief, are going to prevent this with the help of the Nancy Grace Roman Telescope.

How Is This Being Solved Now?

This pressing issue is being tackled through the Nancy Grace Roman Telescope. Don’t underestimate the potential of this instrument just because of its “polite name.” I’m proud to say this telescope surpasses our current buzz in the astrophysics community, the James Webb Space Telescope, holding the power to observe 100x more than another in-space telescope, Hubble. With its ability to manipulate gravitational lenses, the Roman telescope can navigate complications when interacting with stellar objects, which can obscure our analysis of potential habitable planets beyond our solar system. This and more will be fully expanded on within this article. The advanced technologies employed in the Roman telescope will allow us to detect immense sets of data across numerous wavelengths and to “combine” that data in real-time, ultimately helping us chart a clearer path toward our future homes.

The Technology Behind the Nancy Grace Roman Telescope

The technology utilized within the Nancy Grace Roman Telescope will address three main topics of interest; dark matter, dark energy, and exoplanet analysis and exploration. In this article, we will focus on tech intended to further study exoplanet exploration.

An Intro to Advanced Adaptive Optics

Okay — here’s an advanced term for scientists to feel better about themselves. Allow me to simplify; adaptive optics means adapting the orientation and form of mirrors for maximum efficiency in real time. Adaptive optics enhances image quality, especially when observing distant celestial objects. When light from stars and galaxies passes through the Earth’s atmosphere, it encounters turbulence that distorts the light waves, resulting in blurry images. This is particularly problematic for ground-based telescopes (Roman will be launched into space). Here I’ll introduce a similar system to what’s being utilized in the Roman telescope, the ExAO system.

• Extreme Adaptive Optics (ExAO): ExAO systems achieve high performance by utilizing a single bright natural guide star (NGS) (like Sirius or Vega) as a reference point to see how light is affected by turbulence (distortion) within the atmosphere, and change their mirrors to accommodate accordingly.
  Now, how exactly do they “adapt?” The mirrors are deformable and have a reflective surface that changes shape through small actuators inside the mirror, organized in a lattice format (3000 per each of the two mirrors — more on this later). These actuators respond to signals from a wavefront sensor that detects distortions from NGS’ and turbulence.

• The wavefront measures these distortions while the actuators adjust the shape of the mirror to improve image clarity! There isn’t any atmospheric turbulence in space, but the deformable mirrors can be used to correct smaller issues caused by temperature temperatures and space noise, challenges the Nancy Grace Roman Telescope will encounter. The wavefront sensors calculate the exact alterations needed to cancel out the distortions these adjustments can occur multiple times per second, constantly.

This tech will be implemented to acquire different disturbances used in the Roman’s Coronagraph instrument (CGI), with a specific interest in imaging distant exoplanets by blocking light from their parent stars.

The CGI is a system of masks (blocks bright lights), prisms (disperses light into its component colours/wavelengths) and detectors equipped with self-flexing mirrors that image planets in orbit around them. Two mirrors within the coronagraph interact with the light and have the actuators influence them interpretation of these images. You may have guessed by now, but these two mirrors in the coronagraph are indeed part of a similar system to the ExAO system mentioned earlier. The other components of the CGI include the apodizers and lyot stops, which selectively blockout celestial light and allow faint light from potential exponents through while effectively enhancing the contrast between the two; they also feature advanced camera and algorithmic control systems built upon past work on the James Webb Space Telescope (JWST). Advances specific in pixel density, coronagraph usage specifically for exoplanet detection as well as different design features, introduce spectroscopic instruments like PRISM and GRISM to survey dark energy (won’t be further discussed in this article.)

Now coronagraphs have been used in space-based telescopes in the past with the Hubble and JWST featuring either simplified forms in comparison to Romans’ or including similar abilities but don’t have the same starlight suppression features.

Historically, deformable mirrors used mechanical actuators requiring manual adjustment. These actuators were either piezoelectric or electrostrictive, working with the same intentions as Romans in response to light informalities. Let’s make a comparison between the Romans’ actuators and their adjustment technology with JWST.

The JWST has actuators mounted directly on its’ 18 hexagonal mirrors. Three actuators are positioned at the back of each segment, allowing action for precise adjustments in orientation and curvature — similar to Hubbles, to focus light accurately and prevent drift or misalignment.

The actuators in the Roman telescope are located in its’ coronagraph system; such a crossover has been utilized by Hubble but not for real-time adjustments which are the real breakthroughs. The two mirrors are situated within the optical path of the coronagraph, with the actuators enabling real-time adjustments.

The difference between the two? What JWST can do within minutes, Roman can do multiple times per second with even the slightest change being accounted before. Romans’ telescopes were crafted for rapid adjustments according to while-happening events and needed adjustments from external factors. It’s highly responsive to current events. JWST actuators function during initial alignment — they are capable of making adjustments — but not at the degree of Romans’ telescope, they aren’t intended for real-time corrections during observations. They operate on a longer time scale, with changes happening over several minutes.

Example: Digging the Dark Hole

Introducing a technique unique to the Nancy Grace Roman Space Telescope’s Coronagraph Instrument employs the two deformable mirrors, backed by over 2000 tiny pistons to finetune the blocking of starlight, in addition to the already sophisticated adjustment system from the actuators. The results entail an admirable decrease in glare, which will be represented once the Romans’ telescope is launched and catches images of exoplanets. The project was produced in collaboration with NASA, JPL, Caltech and international partners. Read more here: Roman Coronagraph Digging the Dark Hole | NASA Jet Propulsion Laboratory (JPL)

But this isn’t all being offered by the Roman telescope. Not only is its’ method enhancing the accuracy of their reading but allowing for full-range imaging.

How We’re Accomplishing Multiwavelength Observation

Another reason why this telescope is a stand-out against its predecessors is its’ ability for multiwavelength observations. Roman’s telescope captures near-infrared to visible light, covering 0.5–2.3 micrometres. This range allows for less disturbance from dust and gas, atmospheres of exoplanets, and analysis of ancient galaxies (that fall into the infrared stage because of redshift). Now, how is our telescope doing this?!

• Broadband Filters: The telescope is equipped with an array of broadband filters that first separate different wavelengths. These filters enable operators to target specific parts of the light spectrum, revealing features and phenomena that would’ve remained hidden if we only examined visible light. Broadband filters are thin optical elements made of glass occasionally with specialized coating, able to selectively transmit wavelengths while blocking others. They can be manufactured to have varying thicknesses and capture broad ranges of wavelengths — as they intended to in this model. Like the two mirrors, the filters are put in the optical path of the coronagraph. Broadband filters have been used in other astronomical instruments in older and ground-based telescopes.

By capturing this range, the telescope to study in greater detail and will complement other telescopes' data like Euclid's’ to create 3D maps of space at a faster rate (Read more here); utilized for further study of exoplanet atmospheres and distant galaxies.

Main Developers and Experts on This Project

The Nancy Grace Roman Telescope is being developed by NASA’s Goddard Space Flight Center, with contributions from various institutions worldwide. Key figures include:

• NASA Goddard Space Flight Center: the main place for this mission and where all the action is happening;
  Julie McEnery — Senior Project Scientist
  Jeffrey Kruk — Project Scientist
• Other scientists working through team proposals: Olivier Doré, B. Scott Gaudi, Mansi Kasliwal, Dan Scolnic, Rebekah Hounsell, Benjamin Rose, David Rubin, Yun Wang (Read here and here)
• International Partners: the French space agency CNES, European Space Agency (ESA), Japan Aerospace Exploration Agency (JAXA), and the Max Planck Institute for Astronomy
• There are of course more wonderful individuals contributing their time and effort for the eventual launch of the Roman telescope, and I give my respect for those who can’t be named in this article.

Future Challenges

Despite the Roman telescope’s promise and potential to address elementary questions and exoplanet exploration, it is still challenged for its importance and reliability.

Firstly, Roman will collect a full range of data and a wide field of view to measure trillions of individual residuals during its five-year mission. What happens when all this info is too much to tackle — we’ll need to assemble advanced machine learning algorithms to extract usable insights; how do we even ensure that all information gathered is usable and if the filters are reliable enough to combat this? Oh, not to mention, that the telescope will generate up to 11 terabytes of data… per day. Just wanted to put that out there.

The final destination of Roman will also pose more problems, not for data collection — but for communication with the telescope itself. It’ll be positioned 1.5 million km from Earth, with minimal interference from Earth’s radiation and a consistent thermal area. But at this distance, Roman will join other telescopes that rely on NASA’s Deep Space Network (DSN) for data transmission. Considering how much DSN supports other missions, ranging from surrounding telescopes to Mars’ rovers, this could affect how quickly data is being transmitted back to Earth and our ability to transmit instructions and monitor a craft’s conditions. (Read more about NASA’s DSN here; I’d also recommend this book and has similar contents relating to DSN!)

Final note —

The Nancy Grace Roman Telescope is set to revolutionize our understanding of the universe by potentially being completed in May 2027. By leveraging cutting-edge technologies and innovative observational strategies, this telescope aims to uncover the mysteries of dark matter, explore exoplanets, and provide insights into the cosmos that were previously beyond our reach. As we stand on the brink of this new era in astronomy, the potential for groundbreaking discoveries looms large.

Authors Note:

My name is Lovely Gebeyehu, I’m 15 years old and am interested in quantum physics, space exploration and what it holds for our future. Always willing to have a conversation — reach out to me here!

Email: lovelygebeyehu@gmail.com

Linkedln: www.linkedin.com/in/lovely-gebeyehu-155b5632b

Links:

Works Cited

Nancy Grace Roman Space Telescope, https://roman.gsfc.nasa.gov/. Accessed 14 October 2024.

“Digging the dark hole: Coronagraphy and the quest to find other worlds.” SPIE, 1 May 2023, https://spie.org/news/photonics-focus/mayjune-2023/digging-the-dark-hole-to-find-exoplanets#_=_. Accessed 14 October 2024.

Finkelstein, Steven L. “JWST (James Webb Space Telescope).” eoPortal, 5 August 2013, https://www.eoportal.org/satellite-missions/jwst#overview-of-payload-instruments. Accessed 14 October 2024.

“Formulation Science Working Group (FSWG) & Science Team — Roman Space Telescope/NASA.” Roman Space Telescope, https://roman.gsfc.nasa.gov/science/fswg/members.html. Accessed 14 October 2024.

“Found with Webb: a potentially habitable world.” UdeMNouvelles, 8 July 2024, https://nouvelles.umontreal.ca/en/article/2024/07/08/found-with-webb-a-potentially-habitable-world/. Accessed 14 October 2024.

“L3Harris Team Aligns 10 Mirrors for NASA’s Roman Telescope.” L3Harris, 17 April 2024, https://www.l3harris.com/newsroom/editorial/2024/04/l3harris-team-aligns-10-mirrors-nasas-roman-telescope. Accessed 14 October 2024.

Lea, Robert. “How scientists are gearing up for the Roman Space Telescope’s 2027 launch.” Space.com, 17 October 2023, https://www.space.com/roman-space-telescope-scientists-preparing-2027-launch. Accessed 14 October 2024.

“Nancy Grace Roman Space Telescope.” Roman Space Telescope, 1 March 2021, https://roman.gsfc.nasa.gov/science/RRI/ROMAN_Observatory_Reference_Information_20210301.pdf. Accessed 14 October 2024.

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The Fermi and eROSITA bubbles are massive, gaseous, radiation-emitting structures extending symmetrically above and below the Milky Way’s central black hole, Sagittarius A*. This paper delves into the discovery, structure, composition, and potential origins of these bubbles. Through examining the interactions of cosmic rays and magnetic fields, and the roles of shock fronts and past energetic events, we aim to better understand the formation and current state of these enigmatic structures. This exploration includes a discussion on the influence of dark matter and the challenges posed by the bubbles’ sharp edges, as well as speculation on their broader implications for galactic dynamics — taking up the main contributions of this paper.

Introduction
The Fermi and eROSITA bubbles are extraordinary features of our galaxy, revealing much about the energetic outflows at play in the Milky Way’s core. Discovered by the Fermi Gamma-Ray Space Telescope in 2010 and the eROSITA telescope in 2020, respectively, these structures challenge our understanding of galactic dynamics and the activities surrounding the central supermassive black hole, Sagittarius A* (Sgr A*). These bubbles, situated on the accretion disk (where a bunch of gunk and whatnot surrounds the event horizon of black holes) of Sgr A*, exhibit unique characteristics that provide insights into the mechanisms driving their formation and evolution.

Sgr A* is a supermassive black hole (SMBH) with intense gravitational pull, preventing even light from escaping. Its behaviour, rotation, and other properties are critical in understanding the origin and development of the Fermi and eROSITA bubbles. The accretion disk, where these bubbles lay, is a structure formed by material orbiting the black hole, emitting radiation as particles accelerate and collide.
The Fermi bubbles are roughly cylindrical, emitting gamma rays, while the
eROSITA bubbles are more conical, with a narrower base, emitting X-rays. The interaction of cosmic rays with magnetic fields within these bubbles leads to the emission of radiation at different frequencies.

Background: Basics of the Cosmic Ray acceleration mechanisms within FEBs

The Fermi bubbles comprise high-energy particles, primarily accelerated protons and other heavier nuclei. These particles become “excited” and move quite fast due to the gravity of being drawn in by the black hole and can combine to form heavier nuclei from their speed and collision. Cosmic rays (CRs) originate in high-mass regions, gaining energy through interactions with shock fronts and magnetic fields. Shock fronts entail drastic changes in an astronomical environment, in our case temperature and pressure. These interactions lead to the emission of gamma rays, which define the Fermi bubbles. Fermi acceleration, or diffusive shock acceleration, occurs when particles gain energy by interacting with shock fronts. This process involves fast-moving fluids, like plasma, encountering obstacles, resulting in increased temperatures and particle scattering. Plasma temperatures sit in between the range of T ≈ 106.4−7.2 K; Results from [2], show that mean plasma temperatures are lower near the edges in comparison to near the centre of the FEBs (Fermi and eROSITA bubbles) — indicating that the average intensity of the shock that is responsible for heating the plasma decreases with time.

Stochastic acceleration, another mechanism of acceleration, involves particles gaining energy through interactions with turbulent magnetic fields within the bubbles. The gamma-ray emissions from the Fermi bubbles are also influenced by inverse Compton scattering, where high-energy CRs collide with low-energy photons, boosting the photons’ energy. Bremsstrahlung, or braking radiation, occurs when CRs decelerate in the electric fields of atomic nuclei, producing X-ray emissions, prevalent in the eROSITA bubbles (EBS).

Speculative Origins

The formation of the Fermi and eROSITA bubbles is linked to past energetic
events in the Galactic Center (GC). Possible origins include outflows from Sgr A*, nuclear star formation, and supernova feedback. The leptonic jet model, which posits that jets from the supermassive black hole created these bubbles, is widely supported. This model aligns with observed morphologies and brightness distributions from recorded data.
Recent studies suggest that an active galactic nucleus (AGN) jet event from
Sgr A* around 2.6 million years ago could be responsible for the bubbles. This event’s duration, constrained by new X-ray data from the eROSITA bubbles, influences the observed separation between forward shock edges and the continuous structure of the bubbles. The situ acceleration model proposes that CRs accelerated by turbulence within the bubbles explain the gamma-ray emissions of the Fermi bubbles. However, this model struggles to explain the sharp edges and smooth surfaces observed.

Cosmic-ray-driven galactic winds, linked to steady star formation in
the Milky Way may also play a role in the bubbles’ formation.
These two models and their variants aim to explain gamma-ray emissions
and the developed composition of the SBs. The leptonic model, as well as its competitor, the hadronic model, will be discussed in future sections.

Structure of Superbubbles

The Fermi and eROSITA bubbles are vertically extended structures, originating from the GC, Sgr A*. The Fermi bubbles extend approximately 9 kpc (kiloparsec, 1 kpc = 3260 light years) from the galactic disk, while the eROSITA bubbles reach about 14 kpc. Their radii also vary, with the Fermi bubbles at 6 kpc and the eROSITA bubbles at 14 kpc. Understanding the reasons for these differences is an ongoing area of research.

4.1 Actual Conditions of Structure and Borders

The borders of the Fermi and eROSITA bubbles are characterized by enhanced emissions and sharp edges. The Fermi bubbles’ sharp edges and smooth surfaces suggest suppressed hydrodynamic instabilities and possibly anisotropic CR diffusion along magnetic field lines. Several models, including G20, S19, and MB, have been developed to simulate the conditions within these bubbles, but they struggle to accurately represent the bubbles’ narrow bases and brightness distributions.
The Z20 model, incorporating a radially decreasing density profile, allows
for faster jet propagation and energy deposition over longer distances, better matching observed data. This model effectively simulates the narrow bases of the Fermi bubbles and the gas distribution dynamics.
The eROSITA bubbles exhibit enhanced thermal bremsstrahlung emission
in the X-ray band at their borders, likely due to gas compression at shock fronts driven by past activity from the Galactic black hole. The one-sided enhancement on the Galactic northeast side may be due to ram pressure from a circumgalactic medium wind or recent jet heating.

Sharp Edges

The sharp edges of the Fermi bubbles are attributed to suppressed CR diffusion across the bubble surface, possibly due to anisotropic diffusion along magnetic field lines. These edges are indicative of stable propagation conditions and a lack of vigorous hydrodynamic instabilities. The leptonic jet model successfully reproduces the observed sharp and smooth edges, suggesting that AGN jet activity is responsible for these features.
X-ray observations align with the gamma-ray edges of the Fermi bubbles,
supporting the theory of a shock-driven origin from energetic outbursts at the GC. The morphology and sharp edges of the bubbles can be explained by the initial density distribution of the circumgalactic medium (CGM) and the dynamics of jet propagation.

Dark Matter Manipulation

The placement and sharp edges of the Fermi bubbles challenge the notion that they were formed through dark matter interactions, which typically result in more diffuse boundaries. The sharp edges are likely due to shock fronts created by continuous outflows from the GC, resulting in intense particle interactions at these boundaries.

Current Models

The Z20 model best represents the behaviours of superbubbles, particularly in simulating the morphology and dynamics observed in structures like the Fermi bubbles. This model’s radially decreasing density profile allows jets to propagate faster and deposit energy at large distances, effectively reproducing the observed narrow bases and gas distribution dynamics.
Simulations using the Z20 model show better agreement with observed X-
ray surface brightness distributions and the morphology of the Fermi bubbles compared to other models like MB and G20. The Z20 model’s ability to reproduce the observed X-ray and gamma-ray profiles, including their sharp edges and nearly flat intensity profiles, highlights its effectiveness in capturing the essential physics of superbubble dynamics.

Other Environments

Such structures/features like the FEBs are found in 2/3’s of simulated galaxies, even appearing somewhat symmetrical. They vary in structure, having either more bubbles or different morphology which could be used in the future to study SMBH outflows and behavior. What’s interesting is that most simulations find that these shells don’t extend past 10 kpc — remember our own FBs extend a bit above 10 kpc. What’s understood is, that these bubbles slow down as they expand — so in simulations that particularly illustrate young galaxies, these features would
conform to this. It’s predicted that eventual interaction with cosmic microwave background (CMB) is what causes this. The CMB also dilutes emissions from these bubbles. [3] [2]
Specific galaxies explored in his paper were M106 and NGC 4438 (NGC 4438
not as heavily). [3] Possible problems with the detection of other bubbles are simply they’re too distant and their surface brightness. We understand surface brightness decreases with expansion as shown from currently discovered SBs over Sgr A*, M106 and NGC 4438. While the predicted brightness is typically 1035 − 36 erg s1 kpc for the simulated bubbles (with their extents typically ≈ 10kpc [4], compared to 41036 erg s1 kpc2 for the eROSITA bubbles (extent 14 kpcs), 41038 erg s1 kpc2 for the M106 bubbles (8 kpc), or 3 × 1040 erg s1 kpc2 for the northwest nuclear bubble (0.3 kpc) in NGC 4438. From this, we understand that brightness decreases with expansion. [3]
The M106 structures are considered a younger version of the FEBs, which
likely came to be through similar mechanisms and development in comparable environments. Their origins correspond well with simulations from [4], which went under the assumption that some SBs could be the result of AGN (active galactic nuclei) feedback. [4]

Cosmic Ray Propagation

Cosmic ray propagation exhibits distinct characteristics near the borders of
cosmic structures compared to their centers, influenced by various astrophysical processes and environmental conditions. Near the borders of structures like the Fermi bubbles, CR propagation is affected by magnetic draping, which suppresses CR diffusion across the bubble surface, leading to sharp edges.
The intensity of the interstellar radiation field (ISRF) decays with increased distance from the GC, necessitating an enhancement in CR energy density towards higher Galactic latitudes. X-ray surface brightness decreases from the galactic plane towards higher latitudes, indicating lower gas densities at higher altitudes, which influence CR propagation by reducing interactions with matter. The distribution of cosmic ray electrons, as indicated by radio emission, shows a double-humped structure. The more extended high-latitude radio emission correlates with the Fermi bubbles’ propagation, while a secondary lower-latitude radio peak aligns with the interaction zone between the Fermi and eROSITA bubbles.

Hadronic and Leptonic Models

The broad-band spectrum from the bubbles can be explained by a single population of CR electrons transported from the GC by jets, supporting the leptonic jet activity theory. These findings suggest that a single leptonic jet event created the Fermi bubbles, eROSITA bubbles, and the microwave haze near the GC. Specifically, the expansion of the bubbles is credited to an injection of CR energy, thermal gas, and magnetic field energy provided by bipolar jets, perpendicular to our host galaxy. Their vertical expansion continues even after the jets have shut down and are supersonic, reaching Mach numbers (Ma) of 30 (Mach numbers refer to the ratio of an object’s speed to the speed of sound in the surrounding medium).

Lateral expansion is slower, but also supersonic at Ma 10–12. The resulting
forward shock fronts come to suppress the halo gas into a shell around the
bubbles; magnetic fields being morphed accordingly parallel to the surrounding shell. [5].This newly created motion of the fast-moving gas affects the spectra intensity for the CRs, with them diffusing their energy to the upper surface. [5]
The main difference between these models is hadronic models are characterized by emissions dominated by neutral pion decay, which contributes to gamma-ray emission of high intensities (exceeding tens of TeV) where temperatures of such are common — like in galaxy bubbles and collusive interactions with molecular clouds. [6] The leptonic channel where synchrotron emissions are due to Inverse Compton Scattering, diminishes as the SBs expand.

1. Leptonic Model

Under the simulation by Owen et al., the emission spectrum from a leptonic bubble, contributors for CR acceleration were non-thermal bremsstrahlung, and synchrotron emissions — both secondary to inverse Compton acceleration. Low-energy electrons scatter off low-energy photons, ”boosting” them to gamma-ray energies.

2. Limitations and faults

With a decrease in magnetic field strength, the contribution from the primary electrons to the total FB gamma-ray flux increases and at H 2.5 and below guons the origins of gamma rays from the FBs are purely leptonic [7]

3. Hadronic Model
This model successfully illustrates the bubble's hard spectrum, sharp edges and general emissions (a hard spectrum refers to the energetics of particles moving fast). [8] Such interactions between protons and/or thermal nuclei naturally produce high-energy neutrinos (tiny subatomic particles, often called ‘ghost particles’ because they barely interact with anything else). Gamma rays within the bubbles are produced by neutral pion decays, created by proton-proton interactions between energetic cosmic rays and gas. Cosmic rays, accelerated to ≈ 10 − 15eV and possibly beyond in supernova remnants, can be carried by the wind to fill the FB volume. Decays of charged pions and kaons, co-produced with neutral pions, by proton-proton interactions, guarantee a neutrino flux associated with the gamma-ray flux in the hadronic models. [8]

In the current hadronic model formalism [9], we assume a primary proton spectrum in the form of a power law with the exponential cutoff as N(p)(E) = N(O)E(k)exp(E/E(0)). Here N(O), k and E(O) are the normalization factor, spectral index and cutoff energy, respectively. The normalization factor N(O) is adjusted to fit the gamma-ray spectra by using a particle density of 102 cm3 for the gas inside the bubble volumes. The spectral index and the cutoff energy are crucial parameters which can be utilized to constrain the hadronic models from multi-wavelength, multi-messenger and noise observations. The gamma-ray spectrum from the Fermi bubbles is
well described by a power law with an exponential cutoff in the energy range between 100 MeV to 500 GeV; the spectrum is hard, meaning the energies these particles propagate at are high. Its spectal index is approximately -2 in the energy range between 1 GeV and 100 GeV[10]. The spectrum is the same everywhere in the bubble, suggesting that there a uniform mechanism that evenly distributes its’ emission. The radio spectrum observations from the WMAP and the Planck indicate a microwave flux from the FBs with a power-law spectrum, where the spectrum index ranges between 0.5 and 0.63 at GHz frequencies; this
means that the spectrum of the radio-emitting electrons is close to a power law, which is an important differentiation between both the leptonic and hadronic models.

4. Limitations and Faults
• The hadronic model is unable to reproduce the gamma-ray and radio fluxes from the SBs — secondary particles are too soft within the spectrum) if they lose energy from synchrotron radiation and inverse Compton [7]
• The pure hadronic model is unable to reproduce the FB radio spectrum if
the lifetime of secondary electrons is determined by the synchrotron and
IC energy
• The proton-proton collisions can only provide about 80 percent of the FB
gamma-ray flux
• If the magnetic field strength is stronger than 7 gauss up then neither the
hadronic nor leptonic models can reproduce recorded gamma and
radio emissions [7]

Cosmic Ray Energy Density
The cosmic ray energy density profile shows a pronounced enhancement towards higher Galactic latitudes. This profile is attributed to a combination of CR propagation effects and the distribution of the ISRF, which influences the energy density by modulating the rate of inverse Compton scattering and bremsstrahlung processes.
The effective area filling factor (filling factor αeff) of cosmic rays within the Fermi bubbles indicates that CRs are uniformly distributed within the bubbles, leading to a nearly flat intensity profile in both X-ray and gamma-ray emissions. The suppression of CR diffusion across the bubble surface, indicated by the sharp edges, further supports the uniform CR distribution within the bubbles.

1. Gas Density Profile

Gas density profiles play a crucial role in shaping the structure and emission properties of cosmic structures like the Fermi bubbles. The profiles, which describe the distribution of gas density as a function of distance from the Galactic plane, influence the interaction of cosmic rays with matter and the resulting radiation.
The density profile adopted in the Z20 model allows for a more accurate
representation of the gas distribution within the bubbles. This profile, characterized by a radially decreasing density, enables faster jet propagation and energy deposition over longer distances, better matching observed data on the Fermi bubbles’ morphology and brightness distribution.

2. Cooling Function

The cooling function, which describes the rate at which gas loses energy through radiation, is a key factor in the evolution of cosmic structures. For the Fermi bubbles, the cooling function is influenced by the interactions of CRs with the ambient medium, leading to the emission of gamma rays and X-rays. The Z20 model’s cooling function, which accounts for the effects of inverse Compton scattering and bremsstrahlung processes, provides a better match to observed data compared to other models. This cooling function accurately describes the emission properties of the Fermi bubbles, including the sharp edges and nearly flat intensity profiles, supporting the effectiveness of the Z20 model in capturing the essential physics of superbubble dynamics.

Conclusions and Implications
The Fermi and eROSITA bubbles provide valuable insights into the energetic processes at play in the Galactic Center and the interactions between cosmic rays, magnetic fields, and gas within the Milky Way. The leptonic jet model, supported by observations of gamma-ray and X-ray emissions, offers a coherent explanation for the formation and evolution of these bubbles. The Z20 model, with its radially decreasing density profile and effective cooling function, best represents the observed behaviours of the Fermi bubbles. This model’s ability to reproduce the narrow bases, sharp edges, and gas distribution dynamics highlights its effectiveness in capturing the essential physics of superbubble dynamics.
Future research on the Fermi and eROSITA bubbles will continue to refine
our understanding of these enigmatic structures and their broader implications for galactic dynamics, cosmic ray propagation, and the role of magnetic fields in shaping cosmic structures.

Authors Note:

I’m Lovely (yes, the adjective — or occasionally an oxymoron), 15 years of age, and I’m currently researching quantum mechanics, space settlement and exploration. I have lab and professional research experience under university undergrads and aspire to be places beyond that.

Let’s Connect!
Email: gebeyehulovely@gmail.com
Linkedln: linkedin.com/in/lovely-gebeyehu-155b5632b

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