This is not AI art. No generative model painted, styled, or hallucinated anything into this scene. A spectral reconstruction model expands a single linear raw capture into a dense spectral cube spanning the visible and near-infrared. From that cube, a Spectral Angle Mapper (SAM) compares every pixel against a library of known spectra.
Here is exactly what the spectral angle computes:
For every pixel in the scene, we take its reconstructed spectrum \( \mathbf{s} \) (its reflectance across many narrow wavelength bands). We compare that pixel spectrum against a library of known reference material spectra \( \mathbf{r} \). The spectral angle \( \theta \) is the angular distance between these two vectors in \( n \)-dimensional band-space:
I was first introduced to Einstein’s special theory of relativity by a math teacher whose husband, a mathematician, had worked on Einstein’s field equations. Around that time Roger Penrose visited my university and I listened to his lecture. Penrose, together with Hawking, had shown that general relativity predicts the conditions of its own breakdown. That is the theory at its most extreme. The same theory at its least dramatic says something about an airplane. Fly to Tokyo and you land a few nanoseconds displaced from everyone who stayed home. It is real and it has been measured, though not as a clean demonstration of velocity alone. For an airliner, the velocity term that slows the clock competes with the altitude term that speeds it up, and in 1971 Hafele and Keating flew cesium clocks east and west around the world and recorded offsets of opposite sign for the two directions.1
After graduating college, I worked with some folks who had just finished a project on the super collider in Waxahachie and another group out of France and Geneva. It was then that I first started to think about time as something a particle carries with it. Certain particles are created high in the atmosphere and should fall apart long before they ever reach the ground. They arrive anyway. They arrive because they are moving fast enough that their own clock runs slow compared to ours, which buys them the trip down. Rossi and Hall measured this in 1941,2 and particle accelerators have confirmed it since to very high precision. Nothing about the particle itself changes. What changes is the relationship between its clock and ours.
Now the train. Einstein asked us to imagine a long, straight railway track with a train moving along it at a steady speed. Lightning strikes twice: once at the front of the train and once at the rear. On the ground, an observer stands exactly halfway between the two points where the lightning hit. She sees the light from both flashes arrive at the same moment, so she concludes the flashes were simultaneous.
On the train, a passenger sits exactly in the middle of the car. In the ground observer’s frame, the forward flash reaches the passenger first because the train carries her toward the oncoming forward light and away from the rear light. But the passenger herself is at rest in her own inertial frame; for her, light travels at speed c from both ends, and the distances to the front and rear of the car are identical. Since the forward flash arrives before the rear flash despite equal distances and equal light speed, it must have been emitted first in her frame. The two strikes are simultaneous for the ground observer, yet sequential for the passenger.
So did the strikes occur at the same time or not? In special relativity, the question has no absolute answer. The two events are spacelike-separated; no signal could travel from one strike to the other, so their temporal order is frame-dependent. Both observers are correct within their respective frames. There is no universal “now,” and simultaneity depends entirely on your state of motion.
This relativity of time becomes vivid with a light clock. Imagine a spaceship carrying a photon bouncing vertically between two mirrors. To someone on board, each round-trip is a simple up-and-down tick. To an observer on the ground, the photon traces a longer diagonal path because the mirrors move between bounces. Since the speed of light is the same for all observers, the diagonal journey takes longer. So the moving clock is seen to run slow. This is time dilation.
A word about the spaceship, because it is the part people stop on. There is nothing exotic about it. Time only stretches by an amount worth noticing when something travels at a good fraction of the speed of light, and nothing you can ride travels remotely that fast. A train is far too slow. An airplane is too slow, which is why the effect on one is measured in billionths of a second. So the thought experiment needs a vehicle that could actually reach those speeds, and a spaceship is simply the most convenient one to picture, because space is the only place with room enough to get up to speed and nothing in the way. Einstein used trains because a train was the fast thing of his day. The vehicle is a stand-in for speed and nothing else. The point is never the ship. The point is what happens to the clock inside it.
Time dilation is not a metaphor. A traveler moving at high speed ages less than those who stay behind. If you board a spaceship and accelerate to a significant fraction of light speed, you can travel years on your own clock while centuries pass on Earth. This is forward time travel, allowed by special relativity. Backward time travel, however, is not. General relativity offers theoretical loopholes: Gödel’s rotating universe,3 wormholes,4 the interior of a spinning black hole. Each fails for its own reason. Wormholes need exotic matter with negative energy density. Gödel’s solution describes a universe that rotates, which ours does not appear to do. The closed paths inside a spinning black hole sit behind a horizon nothing returns through. Hawking’s chronology protection conjecture suggests the universe forbids closed timelike curves outright.5 Practically, you can journey into the future, but you can never send a message to the past.
That irreversibility is the heart of the matter. The past is sealed. We can only move forward, carrying what we have learned.
What clung to me, what I still carry in my bones, is the cruel elegance of the instrument itself. Those trains, those spaceships: they aren’t just physics. They are lenses. Tools for seeing exactly what light permits and what it ruthlessly forbids.
And thirty years after that miracle year of 1905, Einstein aimed that same sharp, unforgiving lens away from the stars and straight into the quantum mess. He was looking for a new foothold, a new way of seeing the chaos underneath.
In 1935, Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen published a seminal paper arguing that the quantum-mechanical description of physical reality is incomplete.6 The claim was not that quantum mechanics predicts wrongly. It was that a theory can predict correctly and still fail to describe everything that is there. They built the argument on a pair of particles prepared so that measuring the position or the momentum of one lets you predict the corresponding quantity for the other, at any separation, without disturbing it.
Two attributions are worth getting right, because the popular account collapses them. The familiar spin version of the argument (two-outcome measurements along chosen axes, the form in which nearly every modern discussion is conducted) is Bohm's reformulation from 1951, not the 1935 paper.7 And the word entanglement is not Einstein's either; Schrödinger introduced it later that same year, writing in reply.8
It is the quintessential example of a problem in which the whole contains information that cannot be inferred from looking at one part in isolation. An entangled pair can be prepared in a joint quantum state in which particular measurements produce strongly correlated results. Conservation laws can impose those relationships; total angular momentum has to add up. The result is not that each particle secretly carries a classical answer waiting to be revealed, but that quantum mechanics assigns probabilities and correlations to the joint system.
And the correlation is not created by the act of measurement. It is fixed at preparation, written into the joint state rather than into either particle on its own, which is a different claim from saying each particle quietly carried its own answer all along. Bell's result below rules that second reading out. Measuring one particle reveals it, and updates what you should expect from a measurement on the partner, regardless of the distance separating them. That distinction is the whole ballgame, because it is precisely why entanglement cannot be used as a telephone. The formal statement is the no-communication theorem: no local operation on one half of an entangled pair changes the measurement statistics available at the other half. The marginal distribution at each end is untouched, whatever is done at the far end. You need the classical record from both ends, brought together at light speed or slower, before the correlation becomes visible at all. The strangest object in physics still cannot carry a single word backward, or even sideways, faster than light.
So the strange thing about entanglement is not that it provides a faster-than-light telephone; it is that nature permits correlations between separated measurements that cannot be reproduced by ordinary local hidden-variable theories. Einstein objected to the implications of that picture. Bell showed in 1964 that the objection was testable,9 and experiment has since answered. Aspect, Dalibard, and Roger's 1982 measurement with time-varying analyzers10 left two gaps open, the locality loophole and the detection loophole, and both were closed in 2015 by a set of experiments that violated Bell inequalities with no significant loophole remaining.11,12,13 The 2022 Nobel Prize in Physics recognized this line of work. Local hidden variables are gone. Einstein was wrong about the conclusion and right that the question was worth forty years of somebody's life.
The EPR Analogy, and Where It Stops
While the EPR debate centered on the foundations of quantum mechanics, its deeper philosophical lesson, that direct observation can miss profound relationships within a system, resonates with modern imaging. In each case, information that is not apparent from an isolated measurement becomes accessible when measurements are considered together and interpreted through an appropriate mathematical model.
Just as the naked eye perceives only a fraction of the electromagnetic spectrum, a standard RGB sensor records only three broad spectral responses. The information discarded between and beyond those responses can contain clues about the chemical and physical properties of a material. Multispectral and hyperspectral imaging address this limitation by measuring, or in some cases estimating, how materials interact with light across a broader spectral range, and mathematical reconstruction can then infer spectral structure that is not directly represented in the original RGB observation.
The analogy is not that spectral correlations are quantum entanglement. They are not, and the difference in depth is enormous. It is only that both problems reveal the same limitation in taking a partial observation as the whole story.
Silicon Photonic Architecture The realization of this physics in modern hardware is constrained by the physical dimensions and properties of the semiconductor used to capture it. The interaction of incident photons with the silicon lattice, generating electron-hole pairs, is the primary physical process underlying photon detection in a conventional silicon image sensor, and that process sets hard boundaries at both ends of the range.
Silicon's indirect bandgap is approximately 1.1 eV, so photodiode response falls away as wavelengths approach roughly 1100 nm and there is no photoelectric detection beyond it. At the other end, absorption depth collapses: on the order of a few nanometres in the ultraviolet against hundreds of microns in the near-infrared. Ultraviolet photons are absorbed before they can reach the depth at which a front-illuminated sensor's photodiodes sit, which is the substantive reason back-illumination matters for short-wavelength work rather than a marketing distinction.
The Spectral Gatekeeper Before any of that, almost every camera bonds a UV/IR-cut filter directly into the stack above the sensor. That filter, not the lens glass, is the dominant constraint on accessible spectral range: it typically passes roughly 400–650 nm and rejects wavelengths to either side by orders of magnitude. No amount of downstream processing recovers a band the filter rejected, so any work outside that window is a question of optics and filtration rather than algorithms.
A second consequence is easy to miss. Bayer color-filter dyes leak in the near-infrared; past roughly 800 nm all three channels become nearly transparent and nearly identical. Beyond the visible window a silicon sensor therefore stops behaving as a trichromatic device and behaves more like a monochrome detector carrying three largely redundant channels, which means wavelength discrimination in that region cannot come from the color filter array at all.
Sensor Architecture The core of this pipeline is a modern back-illuminated CMOS sensor, optimized for high-resolution imaging and radiometric capture.
Active Sensing Area: The sensor's physical dimensions matter because they influence the total photon flux the device can collect for a given scene and exposure, and therefore the achievable Signal-to-Noise Ratio. No downstream algorithm can recover photons that were never recorded.
Pixel Pitch: Native photodiode pitch varies widely by format, from around a micron in small-format sensors to several microns in full-frame. Pitch, however, is usually not the binding limit.
Diffraction, Not Sampling At realistic working apertures the optics run out of resolution before the pixel grid does. The Airy disc radius is approximately 1.22λN; at f/8 and 550 nm that is about 5.4 µm, several times the pitch of a small-format sensor and larger than a typical full-frame photosite. Stopping down to gain depth of field across a textured surface therefore buys resolution loss at a predictable rate. Fine fiber structure in a document is recoverable only when aperture, wavelength, and working distance are chosen such that the optical transfer function still passes those spatial frequencies. Adding pixels does not help once diffraction has already removed the detail.
Mode Selection The choice between binned and unbinned modes depends on the analysis requirements, and the SNR arithmetic depends on where the binning happens and which noise source dominates.
True charge-domain binning—combining photocharge from neighboring photodiodes before the sense node and before readout—keeps the read-noise contribution essentially constant while the signal scales with the number of pixels summed. In the read-noise-limited regime a 2×2 operation can therefore improve SNR by up to a factor of four. Many modern CMOS sensors, however, implement only digital summation after independent digitization of each pixel, or a hybrid scheme in which charge sharing is possible in one direction only. In the pure digital case the signal still multiplies by four while uncorrelated read noise grows by the square root of four, a factor of two, limiting the SNR gain to a factor of two. In the shot-noise-limited regime (bright scenes, long exposures, controlled illumination) neither approach exceeds a factor of two, because shot noise itself scales as the square root of the collected signal. Binning remains a low-light tool; whether the spatial cost is worthwhile is decided by which noise term actually dominates the exposure.
Full-resolution (native sampling) mode is preferred when spatial detail is the priority—resolving fine fiber patterns in historical documents or detecting micro-scale material boundaries—subject to the diffraction limit above.
The Optical Path The light reaching the sensor passes through a multi-element lens assembly with a fast maximum aperture. A spectral imaging system measures a combination of the material's spectral reflectance R(λ), the illumination spectrum, the optical transmission T(λ), the detector response, and other system characteristics. Modern optical glass and coatings attenuate particular wavelengths, especially toward the near-UV, so those effects must be characterized during calibration if measurements are intended to be quantitatively meaningful. Some coated modern lenses cut off the near-UV so sharply that older uncoated or quartz-element designs are the practical choice for that end of the range.
Calibration: The Three Frames You Cannot Skip A spectral measurement is not a photograph, and the forward model above makes the requirement explicit. Recovering R(λ) means dividing out everything in that product chain that is not the material.
Dark frame: matched exposure time and sensor temperature with no light reaching the sensor, subtracted to remove black-level offset and dark current. Both are temperature-dependent, so the frame has to be acquired close in time and condition to the measurement rather than reused from an earlier session.
Flat field: uniform illumination of a spectrally neutral surface, divided out to remove lens vignetting, pixel response non-uniformity, and illumination falloff across the field. All three are wavelength-dependent, so a single flat does not serve every band.
White reference: a diffuse reflectance standard of known spectral reflectance, imaged under the same illumination in the same geometry. This is what converts raw signal into reflectance rather than an arbitrary sensor unit. Without it the pipeline produces numbers that are internally consistent and externally meaningless. Reflectance is a ratio, and something has to be the denominator.
The Digital Container: DNG and Linearity The accuracy of computational imaging depends heavily on the integrity and characterization of the input data. The Adobe DNG specification can provide a standardized container for raw or rendered image data, but the presence of a DNG extension by itself does not guarantee scientific linearity or calibrated radiometric measurements. The actual camera data, conversion path, metadata, and calibration procedure all matter.
Scene-Referred Linearity For spectral reconstruction, the important property is preservation of a useful linear relationship between recorded sensor signal and scene radiance over the relevant operating range. Raw sensor measurements can generally be treated as approximately linear with respect to accumulated signal before nonlinear display transformations are applied, but black-level offsets, gain, saturation, noise, color-filter responses, and other camera-specific characteristics must be accounted for. Linear image data is not synonymous with photon counts; it is calibrated or calibratable sensor signal.
Gain Maps and Aesthetic Metadata Modern raw-image ecosystems can carry metadata describing transformations, calibration information, or image-rendering behavior separately from the underlying image data. This separation is valuable for scientific workflows because the computational pipeline can choose which transformations are appropriate for measurement and which belong only to visual presentation.
Scientific Stewardship: By keeping measurement-oriented data separate from aesthetic rendering decisions wherever possible, the pipeline avoids allowing display-oriented processing to be confused with the underlying signal used for spectral analysis. The goal is not simply an attractive image; it is a reproducible, characterized measurement from which computational inference can be performed.
Algorithmic Inversion: From 3 Channels to a Dense Spectral Grid Recovering a high-dimensional spectral curve S(λ), potentially comprising hundreds of narrow bands sampled at nanometre-scale intervals, from a low-dimensional RGB input is an ill-posed inverse problem. It is worth being precise about why, because "ill-posed" undersells the situation.
The camera's three spectral sensitivity functions span a three-dimensional subspace of a function space with hundreds of dimensions. Any spectrum lying in the null space of that projection, the metameric blacks, produces identically zero response in all three channels. Not approximately zero: zero. Two spectra differing by a metameric black are the same RGB triple, and no algorithm recovers what the null space swallowed. Reconstruction works instead by ruling out the physically implausible members of that infinite family, using calibration data, physical constraints, statistical priors, and, in learned systems, the distribution represented in the training data. The information loss is a theorem about the projection, not a caveat about implementation quality: no amount of engineering recovers what the null space swallowed. What engineering does determine is how good the remaining guess is, and that depends on how closely the real material resembles what the model was shown.
Wiener Estimation (The Classical Baseline) The classical approach is linear minimum mean-square-error estimation, minimizing expected squared error between estimated and actual spectra through a matrix estimator:
\(W = K_r M^T (M K_r M^T + K_n)^{-1}\)
Here M is the system matrix combining illumination, optical transmission, filter response, and detector sensitivity; Kr is the covariance matrix of the spectral reflectances expected in the sample population; and Kn is the noise covariance. The estimator is optimal among all estimators only when spectra and noise are jointly Gaussian and their second-order statistics are known. Otherwise it is the best linear estimator, which is a materially weaker claim. Kr is where the assumptions hide: the result is only as good as the population you have assumed you are measuring, which is why a Wiener estimator built for one class of material degrades on another.
For decades, linear statistical estimation provided an interpretable route from a low-dimensional observation to an n-band estimate, and it remains a useful reference against which learned methods can be judged. But as a global linear operator it cannot exploit the spatial context or nonlinear relationships that help resolve some of the ambiguity created by spectral compression.
State-of-the-Art: Transformers and Mamba For high-end computational environments, predictive neural architectures can leverage spatial and spectral correlations to resolve ambiguities that simple global linear models cannot. None of them escape the null-space argument above; what they improve is the quality of the prior, not the information content of the measurement. That prior is only as reliable as the distribution on which it was trained. Spectra, illuminants, or material classes that lie outside the training support can produce plausible-looking reconstructions whose errors are invisible to ordinary visual inspection and are not flagged by the network itself. Cross-validation against measured reference spectra under the actual illumination and geometry remains essential; without it the output is an informed guess whose confidence interval is unknown.
MST++ (Spectral Attention Architecture)14: The Multi-stage Spectral-wise Transformer represents a significant development in learned spectral reconstruction. Unlike a single global matrix estimator, MST++ uses attention mechanisms to model relationships between spectral features, allowing the network to learn nonlinear relationships that are difficult to capture with a fixed linear operator. Attention is computationally expensive, particularly as token dimensions and image resolution grow, making memory management important at high resolutions.
State Space Models (Efficient Sequence Processing)15: A newer family of architectures replaces conventional attention with state-space mechanisms. Selective state space models such as Mamba discretize a continuous state-space formulation into a form suitable for efficient sequence processing. Their computational characteristics can be favorable for long sequences, and recent research has adapted Mamba-inspired architectures to spectral reconstruction and spectral compressive imaging.16,17 These approaches are attractive for large images because they model long-range dependencies without relying exclusively on quadratic self-attention. Actual memory and computational cost depends on the architecture and implementation rather than being universally linear in every dimension of the problem.
Multi-Frame Super-Resolution: Approaching the Optical Limit The sampling limits of a single sensor frame can be partly overcome through multi-frame super-resolution compositing, where multiple precisely registered exposures containing sub-pixel shifts are combined into a higher-resolution representation.
What this recovers, precisely, is information above the sampling limit that the optics passed and the pixel grid could not record: aliased and undersampled structure. It cannot exceed the diffraction limit, because that information never arrived at the sensor plane in the first place. The final result remains bounded by the lens's optical transfer function, aberrations, sensor noise, subject and platform motion, registration accuracy, and the information actually present in the source exposures. The objective is not to manufacture detail from nothing, but to make better use of information distributed across multiple measurements.
For spectral work, though, the more valuable gain has nothing to do with resolution. Sub-pixel offsets place different photosites, and therefore different color-filter positions, over the same point on the subject, so the composite can carry genuinely measured R, G, and B values at each output location instead of demosaic-interpolated estimates. Demosaicing invents two of every three color values per pixel, and invents them from neighbouring pixels, which corrupts exactly the per-pixel channel ratios that spectral reconstruction consumes as its input. Eliminating that interpolation matters more to spectral fidelity than the additional pixels do.
These composites preserve the linearity and calibration characteristics of the source data when the processing pipeline is designed appropriately, allowing spectral reconstruction to operate on the resulting representation. The data footprint scales accordingly: floating-point spectral arrays become enormous, and a complete high-resolution multispectral cube may require many gigabytes of storage. The increased spatial detail can enable micro-scale textural analysis that would otherwise be lost, revealing deposition patterns, brushstroke gradients, and surface anomalies at scales approaching the practical resolving capability of the optical system.
Computational Architecture Achieving multispectral precision requires a robust, modular architecture capable of handling massive arrays across a high-dimensional latent space, which in practice means a scientific Python stack running on hardware with substantial memory and bandwidth.
Ingestion: raw decoding is worth one specific warning, because it is a common and silent source of error. Raw decoders do not return linear data by default. Typical defaults apply a gamma curve and automatic brightness scaling, so obtaining sensor-oriented linear values requires disabling those explicitly and handling black-level subtraction as a separate step. Everything downstream inherits whatever was wrong here.
Processing and Analysis: high-performance array libraries handle the matrix algebra required to transform or estimate spectral representations from RGB data, with additional scientific libraries for geometric transforms, image restoration, and spatial filtering, and a plotting layer for spectral signature graphs and false-color composites.
Data Footprint: the scale is significant. A single high-resolution frame converted to floating-point precision produces large files. Intermediate files can exceed hundreds of megabytes for a single three-channel layer, while a full n-band multispectral cube scales proportionally with band count and spatial dimensions. Super-resolution composites multiply those requirements further, producing intermediate arrays that can exceed many gigabytes and necessitating careful memory management, fast storage, and substantial memory bandwidth.
The Spectral Solution Two blue pigments make the argument concrete. Ultramarine and azurite are difficult to separate reliably by eye or by RGB response, and trivially separable once the near-infrared is available, for reasons that come directly from their chemistry:
Spectral Feature
Ultramarine (Lapis Lazuli)
Azurite (Copper Carbonate)
Origin of colour
The S3− radical anion held in the sodalite-type lazurite lattice, producing broad absorption centred near 600 nm
Cu2+ d-d electronic transitions in a basic copper carbonate
Visible-region behaviour
Strong reflectance in the blue-violet region; reduced reflectance through the orange-red where the 600 nm absorption sits
Blue reflectance with a greener bias than ultramarine; spectral shape influenced by particle size, concentration, and binder
Near-infrared behaviour (the discriminator)
Highly reflective through the NIR; remains bright in infrared reflectography
The same Cu2+ transitions produce strong broad absorption extending through the NIR; goes dark in infrared reflectography
Practical requirement
The NIR separation lies outside the roughly 400–650 nm window a stock camera passes, so it depends entirely on the optical and filtration choices discussed above. Inside the visible window alone the two pigments can be genuinely ambiguous.
Note: Measured values vary with pigment composition, particle size, binding medium, concentration, substrate, aging, illumination, and instrument calibration. The NIR contrast between these two is robust because it follows from electronic structure rather than from preparation, but quantitative identification still requires comparison against reference spectra acquired under controlled conditions.
Completing the Picture The successful analysis of complex material properties relies on a convergence of rigorous physics and advanced computation.
Photonic Foundation: A modern back-illuminated CMOS sensor provides high-SNR photonic capture across silicon's usable range, with readout mode driven by which noise regime the exposure actually sits in.
Spectral Access: The accessible range is set by the UV/IR-cut filter first, silicon's 1.1 eV bandgap second, and the optics third. Extending past the visible window is a hardware question, not a software one.
Sensor Diversity: An ingestion layer can normalize black level, white balance, and color filter array geometry across proprietary and standard raw formats. What that produces is format consistency, not radiometric equivalence. Two bodies with different spectral sensitivity functions record different projections of the same spectrum, and harmonizing the containers does not harmonize the measurement. Cross-body comparability requires per-camera SSF characterization, measured against a monochromator or estimated from a calibrated target set, and until a body has been characterized its reconstructions are internally usable but only loosely comparable to another body's.
Data Integrity: A properly characterized raw workflow or linear DNG provides a foundation for preserving scene-referred data, but the file format alone guarantees nothing about radiometric accuracy. Dark, flat, and white-reference frames remain non-optional.
Algorithmic Precision: Wiener estimation remains the classical reference point, while MST++ and Mamba-based architectures model complex nonlinear relationships between image observations and spectral structure. Their output is inference constrained by a learned prior, not recovery of information the camera never measured. Performance outside the training distribution is not guaranteed and must be checked against physical references. Multi-frame compositing improves spatial sampling and, more importantly here, removes demosaic interpolation from the spectral input.
Physical Pattern Analysis: Spectral reconstruction alone cannot resolve every ambiguity. Materials that are spectrally similar can often be separated by their spatial characteristics: texture, edge morphology, and distribution across a surface. Supplementing per-pixel spectral classification with geometric analysis of the spatial domain gives a second, independent axis of evidence, closing a gap that purely spectral methods leave open.
Historical Continuity: The EPR debate of 1935 forced physicists to confront the possibility that a complete description of a system could not be reached through classical intuition about its individual parts. Modern spectral imaging presents a different and far less profound problem that rhymes with it: materials carry structured information across wavelength that is invisible to trichromatic vision. In both cases, completeness requires looking beyond what a single direct observation provides.
Hardware, calibration, file-format stewardship, and reconstruction converge on one thing: a spectral witness to what ordinary vision alone cannot tell us.
And what about the paint? Here is a physical sample: pigment, substrate, history compressed into matter. Light passes through it, scatters from it, carries fragments of its story: yet the full truth remains hidden until we choose to look deeper. Every layer, every faded stroke, every chemical trace is a silent archive. We are not just observers; we are custodians of that archive. When we build tools to see beyond the visible, we are not merely extending sight: we are accepting a quiet responsibility: to bear witness honestly, to preserve what time would erase, to honor what has been made and endured.
Light can expose structure. It cannot carry history.
That part is on us.
We can choose to let the machines we build serve memory rather than erasure, dignity rather than classification, truth rather than convenience. The past does not ask for perfection: it asks only that we refuse to let it be forgotten. In every reconstruction, in every layer we uncover, we have the chance to listen again to what was silenced. That is not just engineering. That is the work of being human.
But tonight, sitting here in the dark, I realize I am still riding that same damn train. Hurtling toward one flash, watching the other recede into a past I can never touch, never text, never warn. Information can race forward, people can race forward, but nothing, nothing gets to go back. We are all just riders, carried away from every moment we have already survived, looking for answers in the one direction the universe actually lets us move. Forward. Always forward. And that is the most beautiful, devastating thing I know.
References
1 Hafele, J. C., & Keating, R. E. (1972). Around-the-World Atomic Clocks: Predicted Relativistic Time Gains; Observed Relativistic Time Gains. Science, 177(4044), 166–168; 168–170.
2 Rossi, B., & Hall, D. B. (1941). Variation of the Rate of Decay of Mesotrons with Momentum. Physical Review, 59(3), 223–228.
3 Gödel, K. (1949). An Example of a New Type of Cosmological Solution of Einstein's Field Equations of Gravitation. Reviews of Modern Physics, 21(3), 447–450.
4 Morris, M. S., & Thorne, K. S. (1988). Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity. American Journal of Physics, 56(5), 395–412.
5 Hawking, S. W. (1992). Chronology protection conjecture. Physical Review D, 46(2), 603–611.
6 Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47(10), 777–780.
7 Bohm, D. (1951). Quantum Theory. Prentice-Hall. (Spin reformulation of the EPR argument.)
8 Schrödinger, E. (1935). Discussion of Probability Relations between Separated Systems. Proceedings of the Cambridge Philosophical Society, 31(4), 555–563.
9 Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Физика, 1(3), 195–200.
10 Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental Test of Bell's Inequalities Using Time-Varying Analyzers. Physical Review Letters, 49(25), 1804–1807.
11 Hensen, B., et al. (2015). Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526, 682–686.
12 Giustina, M., et al. (2015). Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons. Physical Review Letters, 115, 250401.
13 Shalm, L. K., et al. (2015). Strong Loophole-Free Test of Local Realism. Physical Review Letters, 115, 250402.
14 Cai, Y., Lin, J., Lin, Z., Wang, H., Zhang, Y., Pfister, H., Timofte, R., & Van Gool, L. (2022). MST++: Multi-stage Spectral-wise Transformer for Efficient Spectral Reconstruction. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW).
15 Gu, A., & Dao, T. (2023). Mamba: Linear-Time Sequence Modeling with Selective State Spaces. arXiv:2312.00752.
16 Zhang, Y., Li, L., Lin, Q., Ming, Z., Yu, F., & Leung, V. C. M. M3SR: Multi-Scale Multi-Perceptual Mamba for Efficient Spectral Reconstruction. [venue and year to be completed]
17 Qin, M., Feng, Y., Wu, Z., Zhang, Y., & Yuan, X. Detail Matters: Mamba-Inspired Joint Unfolding Network for Snapshot Spectral Compressive Imaging. [venue and year to be completed]
Provenance · Integrity Record
Canonical file hashes · SHA‑512
Hashes are of the byte-identical JPEGs converted from raw sensor data. Verify with sha512sum -c SHA512SUMS.
Arch Linux is known for its high level of customization, and configuring LUKS2 and LVM is a straightforward process. This guide provides a set of instructions for setting up an Arch Linux system with the following features:
Root file system encryption using LUKS2.
Logical Volume Management (LVM) for flexible storage management.
Unified Kernel Image (UKI) bootable via UEFI.
Optional: Detached LUKS header on external media for enhanced security.
Prerequisites
A bootable Arch Linux ISO.
An NVMe drive (e.g., /dev/nvme0n1).
(Optional) A microSD card or other external medium for the detached LUKS header.
Important Considerations
Data Loss: The following procedure will erase all data on the target drive. Back up any important data before proceeding.
Secure Boot: This guide assumes you may want to use hardware secure boot.
Detached LUKS Header: Using a detached LUKS header on external media adds a significant layer of security. If you lose the external media, you will lose access to your encrypted data.
Swap: This guide uses a swap file. You may also use a swap partition if desired.
Step-by-Step Instructions
Boot into the Arch Linux ISO:
Boot your system from the Arch Linux installation media.
Set the System Clock:
# timedatectl set-ntp true
Prepare the Disk:
Identify your NVMe drive (e.g., /dev/nvme0n1). Use lsblk to confirm.
Wipe the drive:
# wipefs --all /dev/nvme0n1
Create an EFI System Partition (ESP):
# sgdisk /dev/nvme0n1 -n 1::+512MiB -t 1:EF00
Create a partition for the encrypted volume:
# sgdisk /dev/nvme0n1 -n 2 -t 2:8300
Set up LUKS2 Encryption:
Encrypt the second partition using LUKS2. This example uses aes-xts-plain64 and serpent-xts-plain ciphers, and SHA512 for the hash. Adjust as needed.
# pacstrap -K /mnt base base-devel linux linux-hardened \
linux-hardened-headers linux-firmware apparmor mesa \
xf86-video-intel vulkan-intel git vi vim ukify
Embedded hardware typically includes an application processor and one or more adjacent processor(s) attached to the printed circuit board. The firmware that resides on the adjacent processor(s) responds to instructions or commands. Different processors on the same board are often produced by different companies. For the system to function properly, it is imperative that the processors communicate without any issues, and that the firmware can handle all types of possible errors.
Formal requirements for firmware related projects may include the validation and verification of the firmware on a co-processor via the application programming interface (API). Co-processors typically run 8, 16, or 32-bit embedded operating systems. If the co-processor manufacturer provides a development board for testing the firmware on a specific co-processor, then the development board may have it's own application processor. Familiarity with all of the applicable bus communication protocols including synchronous and asynchronous communication is important. High-volume testing of firmware can be accomplished using function-like macros and arrays of function pointers. Processor specific firmware is written in C and assembly - 8, 16, 32, or 64-bit. Executing inline assembly from C is straightforward and often required. Furthermore, handling time-constraints such as real-time execution on adjacent processors is easier to deal with in C and executing syscalls, low-level C functions, and userspace library functions, is often more efficient. Timing analysis is often a key consideration when testing firmware, and executing compiled C code on a time-sliced OS, such as Linux, is already constrained.
To read tests based on a custom grammar, a scanner and parser in C can be used. Lex is ideal for building a computationally efficient lexical analyzer that outputs a sequence of tokens. For this case, the tokens comprise the function signatures and any associated function metadata such as expected execution time. Creating a context-free grammar and generating the associated syntax tree from the lexical input is straightforward. Dynamic arrays of function pointers can then be allocated at run-time, and code within external object files or libraries can be executed in parallel using multiple processes or threads. The symbol table information from those files can be stored in multi-dimensional arrays. While C is a statically typed language, the above design can be used for executing generic, variadic functions at run-time from tokenized input, with constant time lookup, minimal overhead, and specific run-time expectations (stack return value, execution time, count, etc.).
At a high level, lists of pointers to type-independent, variadic functions and their associated parameters can be stored within multi-dimensional arrays. The following C code uses arrays of function pointers to execute functions via their addresses. The code uses list management functions from the Linux kernel which I ported to userspace.
On preemptive, timed-sliced UNIX or Linux operating systems such as Solaris, AIX, Linux, BSD, and OS X, program code from one process executes on the processor for a time slice or quantum. After this time has elapsed, program code from another process executes for a time quantum. Linux divides CPU time into epochs, and each process has a specified time quantum within an epoch. The execution quantum is so small that the interleaved execution of independent, schedulable entities – often performing unrelated tasks – gives the appearance of multiple software applications running in parallel.
When the currently executing process relinquishes the processor, either voluntarily or involuntarily, another process can execute its program code. This event is known as a context switch, which facilitates interleaved execution. Time-sliced, interleaved execution of program code within an address space is known as concurrency.
The Linux kernel is fully preemptive, which means that it can force a context switch for a higher priority process. When a context switch occurs, the state of a process is saved to its process control block, and another process resumes execution on the processor.
A UNIX process is considered heavyweight because it has its own address space, file descriptors, register state, and program counter. In Linux, this information is stored in the task_struct. However, when a process context switch occurs, this information must be saved, which is a computationally expensive operation.
Concurrency applies to both threads and processes. A thread is an independent sequence of execution within a UNIX process, and it is also considered a schedulable entity. Both threads and processes are scheduled for execution on a processor core, but thread context switching is lighter in weight than process context switching.
In UNIX, processes often have multiple threads of execution that share the process's memory space. When multiple threads of execution are running inside a process, they typically perform related tasks. The Linux user-space APIs for process and thread management abstract many details. However, the concurrency level can be adjusted to influence the time quantum so that the system throughput is affected by shorter and longer durations of schedulable entity execution time.
While threads are typically lighter weight than processes, there have been different implementations across UNIX and Linux operating systems over the years. The three models that typically define the implementations across preemptive, time-sliced, multi-user UNIX and Linux operating systems are defined as follows - 1:1, 1:N, and M:N where 1:1 refers to the mapping of one user-space thread to one kernel thread, 1:N refers to the mapping of multiple user-space threads to a single kernel thread. M:N refers to the mapping of N user-space threads to M kernel threads.
In the 1:1 model, one user-space thread is mapped to one kernel thread. This allows for true parallelism, as each thread can run on a separate processor core. However, creating and managing a large number of kernel threads can be expensive.
In the 1:N model, multiple user-space threads are mapped to a single kernel thread. This is more lightweight, as there are fewer kernel threads to create and manage. However, it does not allow for true parallelism, as only one thread can execute on a processor core at a time.
In the M:N model, N user-space threads are mapped to M kernel threads. This provides a balance between the 1:1 and 1:N models, as it allows for both true parallelism and lightweight thread creation and management. However, it can be complex to implement and can lead to issues with load balancing and resource allocation.
Parallelism on a time-sliced, preemptive operating system means the simultaneous execution of multiple schedulable entities over a time quantum. Both processes and threads can execute in parallel across multiple cores or processors. Concurrency and parallelism are at play on a multi-user system with preemptive time-slicing and multiple processor cores. Affinity scheduling refers to scheduling processes and threads across multiple cores so that their concurrent and parallel execution is close to optimal.
It's worth noting that affinity scheduling refers to the practice of assigning processes or threads to specific processors or cores to optimize their execution and minimize unnecessary context switching. This can improve overall system performance by reducing cache misses and increasing cache hits, among other benefits. In contrast, non-affinity scheduling allows processes and threads to be executed on any available processor or core, which can result in more frequent context switching and lower performance.
Software applications are often designed to solve computationally complex problems. If the algorithm to solve a computationally complex problem can be parallelized, then multiple threads or processes can all run at the same time across multiple cores. Each process or thread executes by itself and does not contend for resources with other threads or processes working on the other parts of the problem to be solved. When each thread or process reaches the point where it can no longer contribute any more work to the solution of the problem, it waits at the barrier if a barrier has been implemented in software. When all threads or processes reach the barrier, their work output is synchronized and often aggregated by the primary process. Complex test frameworks often implement the barrier synchronization problem when certain types of tests can be run in parallel. Most individual software applications running on preemptive, time-sliced, multi-user Linux and UNIX operating systems are not designed with heavy, parallel thread or parallel, multiprocess execution in mind.
Minimizing lock granularity increases concurrency, throughput, and execution efficiency when designing multithreaded and multiprocess software programs. Multithreaded and multiprocess programs that do not correctly utilize synchronization primitives often require countless hours of debugging. The use of semaphores, mutex locks, and other synchronization primitives should be minimized to the maximum extent possible in computer programs that share resources between multiple threads or processes. Proper program design allows schedulable entities to run parallel or concurrently with high throughput and minimum resource contention. This is optimal for solving computationally complex problems on preemptive, time-sliced, multi-user operating systems without requiring hard, real-time scheduling.
The DE1-SoC from Terasic is an excellent board for hardware design and prototyping. The following VHDL process is from a hardware design created for the Terasic DE1-SoC FPGA. The ten switches and four buttons on the FPGA are used as an n-bit counter with an adjustable multiplier to increase the output frequency of one or more output pins at a 50% duty cycle.
As the switches are moved or the buttons are pressed, the seven-segment display is updated to reflect the numeric output frequency, and the output pin(s) are driven at the desired frequency. The onboard clock runs at 50MHz, and the signal on the output pins is set on the rising edge of the clock input signal (positive edge-triggered). At 50MHz, the output pins can be toggled at a maximum rate of 50 million cycles per second or 25 million rising edges of the clock per second. An LED attached to one of the output pins would blink 25 million times per second, not recognizable to the human eye. The persistence of vision, which is the time the human eye retains an image after it disappears from view, is approximately 1/16th of a second. Therefore, an LED blinking at 25 million times per second would appear as a continuous light to the human eye.
scaler <= compute_prescaler((to_integer(unsigned( SW )))*scaler_mlt); gpiopulse_process : process(CLOCK_50, KEY(0)) begin if (KEY(0) = '0') then -- async reset count <= 0; elsif rising_edge(CLOCK_50) then if (count = scaler - 1) then state <= not state; count <= 0; elsif (count = clk50divider) then -- auto reset count <= 0; else count <= count + 1; end if; end if; end process gpiopulse_process;
The scaler signal is calculated using the compute_prescaler function, which takes the value of a switch (SW) as an input, multiplies it with a multiplier (scaler_mlt), and then converts it to an integer using to_integer. This scaler signal is used to control the frequency of the pulse signal generated on the output pin.
The gpiopulse_process process is triggered by a rising edge of the CLOCK_50 signal and a push-button (KEY(0)) press. It includes an asynchronous reset when KEY(0) is pressed.
The count signal is incremented on each rising edge of the CLOCK_50 signal until it reaches the value of scaler - 1. When this happens, the state signal is inverted and count is reset to 0. If count reaches the value of clk50divider, it is also reset to 0.
Overall, this code generates a pulse signal with a frequency controlled by the value of a switch and a multiplier, which is generated on a specific output pin of the FPGA board. The pulse signal is toggled between two states at a frequency determined by the scaler signal.
It is important to note that concurrent statements within an architecture are executed concurrently, meaning that they are evaluated concurrently and in no particular order. However, the sequential statements within a process are executed sequentially, meaning that they are evaluated in order, one at a time. Processes themselves are executed concurrently with other processes, and each process has its own execution context.
