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A Lens That Takes Derivatives US Patent Basis: US8610839B2 - Optical Processing System for Computing Derivatives. In a 4f Optical Processor, the first lens takes the incoming field and forms its Fourier spectrum. At that middle plane, a tiny optical mask multiplies the spectrum by iξ. This is the... derivative operator written in Fourier language u(x) -> U(ξ) -> iξU(ξ) -> ∂u/∂x Then the second lens brings the field back to the real space. What comes out is no longer just a focused beam. It is the spatial derivative of the input field, computed by light as it propagates. So, this is the serious promise of optical computing. A physical optical train can perform operations that usually live inside numerical code: differentiation, filtering, convolution, edge detection, correlation, and many other linear transforms.show more

Mathelirium

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137,586 次观看 • 1 个月前 •via X (Twitter)

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A Lens Is a Physical Fourier Computer A lens does not only bend light. It computes with the wave. Send several Gaussian beams into the lens, and the field after the glass is no longer just focused. The lens adds a quadratic phase, lets the wave propagate, and converts angle into position at the focal plane. That detector plane is the Fourier plane.

A Lens Is a Physical Fourier Computer A lens does not only bend light. It computes with the wave. Send several Gaussian beams into the lens, and the field after the glass is no longer just focused. The lens adds a quadratic phase, lets the wave propagate, and converts angle into position at the focal plane. That detector plane is the Fourier plane.

Mathelirium

34,626 次观看 • 1 个月前

A lens can perform the Fourier transform! 🔍 This is the 4F system: the first lens converts an image into its frequency components, and the second lens reconstructs it. By adding an aperture at the Fourier plane, we can filter out high frequencies. #Optics #Physics #b3d

A lens can perform the Fourier transform! 🔍 This is the 4F system: the first lens converts an image into its frequency components, and the second lens reconstructs it. By adding an aperture at the Fourier plane, we can filter out high frequencies. #Optics #Physics #b3d

Hans Chiu

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U.S. Air Force Under Secretary Matthew Lohmeier discusses accounts of UAP penetrating solid walls to “observe”, scientific investigation into whether ‘beings exist in the invisible realm’, and a possible connection to The Bible. “If you take a look at the Earth, or the Sun, or any number of things that exist in space using a different lens – not the optical lens, but ultraviolet or infrared – What you’ll see is something that looks like a sea creature flapping its wings swimming through The Great Deep.” “Even though in this, what we used to call the ‘vacuum of space’, it seems to our optical lens as if it’s empty – in fact, it’s filled with plasma. Plasma is highly conductive. So there’s this energy that’s instant and direct and immediate between all of the stars that seems to connect all of us.”

U.S. Air Force Under Secretary Matthew Lohmeier discusses accounts of UAP penetrating solid walls to “observe”, scientific investigation into whether ‘beings exist in the invisible realm’, and a possible connection to The Bible. “If you take a look at the Earth, or the Sun, or any number of things that exist in space using a different lens – not the optical lens, but ultraviolet or infrared – What you’ll see is something that looks like a sea creature flapping its wings swimming through The Great Deep.” “Even though in this, what we used to call the ‘vacuum of space’, it seems to our optical lens as if it’s empty – in fact, it’s filled with plasma. Plasma is highly conductive. So there’s this energy that’s instant and direct and immediate between all of the stars that seems to connect all of us.”

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112,736 次观看 • 11 个月前

$You’ve Seen First and Second Derivatives, But Have You Ever Seen a 0.5 Derivative? You know the first derivative measures slope, the second measures curvature, the third tracks how curvature changes, and so on. What exactly is a fractional derivative?$

You’ve Seen First and Second Derivatives, But Have You Ever Seen a 0.5 Derivative? You know the first derivative measures slope, the second measures curvature, the third tracks how curvature changes, and so on. What exactly is a fractional derivative?

Mathelirium

66,268 次观看 • 3 个月前

OPTICAL AIDS CAUSE 28 DAY MONTHS? NCS does not recommend that we use optical aids for a moonsighting system in Britain for many reasons. The primary reason is that we are seeking a unified solution, and unity is in the sunnah - local, naked eye sightings. Not everybody believes that optical aids are permissible, but naked eye sightings are wholly uncontroversial. Another issue is that optical aids would lead to more and more examples of the moon being “seen” a day early, and out of phase, on the 28th of a lunar month. This has ALREADY HAPPENED to those who use optical aids in the UK - yet has never happened to naked eye moonsighters for over 100 months. Whilst there are procedures from the sunnah of what to do if you were to see a moon on the 28th, we cannot really justify asking people to end their fast a day early on the 28th because of a moon which is invisible to the eye and only visible through optical aids. Hence our stance. Remember - we ourselves use optical aids - and had them on our livestream. We are experienced in them, and it is from our experience we share with you that we have found that it would leave to problems. In any case why are you in a rush to end Ramadan, using technology, and away from the sunnah?

OPTICAL AIDS CAUSE 28 DAY MONTHS? NCS does not recommend that we use optical aids for a moonsighting system in Britain for many reasons. The primary reason is that we are seeking a unified solution, and unity is in the sunnah - local, naked eye sightings. Not everybody believes that optical aids are permissible, but naked eye sightings are wholly uncontroversial. Another issue is that optical aids would lead to more and more examples of the moon being “seen” a day early, and out of phase, on the 28th of a lunar month. This has ALREADY HAPPENED to those who use optical aids in the UK - yet has never happened to naked eye moonsighters for over 100 months. Whilst there are procedures from the sunnah of what to do if you were to see a moon on the 28th, we cannot really justify asking people to end their fast a day early on the 28th because of a moon which is invisible to the eye and only visible through optical aids. Hence our stance. Remember - we ourselves use optical aids - and had them on our livestream. We are experienced in them, and it is from our experience we share with you that we have found that it would leave to problems. In any case why are you in a rush to end Ramadan, using technology, and away from the sunnah?

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18,343 次观看 • 3 个月前

Meet the new Huawei Pura80 Ultra. It features the world's largest telephoto sensor in a smartphone, with a 1/1.28" size. It is also the world's first smartphone to have a switchable telephoto lens structure, with 3.7x and 9.4x optical zoom levels. The hardware is truly outstanding.

Meet the new Huawei Pura80 Ultra. It features the world's largest telephoto sensor in a smartphone, with a 1/1.28" size. It is also the world's first smartphone to have a switchable telephoto lens structure, with 3.7x and 9.4x optical zoom levels. The hardware is truly outstanding.

Alvin

187,196 次观看 • 1 年前

This is what our Tech Experts have to say about the unparalleled pro camera experience of the #Xiaomi13Pro. With the amazing Leica Professional Optical Lens System, now capture moments around you in the most flawless way. Know more:

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Evaluating Neural Networks at the Speed of Light (with Light!). See live optical inference in the video below. Excited to share recent academic work on optical neural networks as a collection of computing elements embedded in the camera lens! These elements perform computation optically even before an image is captured, using the photons in the scene instead of GPU computation after the capture. We were able to achieve ImageNet classification more than two orders of magnitude faster than conventional neural networks on today's GPUs at almost no power consumption! To do this, we developed an array of metalenses that perform this computation on light from the scene. Project: Paper: Amazing collaboration with Kaixuan Wei, Xiao Li, Johannes Froech, Praneeth Chakravarthula, James Whitehead, Ethan Tseng , Arka Majumdar .

Evaluating Neural Networks at the Speed of Light (with Light!). See live optical inference in the video below. Excited to share recent academic work on optical neural networks as a collection of computing elements embedded in the camera lens! These elements perform computation optically even before an image is captured, using the photons in the scene instead of GPU computation after the capture. We were able to achieve ImageNet classification more than two orders of magnitude faster than conventional neural networks on today's GPUs at almost no power consumption! To do this, we developed an array of metalenses that perform this computation on light from the scene. Project: Paper: Amazing collaboration with Kaixuan Wei, Xiao Li, Johannes Froech, Praneeth Chakravarthula, James Whitehead, Ethan Tseng , Arka Majumdar .

Felix Heide

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The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics

The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics

Mathelirium

66,204 次观看 • 5 个月前

😨🌙 Is That a Skinwalker on the Balcony… or Just an Optical Illusion? 👀

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The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics

The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics

Mathelirium

133,454 次观看 • 4 个月前

Ok yeah this USB webcam is not like the rest lol - The "zoom" is a digital crop, yet it looks optical - The simulated bokeh looks pretty damn good - Cropping in looks like a legitimate lens change - CRISP Vid on the [brand gifted] YoloLiv s3 this week. $199. Just nasty.

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Spherical Harmonics 🤝 Fourier Transform I’m modeling the cell surface as a time-varying field u(θ,φ). Budding is energy shifting into higher angular frequencies. Decompose u into spherical harmonics (the Fourier basis on a sphere), evolve the coefficients aₗₘ(t) where growth/smoothing is clean, then inverse-transform back into a breathing, budding 3D surface. #SphericalHarmonics #FourierTransform #HarmonicAnalysis #SpectralMethods #SignalProcessing #AppliedMath #MathAnimation #ScientificVisualization #Biophysics

Mathelirium

25,881 次观看 • 6 个月前

This is huge! A UCLA team managed to build an optical generative model that runs on light instead of GPUs. In their demo, a shallow encoder maps noise into phase patterns, which a free-space optical decoder then transforms into images—digits, fashion, butterflies, faces, even Van Gogh–style art—without any computation during synthesis. ⚡ The results rival digital diffusion models, pointing to ultra-fast, energy-efficient AI powered by photonics. Optical generative models | Nature Paper:

This is huge! A UCLA team managed to build an optical generative model that runs on light instead of GPUs. In their demo, a shallow encoder maps noise into phase patterns, which a free-space optical decoder then transforms into images—digits, fashion, butterflies, faces, even Van Gogh–style art—without any computation during synthesis. ⚡ The results rival digital diffusion models, pointing to ultra-fast, energy-efficient AI powered by photonics. Optical generative models | Nature Paper:

机器之心 JIQIZHIXIN

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