Computational Photography, an AI-powered Slopendium — 33 Computational optics and coded imaging

▸Part 33 COMPUTATIONAL OPTICS AND CODED IMAGING⧉

`fig-editing-lr-vs-ps` · the two digital darkrooms: a Lightroom-style parametric develop panel (WB, exposure/contrast, tone curve, HSL, clarity/dehaze, sharpening/NR, lens corr., local masks) vs a Photoshop-style layer/mask workspace (clone/heal, content-aware fill, dodge/burn, curves) — each tool annotated with the chapter that derives it ⬜

`fig-optics-linear-positive-vs-computation` ·

▸33.1 Wavefront coding⧉

33.1.1 Why you cannot just deblur defocus⧉

33.1.2 The fix: re-engineer the blur⧉

33.1.3 The cubic phase plate⧉

33.1.4 The depth-invariant PSF and a single deconvolution⧉

33.1.5 What it costs⧉

33.1.6 Where it sits⧉

▸33.2 Compressive sensing⧉

33.2.1 Sub-Nyquist: fewer measurements than unknowns⧉

33.2.2 Two ingredients: incoherent measurements and sparsity⧉

33.2.3 Recovery by $\ell_1$: the geometry of basis pursuit⧉

33.2.4 Why it works: the restricted isometry property, intuitively⧉

33.2.5 The single-pixel camera⧉

33.2.6 Where compressive sensing wins, and where it does not⧉

▸33.3 Coded aperture⧉

33.3.1 The bad forward operator of a clear aperture⧉

33.3.2 A mask designed for a flat, zero-free spectrum⧉

33.3.3 One shot, two outputs: depth and an all-in-focus image⧉

33.3.4 The design criterion: which pattern?⧉

33.3.5 Coded-aperture pairs: splitting the trade across two shots⧉

33.3.6 Heterodyning the light field: dappled photography⧉

33.3.7 Where it sits⧉

▸33.4 Phase-coded apertures⧉

33.4.1 A reminder on wavefront coding⧉

33.4.2 Focus sweep⧉

33.4.3 The lattice-focal lens⧉

33.4.4 Where it sits⧉

▸33.5 Code in time (phase, amplitude)⧉

`fig-kernel-spectra` · five common kernels (box, Gaussian, derivative ∂/∂x, Laplacian, unsharp mask) shown in space and as their Fourier magnitudes — a filter's spectrum IS its per-frequency gain (low-pass leaky vs clean, directional/isotropic high-pass, boosting) ✅

33.5.1 Why ordinary motion blur is (almost) unrecoverable⧉

33.5.2 The flutter shutter: chop the exposure into a code⧉

33.5.3 The decode: one deconvolution, a sharp moving object⧉

33.5.4 Amplitude in time, and phase in time⧉

33.5.5 Coded strobing, temporal multiplexing, and compressive video⧉

33.5.6 Motion-invariant photography⧉

33.5.7 Where it sits⧉

▸33.6 Theoretical analysis of imaging systems in the 4D light field Fourier domain⧉

`fig-lightfield-refocus` · **light field → refocus → merge:** refocus a light field by **shift-and-add** (refocused near / refocused far) → the synthesized focal stack merged to one all-in-focus image. placed in **[[11 Advanced computational photography]] § Refocusing** (forward-ref'd from the DoF & focal-stack chapters); registered here next to its focus-stacking siblings ✅

33.6.1 The light field's spectrum, and the one move that explains everything⧉

33.6.2 Every camera is a different slice⧉

33.6.3 Putting cameras on one footing: the Bayesian comparison⧉

33.6.4 The dimensionality gap: most of the 4-D spectrum is afocal⧉

33.6.5 The lattice-focal lens: tiling the wedge⧉

33.6.6 The upper bound, and the gap we have not closed⧉

33.6.7 From cameras to light transport: the same spectral lens⧉

33.6.8 Where this leaves the part⧉

▸33.7 End-to-end optimization⧉

33.7.1 The pipeline as one differentiable graph⧉

33.7.2 Backpropagating into the glass⧉

33.7.3 What gets designed: a height map, not a hyperparameter⧉

33.7.4 A gallery of deep-optics results⧉

33.7.5 What it costs, and where it can go wrong⧉

33.7.6 Where it sits⧉

▸33.8 Fourier optics⧉

⬜ figure not yet created

the spectrum made physical)

equations

coherent image (field) $U_i = \mathcal F^{-1}\{ P\cdot \mathcal F\{U_o\}\}$

**coherent transfer function** $H_{\text{coh}}=P(u,v)$

**incoherent OTF** $H(u,v)=\dfrac{P\star P}{\int|P|^2}$ (normalized autocorrelation of the pupil)

**PSF** $h(x,y)=|\mathcal F\{P\}|^2$

**diffraction-limited cutoff** $f_c = \dfrac{1}{\lambda N}$ (incoherent, $N=f/\#$)

**Abbe limit** $d_{\min}=\dfrac{\lambda}{2\,\mathrm{NA}}$

aberrations as pupil phase $P=A\,e^{i\,2\pi\,W(u,v)/\lambda}$ (wavefront error $W$, Zernike).

33.8.1 Light as a wave: amplitude, phase, and what "coherent" means⧉

33.8.2 Diffraction is a Fourier transform⧉

33.8.3 A lens computes a Fourier transform⧉

33.8.4 The pupil function *is* the transfer function⧉

33.8.5 The diffraction limit⧉

33.8.6 Aberrations are pupil phase⧉

33.8.7 Every code in this part is a choice of pupil⧉

33.8.8 Fourier ptychography: synthesizing a bigger pupil⧉

▸33.9 Exotic / advanced optics⧉

▸33.9.1 Lensless imaging⧉

• cameras with **no lens** at all — a coded **mask** or a **diffuser** directly in front of a bare sensor, plus computational reconstruction: **FlatCam** (Asif et al. 2017 — a separable amplitude mask) and **DiffuserCam** (Antipa et al. 2018 — a diffuser as the encoding optic). The mask/diffuser *is* the (coded) linear operator $A$; recovery is the inverse problem of [[Image formation as a linear system]]. Ultra-thin and wide-FOV, but reconstruction-limited. *(Folded in from its own chapter.)*

33.9.2 GRIN⧉

33.9.3 Metalenses and advanced crazy optics à la Barbastathis (coherent though)⧉

33.9.4 Non-linear optics⧉

▸33.10 Optical modulators (spatial light modulators): DMD and LCD/LCoS⧉

• **DMD** — micromirror array, each mirror tilts ± → **binary amplitude**, very fast (kHz); DLP projectors, single-pixel / compressive imaging, coded exposure & illumination

• **LCD / LCoS** — liquid-crystal pixels rotate polarization → with a polarizer give **grayscale amplitude**; in **phase-only** mode the controllable retardance imposes an arbitrary **phase** profile (programmable lens / hologram / aberration corrector)

• a programmable SLM is the **active** cousin of the fixed coded masks above (and of metalenses) — same idea (shape the wavefront), but reconfigurable on the fly