Bingxi Li CV

Physics undergraduate · EECS minor · UC Berkeley

Bingxi Li

Computational imaging that can show its work.

I work on computational microscopy and multi-frame reconstruction. I want to design optical measurements and reconstruction algorithms together, and to test what a reconstruction recovers.

I’m applying to PhD programs in computational imaging and optics.

GitHub LinkedIn ORCID
Focal stack · pinned weevil specimen Loading slices…
Hover or tap the specimen to see which slice is sharpest at that point.
slice 1
slice 2
slice 3
slice 4

Computed from every slice of the stack with the method and settings of my FocusStack2XR paper: a smoothed Laplacian focus response picks the sharpest slice at each point, the margin over the runner-up gives a confidence, and a 90th-percentile threshold gives a conservative validity mask. PMax blends slices, so the map shows which slice best supports a region, not what PMax used. This specimen has only four slices, rescaled to match the composite and analyzed the same way; with so few slices, confidence and agreement run much higher than in a full stack. Treat the map, and the 2.5D view built from it, as a cue, not as measured depth.

Research

What does a reconstruction actually know?

My interest started with insect specimens at the Essig Museum. With limited depth of field, every specimen needed a stack of photos at different focus settings, and the fused all-in-focus image made me ask which measurements supported each detail it showed. I now work on three versions of that question.

  1. An image is a measurement

    A camera or microscope doesn’t record a scene directly. Optics shape the light, a sensor counts it, and software turns those counts into the picture you see. Computational imaging designs the optics and the software together.

    Measuring a filter from RAW data ↓

  2. Sharp focus is thin

    A lens is sharp at only one distance, and close up that zone can be under a millimetre deep. A focal stack is a series of shots at different focus settings; software fuses the sharpest parts into one all-in-focus image.

    The focal stack at the top ↑

  3. Every point becomes a blur

    Even a good lens spreads a point of light into a small pattern, its point-spread function. Imperfections called aberrations, such as defocus, astigmatism and coma, change that pattern. They are usually written as a sum of standard shapes called Zernike modes.

    My microscopy work ↓

  4. Noise averages down slowly

    Every frame carries random noise. In the ideal case, averaging N frames improves the signal-to-noise ratio by √N: four frames double it and a hundred give ten times. Real data can fall short of that, which is worth checking.

    UIBS and temporal stacks ↓

  5. Measurements have a budget

    Each frame costs time, storage and light. In fluorescence microscopy, light also bleaches the sample and can harm living tissue. So choosing which measurements to take, or which to keep, matters as much as how they are processed.

    My PhD direction ↓

  6. Fitting the data isn’t knowing the answer

    Reconstruction works backwards from measurements to the scene and the optics. Sometimes different answers explain the same data equally well, so a result can fit and still be wrong. A good experiment is designed so the data can tell them apart.

    See one in the playground ↓

Which measurements are worth keeping?

UIBS selects a fixed number of frames from focal stacks and repeated exposures with one shared greedy procedure, and audits when that selection helps and when it doesn’t.

UIBS →

Does a good fit mean the right optics?

In the Na Ji Lab I work with the lab’s neural-field reconstruction pipeline, which estimates a specimen and the microscope’s aberrations together. Investigating a late-stage drift in its aberration estimates led me to ask when a good image fit pins down the optics.

Computational microscopy →

Where did this pixel come from?

FocusStack2XR estimates which focal slice is sharpest in each region of an all-in-focus composite, how decisive that estimate is, and whether the evidence is strong enough to trust, so the basis of a fused image stays visible.

FocusStack2XR →

Publications

Publications & presentations

  1. SPIE Sensors + Imaging 2026OralProceedings under review

    UIBS: a unified formulation for retrospective subset selection in spatial and temporal image stacking

    Bingxi Li

    SPIE Sensors + Imaging 2026, Edinburgh, UK. Paper 14289-43, presented Sep 17, 2026.

    Project summary

  2. IEEE ISMAR 2026Poster paperAccepted

    FocusStack2XR: Provenance-Preserving Depth-Aware Visualization of Focal-Stacked Specimen Images

    Bingxi Li

    IEEE International Symposium on Mixed and Augmented Reality (ISMAR), 2026.

    Paper (PDF)Project summaryInteractive viewer

  3. Berkeley Scientific JournalUndergraduate journalFall 2025

    Experimental Study of Transmission and Color Shift in Neutral Density (ND) Filters

    Bingxi Li

    Berkeley Scientific Journal, Vol. 30, Issue 1 (Prism), Fall 2025, pp. 102–106. Research sponsor: Dr. Peter Oboyski.

    Article (PDF)Project summaryCode (GitHub)

    Erratum: Table B, the Figure 2 caption and the discussion swap the R/G and B/G shifts. The data show R/G rising and B/G falling with density, a warm shift (details).

Projects

Selected projects

UIBSRetrospective frame selection for spatial and temporal image stacking

Independent research · Feb 2026 – present

In plain wordsIf you can keep only 8 frames from a stack of dozens, which 8 should they be, and how much do you lose? UIBS answers that for focus stacks and for repeated exposures, and checks the answer against simple baselines.

Focal stacks and repeated-exposure sequences both combine many frames into one image, but for different reasons: focus stacks need frames that cover different depths, while temporal stacks need frames whose noise averages out. UIBS (unified information-budgeted selection) picks a fixed number of frames from a stack that has already been acquired, using one greedy objective with domain-specific proxies: a focus-response score for focal stacks and a shrinkage-regularized residual-covariance proxy for repeated exposures.

I evaluated it on seven insect focal stacks (519 images; some are different views of the same specimen) and three 64-frame Nikon Z8 RAW runs with matched dark frames and a separate low-noise reference, against random, uniform and single-operator greedy baselines. The baselines carry the main finding. Most of the spatial gain comes from greedy selection itself; my dual-operator score showed no consistent advantage over selecting with a single focus measure, and it can lower retention in the worst-served regions. Retention is scored with the same focus responses the selectors use, so it measures how much focus evidence survives, not the quality of a re-fused image.

0.322→0.553
median focus-response retention at 8 frames: uniform sampling vs greedy selection on one focus measure
0.605
median retention when selecting with UIBS’s combined score (same metric, 8 frames). Paired stack by stack against the better single measure, its median gain is 0 (2 wins, 3 ties, 2 losses).
0.18→0.06
where it hurts: 10th-percentile retention on the elongated-insect stack at 8 frames, uniform vs UIBS
Spatial selection by frame budget
Temporal stacks: why my SNR exponent came out above ½

Data from the UIBS manuscript (SPIE Sensors + Imaging 2026, proceedings under review). Medians hide the lower tail: on some stacks UIBS lowered 10th-percentile retention. Temporal selection showed no consistent advantage over random or uniform subsets.

PythonNumPyOpenCVrawpySciPygreedy selectionLedoit–Wolf shrinkagenoise scaling

FocusStack2XRProvenance-preserving visualization of focal-stacked specimen images

Jun 2026 – present · IEEE ISMAR 2026 poster

In plain wordsA fused photo looks sharp everywhere but hides which original shot each part came from. This tool recovers that, and says how sure it is.

An all-in-focus composite is good documentation but it erases provenance: you can no longer tell which slice supports a region, or whether that assignment is ambiguous. FocusStack2XR keeps that evidence. It computes a focus-index map, a confidence margin, a conservative validity mask and a relative focus-depth layer, and a browser viewer lets you switch overlays, browse slices and click a region to see its predicted source slice. Relative depth is treated as an inspection cue, not calibrated 3D geometry.

The “XR” is the goal, not the current system: the prototype is a desktop browser viewer and hasn’t been tried in a headset or with users. The paper’s argument is that a plausible 2.5D view can imply geometry the data don’t support, so the evidence layers have to come first.

The viewer on the About page shows maps computed with this method from every slice of each stack. The paper evaluates seven stacks across four specimen categories and reports where the method breaks: transparent wings and cluttered scenes.

Laplacian vs Tenengrad focus measures across seven stacks
HTML/CSS/JavaScriptZerene Stacker PMaxfocus measuresuncertainty visualization

Computational microscopyUndergraduate researcher, Na Ji Lab, UC Berkeley

Apr 2026 – present

In plain wordsThe software learns two things at once from the same images: what the sample looks like and how the microscope blurs it. I test whether the blur it learns is the real one.

I apply and analyze the lab’s neural-field-based reconstruction pipeline for two-photon fluorescence microscopy. A learned representation of the specimen is combined with a physical forward model of the microscope, so one optimization estimates both the specimen and the system’s aberrations, written as Zernike modes, and its point-spread function.

One problem caught my attention: a late-stage drift in the estimated optical parameters, which continued after the reconstruction loss had largely settled. I ran controlled tests of learning rates, regularization, shear handling and SLM/pupil geometry, comparing recovered Zernike coefficients with simulation references. Optimizer dynamics, model mismatch or a direction the data don’t constrain could each produce such a drift, and telling them apart is still open. I also extend an existing Gaussian-mixture-based SNR analysis across excitation powers and frame-averaging levels, testing how segmentation and masking choices change the result.

Specimenlearned neural field OpticsZernike modes → pupil → PSF Forward modelimage formation Predicted stackmodel prediction Measured stackmicroscope data loss Specimenneural field OpticsZernike → PSF Forward modelimage formation Predicted stackmodel prediction loss Measured stackmicroscope data
The loss can settle while the recovered aberrations keep moving. Optimizer dynamics, model mismatch, or a direction the data don’t constrain? How this class of method works, drawn generically; no lab data or figures are shown.
Try it: one in-focus image can’t tell +defocus from −defocus
A · your aberrationPSF
B · even modes flippedPSF

Scalar diffraction through a circular pupil with Zernike modes (Noll normalization, waves RMS), imaging a Siemens star; computed in your browser. Flipping the sign of every even mode while keeping the odd ones gives exactly the same in-focus PSF, so a single in-focus image cannot pin down those signs. A second image with a known defocus breaks the tie, which is the idea behind phase diversity. A textbook example of a direction the data don’t constrain, not an explanation of the drift above; generic simulation, no lab data.
forward modelingPSF estimationZernike aberrationsadaptive opticsSNR analysis

Specimen imaging & focus stackingUndergraduate Research Apprentice Program (URAP), Essig Museum of Entomology

Sep 2025 – present

In plain wordsInsects are deeper than a macro lens can keep sharp, so each specimen is photographed dozens to over a hundred times at different focus, and the sharp parts are merged.

I acquire high-resolution focal stacks of pinned insect specimens with controlled illumination and motorized focus stepping, and fuse them into all-in-focus composites with Zerene Stacker PMax. Stacks run from 24 to 127 slices.

Inspecting fine structures and fusion artifacts in those composites made me want to know which measurements supported each displayed detail. I organize the source images for reproducible focal-stack analysis, and this work led directly to my selection experiments (UIBS) and to a tool that shows which source slice most likely supports each detail of a fused image (FocusStack2XR).

Macro imaging station: a camera with a ring flash on a motorized rail and its controller, next to a monitor showing focal slices of the weevil and a fused bee composite
The macro imaging station I use for focal stacks.

Variable ND filter characterizationRAW-domain measurement of transmission and color shift

Sep – Oct 2025 · Berkeley Scientific Journal

In plain wordsA dark camera filter should dim light evenly, by half per stop. I measured one: it dims less than its markings say and tints colors warmer as it darkens.

My first independent measurement project. I built a RAW-domain workflow to test a variable neutral-density filter against the ideal stop law: Nikon Z8 14-bit RAW captures converted to linear TIFFs, a homography-rectified ColorChecker, two illuminants (about 3000 K and 6000 K) and stops ND0 to ND5 with three repeats each. Transmission fell more slowly than the ideal 2−n (fitted log2 slope −0.74 against an ideal −1), and colors drifted warmer with density (R/G up, B/G down), which I quantified with RGB channel ratios and CIE Lab ΔE*ab.

It taught me to keep a pipeline linear until the last step.

Turn the dial: what the marked stop actually does
ND3
–
ideal transmission, 2−n
–
measured transmission
–
stops short of the marking
ND0ND3
~3000 K
~6000 K
Measured points are read from Fig. 1 of the article (screen frames); the solid line is its fit (slope −0.742), the dashed line the ideal 2−n. The swatches apply the measured R/G and B/G changes relative to ND0 (color_shifts_summary.csv) to a neutral gray at a fixed green level, so only the tint shows. They are camera RGB ratios shown on screen, so the rendering is approximate.
PythonRAW / linear TIFFhomographyCIE Lab ΔEcode on GitHub

Optics

Optics, from rays to photons

A short tour of the optics behind imaging, in six parts: four ways of describing light, from rays to photons, plus how real lenses are designed and how computation joins in. Each part comes with a small simulation that runs in your browser.

Rays, lenses and a thin zone of focus

When everything in an optical system is much larger than the wavelength, light can be treated as rays: straight lines that bend where they pass from one material into another, following Snell’s law. A lens is shaped so that the rays leaving one object point meet again at one image point. How far behind the lens they meet depends on the focal length f and on how far away the object is.

Put the sensor anywhere else and each point spreads into a small disk, the blur circle. Its size scales with the aperture diameter D, so a smaller aperture, a larger f-number, deepens the zone that looks sharp. Close up, that zone gets very thin: at life size and f/8 it is about a millimetre deep, which is why insect specimens are photographed as focal stacks.

n1 sin θ1 = n2 sin θ2Snell’s law
1so + 1si = 1fthin lens
m = −si / somagnification
b = D |1 − d / si|blur with the sensor at distance d
Try it: focus a thin lens
On the sensor

Paraxial thin-lens model with distances in millimetres; heights are drawn at three times the horizontal scale. Drag the object or the sensor, or use the sliders. The shaded band marks the object distances that stay sharp to within c = 0.03 mm on the sensor, a common limit for full-frame cameras.

Where it meets my workDepth of field is why the Essig specimens on this site were photographed as focal stacks, and why the focal-stack viewer asks which slice is sharpest where.

Further reading: E. Hecht, Optics, 5th ed. (Pearson, 2017).

Designing a real lens: trace, measure, optimize

The thin-lens equation assumes small angles and a lens of no thickness. Lens-design programs such as Zemax OpticStudio and CODE V instead describe a lens as a list of surfaces, each with a curvature, a thickness and a glass, and trace many real rays through them with the exact form of Snell’s law at every surface. Where those rays land, compared with where they should, measures the lens’s aberrations.

A single lens has two that matter even on axis. Spherical aberration: rays through the edge of the lens focus closer than rays near the centre. Chromatic aberration: glass bends blue light more than red, so colours focus at different distances; the Abbe number measures how strongly a glass does this. The designer picks the variables, such as curvatures, spacings and glasses, and a merit function, often the RMS spot size, and the optimizer, typically damped least squares, adjusts the variables to make it as small as possible.

A classic first exercise is the cemented achromatic doublet: a positive lens of crown glass joined to a weaker negative lens of more dispersive flint glass. The flint undoes the crown’s colour error but only part of its focusing power, and bending the pair also reduces spherical aberration.

n sin θ = n′ sin θ′exact Snell’s law at every surface
V = nd − 1nF − nCAbbe number of a glass
φ1V1 + φ2V2 = 0thin achromat: powers φ = 1/f
MF = Σ wi (vi − ti)2merit function the optimizer minimizes
Try it: design a 100 mm lens
Spot diagram
Longitudinal aberration

A real ray trace in your browser: about 200 rays per colour through spherical surfaces, with glass indices from Schott’s published dispersion formulas, at 486, 588 and 656 nm. The focal length is held at 100 mm by rescaling the curvatures, and an element gets thicker when its edge would drop below 2 mm. The image plane sits at the best focus for all three colours and both field angles together, and the spot size is the RMS radius about the centroid. Optimize runs damped least squares on the sliders, as lens-design programs do, with both field angles in the merit function. The longitudinal plot shows where each ray crosses the axis compared with the paraxial focus, against its height in the aperture.

Where it meets my workZemax OpticStudio is one of the tools I use. This demo runs the same trace, measure and optimize loop on one or two lenses, small enough for a browser.

Further reading: W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008) · R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (Academic Press, 2010).

Interference, diffraction and the resolution limit

Light is an electromagnetic wave; visible wavelengths run from about 400 to 700 nm. By Huygens’ principle, every point on a wavefront acts as a source of new wavelets. Behind two narrow slits the wavelets from each slit overlap: where they arrive in step they add, and where they arrive half a wavelength apart they cancel. Thomas Young’s interference experiments in the early 1800s used fringes like these as evidence that light is a wave.

The same spreading limits every lens. Even a perfect lens images a point as a small Airy pattern, and two points closer than about 0.61 λ/NA (the Rayleigh criterion) blur together until they are hard to tell apart, where NA is the lens’s numerical aperture. Better glass cannot remove this limit. Shorter wavelengths and wider apertures shrink it, and super-resolution microscopy gets around it by changing what is measured.

d sin θ = mλbright fringes, slit spacing d
a sin θ = mλ, m ≠ 0dark fringes, one slit of width a
r = 0.61 λ / NARayleigh resolution
Try it: send a wave through slits

Each slit is a row of point sources of circular waves (the Huygens–Fresnel picture), summed in your browser over a region about 24 × 16 µm. Brightness is boosted with distance so the far waves stay visible. The lower plot is the far-field (Fraunhofer) intensity of the same slits against angle; the dashed lines on the field mark the same angles.

Polarization

The wavelets above are a scalar model, one number at each point. Light’s electric field actually points in a direction across the beam, and that direction is its polarization. Light from the sun or a lamp is unpolarized: its direction changes randomly from moment to moment. A polarizer passes only the part of the field along its axis, so it transmits half of unpolarized light and leaves it polarized; polarized light then follows Malus’s law through a second polarizer. In the 1810s Fresnel and Arago found that two beams polarized at right angles form no interference fringes, one of the clues that light waves are transverse.

A wave plate, a thin slice of birefringent crystal, delays one component of the field behind the other. A quarter-wave delay with the plate at 45° to linear polarization makes it circular, and a half-wave delay rotates it. Reflection polarizes light too, completely at Brewster’s angle, which is why polarized sunglasses cut glare from water and roads. Between crossed polarizers, birefringence shows the stress frozen into plastic parts, and polarized-light microscopes use it to image ordered structures such as muscle fibres and collagen.

E = (Ex, Ey) ei(kz − ωt)Jones vector: two components set the polarization
I = I0 cos2 θMalus’s law, polarizer at θ to the light
tan θB = n2 / n1Brewster’s angle: reflection fully polarized
Try it: polarizers and wave plates
Try
Middle element
From the lamp
After polarizer 1
After the middle
At the detector

Computed with Jones calculus in your browser: each element is a 2 × 2 matrix acting on the field’s two components, and the unpolarized lamp is an equal, incoherent mix of two perpendicular polarizations. Angles are measured from the horizontal, as seen looking back toward the lamp. The side view traces the tip of the electric field along the beam, with the wavelength stretched and the oscillation slowed by about 1015 times; the circles below show the same field end-on.

Where it meets my workThe point-spread function in my aberration playground is this calculation for a circular lens: an Airy pattern, distorted by aberrations.

Further reading: M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

A lens as a Fourier transformer

Any image can be built from sinusoidal stripes of different spacings and directions, its spatial frequencies. In coherent light, a lens forms in its back focal plane the Fourier transform of the field in its front focal plane: coarse features land near the axis and fine detail farther out. A second lens transforms back. This arrangement, the 4f system, lets you edit an image by blocking or phase-shifting parts of its spectrum.

Ernst Abbe explained microscope resolution this way in 1873: to image a fine grating, the objective must collect at least one of the grating’s diffracted orders as well as the undiffracted light. Frits Zernike’s phase contrast, recognized with the 1953 Nobel Prize in Physics, shifts the phase of the undiffracted light by a quarter wave so that transparent cells become visible.

U(fx, fy) = ∬ u(x, y) e−i2π(fxx + fyy) dx dyFourier transform of the field u
x = λf · fxwhere frequency fx lands behind a lens of focal length f
G = H · Ua mask H in that plane filters the spectrum
Try it: filter an image in the Fourier plane
Input
Mask
Input
Fourier plane
Output

A coherent 4f system computed with a 256 × 256 FFT in your browser. Panels show intensity. The Fourier plane is on a log scale, with bright points slightly enlarged so they show and blocked areas dimmed; drag on it to resize the mask. Output brightness is scaled automatically, and the readout gives the share of light that gets through. A real 4f system also turns the image upside down; it is shown upright here.

Where it meets my workThe focus measures in FocusStack2XR are high-pass filters: a slice scores high where its fine detail survives. The aberration playground computes each point-spread function as the Fourier transform of the lens pupil.

Further reading: J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W. H. Freeman, 2017).

Designing the optics and the algorithm together

A conventional camera tries to form the finished picture on the sensor. Computational imaging treats the sensor data as a measurement to be decoded, and designs the optics so that the decoding works well, even if the raw image looks worse.

Defocus is a simple example. A defocused photo is the sharp scene blurred by the shape of the aperture. The blur from a round aperture all but erases some spatial frequencies, and no algorithm can recover those from noisy data. A coded aperture blocks some light but keeps every frequency above the noise, so the same reconstruction recovers more detail. Two papers from 2007, by Levin and colleagues and by Veeraraghavan and colleagues, put patterned masks inside ordinary camera lenses to recover sharp images, and in Levin’s case depth, from defocused photos.

The same idea drives current research: lensless cameras that replace the lens with a diffuser and a reconstruction (DiffuserCam); Fourier ptychography, which combines many low-resolution microscope images taken under tilted illumination into one wide, high-resolution image; single-molecule localization microscopy, which locates each fluorescent molecule far more precisely than the diffraction limit and was part of the 2014 Nobel Prize in Chemistry; and lenses designed end to end together with neural networks.

y = h ∗ x + ncaptured image: scene x blurred by kernel h, plus noise n
X̂ = H∗ Y|H|2 + Sn / SxWiener filter, with noise and image power spectra Sn and Sx
Try it: deblur a round or a coded aperture
Original
Captured
Recovered

Simulated in your browser on a 256 × 256 crop of one of the bee composites, with periodic boundaries. Each aperture blurs the image by the same width, Gaussian noise is added, and the same Wiener filter, given the noise level and the image’s average power spectrum, recovers it. Noise is scaled for the light each aperture passes, as for shot noise. The coded pattern is a 7 × 7 binary mask chosen here for low error, not a copy of either paper’s mask. Press and hold an image to compare it with the original.

Where it meets my workMy projects sit on the reconstruction side: UIBS chooses which frames are worth keeping, FocusStack2XR shows which measurements support each pixel, and in the Na Ji Lab I work with a pipeline that estimates a specimen and the microscope’s aberrations together.

Further reading: A. Levin, R. Fergus, F. Durand and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” SIGGRAPH 2007 · A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” SIGGRAPH 2007 · N. Antipa et al., “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5, 2018 · G. Zheng, R. Horstmeyer and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photonics 7, 2013.

One photon at a time

Light is detected in discrete packets, photons, each carrying energy hν. Make the light in a two-slit experiment so faint that photons pass one at a time, and each lands at a single random spot, yet the fringes still build up in the statistics. If the experiment records which slit each photon went through, the fringes disappear.

Counting photons also sets the basic noise floor of imaging. Laser light gives Poisson-distributed counts, and ordinary camera light nearly so, so a pixel that collects N photons on average has a signal-to-noise ratio of √N: a hundred times the light buys only ten times the SNR. This is the shot-noise limit. Specially prepared quantum states of light can beat it: since 2019 the LIGO and Virgo gravitational-wave detectors have injected squeezed vacuum, a quantum state of light, to lower their noise.

Other quantum effects are becoming imaging tools: two-photon interference (the Hong–Ou–Mandel effect, 1987), ghost imaging with entangled photon pairs (1995), imaging an object with photons that never interacted with it (2014), and single-photon avalanche diode (SPAD) cameras that time individual photons.

E = hν = hc / λphoton energy
P(n) = Nn e−N / n!Poisson counts with mean N
SNR = √Nshot-noise limit
Try it: build the fringes one photon at a time 0 photons

Each detection is drawn at random from the far-field two-slit probability |ψ1 + ψ2|2, with the slit spacing five times the slit width. With the path recorded, the probability becomes |ψ1|2 + |ψ2|2, the sum of two single-slit patterns. Bars count detections; the dashed line is the expected count.
Try it: an image from a handful of photons
Original
Detected photons
Frames averaged

Each pixel’s count is drawn from a Poisson distribution whose mean follows the brightness of the bee photo. Averaging k frames gives the same statistics as one frame with k times the light.

Where it meets my workShot noise is independent from frame to frame, so averaging N frames improves SNR by √N and no more. When a first fit of my UIBS temporal baseline came out slightly faster than √N, that limit is what told me to check the estimator.

Further reading: M. Fox, Quantum Optics: An Introduction (Oxford University Press, 2006) · C. K. Hong, Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987) · G. B. Lemos et al., “Quantum imaging with undetected photons,” Nature 512, 409 (2014) · M. Tse et al., “Quantum-enhanced Advanced LIGO detectors in the era of gravitational-wave astronomy,” Phys. Rev. Lett. 123, 231107 (2019) · F. Acernese et al. (Virgo Collaboration), “Increasing the astrophysical reach of the Advanced Virgo detector via the application of squeezed vacuum states of light,” Phys. Rev. Lett. 123, 231108 (2019).

Experience

Research experience & education

  1. Apr 2026 – present

    Undergraduate Researcher, Computational Microscopy

    Na Ji Lab, UC Berkeley · project ↑

    • Apply the lab’s neural-field reconstruction pipeline for two-photon microscopy: forward-model simulation, PSF and wavefront-aberration estimation, biological image stacks.
    • Investigate late-stage drift in the estimated wavefront and model parameters with controlled tests, comparing recovered Zernike coefficients with simulation references.
    • Extend a Gaussian-mixture-based SNR analysis across excitation powers and frame-averaging levels, testing segmentation and masking choices and comparing the observed scaling with the square-root reference.
  2. Sep 2025 – present

    Undergraduate Researcher (URAP), Specimen Imaging & Focus Stacking

    Essig Museum of Entomology, UC Berkeley · project ↑

    • Acquire focal stacks of 24–127 slices with controlled illumination and motorized focus stepping, fuse them with Zerene Stacker PMax, and organize the source images for reproducible analysis.

Education

University of California, Berkeley

B.A. in Physics, Minor in Electrical Engineering and Computer Sciences · Aug 2023 – May 2027 (expected)

Coursework
Signals and Systems (EE 120) · Electromagnetism and Optics (Physics 110B) · Abstract Linear Algebra (Math 110) · Quantum Mechanics (Physics 137A)
Fall 2026
Introduction to Optical Engineering (EE 118) · Microelectronic Devices and Circuits (EE 105) · Introduction to Circuits & Devices (EE 64)
Activities
Photobears Computational Imaging Community, UC Berkeley: seminars and technical discussions (Oct 2025 – present)

Skills

ProgrammingPython · MATLAB · Java · HTML/CSS/JavaScript · Git
Scientific computingPyTorch · NumPy · SciPy · OpenCV · scikit-image · rawpy
Imaging & opticsForward modeling · learned-PSF analysis · wavefront and Zernike-mode aberration estimation · focus measures · affine registration · RAW-domain processing · SNR and noise-scaling analysis · multi-frame reconstruction
ToolsZemax OpticStudio · Fiji/ImageJ · Zerene Stacker · Nikon RAW/DNG workflows · LaTeX · Typst

Photography

Away from the bench

A few of my photographs, mostly from Edinburgh and around Berkeley. Open one to see it larger, with its exposure settings when the file kept them.

All photographs © Bingxi Li. Please ask before reusing them.

More

Get in touchbingxi.li@berkeley.eduGitHubLinkedInCV (PDF)

Contact

Get in touch

I’m happy to talk about computational imaging, microscopy or any of the projects on this site.

Based inBerkeley, California