Fiducial beads¶

Fiducial beads are bright, stable markers put on a sample to follow its drift: their positions over a movie are the drift, which an SMLM analysis then subtracts. inSiliScope can put beads on any sample (the cell field and the nanorulers), with a type, a density, a size, a height and a share of clumps. They are off by default (density 0). Turn them on with the viewer's Fiducial beads group (Sample section), Micro-Manager's Fiducials device, or the CLI's --fid-* options (below). The beads belong to the sample: they drift with it, and the CLI's <movie>.drift.csv is their ground truth. The bead sample is the beads alone, on a bare coverslip (below).

Bead types¶

Spectra and brightness follow Balinovic, Albrecht and Endesfelder 2019, who compared these markers for SMLM [balinovic2019]. Where the paper has no spectrum, the spectra come from FPbase [lambert2019] and the nominal maxima from the manufacturer [thermofisher_fluospheres]. The data are in data/fiducials/ (README).

Type (`Type`, `--fid-type`)	Size	Colours (ex/em, nm)	Bleaches	Notes
`Gold` (the default type)	100 nm	photoluminescence ~560/575	no	also scatters every laser line (Mie); the filters' blocking floor decides how much reaches the camera
`TetraSpeck`	100 nm	360/430, 505/515, 560/580, 660/680	yes, each dye on its own	one bead in four channels
`FluoSpheresOrange`	200 nm	540/560	yes	a marker that also shows in a 488 nm channel
`FluoSpheresRed`	200 nm	580/605	yes
`FluoSpheresDarkRed`	200 nm	660/680	yes	very bright under 640 nm: can saturate a camera at SMLM powers
`FluoSpheresInfrared`	100 nm	715/755	yes	red-shifted, for imaging next to a 640 nm channel
`Nanodiamond`	100 nm	NV centres, ~640/680	no

The bead types' spectra against the light path — The bead types (data/fiducials: Balinovic et al. 2019, FPbase): each dye's excitation (dashed) and emission (solid), against the light path of the default cell field's labels (488 nm, 561 nm, 640 nm at 1 kW/cm², Chroma ZT405/488/561/640rpc (quad), Chroma ZET405/488/561/640m (quad); grey: what the dichroic and the emission filter pass). The table gives, per component, the wavelength its PSF is made at, its equivalent dyes (ε 10⁵, QY 0.5) at the product size, the photons per second the camera detects from one bead of that size at the beam's peak, the share of its emission detected, and its fluorescence half-time under this light (the 288 s reference is at 1 kW/cm² at the dye's own excitation peak; off the peak a bead bleaches more slowly; – : no line excites it). Gold's scattered laser light passes the filters only through their blocking floor (OD 8).

Type	Component	PSF λ (nm)	Equiv. dyes	Detected (photons/s)	Detected share	Half-time
Gold nanoparticles (100 nm)	photoluminescence	580	2.53	73035	32 %	never
	scattered 488 nm	488	–	502	–	never
	scattered 561 nm	561	–	2670	–	never
	scattered 640 nm	640	–	1809	–	never
TetraSpeck microspheres (100 nm, 4 colours)	blue dye (360/430)	468	705	0	54 %	–
	green dye (505/515)	536	705	4.0×10⁷	67 %	8.4 min
	orange dye (560/580)	584	705	6.6×10⁷	60 %	4.9 min
	dark red dye (660/680)	698	705	8.0×10⁷	73 %	5.9 min
FluoSpheres orange (200 nm, 540/560)	orange dye (540/560)	581	1.00×10⁵	2.8×10⁹	38 %	11 min
FluoSpheres red (200 nm, 580/605)	red dye (580/605)	615	1.00×10⁵	8.7×10⁹	65 %	6.1 min
FluoSpheres dark red (200 nm, 660/680)	dark red dye (660/680)	677	1.00×10⁵	1.1×10¹⁰	72 %	6.3 min
FluoSpheres infrared (100 nm, 715/755)	infrared dye (715/755)	740	1.00×10⁵	1.1×10⁷	58 %	90 h
Red nanodiamonds (100 nm)	NV centres	676	1.93×10⁵	2.8×10¹⁰	83 %	never

How this figure was made (7 cli runs, 52 ms)

Generated by tools/build_physics_figures.py (figure fid-spectra) from the code it documents at commit 72b1b0f, on Linux with 4 threads, 2026-11-01. Commands, in order, with their wall time (those marked [served] ran one after the other in one insiliscope_cli --serve process, which keeps the world and the PSF kernel between commands; their outputs are the same as separate runs'):

insiliscope_cli --setup-json Gold.setup.json --npc-dye Cy3B --laser-488 1 --size 32 --frames 1 --fid-type Gold --prepare 1    # 9.6 ms [served]
insiliscope_cli --setup-json TetraSpeck.setup.json --npc-dye Cy3B --laser-488 1 --size 32 --frames 1 --fid-type TetraSpeck --prepare 1    # 7.6 ms [served]
insiliscope_cli --setup-json FluoSpheresOrange.setup.json --npc-dye Cy3B --laser-488 1 --size 32 --frames 1 --fid-type FluoSpheresOrange --prepare 1    # 7.4 ms [served]
insiliscope_cli --setup-json FluoSpheresRed.setup.json --npc-dye Cy3B --laser-488 1 --size 32 --frames 1 --fid-type FluoSpheresRed --prepare 1    # 7.1 ms [served]
insiliscope_cli --setup-json FluoSpheresDarkRed.setup.json --npc-dye Cy3B --laser-488 1 --size 32 --frames 1 --fid-type FluoSpheresDarkRed --prepare 1    # 6.9 ms [served]
insiliscope_cli --setup-json FluoSpheresInfrared.setup.json --npc-dye Cy3B --laser-488 1 --size 32 --frames 1 --fid-type FluoSpheresInfrared --prepare 1    # 7.0 ms [served]
insiliscope_cli --setup-json Nanodiamond.setup.json --npc-dye Cy3B --laser-488 1 --size 32 --frames 1 --fid-type Nanodiamond --prepare 1    # 7.0 ms [served]

The size in the table is the product size, which picking a type sets as the DiameterNm (below); any other size keeps the type's spectra. The brightness of each dye is an equivalent dye count (dyes with ε = 10⁵ M⁻¹ cm⁻¹ and QY 0.5) at the type's product size, scaling with the bead's volume (d³). For gold, TetraSpeck and the nanodiamonds it was fitted to the paper's counts: each bead's brightest pixel against single dyes (mEos3.2, JF646) in the same images. The FluoSpheres are set to 100 000 equivalent dyes (an estimate) in place of the paper's fits (41 000 for the dark red, 4 × 10⁶ for the infrared, whose far tails the paper's curves underestimate). The fits stay in data/fiducials/types.json as emitters; emittersSet overrides them. The spectral losses stay in the light path, not in the count. A dark-red bead under a 561 nm line behind a 595/50 filter, for example, keeps about 10⁻⁵ of its light, which is why beads of hundreds to tens of thousands of equivalent dyes are usable next to single molecules. The nanodiamonds' calibration also comes out unphysically high, for the same reason as the infrared beads'. A 20 nm bead of a type has its dyes scaled with the volume: (20/100)³ of TetraSpeck's, about 6 per colour, (20/200)³ of the FluoSpheres', 100 (an estimate); 20 nm beads are about as bright as a few to a hundred single dyes. Set DyeCount (Expert, --fid-dyes) to override every component's count.

Placement, size and height¶

Positions are random, with no minimum distance: a Poisson field of DensityPerUm2 beads per µm² of coverslip (--fid-density), so doublets and clusters happen as on a real coverslip. The positions are a pure function of the seed and the place, like every other part of the sample.
Size: DiameterNm (Advanced, Basic on the bead sample in the viewer, --fid-diameter-nm): picking a type sets its product size (100 or 200 nm), and any size can be set after it, such as 20 nm beads (the CLI's −1, its default, is the type's size). The dyes scale with the volume. The bead-to-bead spread is DiameterCvPct (12 %, an estimate within the 10-15 % typical of these products).
Height (Height, Basic, --fid-height):
- Coverslip: the bead's centre one radius above the glass, also under the cells (the beads go down first).
- OnTop (default): on the sample's highest surface there (the cytoplasm or nucleus of a cell; the bare glass between cells), centre one radius above it. Not offered on the bead sample, where it is the glass: mounting it moves OnTop beads to Coverslip.
- Layer: anywhere in a gel layer (e.g. agarose) of LayerUm (10 µm; Advanced, Basic on the bead sample in the viewer) between the coverslip and the layer's top, outside the cells.

On the coverslip	On top of the sample	In a 10 µm gel layer

The same 25.6 µm field of the cell field (256 px of 100 nm, one 50 ms frame, focus 0.5 µm above the coverslip, no labels: only the beads emit) with TetraSpeck beads at 0.05 per µm² (made dim here, 2 equivalent dyes, so none saturates), at the three heights: on the glass (sharp at this focus, also under the cells), on the sample's highest surface (the cells' tops several µm above the focus: wide rings, the bare glass between them sharp) and anywhere in a 10 µm gel outside the cells (most far out of focus).

How this figure was made (3 cli runs, 4.73 s)

Generated by tools/build_physics_figures.py (figure fid-heights) from the code it documents at commit 72b1b0f, on Linux with 4 threads, 2026-11-01. Commands, in order, with their wall time (those marked [served] ran one after the other in one insiliscope_cli --serve process, which keeps the world and the PSF kernel between commands; their outputs are the same as separate runs'):

insiliscope_cli --out h0.movie.tif --x 6.58 --y -5.61 --size 256 --frames 1 --mt-dye None --npc-dye None --laser-561 1 --laser-640 0 --fid-type TetraSpeck --fid-dyes 2 --fid-density 0.05 --fid-height 0    # 4.17 s [served]
insiliscope_cli --out h1.movie.tif --x 6.58 --y -5.61 --size 256 --frames 1 --mt-dye None --npc-dye None --laser-561 1 --laser-640 0 --fid-type TetraSpeck --fid-dyes 2 --fid-density 0.05 --fid-height 1    # 289 ms [served]
insiliscope_cli --out h2.movie.tif --x 6.58 --y -5.61 --size 256 --frames 1 --mt-dye None --npc-dye None --laser-561 1 --laser-640 0 --fid-type TetraSpeck --fid-dyes 2 --fid-density 0.05 --fid-height 2    # 269 ms [served]

Clumps¶

Beads in a suspension stick together, so a coverslip has single beads, pairs and larger clumps. One setting, AggregationPct (Basic, --fid-aggregation-pct, 0 to 90 %, default 0; 40 % on the bead sample), is the chance p that a bead is stuck to the next one. A clump then holds n beads with probability (1 − p) pⁿ⁻¹: a geometric spread of sizes, mean 1 / (1 − p), which is the size distribution of colloids that stick at a constant rate (Smoluchowski coagulation with a constant kernel; the model is an estimate, not fitted to any bead product). At 10 %, 81 % of the beads are single, most of the rest in pairs; at 50 % a clump holds two beads on average. The density counts beads, so clumps make fewer and brighter spots. Each bead of a clump touches one placed before it, chosen at random, without overlapping the others: in the coverslip plane on the coverslip and on top of the sample (each at its own height there), in 3D in a gel layer. A clump stays within 2 µm of its first bead and holds at most 64 beads.

Aggregation 0 %	30 %	70 %

The bead sample at its defaults (a bare coverslip, 100 nm gold at 0.3 beads per µm², 561 nm at 0.1 kW/cm², focus on the beads' centres) but the aggregation, one 50 ms frame of 256 px of 100 nm, one contrast for all three. The density counts beads, so the more stick together, the fewer and brighter the spots: at 30 % half the beads are in clumps (mean 1.4 beads), at 70 % nearly all (mean 3.3); a clump is far smaller than the PSF, so it looks like one brighter bead.

How this figure was made (3 cli runs, 8.91 s)

Generated by tools/build_physics_figures.py (figure fid-clumps) from the code it documents at commit 72b1b0f, on Linux with 4 threads, 2026-11-01. Commands, in order, with their wall time (those marked [served] ran one after the other in one insiliscope_cli --serve process, which keeps the world and the PSF kernel between commands; their outputs are the same as separate runs'):

insiliscope_cli --out a0.movie.tif --x 6.58 --y -5.61 --size 256 --frames 1 --specimen Beads --fid-aggregation-pct 0    # 8.78 s [served]
insiliscope_cli --out a30.movie.tif --x 6.58 --y -5.61 --size 256 --frames 1 --specimen Beads --fid-aggregation-pct 30    # 75 ms [served]
insiliscope_cli --out a70.movie.tif --x 6.58 --y -5.61 --size 256 --frames 1 --specimen Beads --fid-aggregation-pct 70    # 64 ms [served]

The bead sample¶

Bead sample (Beads) is a sample of its own: a bare coverslip with only the fiducial beads, for a PSF or drift calibration, or to look at the beads alone. It has no targets to label: every setting is the Fiducial beads one. Mounting it while no beads are set (density 0) puts 0.3 beads per µm² down, and while the aggregation is 0 sets it to 40 % (the CLI: when --fid-density or --fid-aggregation-pct is not given). Its light is the 561 nm line at 0.1 kW/cm², the other lasers off, through the 561 nm widefield filters (the light preset Beads-561, the automatic preset on this sample, which has no labels for one to follow). The viewer shows the diameter and the gel layer's thickness at Basic here (Micro-Manager creates its properties at one level when the hub starts, so they stay Advanced there). The CLI focuses on the beads' centre when --z is not given (a radius above the glass; the layer's middle in a gel layer).

The image of a bead¶

A bead is not a point: a 200 nm sphere holds dyes over its whole volume. Its image is the PSF averaged over the solid sphere (in z over 10 nm slabs, laterally over its projection), which matters within about a micrometre of the centre and near the focus (where the PSF is not much wider than the bead; off focus the sphere changes it by under 1 % and the point PSF is used). Outside that the bead's halo is the point PSF. A clump is drawn as one bead of the clump's volume (a pair of 100 nm beads as one 126 nm bead) at its centre of mass with all its beads' light; Renderer.Quality Exhaustive (or Renderer.BeadClumpsAsOne Off, Expert; --fid-clumps-as-one 0) draws each bead. A touching pair is longer than that sphere, which shows only for large beads in focus; one splat per clump makes a clumpy sample's frames up to twice as fast. Each bead is one emitter per colour, never 10⁶ dyes. Beads do not blink.

A bead is far brighter than a dye, and above or below the focus its light spreads into a disc several micrometres wide (about 2.4 µm of radius per µm of defocus at NA 1.4). So its halo is not cut at the PSF window the dyes use (±3 µm in the viewer, ±7 µm in Micro-Manager): it comes from a second PSF window twice the field of view (at most ±30 µm), sampled once per camera pixel, and reaches as far as the bead gives at least 0.1 photon per pixel. In z the beads have a PSF stack of their own, 14 µm (PsfZRangeUm, Advanced, --fid-psf-z-range-um; the dyes' stack is the objective's 7 µm; the dyes are cut at CellField.ZRangeUm, ±3.5 µm, the beads are not), so a bead on top of a cell or in a gel layer far from the focus keeps its defocused image instead of vanishing. Beyond the stack (more than 7 µm off focus) a bead is drawn as a blur that grows with the defocus: a Gaussian with all its light, as wide at the stack's edge as the last plane (its second moment) and wider in proportion to the defocus, faded in over the stack's last 0.5 µm, so the bead fades smoothly with no step. This is an approximation (not the defocused PSF's shape). FarDefocus (Expert, --fid-far-defocus 0) leaves such beads out instead: faster with many beads far off focus, whose blurs reach tens of µm. That stack's oversampled point window is at most ±3 µm wide (the halo takes the light beyond it): over 14 µm, Micro-Manager's ±7 µm window would take about 1.2 GB per bead colour. A bright or defocused bead lights the whole frame. Costs: the wide window takes ~0.5 s per colour once (256 px), and the beads take a few per cent of a movie, about 15 % in a drifting one, where every bead is drawn again in every frame.

Bleaching¶

The dyes in a bead bleach one by one, but there are so many that the bead's signal decays smoothly: exp(−t ln 2 / t½). BleachHalfTimeSec (Expert, --fid-bleach-half-sec, 288 s, an estimate) is the half-time at BleachRefKWcm2 (1 kW/cm², --fid-bleach-ref-kwcm2) at the dye's own excitation peak. The bleach rate follows the excitation rate, so a bead bleaches more slowly at less light and off its peak: TetraSpeck's dark-red dye under 561 nm fades about 10 times more slowly than at its peak at the same intensity. Gold and nanodiamonds do not bleach.

In Micro-Manager the beads fade with the sample's illumination history, like every dye: a bead that was lit stays dimmer after a pause, a move away and back, or a change of a bead setting (which keeps the history). CLI and viewer movies start at --start-sec under the movie's own light.

Gold's scattered laser light¶

Gold nanoparticles scatter the excitation light elastically (Mie scattering; gold's optical constants from Johnson and Christy [johnson1972], the method of Bohren and Huffman [bohren1983]). Ideal filters would block it fully, so the emission path is given a blocking floor: every laser line passes the dichroic and the emission filter at least at 10⁻ᴼᴰ (BlockingOD, Expert, --fid-blocking-od, 8: a dichroic ~OD 2 times an emission filter ~OD 6, an estimate). The floor applies to the scattered light only; the dyes' light path is unchanged.

Settings¶

Viewer (Sample > Fiducial beads)	Micro-Manager (`Fiducials`)	CLI	Default
Density	`DensityPerUm2` (Basic)	`--fid-density`	0 (off)
Type	`Type` (Basic)	`--fid-type`	`Gold`
Diameter, Diameter spread	`DiameterNm`, `DiameterCvPct` (Advanced)	`--fid-diameter-nm`, `--fid-diameter-cv-pct`	the type's size, 12 %
Height	`Height` (Basic)	`--fid-height`	`OnTop` (the bead sample: `Coverslip`)
Layer thickness	`LayerUm` (Advanced)	`--fid-layer-um`	10 µm
Aggregation	`AggregationPct` (Basic)	`--fid-aggregation-pct`	0 % (the bead sample: 40 %)
PSF z range	`PsfZRangeUm` (Advanced)	`--fid-psf-z-range-um`	14 µm
Beyond the PSF stack	`FarDefocus` (Expert)	`--fid-far-defocus`	On (a growing blur; Off: not drawn)
Bleach half-time, Reference intensity	`BleachHalfTimeSec`, `BleachRefKWcm2` (Expert)	`--fid-bleach-half-sec`, `--fid-bleach-ref-kwcm2`	288 s, 1 kW/cm²
Equivalent dyes	`DyeCount` (Expert)	`--fid-dyes`	−1 (the type's)
Filter blocking	`BlockingOD` (Expert)	`--fid-blocking-od`	8

The viewer draws the beads in the world view and in its x-z side view as discs of their diameter (the Fiducial beads checkbox, View).

Not modelled: blinking of bead aggregates (their light is the sum of their beads'), single-dye bleaching steps, and the beads' BrightField contrast.