Follow a length from metres to nanometres and picometres. Keep the instrument, conditions and uncertainty beside every reading.
A photon has no universal ruler tick. Optical wavelength, phase sensitivity, readout resolution, localization precision and calibrated distance uncertainty are different quantities. The proposed PRU starts with an exact unit definition; its physical realization still needs evidence.
These entries are your declared values, not acquired scan data. A blank uncertainty stays unknown. Scientific notation keeps a small nonzero result visible; formatting cannot recover information lost during a calculation.
xnm=106xmm,unm=106umm,DnmLnm=DmmLmm
PUBLISHED CAPABILITY / REPRODUCED CALCULATION
Choose a method. Calculate its stated budget.
Use the length entered above to reproduce a named published capability. Each result retains its own measurand, conditions and exclusions.
Measurand: Relative linear displacement measured with XL-80 / XC-80 Scope: published capability evaluated at a hypothetical length; no specimen or scanner calibration is asserted.
Declared length
25,400,000 nm · 2.54 × 10¹⁰ pm · 25.4 mm
Standard uncertainty uc · k = 1
6.18139 nm · 6,181.39 pm · 6.18139 × 10⁻⁶ mm
Expanded uncertainty U · k = 2
12.3628 nm · 12,362.8 pm · 1.23628 × 10⁻⁵ mm
Current XL-80 linear resolution; separately sourced from the 2013 XC-80 budget
1 nm · 1,000 pm · 1 × 10⁻⁶ mm
uc=Lnm10−60.192+0.0252+0.152,U=2uc
Expanded uncertainty is twice the standard uncertainty here. k = 2 is not a universal exact 95% interval. Reproduce the source root-sum-square combination; treat its three standard components as uncorrelated for this named calculation. This does not establish covariance for a new experiment.
Contributions represented in this source budget
Contribution
Standard-equivalent term / contribution
Interpretation
XC-80 compensation
4.826 nm · 4,826 pm · 4.826 × 10⁻⁶ mm
0.38 ppm expanded normal uncertainty, k=2, divided by two.
Laser frequency
0.635 nm · 635 pm · 6.35 × 10⁻⁷ mm
0.05 ppm expanded normal uncertainty, k=2, divided by two.
Air inhomogeneity
3.81 nm · 3,810 pm · 3.81 × 10⁻⁶ mm
0.3 ppm expanded normal uncertainty, k=2, divided by two.
The source’s rounded published expanded figure evaluates to 12.446 nm · 12,446 pm · 1.2446 × 10⁻⁵ mm. The calculation above retains the listed component values before rounding.
Operating conditions, exclusions and source roles
Positive displacement; maximum 80 m from the current XL-80 hardware specification. The 2013 budget itself supplies no separate length interval.
Conditions
Historical XL-80, XC-80 compensator and sensors; compensated air temperature 0–40 °C and stated pressure range.
XC-80 sensor ranges: air pressure 650–1150 mbar; relative humidity 0–95%, non-condensing; material temperature 0–55 °C.
Relative linear displacement in the specified compensated system, not absolute ball diameter or contour length.
Excluded from this example
The 2013 budget excludes system setup/alignment and normalization to material temperature 20 °C.
Current product information discusses XC100; this historical XC-80 budget is not transferred to XC100.
The current 1 nm resolution is a separate specification, not an added independent uncertainty component.
The quadrature result differs slightly from published 0.49 ppm because the source rounds its reported budget.
No calibrated specimen, surface reconstruction, scan acquisition, full PRU budget or physical uncertainty is supplied.
Current product page reviewed 2026-10-07; page discusses XC100 compensation · Separate 1 nm linear-resolution and maximum 80 m hardware specifications; not the historical XC-80 uncertainty budget.
NIST TN 1297 · first-order propagation including covariance · Method provenance: sensitivity coefficients, standard uncertainties and covariance must be stated.
These three examples are different capabilities, not three replications of one specification. Their uncertainties cannot be transferred to a one-inch ball or combined into a universal photonic accuracy.
3D + TIME / CONDITIONAL PHOTON-COUNTING COMPONENT
Follow the point, the time and the noise.
A reproducible prototype adds a local radial error to every prescribed point on the ideal one-inch equatorial circle. A shows the observations at their sample times. B registers them to the declared time-zero frame.
Ideal coherent input, balanced two-port detection, known quadrature, normal-incidence reflection, visibility V = 1 and external phase index n = 1. This generates Gaussian local errors; it does not simulate photon events or reconstruct an unknown ball.
Radial standard uncertainty · shot component
0.0503566 nm · 50.3566 pm · 5.03566 × 10⁻⁸ mm
Expanded radial shot component · k = 2
0.100713 nm · 100.713 pm · 1.00713 × 10⁻⁷ mm
Total expected detected photons
64,000,000 across 64 samples
Complete instrument uncertainty
Not evaluated: calibration, detector, clock and common systematic terms remain outside this prototype.
uϕ=VN1,ur=4πnphaseVNλvac,Ur,local=2ur
k=2 expanded photon-counting component, conditional on the local Gaussian model; total instrument uncertainty is unprovided. Increasing the point count also increases this run’s total photon allocation; it is not a fixed-total-resource comparison.
A / Raw acquisition times
Different sample times can distort an unregistered contour.
B / Registered to t = 0
Subtract the supplied pose translation at each sample.
Sample time: 0 ms over a declared 50 ms schedule. Instants are prescribed; exposure duration, flux, blur and tracking bandwidth are not inferred.
Supplied x pose shift at this time
0 nm · 0 pm · 0 mm
Preserved local radial error Δr
-0.0265774 nm · -26.5774 pm · -2.65774 × 10⁻⁸ mm
Local phase standard uncertainty
0.001 rad
Run seed
417283 · same inputs, seed and JavaScript runtime reproduce the samples
The residual plot has its own noise-scale vertical axis. Noise is too small to resolve on the full 25.4 mm geometry view. Local deltas are retained separately from large floating-point world coordinates. Different JavaScript engines can differ in the last floating-point bits; cross-engine replay uses a stated numerical tolerance.
Complete-run geometry diagnostics · every point in the simulated schedule
Frame
Closed polyline length
Maximum point-pair span
Length / span
Prescribed control
79,764,400 nm · 7.97644 × 10¹⁰ pm · 79.7644 mm
25,400,000 nm · 2.54 × 10¹⁰ pm · 25.4 mm
3.14033
Raw: mixed times
79,762,900 nm · 7.97629 × 10¹⁰ pm · 79.7629 mm
25,425,300 nm · 2.54253 × 10¹⁰ pm · 25.4253 mm
3.13715
Registered: t = 0
79,764,400 nm · 7.97644 × 10¹⁰ pm · 79.7644 mm
25,400,000 nm · 2.54 × 10¹⁰ pm · 25.4 mm
3.14033
The table covers the completed schedule even while the drawing is replayed. It has no propagated contour/span uncertainty. Known π generates the control and angular schedule, so agreement is an implementation check, not an independent proof of π or UNO’s law.
Point vectors, factor status and primary sources
Selected observation / nm: x = 12,700,000, y = 0, z = 0. Registered / nm: x = 12,700,000, y = 0, z = 0.
wavelength
Declared vacuum wavelength; wavelength calibration and drift uncertainty unprovided.
phaseIndex
Declared constant homogeneous external propagation-medium phase index; not the complex internal index of gold. Index uncertainty unprovided.
photonBudget
Expected detected signal photons per point summed across both output ports, after losses. No additional efficiency factor.
Quadrature, a stable surface-reflection phase, and the local phase branch are supplied by a known reference/prior. No absolute-range or fringe-unwrapping inference.
pose
Exact declared x translation and radial directions; no estimated pose, alignment, or registration accuracy.
timestamps
Declared instantaneous acquisition instants; no detector/clock jitter, finite exposure, motion blur, bandwidth, or phase-tracking model.
detector
Background, dark counts, dead time, saturation, read noise and detector correlations unmodeled.
calibration
Full instrument calibration, common systematic errors and radiation-pressure backaction unprovided.
Model conditions
Coherent input and vacuum in the unused port; balanced two-output local interferometric readout at quadrature, with a supplied phase reference.
Normal incidence and one external round trip: dphi/dx = 4pi n_phase/lambda_vac. The reflecting surface phase is assumed stable and known.
Each point is an independently assigned ideal radial scalar readout. Sensor access, normals, geometry and pose are prescribed, not recovered from measurements.
Zero-mean independent Gaussian radial draws approximate the high-count photon-counting component. Photon-count events and quantum optical states are not simulated.
The modeled Cartesian noise is radial and has rank-one covariance u_r^2 e_r e_r^T; it is not three independent coordinate errors or full spatial uncertainty.
The local-demo guard u_phase <= 0.1 rad is chosen for this approximation. Counts >=1000 alone do not guarantee a valid phase estimator or Gaussian interval.
k=2 is an expanded photon-counting component conditional on the local Gaussian model (approximately 95% coverage there), not a total instrument interval.
Scan duration defines the timestamp schedule, not per-point exposure or photon flux. Known pose registration demonstrates a coordinate transform only.
Closed-polyline length and maximum pairwise span describe sampled coordinates in the stated frame; their ratio is a synthetic diagnostic, not an independent measurement of pi.
Raw coordinates have different acquisition times. Registered coordinates share the declared t=0 epoch. Float64 world coordinates can round away a tiny error; local radial deltas remain separately available.
Three primary core documents support different model ingredients. Source review and reproducible arithmetic do not establish three independent experiments or physical validation.
core: The r=0 coherent-input phase baseline is 1/sqrt(p nbar); both outputs of a lossless interferometer are counted. Original PRL study; the author manuscript https://arxiv.org/pdf/0705.4631 is the same study, not independent verification.
core: Normal reflection geometry gives phase change 4pi times displacement divided by the propagation-medium wavelength; wavelength and deadpath matter. Original NIST Journal of Research article, DOI 10.6028/jres.101.065; distinct support for the geometry, not a replication of the photon formula.
core: Standard uncertainty, sensitivity coefficients and covariance, and expanded uncertainty U=k u with justified coverage assumptions. Official JCGM metrology guide; uncertainty methodology, not physical validation of this simulation.
context: Counts can include background; detector efficiency, dead time, timing-jitter width and operating conditions must be distinguished. Official NIST definitions; the detector quantities are unprovided in this prototype.
context: Guidance for propagating specified input distributions and validating uncertainty approximations; no full uncertainty propagation is claimed here. Supplement to JCGM 100; shared JCGM lineage, not another independent validation.
THREE PRIMARY SOURCES PER CATEGORY / REVIEWED 2026-10-07
Compare the quantity each instrument reports.
There is no universal “most accurate ruler.” A calibrated line scale, a hand-read rule and a laser rangefinder have different measurands and operating domains.
Retain metric type, model/configuration, range and conditions. Three sources in a category are not triple verification of each named specification. A rangefinder’s distance to a target is not automatically the diameter or contour of a one-inch ball. A minimum working distance may also exceed that diameter. The named capability calculations above retain their published measurands; no manufacturer figure is assigned to the simulated PRU contour scan.
Precision steel rule
3 primary sources
A physical graduation is different from rule manufacturing tolerance and calibrated-interval uncertainty. These examples establish no most-accurate universal ruler.
Mitutoyo
182-205, full-flexible 6 inch / 150 mm steel rule
Nominal rule length / physical graduation spacing
Smallest metric graduationgraduation
0.5 mmMagnitude in common units: 500,000 nm · 0.5 mm
Customer specified metal-ruler intervals with high-quality graduation marks
Calibrated value of a customer-specified rule interval
Metal-ruler calibration Uexpanded uncertainty
27 + 0.88 * L µm; L in mCoverage factor k = 2
Conditions and interpretation
Comparison to a frequency-stabilized laser with active temperature, pressure and humidity corrections. Graduation quality influences achievable uncertainty.
Calibration uncertainty in reported interval values, not a product manufacturing tolerance or normal visual reading accuracy.
A general lower detection limit is not supplied by this source.
Calibration services achieve nanometre uncertainties under controlled conditions with high-quality artifacts. This is different from visual reading and from sub-nanometre display resolution.
NIST
NIST Line Scale Interferometer (LSI), line-scale/stage-micrometer artifacts
Distance between physical scale graduation centres
Achievable short-interval Uexpanded uncertainty
≤3 nmMagnitude in common units: 3 nm · 3 × 10⁻⁶ mmApplicable interval: max value 10 · unit mm
Achievable metre-interval Uexpanded uncertainty
≤100 nmMagnitude in common units: 100 nm · 1 × 10⁻⁴ mmApplicable interval: approx value 1 · unit m
Conditions and interpretation
Scanning electro-optical line detector and heterodyne displacement interferometer; stabilized helium-neon laser with air-refractive-index correction; monitored temperature-controlled chamber.
Achievable calibrated interval uncertainty depends on artifact quality and operating conditions. Not a guarantee for any ruler or a universal minimum length.
A general lower detection limit is not supplied by this source.
Official NIST search result returned full service text; direct open returned an internal error in this run. Supporting original paper: https://nvlpubs.nist.gov/nistpubs/jres/104/3/html/j43bee.htm
25 nmMagnitude in common units: 25 nm · 2.5 × 10⁻⁵ mmApplicable interval: min value 550 · max value 1000 · unit mm
Conditions and interpretation
Maximum graduation-to-base distance 25 mm and graduation-to-outer-surface distance 160 mm. Service-page table does not display a coverage factor.
Named comparator calibration capability. Preserve the source uncertainty label; do not relabel as expanded k=2 without the missing quality-manual evidence.
A general lower detection limit is not supplied by this source.
Calibrated distances between selected line centres
Best line-scale Uexpanded uncertainty
sqrt(6.2^2 + (82 * L)^2) nm; L in mCoverage factor k = 2Applicable interval: min value 10 · min unit µm · max value 1.12 · max unit m
Conditions and interpretation
20 °C ±0.05 °C, RH45±5%, supported at Airy points; CCD microscope plus special interferometer; air-index and material-temperature corrections. Best class requires excellent low-thermal-expansion scale and graduation quality.
Uncertainty is often larger because of the artifact. At L=1 m, the published formula gives about82.23 nm; that is a derived example, not an extra measurement.
A general lower detection limit is not supplied by this source.
Named handheld meters report millimetre tolerances under specified target, illumination, temperature and range conditions. Laser spot size and distance readout digits are different quantities.
Leica Geosystems
DISTO D2 version described by the 2025 manual; do not mix its150m range with an older100m D2 webpage.
One-way distance to a reflective target
Smallest displayed unitdisplay increment
0.1 mmMagnitude in common units: 100,000 nm · 0.1 mm
Favourable tolerancemanufacturer tolerance
±1.5 mmMagnitude in common units: 1,500,000 nm · 1.5 mmReported confidence: 95%Applicable interval: min value 0.05 · max value 10 · unit m
Unfavourable tolerancemanufacturer tolerance
±3 mmMagnitude in common units: 3,000,000 nm · 3 mmReported confidence: 95%Applicable interval: min value 0.05 · max value 10 · unit m
Measured from front edge, high-reflectivity target,20°C; favourable weak background light; unfavourable strong background light/high elevation. Manual gives no confidence factor for these figures.
Distance-dependent terms and reference-edge conditions must accompany a numerical specification.
A general lower detection limit is not supplied by this source.
Sub-nanometre resolution is available in named interferometer configurations. It is distinct from absolute error, full uncertainty and a procedure-defined lower detection limit.
Renishaw
XL-80 with appropriate environmental compensation
Relative linear displacement / machine calibration
Linear resolutionresolution
1 nmMagnitude in common units: 1 nm · 1 × 10⁻⁶ mm
Compensated linear performancemanufacturer specified relative error
±0.5 ppm
XC-80 historical budgetexpanded uncertainty
0.49 ppmCoverage factor k = 2
Conditions and interpretation
Air-temperature, pressure and humidity compensation required; see separateXC-80 uncertainty-budget source for qualified historical budget.
1 nm resolution differs from ±0.5 ppm system performance. The 2013 XC-80 budget excludes setup/alignment and material20 °C normalization; current product page discusses XC100, so do not transfer that budget to XC100.
A general lower detection limit is not supplied by this source.
5530 system with high-resolution plane-mirror optics
Linear displacement with high-resolution plane-mirror optics
Plane-mirror configuration resolutionresolution
0.25 nmMagnitude in common units: 0.25 nm · 2.5 × 10⁻⁷ mm
Conditions and interpretation
A specific optional optical configuration; brochure identifies traceable calibration and environmental/material sensors but does not provide a complete uncertainty number in the cited passage.
Sub-nanometre resolution example only, not absolute length accuracy.
A general lower detection limit is not supplied by this source.
Differential displacement readout in frequency spectrum
Spectral resolutionspectral resolution
5 pmMagnitude in common units: 0.005 nm · 5 × 10⁻⁹ mm
Conditions and interpretation
Differential measurement with external reference point. Temperature sensitivity<10nm/K; stabilized HeNe wavelength632.8nm and frequency stability2e−8 after warm-up.
Preserve spectral-resolution qualifier. Thermal response/frequency stability are different from a complete distance error or detection limit.
A general lower detection limit is not supplied by this source.
Range quantization, systematic ranging error, point noise and 3D point accuracy differ. These conditional specifications do not establish a universal LiDAR tolerance.
Typical range accuracy is ±25 mm on Lambertian targets and ±50 mm on retroreflective targets beyond 1 m in 1024 at 10 Hz mode. Ouster defines accuracy as the error between the mean of 100 measurements and true range. Range precision is the standard deviation of 100 static-target readings, with stated minimum ±8 mm and maximum ±40 mm. Range resolution is 1 mm, or 8 mm in the low-data-rate profile.
Lambertian typical range accuracymanufacturer typical mean error
±25 mmMagnitude in common units: 25,000,000 nm · 25 mmStatistic: Error of mean of 100 readings vs true range
Retroreflective typical range accuracymanufacturer typical mean error
±50 mmMagnitude in common units: 50,000,000 nm · 50 mmStatistic: Error of mean of 100 readings vs true range
Range resolutionoutput quantization
1 mmMagnitude in common units: 1,000,000 nm · 1 mm
Range precisionstandard deviation
8–40 mmStatistic: 1σof 100 readings
Conditions and interpretation
Lambertian or retroreflective static targets beyond 1 m 1024 at 10 Hz mode Specified hardware and firmware revision
These are conditional typical manufacturer specifications. The 1 mm output increment is not 1 mm accuracy; target, range and mode matter.
A general lower detection limit is not supplied by this source.
Part 1071996; fetched datasheet stamped 2026-09-08
The performance table lists systematic error ±25 mm at 1–10 m and ±35 mm at 10–20 m, alongside statistical error 7 mm and 9 mm over those respective intervals. Its footnote identifies these as typical values that depend on environmental conditions. A separate feature row says measurement accuracy ±12 mm without matching conditions on that row, so the condition-rich performance entries are preferable for a comparison.
9 mmMagnitude in common units: 9,000,000 nm · 9 mm
Conditions and interpretation
Named 2D LiDAR model and part Distance intervals 1–10 m and 10–20 m Actual values depend on environmental conditions
Do not reinterpret the statistical-error line as a guaranteed maximum or known standard deviation. Do not merge the unexplained ±12 mm feature row with the conditioned performance figures.
A general lower detection limit is not supplied by this source.
The 2022 Focus Premium brochure specifies ±1 mm ranging error, defined in its footnote as systematic measurement error around 10 m and 25 m. It separately lists 3D accuracy 2 mm at 10 m and 3.5 mm at 25 m. For a 90% reflective white target, range noise is 0.1 mm at 10 m and 0.2 mm at 25 m, evaluated from repeated readings of a single point at 122,000 points per second. The general accuracy note specifies standard deviations after warm-up within operating temperature range unless otherwise stated.
±1 mmMagnitude in common units: 1,000,000 nm · 1 mmDistances: 10 and 25 m
3D accuracy at 10mmanufacturer 3d accuracy
2 mmMagnitude in common units: 2,000,000 nm · 2 mmStatistic: standard deviation unless stated otherwise
3D accuracy at 25mmanufacturer 3d accuracy
3.5 mmMagnitude in common units: 3,500,000 nm · 3.5 mmStatistic: standard deviation unless stated otherwise
Range noise at 10mrepeated point variation
0.1 mmMagnitude in common units: 100,000 nm · 0.1 mmTarget reflectivity: 90%Point rate: 122,000 points/s
Range noise at 25mrepeated point variation
0.2 mmMagnitude in common units: 200,000 nm · 0.2 mmTarget reflectivity: 90%Point rate: 122,000 points/s
Conditions and interpretation
2022 named Focus Premium models Warm-up and operating temperature requirements Noise evaluated at 122,000 points/s Reflectivity specified for noise
The brochure is a versioned historical model specification, not a claim about every current Focus scanner. Noise and systematic ranging error differ by an order of magnitude here.
A general lower detection limit is not supplied by this source.
The studies measure different quantities: emitter localization, bandwidth-normalized displacement noise and sample-position stabilization. Their values cannot be ranked as one accuracy or merged into a universal photon floor.
These three independent studies appear through two publication outlets. Source coverage is not independent replication of a single specification.
Abberior Instruments/Abberior and Max Planck collaborators
MINFLUX nanometer-scale 3D imaging and microsecond-range tracking on a common fluorescence microscope
2021-03-05
In specified cellular and neurobiological samples, approximately 2,500 detected fluorescence photons yielded localization precision below 1 nm as standard deviation; roughly 800 photons gave 2.2 nm. For Nup96-SNAP labeled with Alexa Fluor 647 in fixed mammalian cells, independently aggregated segments of about 2,100 photons yielded a median localization spread of 0.9 nm with final probing diameter 40 nm. The paper describes 1–3 nm three-dimensional image resolution separately.
<1 nmMagnitude in common units: 1 nm · 1 × 10⁻⁶ mmApproximately 2500 detected photons
3D imaging resolutionreported imaging resolution
1–3 nm
Conditions and interpretation
MINFLUX structured excitation and active stabilization Individually activated labeled fluorophores Named biological samples and photon counts
Emitter localization precision is not the same as structural imaging resolution or absolute macroscopic length accuracy. The ~0.2–0.3 nm technical precision limit at 100,000 photons is a separate high-photon analysis, not the typical cell-imaging result.
A general lower detection limit is not supplied by this source.
Nikhef, TU Delft, AMOLF, UCLouvain and collaborators
The ultimate performance of the Rasnik 3-point alignment system
2023
The authors report a best MicroRas optical displacement readout performance of 7 pm per square root hertz using a mask, lens and imaging pixel sensor. The stated noise floor is attributed to fluctuations in detected photon flux. The demonstrated MicroRas configuration uses a Royal Blue LED, Newport 20× microscope objective and MER-041-302G sensor. Values of 1 or 0.2 pm per square root hertz are discussed as possible future improvements.
Optical displacement noiseamplitude spectral density
The repository abstract's HTML loses the square-root in the unit; the final PDF and author preprint preserve pm/√Hz. Do not render this as a 7 pm absolute error or universal lower detection limit.
A general lower detection limit is not supplied by this source.
Direct-laser writing for subnanometer focusing and single-molecule imaging
2022-02-03
Printed three-dimensional optical fiducials and active stage feedback stabilized the sample with standard deviation 0.4 nm laterally and 0.7 nm axially. The authors measured a duplicate out-of-loop reference and found stability below 0.8 nm across a 0–20 µm depth range, tested in 1 µm increments for one hour per step in three repeats, 63 hours combined. Stage corrections ran at 20 Hz, with an environmental enclosure and recorded temperature stability.
Lateral sample stabilizationstandard deviation
0.4 nmMagnitude in common units: 0.4 nm · 4 × 10⁻⁷ mm
Axial sample stabilizationstandard deviation
0.7 nmMagnitude in common units: 0.7 nm · 7 × 10⁻⁷ mm
Out-of-loop stability over 0–20µm depthpositional stability
<0.8 nmMagnitude in common units: 0.8 nm · 8 × 10⁻⁷ mm
Conditions and interpretation
3D optical fiducials fabricated by two-photon direct-laser writing Independent out-of-loop reference 20 Hz stage correction Environmental temperature control
This is sample/focus stabilization precision, not an object-size accuracy or optical resolution claim. The same article reports much larger biological fluorophore localization spreads.
A general lower detection limit is not supplied by this source.
A material change is zero when temperature and pressure match the reference. Motion bias is zero for a stationary reflector. Uniform isotropic scaling preserves the contour/span ratio. These are legitimate results of the stated models.
Unknown measurement uncertainty
The complete specimen, scanner, reconstruction and calibration uncertainty is not supplied. It remains unknown. A numerical consistency tolerance describes a software check; it is not an instrument’s uncertainty.
Not applicable or not modeled
Water-specific surface tension and capillary diagnostics do not apply to solid rows. Absolute solid density and a general internal optical path are not modeled by the current environment control. Their absence does not mean zero density or zero refraction.
Material source roles also differ: water IAPWS and its NIST implementation share a formulation; diamond’s visible dispersion study cannot be independently checked by an infrared-only dataset; gold optical measurements and fitted models are distinct evidence. Three documents in a family do not give every coefficient three independent confirmations.
Temperature, pressure, refractive index, support and relative motion can affect a declared measurement. The clock calculation uses a hypothetical vertical separation. Earth’s orbital speed is not the same as reflector motion relative to a local instrument.
These are stated reflected-path models. Sub-wavelength displacement sensitivity is possible, while phase ambiguity, noise, air corrections, alignment and calibration still require an uncertainty budget. No published comparison here establishes an exact physical ball or a last digit of π.