LimitsDetection, resolution, and noise

Detection depends on baseline noise, optical background, readout conditions and how efficiently bound mass contributes to the coherent pattern. Distinguish a mass-response threshold from the smallest analyte concentration an assay can detect.

Objective. Separate the sensor’s mass-response threshold from the smallest detectable concentration.

Recommended first: quantification and spatial lock-in.

What a detection limit means here

A simple teaching convention sets a response threshold at three times the baseline standard deviation, σ. State the sampling, filtering, integration time and observation window used to obtain σ. Drift or a changing blank distribution can invalidate a single baseline estimate.

If noise is measured as coherent mass density (CMD), the threshold is 3σ in pg/mm². For analyte efficiency η = Γ_coh/Γ_tot, the corresponding bound-mass threshold is 3σ/η. This separates optical response from mass arrangement; it is not a universal product specification. Frutiger 2019, §§V-VI.

Concentration needs an assay calibration. Molecular weight alone cannot convert pg/mm² into nM: capture capacity, affinity, matrix and measurement time matter. A calibrated response-versus-concentration relation and appropriate blanks are needed.

What the software computes. The Limit of Detection evaluation uses a related rule. The lowest detectable signal is μ_blank + 3.2 σ_blank from repeated blank injections. It is converted to a concentration through a linear fit of the lowest concentrations, fixed through the median blank response. The 3σ figure on this page is the teaching convention; the evaluation's 3.2σ and blank-based fit are the operational definition.

Analyte efficiency and the massless ideal

Analyte efficiency η describes the coherent fraction of bound analyte. A sinusoidal distribution has ideal η = 1/2; equal-width rectangular ridges have η = 2/π. Concentrating the same mass into infinitely narrow lines approaches η = 1, but leaves progressively less space for receptors.

A massless affinity modulation is a different ideal: minimal initial optical contrast before analyte binds. It does not automatically make every subsequently bound molecule coherent. Frutiger 2019, Appendix C.

Why lithography moves the limit

Pattern fidelity changes how much bound mass contributes at the detection frequency. Image-reversal lithography improved the experimental detection limit by changing the patterned surface. Higher analyte efficiency reduces the total mass needed for a given coherent response. It does not, by itself, lower a fixed noise threshold in CMD. Changes in background and readout can separately alter that threshold. Frutiger 2018.

Where the noise comes from

Relevant contributions include residual baseline drift, roughness-induced speckle, photon shot noise, detector noise and instability in illumination or alignment. Their ranking depends on the optical setup and measurement timescale. Laser power can matter through photon statistics and detector saturation; more power is not a universal remedy.

Photon noise sets a floor. For a focus that contains N photons in its Airy disc, the uncertainty of CMD is σ_Γ ≈ Γ_coh / (2√N). The factor 2 comes from the square root that turns intensity into amplitude. With Γ_coh = 10 pg/mm² and N = 10⁴ photons, σ_Γ ≈ 0.05 pg/mm². A brighter focus is therefore measured more precisely, and the reader adapts the exposure time per mologram to bring each toward a target uncertainty without saturating the camera. Longer exposure buys precision only until drift and saturation take over.

Compare published detection limits only when the mass definition, sample matrix, observation time and processing are comparable. Historical demonstrations are evidence for their stated conditions, not guaranteed performance for every assay. Frutiger 2019, §§V-VI.

Worked example. The streptavidin demonstration uses one stated injection concentration. It does not establish a concentration detection limit without an assay calibration and suitable blanks.