ReferenceGlossary & papers

The terms used across the academy, and the peer-reviewed work behind focal molography.

Glossary

Mologram

A pattern of molecular binding sites arranged to focus diffracted light. Target binding changes the coherent signal; patterned non-specific adsorption can also contribute.

Waveguide

The thin high-index film (tantalum pentoxide, Ta₂O₅) that guides light along the chip by total internal reflection.

Guided mode

A discrete field pattern that propagates in the waveguide. This academy models the fundamental transverse-electric (TE) mode; the number of supported modes depends on wavelength, polarization, and layer properties.

Effective index (N_eff)

The index that sets a guided mode's speed and in-plane momentum, below the film index and above both surrounding indices for a bound mode. It fixes the coupling angle and the evanescent reach.

Evanescent field

The part of the guided light that extends past the surface into the sample and decays exponentially with height, about 90 nm in this academy's 785 nm model. Field amplitude and optical intensity have different 1/e decay lengths; intensity decays twice as fast. There is no hard sensing boundary.

Numerical aperture (NA)

NA = n sin α, where n is the refractive index of the focal medium and α is the cone half-angle. For small angles, NA ≈ nD/(2f); D/(2f) applies in air, with width D and focal distance f defined in the same geometry. At fixed wavelength, smaller NA gives a wider diffraction-limited spot.

Phase matching

The condition for coupling light into a guided mode: the in-plane momentum of the beam plus a grating vector equals the mode's momentum.

Airy disc

The central bright disc of the diffraction pattern from an ideal circular, uniformly illuminated aperture. Square apertures and nonuniform illumination produce different patterns.

Affinity modulation

A pattern of binding preference rather than mass. A nearly massless initial pattern is an ideal; real ligand layers can scatter before analyte binds.

Coherent surface mass density (CMD, Γ_coh)

The diffractometric readout: the mass, arranged perfectly in step with the grating, that would give the measured signal. In pg/mm². The diffractometric analog of the refractive index unit.

Optical normalization

Dividing the diffracted power by the incident power at the mologram's own position, read from the coupling camera, so that CMD scales with √(P_out/P_in) and a change in laser power, coupling or position along the beam does not read as binding.

Zero crossing

The point where the ridge-groove contrast changes sign during a run. The trace passes through zero and continues mirrored; the software can invert it from that point so it reads on one scale. The sign of CMD is a convention set at the baseline, not a negative mass.

Reference hologram

A physical hologram engraved into the waveguide with a known equivalent mass. Used to locate the array on the camera, align the chip, and reference the sensing molograms.

Blank mologram

A mologram carrying a non-binding surface, read during the same injections. Its trace is subtracted to remove injection effects and shared patterned interference.

Normalization to immobilization level

Dividing a mologram's response by the ligand it captured, so molograms with different capture become comparable before a fit.

Invisible mass (Γ_inv)

The part of total bound mass that contributes no coherent amplitude at the selected detection location; it may still scatter elsewhere. Total mass is coherent plus invisible.

Analyte efficiency

The fraction of bound analyte that ends up coherent, and so contributes to the signal. It depends on the spatial distribution; concentrating the same mass near a common grating phase increases it. It is not the fraction of ligand that is biologically active.

Spatial lock-in (spatial affinity lock-in)

The principle that reading only at the grating's spatial frequency separates binding from smooth environmental noise, like a lock-in amplifier in space instead of time.

Refractometric mass-density readout (MD)

The second readout, from the lateral position of the focal spot, which shifts when the effective index changes the grating's out-coupling angle. Sensitive to the average refractive index near the surface: responsive to bulk changes, temperature and surface accumulation, including binding. Use alongside CMD to interpret changes.

Backfilling

In the general surface-chemistry sense, passivating grooves with a non-binding molecule after ligand immobilization. Current product procedures specify the actual materials and sequence. The aim is similar non-specific adsorption on ridge and groove; verify it with the relevant blank matrix.

Sensorgram

Coherent mass density plotted against time: baseline, association, and dissociation.

k_on, k_off, K_D

Association k_on (M⁻¹ s⁻¹), dissociation k_off (s⁻¹), and K_D = k_off/k_on (M) for a simple 1:1 interaction.

Papers

1. Gatterdam et al., Focal molography is a new method for the in situ analysis of molecular interactions in biological samples. Nature Nanotechnology, 2017. 10.1038/nnano.2017.168. The founding demonstration.
2. Frutiger et al., Image-reversal reactive immersion lithography improves the detection limit of focal molography. Optics Letters, 2018. 10.1364/OL.43.005801. Patterning and analyte efficiency.
3. Frutiger et al., Principles for Sensitive and Robust Biomolecular Interaction Analysis: The Limits of Detection and Resolution of Diffraction-Limited Focal Molography. Physical Review Applied, 2019. 10.1103/PhysRevApplied.11.014056. Airy discs, resolution, and detection limits.
4. Reichmuth et al., Quantification of molecular interactions in living cells in real time. Analytical Chemistry, 2020. 10.1021/acs.analchem.0c00987.
5. Blickenstorfer et al., Quantitative Diffractometric Biosensing. Physical Review Applied, 2021. 10.1103/PhysRevApplied.15.034023. Coherent surface mass density and modulation shapes.
6. Frutiger et al., Ultra-Stable Molecular Sensors by Sub-Micron Referencing and Why They Should Be Interrogated by Optical Diffraction—Part I. The Concept of a Spatial Affinity Lock-in Amplifier. Sensors, 2021. 10.3390/s21020469.
7. Frutiger et al., Ultra Stable Molecular Sensors by Submicron Referencing and Why They Should Be Interrogated by Optical Diffraction—Part II. Experimental Demonstration. Sensors, 2021. 10.3390/s21010009.
8. Reichmuth et al., Investigating Complex Samples with Molograms of Low-Affinity Binders. ACS Sensors, 2021. 10.1021/acssensors.0c02346.
9. Incaviglia et al., An approach for the real-time quantification of cytosolic protein-protein interactions in living cells. ACS Sensors, 2021. 10.1021/acssensors.0c02480.
10. Fattinger, Focal molography: coherent microscopic detection of biomolecular interaction. Physical Review X, 2014. 10.1103/PhysRevX.4.031024. The original theory.
11. Szekacs et al., Organization and Dynamics of Focal Adhesions: Light Diffraction Analysis of Cellular Adhesion on Nanopatterned Surfaces. ACS Applied Materials & Interfaces, 2026. 10.1021/acsami.6c04698.