PRESBYpath — Personalised Pseudo-Accommodative Profile Designer

Patient-specific multifocal LASIK / PRK profile design — wavefront-guided, pupil-aware, vergence-range-driven.

by Pr Damien Gatinel — Rothschild Foundation Hospital, Paris  ·  © gatinel.com

For education & simulation — not a medical device. See About.
Patient-specific multifocal optics

PRESBYpath

A personalised pseudo-accommodative profile designer for presbyopia treatment — wavefront-guided, pupil-aware, vergence-range-driven.

by Pr Damien Gatinel · Rothschild Foundation Hospital, Paris

A method that goes beyond presbyLASIK

The present build of PRESBYpath is dedicated to excimer-laser presbyopia correction in LASIK or PRK (corneal substrate, Q-asphericity or wavefront-guided ablation). The underlying methodology, however, transfers directly to any refractive corrector whose surface(s) can carry a controlled spherical-aberration trajectory.

Multifocal / EDOF contact lenses

Same Q-modulation and Z40/Z60/Z80 trade-offs, applied to the lens shape rather than the corneal sag.

Multifocal / EDOF IOLs (cataract)

Same optimisation framework — the IOL's optical surface(s) play the role of the modulating element.

Piggyback / IOL exchange

Personalised multifocal add to refine residual post-cataract refraction — not a template add.

The substrate and the surgical workflow change. The optical optimisation problem is the same.

Why presbyopic LASIK has always been a "black box"

Every presbyLASIK / presbyPRK profile in clinical use today relies on a single optical mechanism: manipulating the eye's spherical aberration to extend the depth of field. The lever is most often a programmed change in corneal asphericity (Q); on some platforms it is a direct Zernike target (Z40, Z60, …). Either way, the surgical input is the post-op spherical aberration.

What those commercial modules do not do:

  • they ignore pupil dynamics — the patient's actual mesopic-to-photopic range, and the near miosis triggered by the accommodation–convergence reflex;
  • they do not co-design the treatment around the patient's own higher-order aberrations (HOAs);
  • they apply the same nominal profile across a broad population, with no personalisation of the vergence target, the upper-pupil distance score, or the spherical-aberration trajectory.

These platforms are designed by excellent optical and biomedical engineers — but rarely by clinicians, and never by clinicians using their own optical model. The result is technically sophisticated, yet mathematically decoupled from the individual eye on the table.

What this module does differently

PRESBYpath was designed by a refractive surgeon — with surgical priorities driving every modelling choice, and with the level of care that real optical calculations require.

Behind the UI: rigorous OPD / sag sign conventions, separation of keratometric and physical refractive indices, Zernike rescaling between aberrometer source pupil and analysis pupil, Levenberg–Marquardt biconic ΔK calibration, and dual-pupil through-focus MTFa scoring.

The clinical question comes first. You enter:

  • the patient's refraction, keratometry and asphericity;
  • the measured higher-order wavefront (or any HOA profile of interest);
  • the target pseudo-accommodative vergence range — distance, intermediate, near, or any combination;
  • the two pupil sizes that matter clinically: the mesopic / distance pupil, and the constricted / near pupil.

The optimiser then co-designs the asphericity change, the spherical add, and the radial Zernike modes (Z40, Z60, Z80) so that the through-focus image quality covers the chosen range at both pupil sizes simultaneously.

Every step is patient-specific. No nomogram. No template. The physics adapts to the eye, not the other way around.

Patent — and an open door

A patent application is pending on the methodology of personalised pseudo-accommodative profile design — covering excimer-laser, contact-lens and intraocular-lens implementations.

If a laser manufacturer, an IOL designer or a contact-lens R&D team would like to bring this approach into a clinical or commercial platform, please get in touch. It would save us both a lot of time, and your patients a lot of guesswork.

Direct contact — Pr Damien Gatinel:

gatinel@gmail.com

The point of all this

I hope PRESBYpath helps demystify the optics of presbyopic LASIK for my colleagues, and lets them see what a personalised multifocal correction actually looks like before it is delivered.

Customisation belongs in this field as much as it already does in monofocal refractive surgery — and the conversation about how to do it properly has to start somewhere.

Open scientific transparency. No nomograms. No black box. Just the physics, the patient's eye, and the surgical intent.
Ready to design a profile?
Continue with the patient's clinical data.

Disclaimer

PRESBYpath is an educational and research-oriented simulation tool. It is not a certified medical device, not CE-marked and not FDA-cleared, and must not be used as such to plan or execute treatment on real patients.

Its purpose is to make the optics of presbyopic LASIK / PRK — and, by extension, of contact-lens and IOL multifocal designs — visible, manipulable and teachable. The platform can serve as a reference base for future clinical or industrial implementations, provided it undergoes the usual validation pathway: independent verification of the optical engine, bench testing, prospective clinical evaluation, and regulatory clearance in each jurisdiction of use. Until then, all results displayed here are theoretical and indicative — they are intended to inform, instruct and stimulate clinical reflection, not to drive treatment.

By using PRESBYpath you acknowledge that the author(s) and host institution(s) decline any responsibility for clinical decisions made on the sole basis of its output.

References
  1. Gatinel D, Malet J. Vergence-based ocular wavefront expansions in diopters: orthogonal functions, clinical metrics, and visualization tools. J Opt Soc Am A Opt Image Sci Vis. 2025 Dec 1;42(12):1846-1863. doi:10.1364/JOSAA.576308. PMID: 41411558.
  2. Rahmania N, Salah I, Rampat R, Gatinel D. Clinical Effectiveness of Laser-Induced Increased Depth of Field for the Simultaneous Correction of Hyperopia and Presbyopia. J Refract Surg. 2021 Jan 1;37(1):16-24. doi:10.3928/1081597X-20201013-03. PMID: 33432991.
  3. Courtin R, Saad A, Grise-Dulac A, Guilbert E, Gatinel D. Changes to Corneal Aberrations and Vision After Monovision in Patients With Hyperopia After Using a Customized Aspheric Ablation Profile to Increase Corneal Asphericity (Q-factor). J Refract Surg. 2016 Nov 1;32(11):734-741. doi:10.3928/1081597X-20160810-01. PMID: 27824376.
  4. Gatinel D. Chirurgie de la presbytie [Presbyopia surgery]. Rev Prat. 2008 May 31;58(10):1049-54. French. PMID: 18652400.
PRESBYpath  ·  by Pr Damien Gatinel  ·  Rothschild Foundation Hospital, Paris
Patient Data & Refraction
1 Step 1 — Enter the patient's standard clinical data
Start with the usual presbyopic-LASIK workup: spectacle refraction (sphere, cylinder, axis, vertex distance), keratometry (K1, K2 with the flat-meridian axis A1, asphericity Q1/Q2), and the planned laser optical zone. The next step will display the patient's high-order wavefront (HOA) data — as if just acquired by an aberrometer — on top of these low-order values. All fields here are editable: change any value freely to explore different presentations or to mirror a specific patient profile. Eye dominance is recorded so the design can later be biased toward distance or near as appropriate.
Eye dominance
Spectacle Refraction to Correct
Sphere
Cylinder (negative)
Refractive axis
Vertex distance
S: — D   C: — D   Axis: —°
Auto-calculated
Pre-op Corneal Data
Flat meridian
Principal axis
Asphericity on A1
Steep meridian
Auto: A1+90°
Asphericity on A2
Optical Zone
Optical zone
Reduced eye model
Wavefront analysis — made clinically relevant
2 Step 2 — Wavefront analysis made clinically relevant
A clinically meaningful summary of the optical substrate for a multifocal approach.
This step shows the high-order wavefront data as if it had just been acquired on the patient by an aberrometer. The Zernike pyramid below displays the individual HOA modes (Z3…Z6); together with the low-order refraction entered in step 1, they make up the total ocular wavefront the patient carries through the optical zone. All HOA inputs are editable: enter the measured coefficients, type your own values to study a specific aberration pattern, or click Reset all to 0 for an idealised low-order eye. The « Source ⌀ » field tells the engine on which pupil the coefficients are defined (typical aberrometry diameter: 5–6.5 mm).
No aberrometry available? Use the « No wavefront? Use typical Z(4,0) » button on the Zernike-pyramid card: it sets every HOA mode to 0 except primary spherical aberration Z(4,0) ≈ +0.10 µm at 6 mm — a realistic population mean that already yields a credible post-op rendering.

Zernike HOA Pyramid

No aberrometry data for this patient? Leave most modes at 0 and set Z(4,0) ≈ +0.10 µm at a 6 mm source pupil (typical population mean for primary spherical aberration). The downstream design will already produce a realistic post-op rendering. The button above does this in one click and pre-fills the Source ⌀ field at 6.0 mm.

HOA wavefront map (µm)

Wavefront OPD surface

Below, after the classic wavefront display above, we propose a more clinically intuitive reading of the same optical substrate — one that, to our knowledge, is unique to PRESBYpath and is not used by existing commercial platforms: the wavefront expressed as a map of local optical power in diopters.
Why vergence maps (D), not wavefront (µm)?
For multifocal design and presbyopic-LASIK reading, the relevant clinical quantity is the local optical power in diopters, not the raw optical path difference in microns. A wavefront in µm tells you the shape of the optical error; a vergence in diopters tells you what the eye does optically — where each pupil zone tries to focus light relative to the retina, in the very units used to prescribe glasses, contact lenses or IOLs.
The maps below display the radial vergence component V ≈ −(∂W/∂r)/r in diopters. A central near-add zone reads as a more negative (myopic) vergence at the center — exactly what the patient experiences when fixating a near target. A peripheral plano zone reads close to 0 D — distance vision dominates the upper pupil. The split between total, low-order and high-order contributions lets you see at a glance which part of the local power comes from the spectacle refraction and which part from the patient's own higher-order aberrations.
The classical wavefront map (in µm) is kept on the side as a reference, but the vergence maps are the working tool for evaluating intermediate / near coverage and for anticipating how a personalised multifocal profile will behave across the pupil. This is the central rationale of PRESBYpath: think the design in clinical units, not in microns of OPD.

Radial vergence component — total (low + HOA)

The whole eye. Local refractive error (D) at each pupil point, combining the patient's sphero-cylindrical refraction and the measured high-order aberrations. This is what the eye is doing right now, before any correction.
V ≈ −(∂W/∂r)/r — for non-radial modes (coma, trefoil, oblique cyl) this is one component of the local power matrix; rely on PSF/MTF for quantitative comparison.

Radial vergence component — low order only

The sphero-cylindrical correction alone. Local refractive error (D) from the patient's low-order refraction (sphere, cylinder, axis) only — i.e. what a pair of spectacles or a monofocal IOL targets. Reads as a smooth, symmetric pattern.

HOA radial vergence component

The high-order contribution. Local refractive fluctuations (D) around the low-order correction, caused by HOAs (spherical aberration, coma, trefoil, …). This is the optical residue that a spectacle cannot fix — and the substrate every presbyopic / multifocal design has to work with.
Radial component −(∂W/∂r)/r — for non-radial HOA (coma, trefoil…) this is one component of the full local power matrix; rely on PSF/MTF for quantitative comparison.
M Pre-op image quality — through-focus MTFa
The vergence maps above describe where the eye focuses across the pupil. The through-focus MTFa below describes how well the eye images contrast at each focus depth — i.e. the real visual quality the patient experiences as the target moves from far to near. Together, the two views form the pre-op clinical baseline against which any multifocal profile will be scored.

Pre-op Through-focus MTFa (compensation sweep)

How to read this curve
The MTF (Modulation Transfer Function) measures the eye’s ability to preserve contrast as a function of the spatial frequency of the target (in cycles/mm or cycles/degree). A perfect optical system has MTF = 1 at all frequencies; aberrations, defocus and diffraction reduce the MTF, more strongly at the high spatial frequencies that carry fine detail.

The MTFa shown here is a single scalar derived from the MTF: the area under the MTF curve over a chosen frequency band (here 10–50 lp/mm by default). It compresses the whole MTF into one number that is large when fine details are well preserved and small when the image is blurred. MTFa is therefore a convenient image-quality index.
X axis — Object defocus (D)
The compensation vergence (spectacle plane) added in front of the eye. 0 D ≈ best distance correction; negative values move the target closer (near vision), positive values further (over-minused / accommodated states).
Y axis — MTFa (a.u.)
Image-quality index at each defocus. The peak indicates the best-focus object distance; the curve’s width at a clinical threshold (typically 0.10) is the eye’s depth of focus. A flat-topped, wide curve = good multifocality.
Colours / traces — different pupil sizes are plotted as separate curves. A larger pupil generally produces a higher peak (more light) but narrower DoF (more sensitive to defocus); a smaller pupil flattens and widens the curve. Comparing the two helps anticipate how distance and near tasks will trade off post-op.
This pre-op panel is kept in READ’s historical compensation convention: negative = myopic compensation, positive = hyperopic compensation. It is not the clinical object-vergence convention used in the modern through-focus panels.
Next — Step 3 : Treatment Design. Now that the optical substrate is fully characterised (refraction, HOAs, vergence maps and pre-op through-focus image quality), we move on to designing the personalised multifocal profile: choosing the spatial domain (upper / inner pupil), the target vergence range, and the laser-programming route (Q-asphericity vs spherical-aberration modulation). Each clinical step is built on top of the previous one — that is the spirit of PRESBYpath.
Treatment Design
3 Step 3 — Treatment Design: spatial and optical domains
The presbyopic treatment is programmed on two complementary domains. The spatial domain describes the pupil geometry: two pupil sizes are chosen, each one matching a typical visual task. The optical domain describes the target depth of focus: a vergence range (in diopters) that the treated eye should cover comfortably. Adjust both blocks below — the optimiser will then search for the best laser parameters that satisfy both.
Upper pupil — large (mesopic / distance)
In low-light conditions the pupil dilates (typically 5.5–6.5 mm). This is the geometry used to score distance vision: the optimiser evaluates image quality at the least negative end of the vergence range (Dmax).
Lower pupil — small (near vision)
On a near target the pupil constricts via the accommodation–convergence–miosis triad (typically 3–4 mm). This is the geometry used to score near vision: image quality is evaluated at the most negative end of the vergence range (Dmin).
D Optical domain — target depth of focus
Choose the vergence range (in diopters, spectacle plane) that the treated eye should cover. The pink band visualises the active range; the two bound sliders fine-tune it.
+2+1 0 -1-2 -3-4
⌀ Spatial domain — pupil sizes
The optimiser scores image quality at two pupil sizes. The upper (mesopic / distance) pupil is paired with the far end of the vergence range; the lower (near-vision miosis) pupil with the near end.
Upper pupil — distance / mesopic
Lower pupil — near / accommodation–convergence
Optimization Strategy
Same goal (effective depth of focus) — different programming route. Choose the strategy that matches the laser used in your operating room.
SELECTED
Q
Q-asphericity modulation
Sphere / Cyl / Axis + ΔQ target

Programmes the laser with a clinical refraction plus a target post-op corneal asphericity (Q-factor). The change in Q produces the desired spherical-aberration shift, which extends depth of field.

  • Single intuitive parameter: ΔQ (target post-op asphericity)
  • Output can be compared, for indicative and educational purposes, with vendor-specific multifocal recommendations (e.g. Alcon nomograms)
  • Patient-specific calibration of the targeted post-op shape
Click to switch
Spherical-aberration modulation
Radial Zernike target (Z40, Z60, Z80)

Programmes the laser with a target wavefront expressed as radial Zernike modes. The optimiser shapes Z40/Z60/Z80 so the post-op spherical-aberration trajectory matches the surgical intent.

  • Wavefront-guided / topo-guided platforms
  • Finer high-order tuning across the vergence range
  • Full transparency on every coefficient + ablation depth
Same surgical goal — same scoring objective. Both routes share an identical patient-specific objective: maximising a combined optical-quality score built from a series of through-focus optical metrics (modulation transfer function, point-spread function, Strehl ratio and depth-of-focus) evaluated across the chosen vergence range and pupil pair. The card you click drives every downstream calculation — ablation profile, image-quality maps, laser-entry contract.
Advanced Settings ▼
Surgery / Pupil Sweep
Step D
Stage 1 — Target Q values
Stage 2 — Global Criterion
Stiles-Crawford Effect (currently disabled in engine)
Reserved / not applied by the optimizer in this build (would drift the modal search). Keep disabled.
A(ρ)=exp(−(ρ/r0)²). Typical 0.3–0.6
About to compute — please allow some time. The treatment optimisation is fully personalised for this eye: it scans the optical parameter space (Q-asphericity or radial Zernike modes plus a spherical add), and at each candidate it reconstructs the post-op wavefront, evaluates through-focus image quality at both pupil sizes, and refines around the best score. Depending on the chosen strategy and parameter ranges, this typically takes a few tens of seconds to a couple of minutes. The Results page will open automatically as soon as the laser-entry numbers are ready, and the secondary plots will fill in progressively. Do not navigate away from this tab during the computation.
Optimization in Progress
4 Step 4 — What the optimiser is doing right now
A two-parameter sweep is being run over the laser settings you selected on the previous step. For each combination of settings, the engine simulates the post-op eye at the two pupil sizes you defined, computes a through-focus MTFa curve, and aggregates everything into a single score. The combination with the highest score wins.
Axes of the heat-map
In biconic mode: X = ΔQ (induced asphericity change), Y = sphere add (D). In modal mode: the sweep visits the (Z20, Z40) plane (or a section of higher-order pairs), with the remaining modes set to their best partial solution. Each cell = one full evaluated solution.
Colours and trajectory
The colour-map shows the score: warm = good, cool = poor. The bright peak is the current best candidate; the visible trajectory traces the order in which the search visited the cells (coarse-to-fine refinement around the best region).
What the score is made of — a weighted combination of:
  • Depth of focus (DoF): width of the through-focus MTFa curve above a clinical threshold, averaged over the swept pupils.
  • Upper-pupil quality at Dmax: MTFa at the far end of the vergence range (distance vision, mesopic pupil).
  • Lower-pupil quality at Dmin: MTFa at the near end of the vergence range (near vision, miotic pupil).
  • Penalties: fragmentation (multiple disconnected DoF segments), peak displacement (best focus drifting away from target), and a hard floor if either MTFa drops below its minimum acceptable value.
The chosen optimisation objective (Max DoF, Distance quality, DoF + upper, Upper/Lower balanced) controls the relative weights.
You can read this banner while the engine sweeps — the next page will summarise the chosen laser settings and the through-focus performance of the winning solution.
Starting optimization...

Search landscape

Treatment Results & Laser Parameters
5 Step 5 — Results: what to program, what to expect
This page is organised in four thematic sections. (A) the laser-entry parameters and the ablation profile — what you actually program. (B) the predicted vergence outcome maps — how the eye’s local optical power changes after surgery. (C) the expected post-op visual performance computed on the realistic post-op wavefront Wplaced (MTFa, multi-frequency MTF, PSF and letter convolution — what the patient will actually experience). (D) the search-landscape audit. Scroll down to read them in order.
A Treatment to program — laser entry & ablation profile
These are the parameters you enter into the excimer console. In biconic mode, you program a spectacle-equivalent Sphere / Cylinder / Axis plus a target post-op Q (asphericity) on each meridian — the laser handles ablation shaping internally. The numerical output is purely a personalised design and is not vendor-specific; depending on the laser platform available in your operating room, it may be compared, for indicative and educational purposes, with the corresponding vendor-specific multifocal recommendations. In modal mode, the platform may accept either a clinical refraction or a set of Zernike treatment coefficients; pick the contract that matches your laser interface and do not enter both at once (block A vs. block C). The ablation profile below shows the per-point tissue depth derived from the chosen treatment — it lets you sanity-check the maximum depth and the spatial distribution before clicking Treat.

Laser Correction to Program

Biconic laser entry — Sphere / Cylinder / Axis derived from calibrated biconic ΔK
Sphere (D)
—
Cylinder (D)
—
Axis (°)
—
Audit / low-order target (NOT the value to type into the laser): Slow-order = Sbase + sphereAdd = — D. The fields above come from the calibrated biconic dK (post-LM optimisation), not from this low-order seed.
Biconic — target asphericity to program (post-op corneal Q)
Q1 target
—
Q2 target
—
Induced change
ΔQ (post − pre)
—

Ablation Profile — idealised target (inside OZ, inert cornea)

The 2D map on the left shows the depth of corneal tissue (µm) removed at each (x, y) inside the optical zone. Hot colours = deeper ablation. The cross-section on the right shows the ablation depth along a slice through the cornea at the angle you choose with the slider; this is helpful to verify the central-vs-paracentral pattern (a presbyopic profile typically shows a central hill or a paracentral plateau). Maximum ablation depth is one of the most important clinical safety numbers — read it from the map’s colourbar before treating.
What this profile is — and what it is not
What you see is the exact mathematical/physical subtraction ablation(x, y) = zpre(x, y) − zpost(x, y) inside the optical zone, computed with the physical corneal refractive index (n = 1.376). It represents the tissue depth an ideal laser would need to remove from an inert cornea to convert the pre-op shape into the targeted post-op shape. Outside the OZ the ablation is shown as zero (sharp cut-off).
It deliberately does NOT model:
  • Transition zone (TZ): real lasers extend the ablation outside the OZ over ~1–2 mm with a smooth taper (cosine, tanh or vendor-specific blend) to avoid an abrupt optical/non-optical edge. The TZ shape, width and ablation strategy are proprietary to each laser platform.
  • Epithelial remodelling: 3–6 months post-LASIK the epithelium redistributes over the ablated cornea. After myopic ablations the epithelium thickens centrally over the flat zone (typically 5–15 µm) and masks part of the intended optical effect (~12 % regression typical). After hyperopic / presbyopic ablations the pattern is partly reversed: the epithelium can also thicken in the peripheral / paracentral zone where the cornea has been left steeper, on top of central thinning, contributing to a larger regression (up to ~25 % in hyperopic / multifocal corrections — Reinstein nomograms). Clinical implication. Because this regression is partly predictable, a controlled slight overcorrection of the optical target (sphere add and/or ΔQ amplitude) is commonly used to land at the intended stable post-op state once the epithelial response has matured. PRESBYpath outputs the ideal optical design — the surgeon's nomogram applies the regression-compensating margin on top.
  • Biomechanical response: flap creation and stromal ablation reduce the stromal load-bearing capacity, producing a small forward shift of the residual stroma and a typical ~5–10 % under-correction for myopic spheres > 3 D, more for higher corrections (Roberts model).
  • Laser-specific implementation: spot profile (Gaussian vs top-hat), spot size, repetition rate, ablation rate per pulse, eye-tracker latency, hydration compensation, pulse-by-pulse smoothing algorithm — all differ between platforms (Alcon Wavelight EX500, Schwind Amaris, Zeiss MEL 90 — which natively handles spherical-aberration modulation —, Bausch Teneo, …). Each vendor applies its own nomogram on top of the theoretical Zernike / biconic recipe.
Use this map as a theoretical reference for safety checks (max depth, symmetry, paracentral hill placement) and to inspect the optical recipe. The actually shot profile and the stable post-op result will differ by the four mechanisms above; clinical nomograms and laser-specific calibration are required to bridge that gap.
B Predicted vergence outcome — where light will focus across the pupil
Each map below displays the radial vergence component V ≈ −(∂W/∂r)/r in diopters — the local optical power read across the pupil. Negative values indicate myopic (near) focus, positive values indicate hyperopic (over-corrected) focus. The three maps together tell the full story of the treatment.
1 — To correct (pre-op)
The eye’s current vergence map. The patient’s low-order refraction and high-order aberrations determine where each ray of light focuses across the pupil.
2 — Treatment-induced change
The vergence change the laser will add at each pupil point. Hot/cold zones show how the multifocal profile redistributes optical power between distance and near.
3 — Post-op residual vergence
The vergence the eye will carry after surgery (= map 1 + map 2). A well-designed presbyopic profile shows a smooth central-vs-paracentral gradient covering the chosen DoF range.

1 — Radial vergence to correct (pre-op)

2 — Treatment-induced net vergence change

3 — Post-op radial residual vergence component

C Expected post-op visual performance — what the patient will actually experience
Every plot in this section is computed on the realistic post-op wavefront Wplaced — the wavefront actually left in the eye after the laser correction is applied. In modal mode Wplaced ≡ Wfull; in biconic mode Wplaced = Wfull + W2base, capturing what remains after the Sphere/Cylinder + Q programming. These four metrics (MTFa, multi-frequency MTF, PSF, letter convolution) together describe the patient’s expected visual experience and should drive the final clinical decision.

Headline metrics

DoF = depth of focus (D), width of the through-focus MTFa curve above the clinical threshold.  Peak MTFa = best image-quality index across defocus.  Peak Strehl = ratio of the actual PSF peak to a diffraction-limited PSF (1.0 = perfect).  Sphere Add = spherical equivalent added by the design.
DoF (D)
—
Peak MTFa
—
Peak Strehl
—
Sphere Add (D)
—

Zernike Spherical Aberration Analysis

Per-mode comparison of the rotationally-symmetric (radial) Zernike coefficients pre-op vs. post-op, with the induced Δ in the right column. A negative Δ on Z(4,0) (primary spherical aberration) typically signals a paracentral myopic shift used to extend near vision.
CoefficientPre-opPost-opΔ (post-op − pre-op)

Through-focus MTFa (upper & lower pupil)

MTFa as a function of object vergence (D), computed on the realistic post-op wavefront Wplaced. The blue curve is the upper (mesopic / distance) pupil, the orange curve is the lower (near) pupil. The width of each curve above the threshold defines that pupil’s usable DoF; their overlap drives the perceived multifocal range.

Through-focus multi-frequency MTF

Same idea as the MTFa above (on Wplaced) but broken down by spatial frequency (lp/mm). Low frequencies (10–20 lp/mm) correspond to large optotypes — they tolerate a lot of defocus; high frequencies (50+ lp/mm) correspond to fine detail (20/20 letters) and collapse much faster off-focus. Looking at multiple frequencies lets you anticipate which acuity lines the patient will maintain across the DoF.

PSF through defocus

The Point-Spread Function (PSF) is the image that a single point source forms on the retina, computed here on Wplaced. Each tile shows the PSF at one defocus step; a compact central peak indicates good focus, a spread-out cloud indicates aberration or defocus. This is the convolution kernel that, combined with a letter, produces the on-retina image shown in the next panel.

Letter convolution with PSF across defocus

Each PSF tile from the strip above is convolved with a letter at a chosen acuity, for two pupil sizes (orange = pupil 1, blue = pupil 2). This is the closest visual proxy to “what the patient will see” at each defocus and is the most intuitive panel to interpret — if the letter remains legible across several defocus steps, the eye carries depth of focus at that acuity.
Realistic photometric rendering (no auto-contrast). The optotype is rasterised at the physically calibrated Snellen size (20/20 ↔ 5 arcmin retinal height, ≈ 24.7 µm on a 17 mm reduced eye); the convolution is computed in a wider retinal field (≈ 40–80 arcmin) so PSF halos are integrated without truncation, then a central ≈ 20 arcmin crop is displayed — purely an observation-window change, the absolute contrast is preserved. The display layer is not renormalised so a blurred letter stays grey. The caption under each tile shows max ink %: a tile with max ink ≲ 3 % is below the typical recognition threshold even though something was computed. The defocus sweep covers +1 D → -3 D, with a fine 0.25 D step between 0 and -3 D for better resolution in the near-vision band. The model is monochromatic, scalar, no neural contrast sensitivity, no Stiles–Crawford apodisation: this rendering is therefore an optical upper bound; real-world legibility is typically a bit worse.
D Optimisation audit — search landscape
Final view of the score map explored by the optimiser. Same axes and colour code as on the Step 4 page, plus the trajectory and the winning point. Useful for documentation, for sanity-checking that the optimum is not at the edge of the search domain, and for exporting a GIF of the sweep for case reports or training.

Search landscape

In summary
From this patient's refraction, keratometry, asphericity and wavefront, PRESBYpath has designed a fully personalised multifocal profile that targets the requested vergence range at both pupil sizes simultaneously, audited through pre-op vergence maps, ablation depth, through-focus image quality and a simulated optotype rendering. Use the laser-entry values above as a theoretical baseline — your clinical nomogram (regression-compensating overcorrection, transition-zone strategy, vendor-specific ablation calibration) is the final step that bridges this optical design to the actual treatment delivered on the patient.