Coefficients
Noll Z1–Z66Values in waves (λ), RMS-normalized — 1.00 on a mode = 1 λ RMS of wavefront error on that mode.
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Wavefront map
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How to read this. Circular clear aperture, no obstruction, pupil normalized to unit radius. Axes are physical units derived from the pupil radius set on the right. Coefficients are in waves (λ), RMS-normalized — a value of 1.00 on a mode contributes exactly 1 λ RMS of wavefront error.
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Peak & valley markers. Marks the exact point of maximum wavefront error (P, amber) and minimum (V, blue) over the pupil. Together they define the PV metric shown on the right — useful for spotting where the largest deviation actually occurs, not just its magnitude.
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Cross-section axis. Draws the exact line the "Cross-section" plot below is cutting along, at the angle set there. Drag that angle and watch this line rotate on the map to see where the profile is being sampled.
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3D view. Renders the wavefront as an interactive height surface. Drag to orbit, scroll to zoom, right-click-drag to pan. Height is exaggerated for visibility (not a physical scale) and respects the same colormap, display filters, and percentile clipping as the 2D map.
Cross-section (0°, along X)
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Value distribution (no clipping)
RMS by order
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RMS contribution per radial order. Since Zernike modes are orthogonal, the RMS contributed by an order equals the square root of the sum of squares of its active coefficients (in that order alone). These combine in quadrature to the total RMS shown in Wavefront metrics.
PSF (√ scale)
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Point spread function. Computed from the pupil function (uniform amplitude × the phase from your coefficients) via a 2D FFT — it reflects whatever aberrations are currently set, not necessarily a diffraction-limited result. Axes default to λ/D (Airy units) — the first null of a diffraction-limited Airy pattern falls at 1.22 λ/D. Set an F-number in Display settings (same field used for the MTF's lp/mm axis) to switch both the 2D map and the cross-section to real µm at the focal plane instead — 1 λ/D then corresponds to (wavelength × F-number) µm. The diffraction rings around an unaberrated Airy disk are very faint — the first ring peaks at only ~1.75% of the central peak — so on a strict linear intensity scale they're essentially invisible. Use the scale selector (Linear/√/Log) to stretch faint intensity and reveal them; √ is a good default, Log shows even fainter structure at the cost of exaggerating noise. Assumes a clear, unobstructed, unapodized aperture — a simplified preview, not a full optical design.
MTF
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Modulation transfer function. Contrast transmitted by the system vs. spatial frequency f (line pairs per unit angle), derived from the same pupil (magnitude of the Fourier transform of the PSF). By default the X-axis is normalized to fc = D/λ, the diffraction cutoff — the maximum spatial frequency any system with this aperture and wavelength can transmit, regardless of how well corrected it is. Set an F-number in Display settings to switch the axis to real lp/mm instead — the exact cutoff value (fc = 1/(λ·F#)) is shown next to the title once you do. Beyond the cutoff, contrast is exactly zero for any real system. Since the aberration isn't rotationally symmetric, two directional cuts are shown — along 0° and along 90° of the pupil. The dashed diffraction limit curve is the exact closed-form MTF of a perfect, unaberrated circular aperture: (2/π)[cos⁻¹(ν) − ν√(1−ν²)] with ν = f/fc — the theoretical ceiling no real system can exceed.
Diffraction limit
0° cut
90° cut
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First MTF null. The first spatial frequency (per cut) where contrast drops to ~0, given your current aberrations. Unlike fc, this depends on the aberrations — it's the practical resolution limit for this state, not a hard ceiling. For some aberrations (e.g. spherical) contrast can partially recover into a secondary lobe past this point, so it doesn't mean "nothing resolvable beyond here" — just where contrast first vanishes.
Display settings
µm
mm
f/#
%
Wavefront metrics
- PV
- 0.000 µm 0.000 λ
- RMS
- 0.000 µm 0.000 λ
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Strehl (est.)
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Strehl ratio. PSF peak intensity with your current aberrations, divided by the peak of a perfect (unaberrated) system — 1.0 means diffraction-limited. Computed directly from the simulated PSF (same FFT pipeline as the PSF/MTF plots), not from an approximation. You can hand-check it: for a single small coefficient (RMS ≲ 0.1λ), the classic Maréchal approximation Strehl ≈ exp(-(2π·RMS)²) should be within ~1% of the value shown here. - 1.000
Sampling
- Grid
- 256 × 256
- Pupil fill
- 78.5%
- Active terms
- 1 / 66
Active terms
No active terms.
Convention
Coefficients follow Noll (1976) indexing and ordering — the same convention used by Zemax's "Standard Zernike Coefficient" surface (Z1 = piston … Z66 = order 10). Even j → cosine term (m ≥ 0); odd j → sine term (m < 0).